Mathematics Support Guide · 2018-11-14 · Mathematics Support Guide ... Key Concept: Reasoning...
Transcript of Mathematics Support Guide · 2018-11-14 · Mathematics Support Guide ... Key Concept: Reasoning...
Mathematics
Support Guide
Published: April 26, 2018
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TABLE OF CONTENTS
Mathematics Support Guide ...................................................................................................................... 1
Number Sense and Base Ten ...................................................................................................................... 2
The Number System ................................................................................................................................... 2
Arithmetic with Polynomials and Rational Expressions ......................................................................... 2
Creating Equations/Structure and Expressions ....................................................................................... 2
Reasoning with Equations and Inequalities .............................................................................................. 2
Key Concept: Number Sense and Base Ten ............................................................................................. 3
Key Concept: Number Sense and Base Ten ............................................................................................. 5
Key Concept: Number Sense and Base Ten ............................................................................................. 7
Key Concept: The Number System ........................................................................................................ 10
Key Concept: The Number System ........................................................................................................ 14
Key Concept: The Number System ........................................................................................................ 17
Key Concept: Arithmetic with Polynomials and Rational Expressions .................................................. 19
Key Concept: Creating Equations........................................................................................................... 20
Key Concept: Structure and Expressions ................................................................................................ 21
Key Concept: Reasoning with Equations and Inequalities ..................................................................... 22
Number Sense – Fractions ........................................................................................................................ 24
Number Sense and Operations – Fractions ............................................................................................ 24
Ratios and Proportional Relationships ................................................................................................... 24
Key Concept: Number Sense – Fractions ............................................................................................... 25
Key Concept: Number Sense and Operations – Fractions ...................................................................... 27
Key Concept: Number Sense and Operations – Fractions ...................................................................... 30
Key Concept: Ratios and Proportional Relationships ............................................................................. 32
Key Concept: Ratios and Proportional Relationships ............................................................................. 33
Algebraic Thinking and Operations ........................................................................................................ 35
Expressions, Equations, and Inequalities ............................................................................................... 35
Key Concept: Algebraic Thinking and Operations ................................................................................. 36
Key Concept: Algebraic Thinking and Operations ................................................................................. 39
Key Concept: Algebraic Thinking and Operations ................................................................................. 41
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Key Concept: Expressions, Equations, and Inequalities ......................................................................... 43
Key Concept: Expressions, Equations, and Inequalities ......................................................................... 45
Key Concept: Expressions, Equations, and Inequalities ......................................................................... 47
Geometry ................................................................................................................................................... 49
Geometry and Measurement.................................................................................................................... 49
Key Concept: Geometry ......................................................................................................................... 52
Key Concept: Geometry ......................................................................................................................... 54
Key Concept: Geometry and Measurement ............................................................................................ 56
Key Concept: Geometry and Measurement ............................................................................................ 57
Key Concept: Geometry and Measurement ............................................................................................ 59
Measurement and Data Analysis ............................................................................................................. 60
Key Concept: Measurement and Data Analysis...................................................................................... 61
Key Concept: Measurement and Data Analysis...................................................................................... 63
Key Concept: Measurement and Data Analysis...................................................................................... 65
Data Analysis and Statistics ..................................................................................................................... 68
Data Analysis, Statistics, and Probability ............................................................................................... 68
Functions .................................................................................................................................................... 68
Interpreting Functions .............................................................................................................................. 68
Interpreting Data ...................................................................................................................................... 68
Quantities ................................................................................................................................................... 68
Real Number System ................................................................................................................................ 68
Key Concept: Data Analysis and Statistics............................................................................................. 69
Key Concept: Data Analysis, Statistics, and Probability ........................................................................ 70
Key Concept: Functions .......................................................................................................................... 72
Key Concept: Interpreting Functions ...................................................................................................... 75
Key Concept: Data Analysis, Statistics, and Probability ........................................................................ 77
Key Concept: Interpreting Data .............................................................................................................. 79
Key Concept: Quantities ......................................................................................................................... 81
Key Concept: Real Number System ....................................................................................................... 83
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Introduction
The South Carolina Alternate Assessments (SC-Alt): Mathematics Assessment and Instructional Support Guide document was developed to
provide guidance to teachers for including students with significant cognitive disabilities in challenging academic instruction. The South Carolina
College- and Career-Ready Standards for Mathematics have been prioritized for students participating in the alternate assessment. This prioritized
content preserves the essence of the grade-level expectations while narrowing the depth and breadth of content that students with significant
cognitive disabilities are exposed to during instruction and assessment. This support guide identifies prioritized content by grade level, core
concept, and standard.
What Are Prioritized Standards?
Prioritized standards are a subset of the South Carolina College- and Career-Ready Standards that are considered essential for all students to attain.
This subset includes the standards that are assessed in the South Carolina Alternate Assessments for Mathematics. The prioritized standards are
intended to help teachers focus instruction on the most critical of the knowledge and skills included in the South Carolina College- and Career-
Ready Standards. The prioritized standards provide suggestions that are intended to help teachers make content accessible to students with a
varying range of abilities within the classroom. The activities and adaptations included here serve as a model for how students participating in the
South Carolina Alternate Assessments for Mathematics assessment may receive academic instruction in math.
What’s Included?
This guide includes the following sections:
• A list of the South Carolina College- and Career-Ready Standards has been prioritized for students with significant cognitive disabilities.
The Prioritized Standards are presented in a matrix to show the continuum of the concepts across complexity levels. The matrix shows
the range of access points to the prioritized standards. This matrix should not be perceived as a linear progression; students may be
stronger in one skill than another, so the matrix should be used as appropriate.
• A section called It Is Essential for Students to Know provides a “big picture” description of the content.
• Vocabulary and Skills sections describe the mathematical processes that students need to meet proficiency.
• Sections describing Daily Activities and Functional Activities provide suggestions for tying academic instruction to functional skills.
• A Resources section lists materials that may be helpful in instruction.
This document was developed to provide a foundation that supports and enhances the day-to-day activities which will lead to positive outcomes
for students with significant cognitive disabilities as they access the SCCCR Standards.
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Number Sense and Base Ten
The Number System
Arithmetic with Polynomials and Rational Expressions
Creating Equations/Structure and Expressions
Reasoning with Equations and Inequalities
3rd Grade 4th Grade 5th Grade 6th Grade 7th Grade 8th Grade 11th Grade 11th Grade 11th Grade
3.NSBT 4.NSBT 5.NSBT 6.NS 7.NS 8.NS 11.AAPR 11.ACE
11.ASE
11.AREI
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3rd Grade
Key Concept: Number Sense and Base Ten
SCCCR Standards: Use place value understanding to round whole numbers to the nearest 10 or 100 (3.NSBT.1). Add and subtract whole
numbers fluently to 1,000 using knowledge of place value and properties of operations (3.NSBT.2). Multiply one-digit whole numbers by
multiples of 10 in the range 10–90, using knowledge of place value and properties of operations (3.NSBT.3). Read and write numbers through
999,999 in standard form and equations in expanded form (3.NSBT.4). Compare and order numbers up to 999,999 and represent the comparison
using the symbols >, =, or < (3.NSBT.5).
Prioritized Standard Level 4: Exceeds Standard Level 3: Meets Standard Level 2: Emerging Level 1: Foundational
3.NSBT.1: Round whole
numbers up to 100 to the
nearest 10.
3.NSBT.1: Round whole
numbers from 0–100 to the
nearest 10.
3.NSBT.1: Round whole
numbers from 0–30 to the
nearest 10.
3.NSBT.1: Understand the
point when a number should
be rounded up (limited to
numbers from 1–10).
3.NSBT.1: Recognize a unit
in the place value system
(limited to ones and tens
place values).
3.NSBT.2: Add and subtract
single-digit numbers.
3.NSBT.2: Determine the
unknown in an addition or
subtraction equation.
3.NSBT.2: Demonstrate the
concept of addition and
subtraction (limited to
single-digit numbers from 1–
10).
3.NSBT.2: Identify the
functions of addition,
subtraction, and equal signs
(limited to numbers 1–5).
3.NSBT.2: Recognize the
addition, subtraction, and
equal signs.
3.NSBT.3: Multiply one-
digit whole numbers by 10.
3.NSBT.3: Count by tens
starting at a multiple of 10
(using a set of 10 objects,
numbers, etc., e.g., count
with dimes).
3.NSBT.3: Demonstrate the
concept of counting by 10 by
counting the sets of 10 and
adding a zero to the end of
number of sets (limited to
numbers 1–50).
3.NSBT.3: Identify sets of
numbers in tens using
numbers 1–30.
3.NSBT.3: Recognize the
numbers 1–10 as a set for the
tens place.
3.NSBT.4: Read numbers up
to 999.
3.NSBT.4: Read numbers up
to 999.
3.NSBT.4: Identify numbers
in word form (numbers
ranging from 1–100).
3.NSBT.4: Identify numbers
in word form (numbers
ranging from 1–50).
3.NSBT.4: Identify numbers
in word form (limit to
numbers 1–50).
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Prioritized Standard Level 4: Exceeds Standard Level 3: Meets Standard Level 2: Emerging Level 1: Foundational
3.NSBT.5: Compare and
order numbers up to 999
using the symbols >, =, or <.
3.NSBT.5: Compare two
numbers up to 100 using
symbols (=, <, >).
3.NSBT.5: Compare two
numbers up to 50 using
symbols (=, <, >).
3.NSBT.5: Arrange a set of
numbers from least to
greatest.
3.NSBT.5: Recognize the <,
>, and = signs.
It Is Essential for Students to Know: Students need to recognize place value up to hundreds place and recognize mathematical symbols in order
to round whole numbers, compare numbers, add and subtract numbers, and multiply one-digit whole numbers by 10.
Applications to Daily Tasks, Activities, Routines, or Life Experiences
• Using a hundred chart or ones place value chart, demonstrate place value concepts by showing students that a collection of 10 pennies is
the same value as one dime.
• Demonstrate addition and subtraction of single-digit numbers using student-preferred items such as crackers, stickers, coins, counting
bears, etc. This can be done as a group activity or individually with students.
• Using items two students have in their desks or pencil boxes, demonstrate comparing numbers by counting the number of items each
student has and comparing who has the most or least amount.
Standard Vocabulary Skills Daily Activities Functional Activities
3.NSBT Round
Addition/
Subtraction
Multiply
Compare
Greater than
Less than
Order
Equal
Place Value
Ones
Tens
Count by ones and tens
Add with numbers to 10
Subtract with numbers to
10
Recognize numbers
Read number words
Order numbers
Compare numbers
Recognize symbols (+, –,
=, <, >)
Round numbers from 0–
30 to nearest 10
Play bingo (digit, number words, sets)
Use various number cubes (6-sided, 20-sided, etc.)
Count with pennies, dimes, and dollar bills
Play games that include number cubes, but use numbered
cubes that have digits or words on sides or use spinners
Practice place value using a weekly pill case with
numbered cubes
Scavenger hunt in newspaper, magazine, cupboards to find
numbers, number words
Color by number – in spaces include words, digits,
equations
Play dominos
Match words to numbers
Making a grocery list
Cooking
Learning room numbers (such as by
collecting items from classrooms)
Comparing scores to determine game
winners
Finding seats at events using seat numbers
Reading numbers on buses or cars
Reading addresses and telephone numbers
Counting objects
Identifying page numbers
Identifying dates on calendars
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4th Grade
Key Concept: Number Sense and Base Ten
SCCCR Standards: Recognize math periods and number patterns within each period to read and write in standard form large numbers through
999,999,999 (4.NSBT.2). Use rounding as one form of estimation and round whole numbers to any given place value (4.NSBT.3). Fluently add
and subtract multi-digit whole numbers using strategies to include a standard algorithm (4.NSBT.4). Multiply up to a four-digit number by a one-
digit number and multiply a two-digit number by a two-digit number using strategies based on place value and the properties of operations.
Illustrate and explain the calculation by using rectangular arrays, area models and/or equations (4.NSBT.5). Divide up to a four-digit dividend by a
one-digit divisor using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division
(4.NSBT.6).
Prioritized Standard Level 4: Exceeds Standard Level 3: Meets Standard Level 2: Emerging Level 1: Foundational
4.NSBT.2: Recognize mathematical
periods through 999,999.
4.NSBT.2: Recognize word
form for numbers through
999,999.
4.NSBT.2: Recognize word
form for numbers through
999.
4.NSBT.2: Recognize
word form for numbers
through 99.
4.NSBT.2: Recognize
word form for numbers
through 9.
4.NSBT.3: Round whole numbers up
to 1,000 to the nearest 10 or 100.
4.NSBT.3: Round whole
numbers 0–100 to the
nearest 10 or nearest 100.
4.NSBT.3: Round whole
numbers from 0–30 to the
nearest 10.
4.NSBT.3: Identify when
a number can be rounded
up to the nearest unit.
4.NSBT.3: Recognize a
place value unit.
4.NSBT.4: Add and subtract two-digit
whole numbers.
4.NSBT.4: Solve addition
and subtraction word
problems with numbers up
to 100.
4.NSBT.4: Add and
subtract numbers up to 100
with a two-digit number
and a multiple of 10.
4.NSBT.4: Add and
subtract two-digit whole
numbers up to 20.
4.NSBT.4: Recognize
the addition or
subtraction symbols.
4.NSBT.5: Demonstrate basic
multiplication facts of products
through 100.
4.NSBT.5: Multiply two
whole numbers using 0–10.
4.NSBT.5: Multiply two
single-digit whole numbers
using 0–5.
4.NSBT.5: Demonstrate
the concept of
multiplication.
4.NSBT.5: Recognize
multiplication factors
and products.
4.NSBT.6: Divide up to a two-digit
dividend by a one-digit divisor without
remainders using strategies based on
place value, the properties of
operations, and/or the relationship
4.NSBT.6: Solve a division
word problem using a two-
digit dividend by a one-digit
divisor.
4.NSBT.6: Demonstrate the
concept of division using
manipulatives to divide into
equal groups.
4.NSBT.6: Identify the
components of a division
problem (i.e., What is the
dividend? What is the
4.NSBT.6: Recognize
the division sign.
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Prioritized Standard Level 4: Exceeds Standard Level 3: Meets Standard Level 2: Emerging Level 1: Foundational
between multiplication and division
(excluding long division).
divisor? What is the
quotient?).
It Is Essential for Students to Know: Students need to recognize place value up to the thousands place and recognize the written form of
numbers. Students need to be able to add and subtract two-digit whole numbers and recognize multiplication facts.
Applications to Daily Tasks, Activities, Routines, or Life Experiences
• Read and recognize the word form of numbers through bingo game activities.
• Demonstrate solving addition, subtraction, multiplication, and division problems using preferred objects.
• Demonstrate multiplication and division facts with preferred objects displayed in arrays.
Standard Vocabulary Skills Daily Activities Functional Activities
4.NSBT Round
Place value
Addition/Subtraction
Symbol
Multiply
Division/Quotient
Periods
Single-digit/two-digit
Dividend
Divisor
Divide into equal groups
Add and subtract with
numbers to 100
Multiply with whole
numbers to 5
Recognize division symbol
Build shapes with building blocks
Cut a sheet of stickers
Teach arrays with preferred objects
(egg cartons, ice cube trays, pill boxes,
paint palette, cookie trays, muffin tins,
boxes with dividers, teacher mailboxes)
Practice play-dough math
Practice menu math
Sharing – do you have enough for everyone?
Planning a party – do you have enough seating and
food for everyone?
Planning a pizza party – counting toppings
(addition/multiplication), cutting/sharing
(subtraction/division)
Breaking apart a chocolate bar
Cutting wood
Sorting supplies for activities
Asking “Do I have enough money?” for a purchase
Doubling or dividing a recipe
Purchasing tickets – if three tickets cost $5, how
much money do you need to buy three tickets?
Calculating hourly wages/piece pay
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5th Grade
Key Concept: Number Sense and Base Ten
SCCCR Standards: Use whole number exponents to explain: a. patterns in the number of zeroes of the product when multiplying a number by
powers of 10; b. patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10 (5.NSBT.2). Read and
write decimals in standard and expanded form. Compare two decimal numbers to the thousandths using the symbols >, =, or < (5.NSBT.3). Round
decimals to any given place value within thousandths (5.NSBT.4). Fluently multiply multi-digit whole numbers using strategies to include a
standard algorithm (5.NSBT.5). Divide up to a four-digit dividend by a two-digit divisor, using strategies based on place value, the properties of
operations, and the relationship between multiplication and division (5.NSBT.6). Add, subtract, multiply, and divide decimal numbers to
hundredths using concrete area models and drawings (5.NSBT.7).
Prioritized Standard Level 4: Exceeds Standard Level 3: Meets Standard Level 2: Emerging Level 1: Foundational
5.NSBT.2: Use whole number exponents to
explain patterns in the number of zeroes of the
product when multiplying a number by
powers of 10.
5.NSBT.2: Identify the power
of 10, given the product.
5.NSBT.2: Identify the
product, given the
number 10, with an
exponent.
5.NSBT.2:
Multiply a product
of 10 by 10.
5.NSBT.2: Identify or
continue a pattern.
5.NSBT.3: Read and write decimals in
standard form. Compare two decimal numbers
to the hundredths using the symbols >, =, or
<.
5.NSBT.3: Compare two
decimals to the hundredths
(=, <, >). Read and write
monetary values.
5.NSBT.3: Compare two
decimals to the
hundredths (=, <, >).
5.NSBT.3: Identify
and define a
decimal.
5.NSBT.3: Recognize
larger, smaller, and
equal.
5.NSBT.4: Round decimals to the nearest
whole number.
5.NSBT.4: Round a decimal
to the nearest whole number.
5.NSBT.4: Round a
decimal to the nearest
whole number (limit to
decimals over 0.50).
5.NSBT.4: Identify
a decimal.
5.NSBT.4: Identify a
unit.
5.NSBT.5: Multiply a multi-digit whole
number by a one-digit whole number using
strategies to include a standard algorithm.
5.NSBT.5: Multiply by 1, 2,
3, 4, and/or 5.
5.NSBT.5: Demonstrate
the concept of
multiplication related to
repeated addition.
5.NSBT.5: Solve
repeated addition
problems.
5.NSBT.5: Identify and
represent repeated
addition with an
equation.
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Prioritized Standard Level 4: Exceeds Standard Level 3: Meets Standard Level 2: Emerging Level 1: Foundational
5.NSBT.6: Divide up to a four-digit dividend
by a one-digit divisor, using strategies based
on place value, the properties of operations,
and the relationship between multiplication
and division.
5.NSBT.6: Divide by 1, 2, 3,
4, and/or 5.
5.NSBT.6: Apply the
relationship between
multiplication and
division.
5.NSBT.6:
Understand that
equal groups can be
represented by
division.
5.NSBT.6: Identify
equal groups.
5.NSBT.7: Add and subtract decimal
numbers to hundredths using concrete area
models and drawings.
5.NSBT.7: Add and subtract
multi-digit decimal numbers
without regrouping. Add and
subtract monetary amounts
including dollars and cents.
Students may use a model or
drawing.
5.NSBT.7: Add and
subtract monetary
amounts, including in
whole numbers (with the
$.00 included). Students
may use a model or
drawing.
5.NSBT.7: Identify
a whole number
when presented in
monetary form.
Identify a decimal
when presented in
monetary form.
5.NSBT.7: Identify
whole and part.
It Is Essential for Students to Know: Students need to be able to continue a pattern and identify equal groups. Students need to be able to
recognize multiplication facts up to 100. Students also need to be able to define decimals, compare decimals up to hundredths place, and recognize
decimals when written as money.
Applications to Daily Tasks, Activities, Routines, or Life Experiences
• Use advertisements, printed website pages, or sales flyers to demonstrate adding, subtracting, and comparing decimals.
• Use student-preferred objects to demonstrate that repeated addition is the same as a multiplication array and multiplication expression.
• Use student-preferred objects to demonstrate similarities between multiplication facts and division.
Standard Vocabulary Skills Daily Activities Functional Activities
5.NSBT Decimal
Standard form
Tenths
Hundredths
Expanded form
Comparing decimals
Rounding decimals
Multiply by 10
Adding and subtracting
monetary amounts
Practice menu math
Practice play-dough math
Use seed trays
Make arrays with preferred objects
Add money (coins)
Reading sale ads
Calculating prices while using coupons
Comparing prices
Sharing – do you have enough for everyone?
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Standard Vocabulary Skills Daily Activities Functional Activities
Algorithm
Exponent
Unit
Equivalent
+, -, =, x, ÷
<, >
Pattern
Larger
Smaller
Equal
Whole
Part
Repeated addition
Using models
Sort money and make change using a
money tray
Play card games
Planning a party – do you have enough seating
and food for everyone?
Planning a pizza party – counting toppings
(addition/multiplication), cutting/sharing
(subtraction/division)
Breaking apart a chocolate bar
Cutting wood
Sorting supplies for activities
Asking “Do I have enough money?”
Forming relay teams
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6th Grade
Key Concept: The Number System
SCCCR Standards: Fluently divide multi-digit whole numbers using a standard algorithmic approach (6.NS.2). Fluently add, subtract, multiply
and divide multi-digit decimal numbers using a standard algorithmic approach (6.NS.3). Find common factors and multiples using two whole
numbers. a. Compute the greatest common factor (GCF) of two numbers both less than or equal to 100. b. Compute the least common multiple
(LCM) of two numbers both less than or equal to 12. c. Express sums of two whole numbers, each less than or equal to 100, using the distributive
property to factor out a common factor of the original addends (6.NS.4). Understand that the positive and negative representations of a number are
opposites in direction and value. Use integers to represent quantities in real-world situations and explain the meaning of zero in each situation
(6.NS.5). Extend the understanding of the number line to include all rational numbers and apply this concept to the coordinate plane. a. Understand
the concept of opposite numbers, including zero, and their relative locations on the number line. b. Understand that the signs of the coordinates in
ordered pairs indicate their location on an axis or in a quadrant on the coordinate plane. c. Recognize when ordered pairs are reflections of each
other on the coordinate plane across one axis, both axes, or the origin. d. Plot rational numbers on number lines and ordered pairs on coordinate
planes (6.NS.6). Understand and apply the concepts of comparing, ordering, and finding absolute value to rational numbers. a. Interpret statements
using equal to (=) and not equal to (≠) (6.NS.7a). b. Interpret statements using less than (<), greater than (>), and equal to (=) as relative locations
on the number line (6.NS.7b). c. Use concepts of equality and inequality to write and to explain real-world and mathematical situations (6.NS.7c).
d. Understand that absolute value represents a number’s distance from zero on the number line and use the absolute value of a rational number to
represent real-world situations (6.NS.7d). Investigate and translate among multiple representations of rational numbers (fractions, decimal
numbers, percentages). Fractions should be limited to those with denominators of 2, 3, 4, 5, 8, 10, and 100 (6.NS.9).
Prioritized Standard Level 4: Exceeds Standard Level 3: Meets Standard Level 2: Emerging Level 1: Foundational
6.NS.2: Fluently divide multi-digit
whole numbers limited to four-digit
dividends and two-digit divisors
using a standard algorithmic
approach.
6.NS.2: Divide by numbers up
to and including 10.
6.NS.2: Divide by 1, 2, 3,
4, and 5.
6.NS.2: Apply the
relationship between
multiplication and
division.
6.NS.2: Demonstrate
the concept of division.
6.NS.3: Fluently add and subtract
multi-digit decimal numbers to the
hundredths place using a standard
algorithmic approach.
6.NS.3: Add and subtract
multi-digit decimal numbers
without regrouping. Add and
subtract monetary amounts
including dollars and cents;
students may use a model or
drawing.
6.NS.3: Add and subtract
monetary amounts
including in whole
numbers (with the $.00
included); students may
use a model or drawing.
6.NS.3: Identify a whole
number when presented in
monetary form. Identify a
decimal when presented in
monetary form.
6.NS.3: Identify whole
and part.
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Prioritized Standard Level 4: Exceeds Standard Level 3: Meets Standard Level 2: Emerging Level 1: Foundational
6.NS.4: Find common factors and
multiples using two whole numbers
up to 50 for factors, and less than or
equal to 10 for multiples.
6.NS.4: Find common factors
for whole numbers up to 50
and less than or equal to 10 for
multiples.
6.NS.4: Given the factors
of two numbers, identify
the common factors (for
two whole numbers up to
50 and multiples of 5 or
10).
6.NS.4: Find the factors of
a number (limit to fact
families under 50).
6.NS.4: Identify fact
families of a number
using multiplication.
6.NS.5: Understand that the positive
and negative representations of a
number are opposites in direction
and value. Use integers to represent
quantities in real-world situations.
6.NS.5: Given a real-world
context, identify the value of
the situation which may
include negative numbers.
6.NS.5: Given a real-
world context, identify
whether the value in the
situation is positive,
negative, or zero.
6.NS.5: Given a real-
world context, identify the
value of the situation
(limit to positive numbers
under 100).
6.NS.5: Given a real-
world context, identify
the value of the
situation (limit to
positive numbers under
15).
6.NS.6: Plot integers on number
lines and ordered pairs on the
coordinate plane.
6.NS.6: Plot an ordered pair
on a coordinate plane.
6.NS.6: Identify an
ordered pair on a
coordinate plane.
6.NS.6: Plot a number on
a vertical or horizontal
number line.
6.NS.6: Identify a
number on a vertical or
horizontal number line.
6.NS.7a: Interpret statements using
equal to (=) and not equal to (≠).
6.NS.7a: Identify the absolute
value of a number as the
distance from zero on a
number line.
6.NS.7a: Given a real-
world or mathematical
situation, identify a
statement of equality or
inequality that describes it.
6.NS.7a: Given two points
on a number line, identify
a statement using less than
(<), greater than (>), and
equal to (=) to describe
their locations on the
number line.
6.NS.7a: Identify if two
statements are equal (=)
or not equal (≠).
6.NS.7b: Interpret statements using
less than (<), greater than (>), and
equal to (=) as relative locations on
the number line.
6.NS.7b: Identify the absolute
value of a number as the
distance from zero on a
number line.
6.NS.7b: Given a real-
world or mathematical
situation, identify a
statement of equality or
inequality that describes it.
6.NS.7b: Given two points
on a number line, identify
a statement using less than
(<), greater than (>), and
equal to (=) to describe
their locations on the
number line.
6.NS.7b: Identify if
two statements are
equal (=) or not equal
(≠).
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Prioritized Standard Level 4: Exceeds Standard Level 3: Meets Standard Level 2: Emerging Level 1: Foundational
6.NS.7c: Use concepts of equality
and inequality to write and to explain
real-world and mathematical
situations.
6.NS.7c: Identify the absolute
value of a number as the
distance from zero on a
number line.
6.NS.7c: Given a real-
world or mathematical
situation, identify a
statement of equality or
inequality that describes it.
6.NS.7c: Given two points
on a number line, identify
a statement using less than
(<), greater than (>), and
equal to (=) to describe
their locations on the
number line.
6.NS.7c: Identify if two
statements are equal (=)
or not equal (≠).
6.NS.7d: Understand that absolute
value represents a number’s distance
from zero on the number line and
use the absolute value of an integer
number to represent real-world
situations.
6.NS.7d: Identify the absolute
value of a number as the
distance from zero on a
number line.
6.NS.7d: Given a real-
world or mathematical
situation, identify a
statement of equality or
inequality that describes it.
6.NS.7d: Given two points
on a number line, identify
a statement using less than
(<), greater than (>), and
equal to (=) to describe
their locations on the
number line.
6.NS.7d: Identify if
two statements are
equal (=) or not equal
(≠).
6.NS.9: Explore and translate among
multiple representations of rational
numbers (fractions, decimal
numbers, percentages). Fractions
should be limited to those with
denominators of 2, 3, 4, 5, 8, 10, and
100.
6.NS.9: Translate multiple
representations of rational
numbers (fractions, decimal
numbers, and percentages).
Fractions should be limited to
those with denominators of 2,
3, 4, 5, 8, 10, and 100.
6.NS.9: Identify multiple
representations of a
rational number.
6.NS.9: Identify the
definition of a rational
number.
6.NS.9: Identify a
whole number.
It Is Essential for Students to Know: Students need to be able to add and subtract decimals to the hundredths place. Students need to know
multiplication and division fact families. Students need to be able to recognize and compare points on a number line. Students also need to
recognize points on the first quadrant of a coordinate plane.
Applications to Daily Tasks, Activities, Routines, or Life Experiences
• Identify equality statements when given a real-world situation. For example, Mary is 12 years old, and Chris is 11 years old. Which
statement correctly compares Mary and Chris’s ages?
• Create a number line using painter’s tape on the ground and measure steps from zero in both directions to demonstrate the concept of
absolute value.
-13-
• Add and subtract monetary amounts including dollars and cents. For example, Craig has $20.45. He spends $2.65 to buy a notebook and
$1.50 on an eraser from the school store. How much money does Craig have left?
• Calculate the final price when things are on sale. For example, calculate 25% off a pair of jeans that are $25.50.
Standard Vocabulary Skills Daily Activities Functional Activities
6.NS Positive
Negative
Zero
Coordinate Plane
Equality
Inequality
Rational number
LCM
GCF
Factors
Integers
Vertical
Horizontal
Not equal to
Plot
Order pair
Whole/part
Add
Subtract
Fact families
Factor
Divide by 1, 2, 3, 4
Use arrays or models for division and
multiplying and factors
Buy items in the school stores
Play “Battleship” on a coordinate plane
Use maps during a scavenger hunt
Use a thermometer to find the temperature
Use an elevator or stairs to understand positive,
negative, zero
Throw objects and compare distance
Practice number line activities (placing number
words, digits, sets on points)
Use spreadsheets.
Using maps of amusement parks, zoos, etc.
to find places
Reading thermometers to decide what
clothes to wear
Practicing banking (making deposits,
withdrawals)
Weighing grocery items
Comparing food labels
Determining price of produce based on
weight
Locating objects on shelves (coordinate
plane)
Using a balance to compare amounts
-14-
7th Grade
Key Concept: The Number System
SCCCR Standards: Extend prior knowledge of operations with positive rational numbers to add and to subtract all rational numbers and
represent the sum or difference on a number line. a. Understand that the additive inverse of a number is its opposite and their sum is equal to zero.
b. Understand that the sum of two rational numbers (𝑝 + 𝑞) represents a distance from p on the number line equal to |q| where the direction is
indicated by the sign of q. c. Translate between the subtraction of rational numbers and addition using the additive inverse, 𝑝 – 𝑞 = 𝑝 + (−𝑞). d.
Demonstrate that the distance between two rational numbers on the number line is the absolute value of their difference. e. Apply mathematical
properties (e.g., commutative, associative, distributive, or the properties of identity and inverse elements) to add and subtract rational numbers
(7.NS.1). Extend prior knowledge of operations with positive rational numbers to multiply and to divide all rational numbers. a. Understand that
the multiplicative inverse of a number is its reciprocal and their product is equal to one. b. Understand sign rules for multiplying rational numbers.
c. Understand sign rules for dividing rational numbers and that a quotient of integers (with a non-zero divisor) is a rational number. d. Apply
mathematical properties (e.g., commutative, associative, distributive, or the properties of identity and inverse elements) to multiply and divide
rational numbers. e. Understand that some rational numbers can be written as integers and all rational numbers can be written as fractions or
decimal numbers that terminate or repeat (7.NS.2). Apply the concepts of all four operations with rational numbers to solve real-world and
mathematical problems (7.NS.3). Understand and apply the concepts of comparing and ordering to rational numbers. a. Interpret statements using
less than (<), greater than (>), less than or equal to (≤), greater than or equal to (≥), and equal to (=) as relative locations on the number line. b. Use
concepts of equality and inequality to write and explain real-world and mathematical situations (7.NS.4). Extend prior knowledge to translate
among multiple representations of rational numbers (fractions, decimal numbers, percentages). Exclude the conversion of repeating decimal
numbers to fractions (7.NS.5).
Prioritized Standard Level 4: Exceeds Standard Level 3: Meets Standard Level 2: Emerging Level 1: Foundational
7.NS.1: Extend prior knowledge
of operations with positive
rational numbers to add and to
subtract all rational numbers and
represent the sum or difference on
a number line.
7.NS.1: Extend prior
knowledge of operations with
positive rational numbers to add
and subtract all rational
numbers and represent the sum
or difference on a number line.
7.NS.1: Extend prior
knowledge of operations
with positive rational
numbers to add and subtract
all rational numbers.
7.NS.1: Convert a whole
number into a fraction.
7.NS.1: Identify a whole
number or a fraction.
7.NS.2: Extend prior knowledge
of operations with positive
rational numbers to multiply and
divide all rational numbers.
7.NS.2: Extend prior
knowledge of operations with
positive rational numbers to
multiply and divide all rational
numbers and represent the
result on a number line.
7.NS.2: Extend prior
knowledge of operations
with positive rational
numbers to multiply and
divide all rational numbers.
7.NS.2: Convert a whole
number into a fraction.
7.NS.2: Identify a whole
number or a fraction.
-15-
Prioritized Standard Level 4: Exceeds Standard Level 3: Meets Standard Level 2: Emerging Level 1: Foundational
7.NS.3: Apply the concepts of all
four operations with positive
rational numbers to solve one-
step, real-world and mathematical
problems.
7.NS.3: Apply the concepts of
all four operations with positive
rational numbers to solve two-
step, real-world and
mathematical problems.
7.NS.3: Apply the concepts
of all four operations with
positive rational numbers to
solve one-step, real-world
and mathematical problems.
7.NS.3: Apply the
concepts of the operations
of multiplication and
division with positive
rational numbers to solve
one-step, real-world and
mathematical problems.
7.NS.3: Apply the
concepts of the
operations of addition
and subtraction with
positive rational
numbers to solve one-
step, real-world and
mathematical problems.
7.NS.4: Understand and apply the
concepts of comparing and
ordering rational numbers on a
number line. Interpret statements
using less than (<), greater than
(>), less than or equal to (≤),
greater than or equal to (≥), and
equal to (=) as relative locations
on the number line.
7.NS.4: Understand and apply
the concepts of comparing and
ordering rational numbers on a
number line. Interpret
statements using less than (<),
greater than (>), less than or
equal to (≤), greater than or
equal to (≥), and equal to (=) as
relative locations on the number
line.
7.NS.4: Understand and
apply the concepts of
comparing and ordering
rational numbers on a
number line. Interpret
statements using less than
(<), greater than (>), and
equal to (=) as relative
locations on the number line.
7.NS.4: Understand and
apply the concepts of
comparing and ordering
whole numbers on a
number line. Interpret
statements using less than
(<), greater than (>), and
equal to (=) as relative
locations on the number
line.
7.NS.4: Understand and
apply the concepts of
comparing and ordering
whole numbers on the
number line.
7.NS.5: Extend prior knowledge
to translate among multiple
representations of rational
numbers (fractions, decimal
numbers). Exclude the conversion
of repeating decimal numbers to
fractions.
7.NS.5: Extend prior
knowledge to translate among
multiple representations of
rational numbers (fractions,
decimal numbers). Exclude the
conversion of repeating decimal
numbers to fractions.
7.NS.5: Extend prior
knowledge to translate
among fractions and decimal
numbers up to 100. Exclude
the conversion of repeating
decimal numbers to
fractions.
7.NS.5: Identify
equivalent fractions and
decimal numbers up to
100. Exclude the
conversion of repeating
decimal numbers to
fractions.
7.NS.5: Identify same
and different fractions or
decimal numbers from
pictorial representations.
It Is Essential for Students to Know: Students need to be able to differentiate between a whole number, a fraction, and a decimal. Students need
to be able to order whole numbers, fractions, and decimals on a number line. Students need to be able to convert a fraction (with single-digit
numerators and a denominator of 10) to the equivalent decimal. Students also need to be able to apply all four operations to solve problems with
decimals in the tenths place.
-16-
Applications to Daily Tasks, Activities, Routines, or Life Experiences
• Using a scale and some fruits and vegetables, create a store scenario and have the students calculate the total cost of the fruits and
vegetables per pound by weighing the fruits and vegetables and then multiplying by the price per pound.
• Have students calculate the price of an item that is discounted to practice solving real-world problems involving all rational numbers.
Standard Vocabulary Skills Daily Activities Functional Activities
7.NS Order of operations
Repeating decimals
Signs (<, >, +, =, -)
Solve
Number line
Fraction
Decimal
Add and subtract
Multiply and divide
Convert whole numbers
into fractions
Convert decimals into
fractions up to 100
Add and subtract with models
Multiply and divide with models
Shopping, budgeting
Cooking or baking using recipes
Taking inventory to determine what you have and
what you need
Feeding pet, watering plant using measuring cups
(combinations of cups)
-17-
8th Grade
Key Concept: The Number System
SCCCR Standards: Explore the real number system and its appropriate usage in real-world situations. a. Recognize the differences between
rational and irrational numbers. b. Understand that all real numbers have a decimal expansion. c. Model the hierarchy of the real number system,
including natural, whole, integer, rational, and irrational numbers (8.NS.1). Estimate and compare the value of irrational numbers by plotting them
on a number line (8.NS.2). Extend prior knowledge to translate among multiple representations of rational numbers (fractions, decimal numbers,
percentages). Include the conversion of repeating decimal numbers to fractions (8.NS.3).
Prioritized Standard Level 4: Exceeds Standard Level 3: Meets Standard Level 2: Emerging Level 1: Foundational
8.NS.1: Recognize the
differences between rational and
irrational numbers. Understand
that all real numbers have a
decimal expansion.
8.NS.1: Recognize the
differences between rational and
irrational numbers. Understand
that all real numbers have a
decimal expansion.
8.NS.1: Recognize the
differences between
rational and irrational
numbers.
8.NS.1: Identify rational
numbers.
8.NS.1: Identify whole
numbers and fractions.
8.NS.2: Estimate the value of
irrational and rational numbers
by plotting them on a number
line.
8.NS.2: Estimate the value of
irrational and rational numbers
by plotting them on a number
line.
8.NS.2: Plot irrational and
rational numbers on a
number line.
8.NS.2: Plot rational
numbers on a number line.
8.NS.2: Plot whole
numbers and fractions
on a number line.
8.NS.3: Extend prior knowledge
to translate among multiple
representations of rational
numbers (fractions, decimal
numbers, percentages). Exclude
the conversion of repeating
decimal numbers to fractions.
8.NS.3: Translate among
multiple representations of
rational numbers (fractions,
decimal numbers, percentages).
Exclude the conversion of
repeating decimal numbers to
fractions.
8.NS.3: Translate among
multiple representations of
rational numbers (fractions
and decimal numbers).
Exclude the conversion of
repeating decimal numbers
to fractions.
8.NS.3: Translate fractions
with the denominators 2, 4,
6, 8, and 10 into decimals.
8.NS.3: Identify
fractions.
It Is Essential for Students to Know: Students need to be able to identify rational numbers and plot fractions on a number line. Students need to
be able to convert fractions with denominators of 2, 4, 6, and 8 to equivalent decimals.
Applications to Daily Tasks, Activities, Routines, or Life Experiences
• Students can practice translating among multiple representations of rational numbers by doing everyday things like making a monthly
lunch budget and calculating a percentage of their monthly allowance that they want to save.
-18-
Standard Vocabulary Skills Daily Activities Functional Activities
8.NS Percentage
Rational
Irrational
Recognize difference between
rational and irrational numbers
Plot rational and irrational
numbers
Use painter’s tape on the floor or wall to
practice number line activities such as
whole numbers and fractions
Use a hundred chart to illustrate percentage
Creating pie chart of data collected in class (eye color,
hair color, etc.)
Practicing money activities (quarters, parts of dollar)
Comparing calories of various foods
Calculating fractions of time
-19-
11th Grade
Key Concept: Arithmetic with Polynomials and Rational Expressions
SCCCR Standards: Add, subtract, and multiply polynomials and understand that polynomials are closed under these operations (A1.AAPR.1).
Prioritized Standard Level 4: Exceeds Standard Level 3: Meets Standard Level 2: Emerging Level 1: Foundational
A1.AAPR.1: Add and
subtract polynomials (limit
to linear).
A1.AAPR.1: Add and
subtract like terms with
simple expressions.
A1.AAPR.1: Add and
subtract like terms that may
include a variable.
A1.AAPR.1: Add and
subtract like terms (limited
to constants).
A1.AAPR.1: Add two like
terms (limited to constants).
It Is Essential for Students to Know: Students need to be able to add and subtract like terms.
Applications to Daily Tasks, Activities, Routines, or Life Experiences
• The students can practice adding and subtracting polynomials by determining which objects should be grouped together. For example,
comedy movies should be grouped with other comedy movies, action movies with other action movies, and drama movies with other
drama movies.
Standard Vocabulary Skills Daily Activities Functional Activities
11.AAPR Variable
Term
Like terms
Add and subtract
like terms
Use manipulatives to group and
add/subtract
Sorting laundry – if two people add their amounts together, how many
shirts and pants do they have together?
Creating job-related materials
Using any preferred objects to add and subtract like terms
Calculating amounts using money
-20-
11th Grade
Key Concept: Creating Equations
SCCCR Standards: Create and solve equations and inequalities in one variable that model real-world problems involving linear, quadratic,
simple rational, and exponential relationships. Interpret the solutions and determine whether they are reasonable (A1.ACE.1).
Prioritized Standard Level 4: Exceeds Standard Level 3: Meets Standard Level 2: Emerging Level 1: Foundational
A1.ACE.1: Solve linear
equations with one variable.
A1.ACE.1: Solve a linear
equation with one variable.
A1.ACE.1: Solve a linear
equation with one variable
with one step (addition,
subtraction).
A1.ACE.1: Solve an
equation written with the
variable isolated on the left
side.
A1.ACE.1: Given a linear
equation, identify parts of
the equation (variable,
constant, and coefficient).
It Is Essential for Students to Know: Students need to be able to identify a variable, coefficient, and constant in a linear equation. Students need
to be able to solve one-step equations with the variable isolated to one side (i.e., x = 2 * 4; x = 8 + 9).
Applications to Daily Tasks, Activities, Routines, or Life Experiences
• Solve simple linear equations with one variable. For example, if John earns $10 per hour, how many hours should he work to earn $100?
Standard Vocabulary Skills Daily Activities Functional Activities
11.ACE
Constant
Variable
Coefficient
Term
Expression
Solve equation with one
variable with one step
Identify parts of equation
Model real-life situations
Example: Give a student $5 for the week and then give a
quarter for every day of attendance. If the student comes to
school for three days, how much money would he have?
Calculating amounts using savings
accounts
Calculating amounts using piggy banks
(with a starting amount as constant)
-21-
11th Grade
Key Concept: Structure and Expressions
SCCCR Standards: Interpret the meanings of coefficients, factors, terms, and expressions based on their real-world contexts. Interpret
complicated expressions as being composed of simpler expressions. (A1.ASE.1).
Prioritized Standard Level 4: Exceeds Standard Level 3: Meets Standard Level 2: Emerging Level 1: Foundational
A1.ASE.1: Determine the
meanings of coefficients,
variables, terms, and
expressions based on their
real-world contexts.
A1.ASE.1: Determine the
meanings of coefficients,
variables, terms, and
expressions based on their
real-world contexts.
A1.ASE.1: Given a real-
world context and a variable,
determine what the variable
represents.
A1.ASE.1: Identify the
meaning of the unknown in a
real-world context.
A1.ASE.1: Given an
expression, identify a part
(variable, term).
It Is Essential for Students to Know: Students need to be able to differentiate between an equation and an expression. Students need to be able to
identify the unknown.
Applications to Daily Tasks, Activities, Routines, or Life Experiences
• Create a real-world context and expression, and determine the meaning of each part of the expression. For example, Jim is using the
expression 5x + 20 to calculate his savings based on his weekly allowance. What does each part of the expression represent? The slope,
which represents Jim’s weekly allowance, is $5. The variable represents the number of weeks, and the y-intercept represents the amount of
money that Jim has already saved.
Standard Vocabulary Skills Daily Activities Functional Activities
11.ASE Constant
Variable
Coefficient
Term
Expression
Solve equation with one
variable with one step
Identify parts of
equations
Model real-life situations
Example: Give a student $5 for the week and then give a
quarter for every day of attendance. If the student comes to
school for three days, how much money would he have?
Calculating amounts using savings
accounts
Calculating amounts using piggy banks
(with a starting amount as constant)
-22-
11th Grade
Key Concept: Reasoning with Equations and Inequalities
SCCCR Standards: Understand and justify that the steps taken when solving simple equations in one variable create new equations that have the
same solution as the original (A1.AREI.1). Solve systems of linear equations algebraically and graphically focusing on pairs of linear equations in
two variables. (Note: AREI.6a and 6b are not Graduation Standards.) a. Solve systems of linear equations using the substitution method. b. Solve
systems of linear equations using linear combination (A1.AREI.6). Explain that the graph of an equation in two variables is the set of all its
solutions plotted in the coordinate plane (A1.AREI.10). Graph the solutions to a linear inequality in two variables (A1.AREI.12).
Prioritized Standard Level 4: Exceeds Standard Level 3: Meets Standard Level 2: Emerging Level 1: Foundational
A1.AREI.1: Understand
that the steps taken when
solving simple equations
in one variable create new
equations that have the
same solution as the
original.
A1.AREI.1: Understand that
the steps taken when solving
simple equations in one
variable create new equations
that have the same solution as
the original.
A1.AREI.1: Identify the
possible next step in solving an
equation.
A1.AREI.1: Identify the
possible first step in solving
an equation.
A1.AREI.1: Determine if
two expressions are equal
(2 x 3, 3 x 2,
commutative property,
associative property).
A1.AREI.6: Solve
systems of linear equations
graphically focusing on
pairs of linear equations in
two variables.
A1.AREI.6: Solve systems of
linear equations, graphically
focusing on pairs of linear
equations in two variables.
A1.AREI.6: Given the graph of
one equation and a simple
equation, identify the graph that
models the solution.
A1.AREI.6: Identify the
point at which a given set of
lines intersect.
A1.AREI.6: Identify a
set of lines that intersect.
A1.AREI.10: Understand
that the graph of an
equation in two variables
is the set of all its
solutions plotted in the
coordinate plane.
A1.AREI.10: Understand that
the graph of an equation in two
variables is the set of all its
solutions plotted in the
coordinate plane.
A1.AREI.10: Identify the graph
of an equation in two variables
that models the set of all its
solutions plotted in the
coordinate plane (limit to the
first quadrant).
A1.AREI.10: Identify an
equation in the first
quadrant.
A1.AREI.10: Identify a
point in the first quadrant.
-23-
Prioritized Standard Level 4: Exceeds Standard Level 3: Meets Standard Level 2: Emerging Level 1: Foundational
A1.AREI.12: Graph the
solutions to a simple
inequality with one
variable on a number line.
A1.AREI.12: Identify a simple
inequality with one variable on
the number line (include
greater than or equal to).
A1.AREI.12: Identify an
inequality on the number line
(where the solution is a positive
number but the number line may
include negative numbers).
A1.AREI.12: Identify an
inequality on the number
line (limit to greater than and
less than, limit to positive
number line starting at zero).
A1.AREI.12: Identify a
point on the number line.
It Is Essential for Students to Know: Students need to be able to differentiate between an equation and an inequality. Students need to be able to
identify an inequality on a number line (i.e., x > 4). Students also need to be able to recognize the first step to solve an equation.
Applications to Daily Tasks, Activities, Routines, or Life Experiences
• To solve real-world inequality problems, students must determine if they have enough money to make a certain purchase. For example,
Jim gets $5 per week for his allowance. He already has $20 saved. How many more weeks will Jim need to save his allowance to have
$60? 60 = 5x + 20, solve for x, which is the number of weeks, x = 8. Jim needs to save his allowance for 8 more weeks to reach his goal.
Standard Vocabulary Skills Daily Activities Functional Activities
11.AREI Graph
Equation
Quadrant
Intersect
Commutative
Associative
Compare expressions
Determine that
expressions are equal
Intersecting lines
Identify point of
intersection
Compare similar groups of objects that are in containers
Compare arrays of pictures (e.g., 2x3 is the same as 3x2 – same
amount of objects)
Compare steps taken (e.g., one student takes 6 steps and then 4;
the other student takes 4 steps and then 6)
Have students dip the wheels of toy cars in paint and “drive”
them on chart paper to illustrate intersecting lines
Place sticky notes or ink with a dot stamper on chart paper with
X and Y axes, and then plot the points
Cooking recipes to compare amounts
Using directions to and from places to
illustrate the commutative property
Using maps to understand intersections
Comparing amounts using objects on
shelves
Using shoe storage containers to
compare groups of objects
-24-
Number Sense – Fractions
Number Sense and Operations –
Fractions
Ratios and Proportional Relationships
3rd Grade 4th Grade 5th Grade 6th Grade 7th Grade
3.NSF 4.NSF 5.NSF 6.RP 7.RP
-25-
3rd Grade
Key Concept: Number Sense – Fractions
SCCCR Standards: Develop an understanding of fractions (i.e., denominators 2, 3, 4, 6, 8, 10) as numbers. a. A fraction 1
𝑏 (called a unit
fraction) is the quantity formed by one part when a whole is partitioned into 𝑏 equal parts; b. A fraction 𝑎
𝑏 is the quantity formed by 𝑎 parts of
size 1
𝑏; c. A fraction is a number that can be represented on a number line based on counts of a unit fraction; d. A fraction can be represented
using set, area, and linear models (3.NSF.1) Explain fraction equivalence (i.e., denominators 2, 3, 4, 6, 8, 10) by demonstrating an
understanding that: a. two fractions are equal if they are the same size, based on the same whole, or at the same point on a number line; b.
fraction equivalence can be represented using set, area, and linear models; c. whole numbers can be written as fractions (e.g., 4 = 4/1 and 1=
4/4); d. fractions with the same numerator or same denominator can be compared by reasoning about their size based on the same whole
(3.NSF.2).
Prioritized Standard Level 4: Exceeds Standard Level 3: Meets Standard Level 2: Emerging Level 1: Foundational
3.NSF.1: Develop an
understanding of fractions (i.e.,
denominators 2, 3, 4, 6, 8, 10) as
numbers.
3.NSF.1: Match fractions to
their models (i.e.,
denominators to 2, 3, 4, 6, 8,
10).
3.NSF.1: Identity a part of a
whole using fraction models.
3.NSF.1: Identify
parts of a fraction
(denominator and
numerator).
3.NSF.1: Identify a fraction
from a list of numbers (i.e.,
3 choices, 2 whole
numbers, and 1 fraction).
3.NSF.2: Explain fraction
equivalence (i.e., denominators 2,
3, 4, 6, 8, 10) by demonstrating an
understanding that two fractions
are equal if they are the same size,
based on the same whole, or at the
same point on a number line.
3.NSF.2: Identify equal
fractions that are the same
size but have different
fraction sizes using models
and numbers to show
fractions using the
denominators 2, 3, 4, 6, 8, 10.
3.NSF.2: Recognize that two
fractions are equal if they are
the same using different
numbers in the denominators
(using pictures limiting the
denominators to 2, 3, and 4).
3.NSF.2: Identify
fraction models that
are divided into the
same number of parts.
3.NSF.2: Identify shapes
divided into equal parts.
It Is Essential for Students to Know: Students need to identify parts of a fraction and recognize when a fraction model is divided into equal
parts. Students can share a bar of chocolate equally between two people to practice being able to recognize equal parts.
Applications to Daily Tasks, Activities, Routines, or Life Experiences
• Use pizza or square crackers to practice fractions. Demonstrate breaking or cutting the item into equal parts such as halves or fourths.
-26-
• Demonstrate the denominator and numerator; the total number of parts of the cracker or slices of pizza (denominator) and the number of
parts remaining, eaten, or shared (numerator).
Standard Vocabulary Skills Daily Activities Functional Activities
3NSF Numerator
Denominator
Fraction
Distinguish between fractions
and whole numbers
Identify parts of a fraction
Compare equal fractions
Color or cut paper plates into fractions
Practice menu math
Practice play-dough math
Use seed trays
Use arrays with preferred objects
Add and subtract money (coins)
Use a money tray to sort money and make change
Play card games
Hosting a fraction picnic
Comparing groups of boys or girls to the
whole group (at recess, at lunch)
Sorting parts/whole for everyday objects
Folding towels into ½, ¼, etc.
-27-
4th Grade
Key Concept: Number Sense and Operations – Fractions
SCCCR Standards: Explain why a fraction (i.e., denominators 2, 3, 4, 5, 6, 8, 10, 12, 25, 100), 𝑎
𝑏 , is equivalent to a fraction,
𝑛 × 𝑎
𝑛 × 𝑏, by using visual
fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this
principle to recognize and generate equivalent fractions (4.NSF.1). Compare two given fractions (i.e., denominators 2, 3, 4, 5, 6, 8, 10, 12, 25,
100) by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1
2 and represent the comparison using the
symbols >, =, or < (4.NSF.2). Develop an understanding of addition and subtraction of fractions (i.e., denominators 2, 3, 4, 5, 6, 8, 10, 12, 25, 100)
based on unit fractions. a. Compose and decompose a fraction in more than one way, recording each composition and decomposition as an
addition or subtraction equation; b. Add and subtract mixed numbers with like denominators; c. Solve real-world problems involving addition and
subtraction of fractions referring to the same whole and having like denominators (4.NSF.3). Express a fraction with a denominator of 10 as an
equivalent fraction with a denominator of 100 and use this technique to add two fractions with respective denominators of 10 and 100 (4.NSF.5).
Compare and order decimal numbers to hundredths, and justify using concrete and visual models (4.NSF.7).
Prioritized Standard Level 4: Exceeds Standard Level 3: Meets Standard Level 2: Emerging Level 1: Foundational
4.NSF.1: Using visual
fraction models, recognize
equivalent fractions (i.e.,
denominators 2, 3, 4, 5, 6, 8,
10, 12, 25, 100).
4.NSF.1: Use same-size
models that have been
divided differently to solve
equivalent fraction problems
(i.e., denominators 2, 3, 4, 5,
6, 8, 10, 12, 25, 100).
4.NSF.1: Use same-size models
that have been divided
differently to solve equivalent
fraction problems (i.e.,
denominators 2, 3, 4, 5, 6, 8, 10,
12, and 25).
4.NSF.1: Identify models that
have been divided in half or
equal parts (i.e., denominators
limited to 2–10).
4.NSF.1: Identify a
fraction from a whole
number.
4.NSF.2: Compare two given
fractions (i.e., denominators
2, 3, 4, 5, 6, 8, 10, 12, 25,
100) with common
denominators using the
symbols >, =, or <.
4.NSF.2: Compare two
fractions with like
denominators (=, <, >).
4.NSF.2: Compare two fractions
with like denominators using a
pictorial model (=, <, >).
4.NSF.2: Demonstrate the
concepts of greater than and
less than using models/groups
of manipulatives to choose
which ones have more, less,
or equal amounts (<, >, =).
4.NSF.2: Recognize
greater than and less
than signs.
-28-
Prioritized Standard Level 4: Exceeds Standard Level 3: Meets Standard Level 2: Emerging Level 1: Foundational
4.NSF.3: Develop an
understanding of addition and
subtraction of fractions with a
common denominator (i.e.,
denominators 2, 3, 4, 5, 6, 8,
10, 12, 25, 100) based on unit
fractions. a. Develop an
understanding of mixed
numbers.
4.NSF.3: Add and subtract
fractions with common
denominators (denominators
limited to 2, 3, 4, 5, 6, 8, 10,
12, 25, 100). Develop an
understanding of mixed
numbers.
4.NSF.3: Using simple fractions
with common denominators
(limited between the numbers 2–
9), add or subtract the
numerators in the fraction.
4.NSF.3: Identify numerators
and denominators in
fractions.
4.NSF.3: Identify
common denominators
in fractions.
4.NSF.5: Express a fraction
with a denominator of 10 as
an equivalent fraction with a
denominator of 100 and use
this technique to add two
fractions with respective
denominators of 10 and 100.
4.NSF.5: Identify fractions
with the denominators of 10
and 100 when comparing
two fractions.
4.NSF.5: Identify when two
fractions are equivalent with the
denominators of 10 and 100.
4.NSF.5: Given a model,
recognize tenths/hundredths
using a model.
4.NSF.5: Recognize
part of a whole using
models.
4.NSF.6: Write a fraction
with a denominator of 10 or
100 using decimal notation.
4.NSF.6: Write a fraction
with denominator of 10 or
100 as a decimal.
4.NSF.6: Write a fraction from a
decimal notation with the
denominator of 10.
4.NSF.6: Demonstrate the
function of a decimal point as
it represents a fraction using a
place value chart.
4.NSF.6: Identify
where a decimal point
is on the place value
chart. Identify the
tenths and hundredths
place on the value
chart.
4.NSF.7: Compare decimal
numbers to hundredths using
visual models.
4.NSF.7: Compare decimal
numbers to hundredths
place.
4.NSF.7: Using visual models,
compare decimals to hundredths
place.
4.NSF.7: Demonstrate the
function of a decimal point as
it represents a fraction using a
place value chart.
4.NSF.7: Recognize
greater than, less than,
and equal signs.
It Is Essential for Students to Know: Students need to be able to identify a fraction of a whole and compare fractions using models. Students
also need to recognize decimals, understand the place value of decimals using models, and compare decimals using symbols.
-29-
Applications to Daily Tasks, Activities, Routines, or Life Experiences
• Demonstrate adding and subtracting fractions by sharing objects that can be divided, such as a piece of paper or large crackers.
• Demonstrate decimals using a hundred chart with pennies and dimes. Connect the decimals shown with the coins to the written decimal
number.
• Compare decimals using a hundred chart and two sets of pennies and dimes (e.g., 2 dimes and 1 penny is greater than 4 pennies).
Standard Vocabulary Skills Daily Activities Functional Activities
4NSF Mixed number
Tenths
Hundredths
Comparing fractions –
greater than, less than,
and equal to
Fold or cut objects (construction paper, newspaper)
into equal parts
Tabulate voting results to find votes of groups
compared to total of votes
Compare attributes, clothing of students, etc. to
understand fractions represented and compare groups
Use tangrams to make a whole
Using shirts, socks, etc. with fractions
written on them to compare and order
fractions
Using pizza toppings representing fractions
to compare amounts to the whole
Practicing measurement using cups and
spoons
-30-
5th Grade
Key Concept: Number Sense and Operations – Fractions
SCCCR Standards: Add and subtract fractions with unlike denominators (including mixed numbers) using a variety of models, including an area
model and number line (5.NSF.1). Extend the concept of multiplication to multiply a fraction or whole number by a fraction. a. Recognize the
relationship between multiplying fractions and finding the areas of rectangles with fractional side lengths; b. Interpret multiplication of a fraction
by a whole number and a whole number by a fraction and compute the product; c. Interpret multiplication in which both factors are fractions less
than one and compute the product (5.NSF.4).
Prioritized Standard Level 4: Exceeds Standard Level 3: Meets Standard Level 2: Emerging Level 1: Foundational
5.NSF.1: Add and subtract
fractions with unlike
denominators using a variety
of models, including an area
model and number line.
5.NSF.1: Add or subtract
fractions with unlike
denominators (limit to
halves, thirds, fourths, sixths,
and use visual models).
5.NSF.1: Add or subtract
fractions with like
denominators using models
(limit to halves, thirds,
fourths, sixths, and eighths).
5.NSF.1: Create a model of
a fraction (partition and
shade).
5.NSF.1: Partition any shape
into equal parts.
5.NSF.4: Multiply a whole
number by a fraction.
5.NSF.4: Multiply a whole
number by a fraction.
5.NSF.4: Multiply a whole
number by a fraction (limit
to compatible numbers that
result in a whole number
product).
5.NSF.4: Understand the
relationship between adding
and multiplying the fraction.
5.NSF.4: Add two of the
same fraction (limit to
halves, thirds, fourths).
It Is Essential for Students to Know: Students need to be able to divide a whole into equal parts. Students need to be able to add, subtract, and
multiply fractions using models.
Applications to Daily Tasks, Activities, Routines, or Life Experiences
• Have students add and subtract fractions with like denominators by using a large measuring cup and an individual measuring spoon.
-31-
Standard Vocabulary Skills Daily Activities Functional Activities
5NSF Add
Subtract
Fractions
Partition
Denominator
Numerator
Halves
Thirds
Fourths
Sixths
Eights
Shade
Compatible
Adding fractions
Subtracting fractions
Multiplying fractions with
whole numbers
Practice with fractions using concrete models;
example: 5 x ½ – give students five halves of an
apple and have them put the halves together to
determine how many total apples there are (2 ½)
Doubling or halving a recipe
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6th Grade
Key Concept: Ratios and Proportional Relationships
SCCCR Standards: Interpret the concept of a ratio as the relationship between two quantities, including part-to-part and part-to-whole (6.RP.1).
Prioritized Standard Level 4: Exceeds Standard Level 3: Meets Standard Level 2: Emerging Level 1: Foundational
6.RP.1: Understand the
concept of a ratio as the
relationship between two
quantities, including part-to-
part and part-to-whole.
6.RP.1: Understand the
concept of a ratio as the
relationship between two
quantities, including part-to-
part and part-to-whole.
6.RP.1: Understand the
concept of a ratio as the
relationship between two
quantities (limit to part-to-
whole).
6.RP.1: Identify a ratio that
matches a context.
6.RP.1: Identify a ratio.
It Is Essential for Students to Know: Students need to be able to recognize ratios.
Applications to Daily Tasks, Activities, Routines, or Life Experiences
• Determine solutions to real-world problems. For example, the recipe for 12 muffins uses 2 eggs. How many eggs are needed to make 36
muffins?
Standard Vocabulary Skills Daily Activities Functional Activities
6RP Ratio
Context
Part
Whole
Identify ratio
Understand part-to-whole
relationships
Color or cut paper plates into fractions
Practice menu math
Practice play-dough math
Use seed trays
Use arrays with preferred objects
Add and subtract money (coins)
Use a money tray to sort money and make change
Hosting a fraction picnic
Comparing groups of boys or girls to the
whole group (at recess, at lunch)
Sorting parts/whole for everyday objects
Folding towels into ½, ¼, etc.
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7th Grade
Key Concept: Ratios and Proportional Relationships
SCCCR Standards: Identify and model proportional relationships given multiple representations, including tables, graphs, equations, diagrams,
verbal descriptions, and real-world situations (7.RP.2). Determine when two quantities are in a proportional relationship (7.RP.2a). Investigate the
graph of a proportional relationship and explain the meaning of specific points (e.g., origin, unit rate) in the context of the situation (7.RP.2e).
Solve real-world and mathematical problems involving ratios and percentages using proportional reasoning (e.g., multi-step dimensional analysis,
percent increase/decrease, tax) (7.RP.3).
Prioritized Standard Level 4: Exceeds Standard Level 3: Meets Standard Level 2: Emerging Level 1: Foundational
7.RP.2: Identify proportional
relationships given multiple
representations, including
tables, graphs, and real-world
situations. a. Determine when
two quantities are in a
proportional relationship.
e. Identify the graph of a
proportional relationship in a
real-world situation.
7.RP.2: Identify proportional
relationships given multiple
representations, including tables,
graphs, and real-world
situations. a. Determine when
two quantities are in a
proportional relationship. e.
Identify the graph of a
proportional relationship in a
real-world situation.
7.RP.2: Identify proportional
relationships given multiple
representations, including
tables, graphs, and real-world
situations. a. Determine when
two quantities are in a
proportional relationship.
7.RP.2: Identify
proportional relationships
in real-world situations.
7.RP.2: Identify
equivalent relationships
in real-world situations.
7.RP.3: Solve real-world and
mathematical problems
involving ratios and
percentages.
7.RP.3: Solve real-world and
mathematical problems
involving ratios and percentages.
7.RP.3: Solve real-world
problems involving ratios and
percentages.
7.RP.3: Solve real-world
problems involving
percentages.
7.RP.3: Understand part
and whole relationships.
It Is Essential for Students to Know: Students need to be able to recognize part-to-whole relationships. Students need to be able to recognize
ratios in real-world settings, such as what proportion of the class is made up of boys or what proportion is made up of girls.
Applications to Daily Tasks, Activities, Routines, or Life Experiences
• The students can collect data on how many boys and girls are in the classroom and discuss the proportion of boys to the whole class and
the proportion of girls to the whole class. This can be extended to collecting data and identifying proportions with other objects and
resources in the classroom.
-34-
Standard Vocabulary Skills Daily Activities Functional Activities
7RP Proportional
Ratio
Percentages
Unit rate
Solve problems
with ratio
percentages
(equivalent
fractions)
Fold or cut objects (construction paper, newspaper) into equal parts
Tabulate voting results to find groups compared to whole)
Compare attributes, clothing of students, etc. to understand
fractions represented and compare groups
Use tangrams to make a whole
Calculating mileage and miles/hour
Calculating distances in inches and feet
Taking a medication a specified
number of times per day
Calculating an hourly rate of pay
-35-
Algebraic Thinking and Operations
Expressions, Equations, and Inequalities
3rd Grade 4th Grade 5th Grade 6th Grade 7th Grade 8th Grade
3.ATO 4.ATO 5.ATO 6.EE 7.EE 8.EE
-36-
3rd Grade
Key Concept: Algebraic Thinking and Operations
SCCCR Standards: Use concrete objects, drawings and symbols to represent multiplication facts of two single-digit whole numbers and
explain the relationship between the factors (i.e., 0–10) and the product (3.ATO.1). Solve real-world problems involving equal groups,
area/array, and number line models using basic multiplication and related division facts. Represent the problem situation using an equation
with a symbol for the unknown (3.ATO.3). Determine the unknown whole number in a multiplication or division equation relating three
whole numbers when the unknown is a missing factor, product, dividend, divisor, or quotient (3.ATO.4). Apply properties of operations
(i.e., Commutative Property of Multiplication, Associative Property of Multiplication, Distributive Property) as strategies to multiply and
divide and explain the reasoning (3.ATO.5). Demonstrate fluency with basic multiplication and related division facts of products and
dividends through 100 (3.ATO.7). Solve two-step real-world problems using addition, subtraction, multiplication, and division of whole
numbers and having whole number answers. Represent these problems using equations with a letter for the unknown quantity (3.ATO.8).
Identify a rule for an arithmetic pattern (e.g., patterns in the addition table or multiplication table) (3.ATO.9).
Prioritized Standard Level 4: Exceeds Standard Level 3: Meets Standard Level 2: Emerging Level 1: Foundational
3.ATO.1: Use concrete objects,
drawings, and symbols to represent
multiplication facts of two single-
digit whole numbers (i.e., 0–5).
3.ATO.1: Multiply two
single-digit whole numbers
using 0–5.
3.ATO.1: Demonstrate the
concept of multiplication
using the multiplication sign
and numbers (limited to
numbers 0–3).
3.ATO.1: Demonstrate the
concept of multiplication
by using the repeated
addition strategy (limited
to numbers 0–2).
3.ATO.1: Identify the
multiplication symbol.
3.ATO.3: Solve real-world problems
involving equal groups, area/array,
and number line models using basic
multiplication (i.e., 0–5).
3.ATO.3: Solve a real-world
problem using basic
multiplication with equal
groups, arrays, and/or the
number line.
3.ATO.3: Apply the concept
of multiplying using equal
groups by solving a simple
word problem (limited to
numbers 0–5).
3.ATO.3: Match a basic
multiplication expression
with its model.
3.ATO.3: Recognize a
group, an array, and a
number line using
models or pictures.
-37-
Prioritized Standard Level 4: Exceeds Standard Level 3: Meets Standard Level 2: Emerging Level 1: Foundational
3.ATO.4: Determine the unknown
whole number in a multiplication
equation relating three whole
numbers when the unknown is a
missing factor or product.
3.ATO.4: Determine the
unknown whole number in a
multiplication equation by
selecting the missing factor
and product from a set of
whole numbers (limited to
numbers 0–5).
3.ATO.4: Determine the
unknown whole number in a
multiplication equation by
selecting the missing factor
from a set of whole numbers
(one missing factor between
the numbers 0 and 5).
3.ATO.4: Determine the
unknown whole number in
a multiplication equation
by selecting the missing
product from a set of
whole numbers (limited to
numbers 0–5).
3.ATO.4: Identify the
key terms,
factor/product, in a
multiplication equation.
3.ATO.5: Apply the Commutative
Property of Multiplication.
3.ATO.5: Demonstrate
understanding of the concept
by filling in the missing
factors in a commutative
property equation (filling in
one missing factor from both
sides).
3.ATO.5: Match equivalent
multiplication expressions
using models.
3.ATO.5: Match a basic
multiplication expression
with its model.
3.ATO.5: Identify
multiplication
problems.
3.ATO.7: Demonstrate basic
multiplication facts of products
through 25.
3.ATO.7: Demonstrate basic
multiplication facts of
products through 25.
3.ATO.7: Demonstrate the
concept of multiplication by
matching pictures of
multiplication to the correct
multiplication equation
(limited to factors between 0
and 5).
3.ATO.7: Demonstrate the
concept of multiplication
by using pictures of group
members being distributed
as a set number of items.
3.ATO.7: Recognize
basic multiplication sets
(limited to the multiples
of 0, 1, and 2).
3.ATO.8: Solve one-step, real-world
problems using addition and
subtraction of whole numbers and
having whole number answers.
3.ATO.8: Solve addition or
subtraction word problems
(limited to products up to
10).
3.ATO.8: Determine the
unknown in an addition or
subtraction equation.
3.ATO.8: Demonstrate
addition or subtraction
problems using
manipulatives.
3.ATO.8: Recognize
one-step equations.
3.ATO.9: Identify a rule for an
arithmetic pattern limited to
multiples of 1, 2, 5, 10, and 25, up to
100.
3.ATO.9: Identify a rule for
an arithmetic pattern limited
to multiples of 1, 2, 5, 10,
and 25, up to 100.
3.ATO.9: Identify a rule for
an arithmetic pattern limited
to multiples of 1, 2, 5, and
10.
3.ATO.9: Count by 10. 3.ATO.9: Count by 1,
2, and 5.
-38-
It Is Essential for Students to Know: Students need to be able to count by multiples and recognize number patterns. Students need to also
recognize visual models of expressions (e.g., 2 rows of 3 apples is the same as 2 x 3).
Applications to Daily Tasks, Activities, Routines, or Life Experiences
• The teacher can use real objects to show 3 groups of 2, which demonstrates the multiplication expression “3 x 2.” The students can match
or name the multiplication expression that is being demonstrated and find the solution. For example, there are 3 baskets and there are 2
apples in each basket. This shows 3 x 2, so how many apples are there in all?
• Using a hundred chart and preferred objects, the teacher can demonstrate counting multiples of 2, 5, and 10.
Standard Vocabulary Skills Daily Activities Functional Activities
3ATO Multiplication
Equal
Array
Factors
Expressions
Word problems
Number line
Patterns
Multiply whole numbers
Determine unknowns
Identify the multiplication sign
Count by 1, 2, 5, and 10
Solve addition/subtraction story
problems with missing addend
Practice skip counting
Using preferred objects, create addition and
subtraction stories
Use a hundred chart to color in patterns
Assign class jobs to students (water plants
every 5th day)
Create concrete models of arrays using muffin
tins, beads on pipe cleaners, blocks on wall,
etc. and match to written expression
Lacing – counting by multiples (2, 5, 10)
Ordering combo meals at restaurants – 2
combo meals equal how many of each
item in each combo meal?
Comparing prices (e.g., 2 for $2,
3 for $5; which is the better price?)
-39-
4th Grade
Key Concept: Algebraic Thinking and Operations
SCCCR Standards: Solve real-world problems using multiplication (product unknown) and division (group size unknown, number of groups
unknown) (4.ATO.2). Recognize that a whole number is a multiple of each of its factors. Find all factors for a whole number in the range 1–100
and determine whether the whole number is prime or composite (4.ATO.4). Generate a number or shape pattern that follows a given rule and
determine a term that appears later in the sequence (4.ATO.5).
Prioritized Standard Level 4: Exceeds Standard Level 3: Meets Standard Level 2: Emerging Level 1: Foundational
4.ATO.2: Solve one-step,
real-world problems using
basic multiplication (0–10)
or division (with no
remainders).
4.ATO.2: Solve one-step
multiplication or division
word problems.
4.ATO.2: Determine the
unknown in a multiplication
or division equation.
4.ATO.2: Demonstrate the
concepts of multiplication
and division.
4.ATO.2: Identify the
components of a
multiplication problem.
4.ATO.4: Find all factor
pairs for whole numbers 1–
24.
4.ATO.4: Identify factors
for whole numbers 1–24.
4.ATO.4: Identify factors
for whole numbers 1–10.
4.ATO.4: Identify factors
for whole numbers 1–5.
4.ATO.4: Recognize what a
factor pair is for a whole
number.
4.ATO.5: Given the rule for
a pattern, determine the next
term in the sequence/pattern.
4.ATO.5: Given the rule,
determine the next term in a
number pattern or sequence.
4.ATO.5: Given the rule,
determine the next term in a
picture pattern or sequence.
4.ATO.5: Identify symbolic,
repeating, and pictorial
patterns.
4.ATO.5: Recognize
patterns.
It Is Essential for Students to Know: Students need to be able to recognize symbol and picture patterns. Students need to also recognize
multiplication facts for numbers 1–10 to solve multiplication and division problems.
-40-
Applications to Daily Tasks, Activities, Routines, or Life Experiences
• Use a rug with a pattern or another familiar object with a pattern, and have the student identify the pattern shown on the object.
• Use student-preferred objects and create real-life word problems demonstrating multiplication facts for numbers 1–10.
• Show the student a multiplication fact they know using objects and the written fact (e.g., 2 x 3 = 6). Connect how the multiplication fact
helps solve the related division problem (6 / 2 = 3 or 6 / 3 = 2).
Standard Vocabulary Skills Daily Activities Functional Activities
4ATO Multiplication
Equal
Array
Factors
Expressions
Word problems
Number line
Patterns
Division
Sequence
Multiply whole numbers
Determine unknowns
Identify multiplication sign
Count by 1, 2, 5, and 10
Solve addition/subtraction
story problems with
missing addend
Find next number in a
sequence or picture pattern
Practice skip counting
Use preferred objects to create addition and subtraction
stories
Use a hundred chart to fill in or color patterns
Assign class jobs to students (water plants every 5th day)
Use concrete models of arrays such as muffin tins,
beads on pipe cleaners, blocks on wall, etc. and match
to written expression
Use pattern blocks or containers
Use tally marks to count by 5
Making jewelry to create
patterns (use beads or cereal)
Making fruit or vegetable
kabobs to create patterns
-41-
5th Grade
Key Concept: Algebraic Thinking and Operations
SCCCR Standards: Evaluate numerical expressions involving grouping symbols (i.e., parentheses, brackets, braces) (5.ATO.1). Translate verbal
phrases into numerical expressions and interpret numerical expressions as verbal phrases (5.ATO.2).
Prioritized Standard Level 4: Exceeds Standard Level 3: Meets Standard Level 2: Emerging Level 1: Foundational
5.ATO.1: Evaluate two-step
numerical expressions involving
grouping symbols (i.e.,
parentheses, brackets, braces).
5.ATO.1: Evaluate two-step
numerical expressions involving
grouping symbols (i.e.,
parentheses, brackets, braces;
limit to addition and subtraction).
5.ATO.1: Evaluate a two-step
numerical expression
involving grouping symbols
(limit to addition and
subtraction).
5.ATO.1: Evaluate a
one-step expression
that contains grouping
symbols.
5.ATO.1: Identify
grouping symbols in an
expression (parentheses,
brackets, braces).
5.ATO.2: Translate verbal
phrases into simple numerical
expressions.
5.ATO.2: Translate verbal
phrases into simple numerical
expressions.
5.ATO.2: Translate verbal
phrases into simple numerical
expressions (limit to one-step
addition or subtraction).
5.ATO.2: Given a
verbal phrase, identify
the operation.
5.ATO.2: Identify the
symbol that correlates
with sum, product, take
away, divide.
It Is Essential for Students to Know: Students need to be able to recognize computation terms (e.g., how many are left, altogether). Students
need to be able to create and solve one-step addition and subtraction equations.
Applications to Daily Tasks, Activities, Routines, or Life Experiences
• Demonstrate solving one-step addition and subtraction problems using student-preferred objects. For example, have students count how
many items they have in their pencil box. Then, have students give away or add more items to the box. Create addition or subtraction
expressions demonstrating how the amount of supplies changed.
Standard Vocabulary Skills Daily Activities Functional Activities
5ATO Expression
Parenthesis
Brackets
Braces
Using grouping symbols
Identify operation needed
Write expressions into
numerical form
Use hula hoops, jump ropes, wiki sticks to
illustrate grouping symbols
Play games with cards (grouping)
Use real life examples with preferred objects to
explain operational vocabulary
Sponsoring a canned food drive to
compare class totals and practice
addition, subtraction, multiplication,
and division
-42-
Standard Vocabulary Skills Daily Activities Functional Activities
Take away
Sum
Product
Use building blocks
-43-
6th Grade
Key Concept: Expressions, Equations, and Inequalities
SCCCR Standards: Write and evaluate numerical expressions involving whole-number exponents and positive rational number bases using the
Order of Operations (6.EEI.1). Extend the concepts of numerical expressions to algebraic expressions involving positive rational numbers.
a. Translate between algebraic expressions and verbal phrases that include variables. b. Investigate and identify parts of algebraic expressions
using mathematical terminology, including term, coefficient, constant, and factor. c. Evaluate real-world and algebraic expressions for specific
values using the Order of Operations. Grouping symbols should be limited to parentheses, braces, and brackets. Exponents should be limited to
whole numbers (6.EEI.2). Write and solve one-step linear equations in one variable involving nonnegative rational numbers for real-world and
mathematical situations (6.EEI.7).
Prioritized Standard Level 4: Exceeds Standard Level 3: Meets Standard Level 2: Emerging Level 1: Foundational
6.EEI.1: Write numerical
expressions involving whole
numbers using the Order of
Operations.
6.EEI.1: Write numerical
expressions involving whole
numbers using the Order of
Operations.
6.EEI.1: Given an equation,
identify the Order of
Operations.
6.EEI.1: Given an equation,
identify the first step for
Order of Operations.
6.EEI.1: Given an equation,
identify the symbols for the
four functions (+, –, x, ÷).
6.EEI.2: Identify parts of
algebraic expressions using
mathematical terminology,
including term, coefficient,
constant, and variable.
6.EEI.2: Identify parts of
algebraic expressions using
mathematical terminology,
including term, coefficient,
constant, and variable.
6.EEI.2: Identify the parts of
an expression using
mathematical terminology
(limit to term and variable).
6.EEI.2: Identify an
algebraic expression.
6.EEI.2: Distinguish
between a number and a
letter.
6.EEI.7: Identify linear
equations for real-world
situations.
6.EEI.7: Identify linear
equations related to wages,
finances, time, and distance.
6.EEI.7: Identify a situation
where the variables create an
increasing linear equation
(e.g., the more hours you
work, the higher your
paycheck; the farther your
destination, the longer the
bus ride).
6.EEI.7: Identify the
relationship between two
variables.
6.EEI.7: Recognize that an
unknown value can be
represented by a variable.
It Is Essential for Students to Know: Students need to be able to differentiate between a variable and a number, and to recognize expressions and
equations. Students also need to know the Order of Operations.
-44-
Applications to Daily Tasks, Activities, Routines, or Life Experiences
• Read articles with graphs and interpret the graphs.
• Identify linear equations that represent real-life situations. For example, Peter is paid $5 for walking 1 dog, $10 for walking 2 dogs, and
$15 for walking 3 dogs. Which line shows how much Peter gets paid for walking dogs?
Standard Vocabulary Skills Daily Activities Functional Activities
6EE Variables
Term
Symbols
Increasing
Linear
Use Order of Operations
Understand money and
measurement
Distinguish between
numbers/letters
Play the Twenty-four game
Sort magnetic numbers and letters
Use an outside activity such as running to
determine distance ran in a time or time to
run a distance, and then graph results
Play hopscotch to practice using the Order
of Operations
Use hula hoops, jump ropes, wiki sticks to
illustrate grouping symbols
Use visual schedule for Order of Operations
“Hiring” students for jobs and determining “pay”
Using a map of familiar places (school or town)
determine distance
Running a school store
Growing plants and measuring growth
Using a thermometer to understand temperature
Calculating electricity usage
Using a toaster and adjusting time for darkness of bread
Using a dryer to understand that a longer drying time
creates drier clothes
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7th Grade
Key Concept: Expressions, Equations, and Inequalities
SCCCR Standards: Apply mathematical properties (e.g., commutative, associative, distributive) to simplify and to factor linear algebraic
expressions with rational coefficients (7.EEI.1). Extend previous understanding of Order of Operations to solve multi-step real-world and
mathematical problems involving rational numbers. Include fraction bars as a grouping symbol (7.EEI.3).
Prioritized Standard Level 4: Exceeds Standard Level 3: Meets Standard Level 2: Emerging Level 1: Foundational
7.EEI.1: Apply mathematical
properties (e.g., commutative,
associative) to simplify linear
algebraic expressions with
whole number coefficients.
7.EEI.1: Apply mathematical
properties (e.g., commutative,
associative) to simplify linear
algebraic expressions with whole
number coefficients.
7.EEI.1: Apply mathematical
commutative property to simplify
linear algebraic expressions with
whole number coefficients.
7.EEI.1: Apply
mathematical
commutative
property of addition
and multiplication.
7.EEI.1: Apply
mathematical
commutative property
of addition.
7.EEI.3: Extend previous
understanding of Order of
Operations to solve multi-step
real-world and mathematical
problems involving whole
numbers. Exclude exponents
and fraction bars as a grouping
symbol.
7.EEI.3: Extend previous
understanding of Order of
Operations to solve multi-step
real-world and mathematical
problems involving whole
numbers. Exclude exponents and
fraction bars as a grouping
symbol.
7.EEI.3: Extend previous
understanding of the Order of
Operations to solve two-step real-
world problems involving whole
numbers. Exclude exponents and
fraction bars as a grouping symbol.
7.EEI.3: Know the
Order of Operations
in a mathematical
expression.
7.EEI.3: Identify a
mathematical operation
by its symbol.
It Is Essential for Students to Know: Students need to be able apply the Order of Operations and commutative property of addition and
multiplication.
Applications to Daily Tasks, Activities, Routines, or Life Experiences
• Use simple directions to show the real-world use of the commutative property. For example, here are directions to the principal’s office:
take a right out of the classroom door, walk 10 feet, then take a left, walk 5 feet, and the office is in front of you. When going back to
class, walk 5 feet from the principal’s office and then take a right, walk 10 feet, and the class will be on your left.
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Standard Vocabulary Skills Daily Activities Functional Activities
7EE Commutative
Coefficient
Linear
Add and subtract with
commutative property
Use Order of
Operations
Two-step equations
Compare steps taken (one student takes 6 steps then 4;
the other takes 4 steps and then 6)
Use sentence strips to take word problems apart and
put back together; put in correct order to match model
Use a calculator to get to correct answer (give answer
first and they determine order to get answer)
Using directions to and from places to
understand the commutative property (tasks
where order does not matter)
Completing activities where order does matter
(task analysis) such as making a sandwich,
getting dressed, or building something
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8th Grade
Key Concept: Expressions, Equations, and Inequalities
SCCCR Standards: Understand and apply the laws of exponents (i.e., product rule, quotient rule, power to a power, product to a power, quotient
to a power, zero power property, negative exponents) to simplify numerical expressions that include integer exponents (8.EEI.1). Investigate
concepts of square and cube roots. a. Find the exact and approximate solutions to equations of the form 𝑥2 = 𝑝 and 𝑥3 = 𝑝 where 𝑝 is a positive
rational number. b. Evaluate square roots of perfect squares. c. Evaluate cube roots of perfect cubes. d. Recognize that square roots of non-perfect
squares are irrational (8.EEI.2). Apply concepts of proportional relationships to real-world and mathematical situations. a. Graph proportional
relationships. b. Interpret unit rate as the slope of the graph. c. Compare two different proportional relationships given multiple representations,
including tables, graphs, equations, diagrams, and verbal descriptions (8.EEI.5).
Prioritized Standard Level 4: Exceeds Standard Level 3: Meets Standard Level 2: Emerging Level 1: Foundational
8.EEI.1: Understand
exponents to simplify
numerical expressions that
include integer exponents.
8.EEI.1: Understand exponents to
simplify numerical expressions that
include integer exponents.
8.EEI.1: Understand
exponents to simplify
numerical expressions.
8.EEI.1: Expand
exponents into repeated
multiplication.
8.EEI.1: Identify
repeated multiplication
(4 x 4 x 4) as the
exponent notation (43).
8.EEI.2: Investigate
concepts of square roots.
8.EEI.2: Understand that the square
root is the inverse of squaring a number.
8.EEI.2: Understand how
to square a number.
8.EEI.2: Understand
multiplication facts of
whole numbers with
products up to 100.
8.EEI.2: Understand
multiplication as
repeated addition.
8.EEI.5: Compare two
different proportional
relationships using tables
and graphs.
8.EEI.5: Compare two different
proportional relationships given
multiple representations, including
tables, graphs, equations, diagrams, and
verbal descriptions.
8.EEI.5: Compare two
different proportional
relationships using tables
and graphs.
8.EEI.5: Compare two
relationships using tables
and graphs.
8.EEI.5: Identify a table
or graph.
It Is Essential for Students to Know: Students need to be able to recognize the relationship between repeated addition and multiplication.
Students need to be able to convert repeated multiplication into exponents (i.e., 2 x 2 x 2 = 23). Students also need to be able recognize a
proportional relationship when displayed in a table or graph.
-48-
Applications to Daily Tasks, Activities, Routines, or Life Experiences
• Show repeated multiplication using objects.
Standard Vocabulary Skills Daily Activities Functional Activities
8EE Square of a number
Exponent
Table
Graph
Proportion
Simplify
Product
Repeated addition
Repeated multiplication
Read tables and graphs
Use bingo dotters to illustrate repeated
multiplication
Use muffin tins to understand repeated
multiplication; put the same number of
objects in each space and then group
together to calculate answer
Grouping similar items or cans in a pantry or
grocery store and counting the totals
Stocking vending machines or items in the
school store
Filling class orders (such as using health
supplies, paper towels, Band-Aids, gloves, etc.)
-49-
Geometry
Geometry and Measurement
3rd Grade 4th Grade 5th Grade 6th Grade 7th Grade 8th Grade
3.G 4.G 5.G 6.GM 7.GM 8.GM
-50-
3rd Grade
Key Concept: Geometry
SCCCR Standards: Understand that shapes in different categories (e.g., rhombus, rectangle, square, and other 4-sided shapes) may share
attributes (e.g., 4-sided figures) and the shared attributes can define a larger category (e.g., quadrilateral). Recognize rhombuses, rectangles,
and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories (3.G.1). Partition two-dimensional shapes into 2, 3, 4, 6, or 8 parts with equal areas and express the area of each part using the same unit fraction.
Recognize that equal parts of identical wholes need not have the same shape (3.G.2).
Prioritized Standard Level 4: Exceeds Standard Level 3: Meets Standard Level 2: Emerging Level 1: Foundational
3.G.1: Recognize
rhombuses, rectangles, and
squares as quadrilaterals.
3.G.1: Identify all attributes
of quadrilaterals (i.e., 4
sides, 4 angles).
3.G.1: Recognize
rhombuses, rectangles, and
squares as quadrilaterals.
3.G.1: Identify
quadrilaterals.
3.G.1: Identify sides or
angles of a quadrilateral.
3.G.2: Partition two-
dimensional shapes into two
parts with equal areas.
3.G.2: Recognize when a
shape is not equal to one
half.
3.G.2: Recognize one half
on an area model.
3.G.2: Recognize the equal
parts of a two-dimensional
shape.
3.G.2: Identify two-
dimensional shapes.
It Is Essential for Students to Know: Students need to be able to recognize quadrilaterals and their attributes, such as having 4 sides and 4
angles.
Applications to Daily Tasks, Activities, Routines, or Life Experiences
• Identify quadrilaterals in everyday objects; for example, unfold a box of cereal to see that it is made up of three differently sized
rectangles.
Standard Vocabulary Skills Daily Activities Functional Activities
3G Rectangle
Rhombus
Square
Quadrilateral
Half
Recognize 2D shapes
Divide shapes in half
Sort shapes
Find shapes in environment
Take pictures with students and create a book of shapes
Build a “house”
Sweeping into shape
Recognizing street signs
Recognizing sports fields/courts
Sorting or stocking items in a pantry
-51-
Standard Vocabulary Skills Daily Activities Functional Activities
Build shapes with toothpicks, cotton swabs, pipe cleaners,
geoboards, wiki sticks
Create a shape person (robot)
Play “Four Corners”
-52-
4th Grade
Key Concept: Geometry
SCCCR Standards: Draw points, lines, line segments, rays, angles (i.e., right, acute, obtuse), and parallel and perpendicular lines. Identify these
in two-dimensional figures (4.G.1). Classify quadrilaterals based on the presence or absence of parallel or perpendicular lines (4.G.2).
Prioritized Standard Level 4: Exceeds Standard Level 3: Meets Standard Level 2: Emerging Level 1: Foundational
4.G.1: Identify points, line
segments, and angles in two-
dimensional figures.
4.G.1: Recognize angles,
points, or line segments in a
two-dimensional figure.
4.G.1: Recognize different
types of angles (acute, right,
obtuse, and straight).
4.G.1: Identify a line or line
segment.
4.G.1: Recognize a point.
4.G.2: Identify parallel and
perpendicular lines.
4.G.2: Identify parallel and
perpendicular lines in
shapes.
4.G.2: Identify parallel and
perpendicular lines.
4.G.2: Identify shapes with
parallel lines.
4.G.2: Identify lines.
It Is Essential for Students to Know: Students need to be able to recognize points, lines, and line segments. Students need to be able to recognize
parallel and perpendicular lines.
Applications to Daily Tasks, Activities, Routines, or Life Experiences
• Place marking spots on the classroom floor and engage students to “act” or show points, lines, and line segments by moving to the
different marking spots in the classroom.
• Use objects in the classroom to demonstrate parallel and perpendicular lines.
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• Use objects in the classroom or pictures of familiar places to demonstrate parallel and perpendicular lines.
Standard Vocabulary Skills Daily Activities Functional Activities
4G Acute
Obtuse
Right angle
Straight
Parallel
Perpendicular
Recognize points
Identify lines
Identify shapes with parallel
and perpendicular lines
Recognize angles
Host a scavenger hunt that relies on lines
In gymnasium, find angles and lines
Use toothpicks/marshmallows to create angles
Find points in environment (pencil point, top of bottle)
Find angles in environment (clock, hallways, etc.)
Play shape bingo
Drawing hallways/maps
Looking at crosswalks to
understand parallel lines
Writing names on point or line
Creating parallel lines by pushing
strollers or wheelchairs outside
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5th Grade
Key Concept: Geometry
SCCCR Standards: Define a coordinate system (5.G.1). The x- and y-axes are perpendicular number lines that intersect at 0 (the origin) (5.G.1a).
Any point on the coordinate plane can be represented by its coordinates (5.G.1b). The first number in an ordered pair is the x-coordinate and
represents the horizontal distance from the origin (5.G.1c). The second number in an ordered pair is the y-coordinate and represents the vertical
distance from the origin (5.G.1d). Plot and interpret points in the first quadrant of the coordinate plane to represent real-world and mathematical
situations (5.G.2).
Prioritized Standard Level 4: Exceeds Standard Level 3: Meets Standard Level 2: Emerging Level 1: Foundational
5.G.1: Define a coordinate system. 5.G.1: Identify an ordered
pair on a coordinate plane.
5.G.1: Plot a number on a
vertical or horizontal
number line.
5.G.1: Identify a number
on a vertical or horizontal
number line.
5.G.1: Recognize a point
on a number line (limit to
numbers greater than 0).
5.G.1a: The x- and y-axes are
perpendicular number lines that
intersect at 0 (the origin).
5.G.1a: Identify an ordered
pair on a coordinate plane.
5.G.1a: Plot a number on
a vertical or horizontal
number line.
5.G.1a: Identify a
number on a vertical or
horizontal number line.
5.G.1a: Recognize a point
on a number line (limit to
numbers greater than 0).
5.G.1b: Any point on the coordinate
plane can be represented by its
coordinates.
5.G.1b: Identify an ordered
pair on a coordinate plane.
5.G.1b: Plot a number on
a vertical or horizontal
number line.
5.G.1b: Identify a
number on a vertical or
horizontal number line.
5.G.1b: Recognize a point
on a number line (limit to
numbers greater than 0).
5.G.1c: The first number in an
ordered pair is the x-coordinate and
represents the horizontal distance
from the origin.
5.G.1c: Identify an ordered
pair on a coordinate plane.
5.G.1c: Plot a number on
a vertical or horizontal
number line.
5.G.1c: Identify a number
on a vertical or horizontal
number line.
5.G.1c: Recognize a point
on a number line (limit to
numbers greater than 0).
5.G.1d: The second number in an
ordered pair is the y-coordinate and
represents the vertical distance from
the origin.
5.G.1d: Identify an ordered
pair on a coordinate plane.
5.G.1d: Plot a number on
a vertical or horizontal
number line.
5.G.1d: Identify a
number on a vertical or
horizontal number line.
5.G.1d: Recognize a point
on a number line (limit to
numbers greater than 0).
5.G.2: Plot points in the first
quadrant.
5.G.2: Plot a point on a map
given the x and y variables.
5.G.2: Recognize
perpendicular lines and
line segments.
5.G.2: Recognize
intersecting lines and line
segments.
5.G.2: Recognize a point.
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It Is Essential for Students to Know: Students need to be able to identify various points on a number line. Students need to be able to recognize
line segments and intersecting lines.
Applications to Daily Tasks, Activities, Routines, or Life Experiences
• Have students roll a die and place a marker on a number line corresponding to the number rolled on the die.
• Using pictures of real life locations and objects, demonstrate the difference between line segments and intersecting lines.
Standard Vocabulary Skills Daily Activities Functional Activities
5G Vertical
Horizontal
Point
Plot
Line segment
Perpendicular
Intersecting
Plot a number on a line Use painter’s tape on the floor or wall to practice
number line activities
Place sticky notes or ink with a dot stamper on chart
paper with X and Y axes illustrated, and plot the points
Practicing reading temperature
from thermometers
-56-
6th Grade
Key Concept: Geometry and Measurement
SCCCR Standards: Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or
decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems (6.GM.1).
Prioritized Standard Level 4: Exceeds Standard Level 3: Meets Standard Level 2: Emerging Level 1: Foundational
6.GM.1: Find the area of
right triangles and
rectangles.
6.GM.1: Find the area of
right triangles and rectangles
when given side lengths.
6.GM.1: Find the area of a
rectangle given the side
lengths and tiles.
6.GM.1: Identify a triangle
that has a right angle.
6.GM.1: Identify a triangle.
It Is Essential for Students to Know: Students need to be able to identify triangles and right angles.
Applications to Daily Tasks, Activities, Routines, or Life Experiences
• Students can practice finding the area by measuring the length and width of a window to determine what size curtains are needed, or they
can measure the length and width of the classroom and their desks to determine approximately how many desks would fit in the
classroom.
• Have students identify triangles inside everyday objects, such as pictures on flags, road signs, or the entrance of a tent.
Standard Vocabulary Skills Daily Activities Functional Activities
6GM Triangle
Area
Rectangle
Find area
Identify right triangles
Identify triangles
Area formula
Use painter’s tape on the floor or count tiles to find area
Use square foods such as crackers to create rectangles and
triangles, and then find the area
Measure objects in class, such as tables, windows, etc.
Use pool table rack to illustrate the area of a triangle and
calculate how many of same object can fit inside
Use coat hangers to illustrate the area of a triangle and
calculate how many of same object can fit inside
Play area games, such as rolling number cubes, coloring in
the area of a shape on graph paper, and illustrating
percentage using 10x10 grid paper
Measuring area by making curtains,
bandanas, or pennants for sports teams
Making a simple floor plan
Cutting fabric and calculating area
Using pizza slices to understand how
many toppings fill slice
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7th Grade
Key Concept: Geometry and Measurement
SCCCR Standards: Apply the concepts of two- and three-dimensional figures to real-world and mathematical situations. a. Understand that the
concept of area is applied to two-dimensional figures such as triangles, quadrilaterals, and polygons. b. Understand that the concepts of volume
and surface area are applied to three-dimensional figures such as cubes, right rectangular prisms, and right triangular prisms. c. Decompose cubes,
right rectangular prisms, and right triangular prisms into rectangles and triangles to derive the formulas for volume and surface area. d. Use the
formulas for area, volume, and surface area appropriately (7.GM.6).
Prioritized Standard Level 4: Exceeds Standard Level 3: Meets Standard Level 2: Emerging Level 1: Foundational
7.GM.6: Understand that the
concept of area applies to
two-dimensional figures.
Understand that the concept
of volume applies to three-
dimensional figures.
7.GM.6: Understand that the
concept of area applies to
two-dimensional figures.
Understand that the concept
of volume applies to three-
dimensional figures.
Understand which formula to
use to calculate either area or
volume.
7.GM.6: Understand that the
concept of area applies to
two-dimensional figures.
Understand that the concept
of volume applies to three-
dimensional figures.
7.GM.6: Understand the
concept of area. Understand
the concept of volume.
7.GM.6: Understand the
difference between two-
dimensional and three-
dimensional figures.
It Is Essential for Students to Know: Students need to be able to differentiate between two- and three-dimensional objects. Students also need to
be able to determine when to find the area or volume of an object, such as how one finds the area of a window or the volume of a cereal box.
Applications to Daily Tasks, Activities, Routines, or Life Experiences
• Explore the concept of area by measuring the length and width of papers, then use unit squares to determine if your calculation methods
were correct.
• Explore the concept of volume by estimating the number of dried beans that can fill a three-dimensional object. First, count the number of
beans that cover the bottom of the shape. Then count the number of beans needed to make the height of the object and multiply the
numbers. Verify your findings by counting the number of beans in the container.
-58-
Standard Vocabulary Skills Daily Activities Functional Activities
7GM Volume (3D)
Area (2D)
Link volume
to 3D figures
Link area to
2D figures
Fill bottles with objects (how many objects fill bottle?)
Use blocks/beans to fill 2D shapes and 3D objects
Use a flat square or open cube to illustrate volume;
“pour” contents to show which one will hold
Packing boxes for class picnics – how many boxes
are needed?
Packing book boxes for classes
Cooking
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8th Grade
Key Concept: Geometry and Measurement
SCCCR Standards: Investigate the properties of rigid transformations (rotations, reflections, translations) using a variety of tools (e.g.,
grid paper, reflective devices, graphing paper, technology). a. Verify that lines are mapped to lines, including parallel lines. b. Verify that
corresponding angles are congruent. c. Verify that corresponding line segments are congruent (8.GM.1).
Prioritized Standard Level 4: Exceeds Standard Level 3: Meets Standard Level 2: Emerging Level 1: Foundational
8.GM.1: Investigate the properties
of rigid transformations (rotations,
reflections, translations) using a
variety of tools to recognize
congruence.
8.GM.1: Investigate the properties
of rigid transformations (rotations,
reflections, translations) using a
variety of tools to recognize
congruence.
8.GM.1: Investigate the
properties of rigid
transformations (rotations,
reflections, translations).
8.GM.1: Recognize
congruent figures.
8.GM.1: Recognize
when two-dimensional
shapes are the same.
It Is Essential for Students to Know: Students need to be able to recognize that two shapes are congruent when displayed in different
orientations.
Applications to Daily Tasks, Activities, Routines, or Life Experiences
• Explore properties of rigid transformations by moving a small rug around the room or a desk. Describe how the orientation of the rug or
desk changes based on the transformation.
Standard Vocabulary Skills Daily Activities Functional Activities
8GM 2D
Reflection
Translation
Rotation
Congruent
Recognize shapes
Understand reflection,
translation, and rotation
Sort objects by shape or size
Host a scavenger hunt to find congruent shapes
Create a color mandala by coloring congruent shapes the same color
Use a mirror to illustrate congruence
Create shapes using Tangrams
Use straws to create congruent shapes
Use grid paper to illustrate congruence
Sorting clothing or dishes
by shape/size
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Measurement and Data Analysis
3rd Grade 4th Grade 5th Grade
3.MDA 4.MDA 5.MDA
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3rd Grade
Key Concept: Measurement and Data Analysis
SCCCR Standards: Use analog and digital clocks to determine and record time to the nearest minute, using a.m. and p.m.; measure time
intervals in minutes; and solve problems involving addition and subtraction of time intervals within 60 minutes (3.MDA.1). Estimate and
measure liquid volumes (capacity) in customary units (i.e., c., pt., qt., gal.) and metric units (i.e., mL, L) to the nearest whole unit
(3.MDA.2). Collect, organize, classify, and interpret data with multiple categories and draw a scaled picture graph and a scaled bar
graph to represent the data (3.MDA.3). Generate data by measuring length to the nearest inch, half-inch and quarter-inch and organize the
data in a line plot using a horizontal scale marked off in appropriate units (3.MDA.4).
Prioritized Standard Level 4: Exceeds Standard Level 3: Meets Standard Level 2: Emerging Level 1: Foundational
3.MDA.1: Use analog and
digital clocks to record time to
the nearest hour and half-hour,
using a.m. and p.m.
3.MDA.1: Demonstrate the
concept of telling time to the
hour and half-hour on both
types of clocks.
3.MDA.1: Use analog and digital
clocks to record time to the nearest
hour and half-hour, using a.m.
and p.m.
3.MDA.1: Match
the time to an
activity from a list.
3.MDA.1: Identify a
clock as a tool to
measure time.
3.MDA.2: Measure liquid
volumes (capacity) in
customary units (i.e., c., pt., qt.,
gal.) and metric units (i.e., mL,
L) to the nearest whole unit.
3.MDA.2: Demonstrate the
concept by choosing the
appropriate volume unit for
various given substances to be
measured.
3.MDA.2: Demonstrate the concept
by choosing the appropriate volume
unit for a given substance to be
measured (e.g., what is the best unit
to measure for a box of cereal?)
3.MDA.2: Identify
shapes that can have
volume.
3.MDA.2: Identify
three-dimensional
shapes.
3.MDA.3: Interpret data from a
picture graph and a bar graph.
3.MDA.3: Interpret data from
a picture graph and a bar
graph.
3.MDA.3: Identify information from
a picture graph.
3.MDA.3: Identify
information from a
bar graph.
3.MDA.3: Identify a
bar graph.
3.MDA.4: Measure length to
the nearest inch.
3.MDA.4: Measure length to
the nearest inch.
3.MDA.4: Recognize inches as a
measure of length.
3.MDA.4: Identify
an inch on a ruler.
3.MDA.4: Identify a
ruler.
It Is Essential for Students to Know: Students need to be able to identify tools of measurement. Students need to be able to read time (e.g., 2:30),
length with a ruler, and bar graphs. Students need to also identify objects that have volume (e.g., a cup can contain water).
-62-
Applications to Daily Tasks, Activities, Routines, or Life Experiences
• The students can practice reading a digital and/or analog clock or watch by incorporating activities throughout the day that require the
students to read the clock and compare the time to a class schedule that shows what is happening at different times in the day.
• Students can measure liquids using measuring cups or weigh objects using a scale to help with understanding of volume and units of
measure.
• Use bar graphs in newspapers and magazine articles to demonstrate how to interpret the graph data.
• Students can measure objects using an inch ruler; for example, the students can measure the length and width of a picture to see if it can fit
in a certain frame size.
Standard Vocabulary Skills Daily Activities Functional Activities
3MDA Analog
Digital
AM
PM
Hour
Half Hour
Inches
Graph
Ruler
Volume
Tell time to hour
and half hour
Recognize numbers
Count by 5s
Read rulers
Rote count
Use hula hoops or paper plates to create clocks
Draw a large circle on the floor and let students become the
hands on the clock
Use timers to show the passage of time
Play clock bingo
Measure objects in classroom
Measure preferred food items
Create an art project using sand art to measure depth of different
colors of sand
Measure shoes, feet
Creating a daily schedule with clocks
Hosting a Classroom Olympics –
measure distances ran, objects
thrown, distances jumped
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4th Grade
Key Concept: Measurement and Data Analysis
SCCCR Standards: Convert measurements within a single system of measurement, customary (i.e., in., ft., yd., oz., lb., sec., min., hr.) or metric
(i.e., cm, m, km, g, kg, mL, L) from a larger to a smaller unit (4.MDA.1). Apply the area and perimeter formulas for rectangles (4.MDA.3).
Determine the value of a collection of coins and bills greater than $1.00 (4.MDA.8).
Prioritized Standard Level 4: Exceeds Standard Level 3: Meets Standard Level 2: Emerging Level 1: Foundational
4.MDA.1: Distinguish
measurements within a single
system of measurement—
customary (i.e., in., ft., yd., min.,
hr.) or metric (i.e., cm, m, km, g,
kg, mL, L)—as larger or smaller.
4.MDA.1: Compare the size of
measurements within one system
measure—customary (i.e., in.,
ft., yd., min., hr.) or metric (i.e.,
cm, m, km, g, kg, mL, L).
4.MDA.1: Determine if
measurements within one
system are larger or
smaller (i.e., in., ft., min.,
hr., mL, L).
4.MDA.1: Distinguish
between systems of
measurement.
4.MDA.1: Compare
two pieces of data with
the same unit of
measurement.
4.MDA.3: Find the area and
perimeter for rectangles when given
the side lengths.
4.MDA.3: Find the area and
perimeter for rectangles when
given the side lengths.
4.MDA.3: Find the area
and perimeter by counting
squares.
4.MDA.3: Recognize a
rectangle.
4.MDA.3: Recognize
side lengths.
4.MDA.8: Determine the value of a
collection of coins and bills greater
than $1.
4.MDA.8: Determine the value
of a collection of coins and bills
greater than $1.
4.MDA.8: Identify the
value of a penny, a nickel,
a dime, and a quarter.
4.MDA.8: Identify a
penny, a nickel, a dime,
and a quarter.
4.MDA.8: Recognize
money.
It Is Essential for Students to Know: Students need to be able to identify length and width of a shape. Students need to be able to distinguish
between and compare types of measurement (e.g., inches, minutes, feet). Students also need to be able to recognize coins.
Applications to Daily Tasks, Activities, Routines, or Life Experiences
• Show advertisements and sales flyers and have students select the appropriate coins needed to purchase certain items.
• Use classroom objects to measure side lengths.
• Use classroom objects and using counting squares to determine perimeter and area.
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Standard Vocabulary Skills Daily Activities Functional Activities
4MDA Inches
Feet
Minutes
Hours
Perimeter
Liters
Milliliters
Area
Coins
Compare
measurements with
same unit of
measurement
Count objects
Find area
Identify coins and
value of coins
Create a garden; plan size and shape, and then measure heights of plants
Weigh produce and compare weights
Measure distances using popcorn; without using the lid of the popper,
make popcorn and then measure the distance popcorn travels from
popper (extend into geometry – draw connecting lines and determine
area)
Make and launch paper helicopters activity
Measure heights of students and compare heights
Measuring and comparing
distances at school
Predicting sizes and shapes;
do we have room for 4 trays at
this table?
Counting money, making
purchases, and making change
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5th Grade
Key Concept: Measurement and Data Analysis
SCCCR Standards: Convert measurements within a single system of measurement: customary (i.e., in., ft., yd., oz., lb., sec., min., hr.) or metric
(i.e., mm, cm, m, km, g, kg, mL, L) from a larger to a smaller unit and a smaller to a larger unit (5.MDA.1). Differentiate among perimeter, area,
and volume and identify which application is appropriate for a given situation (5.MDA.4).
Prioritized Standard Level 4: Exceeds Standard Level 3: Meets Standard Level 2: Emerging Level 1: Foundational
5.MDA.1: Convert
measurements within a
single system of
measurement—customary
(i.e., in., ft., yd., min., hr.) or
metric (i.e., cm, m, km, mL,
L)—from a larger to a
smaller unit.
5.MDA.1: Convert
measurements within a
single system of
measurement.
5.MDA.1: Use an
appropriate tool for
measuring length using
inches; use an appropriate
tool for measuring length
using feet; use an appropriate
tool for measuring mass in
pounds; use an appropriate
tool for measuring mass in
ounces.
5.MDA.1: Make direct
comparison of two lengths.
Make direct comparison of
two masses.
5.MDA.1: Recognize
measurable attributes.
5.MDA.4: Differentiate
among perimeter, area, and
volume and identify which
application is appropriate for
a given situation.
5.MDA.4: Solve word
problems by using perimeter,
area, or volume.
5.MDA.4: Solve word
problems involving the
perimeter of polygons.
5.MDA.4: Calculate the
perimeter by adding all the
side lengths. Calculate the
area by counting the square
units.
5.MDA.4: Recognize
measurable attributes.
It Is Essential for Students to Know: Students need to be able to determine and compare the length of two objects or the mass of two objects.
Students need to be able to determine the perimeter and area of a shape.
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Applications to Daily Tasks, Activities, Routines, or Life Experiences
• The students can practice the difference among perimeter, area, and volume by identifying which is needed for certain real-life activity.
For example:
The amount of water in the beaker requires calculating volume.
Determining where the rug can fit requires calculating area.
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Determining the amount of fencing needed for the vegetable garden requires calculating perimeter.
Standard Vocabulary Skills Daily Activities Functional Activities
5MDA Attributes
Tool (measurement)
Mass
Perimeter
Length
Polygon
Calculate
Use measuring tools
Compare lengths and
masses
Calculate perimeter
Use a see-saw to compare weights
Find perimeter throughout classroom,
school, etc. and compare
Using a kitchen scale, cups, and measurements
during cooking
Building or planning a project
Planning and creating a school garden; measure
perimeter, height of plants, etc.
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Data Analysis and Statistics
Data Analysis, Statistics, and Probability
Functions
Interpreting Functions
Interpreting Data
Quantities
Real Number System
6th Grade 7th Grade 8th Grade 11th Grade 8th Grade 11th Grade 11th Grade 11th Grade
6.DS 7.DSP 8.F 11.FIF 8.DSP 11.SPID 11.NQ 11.NRNS
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6th Grade
Key Concept: Data Analysis and Statistics
SCCCR Standards: Differentiate between statistical and non-statistical questions (6.DS.1).
Prioritized Standard Level 4: Exceeds Standard Level 3: Meets Standard Level 2: Emerging Level 1: Foundational
6.DS.1: Find the mean,
median, mode, and range.
6.DS.1: Identify the median
and/or range of a data set.
6.DS.1: Determine the middle
point of a collection of objects.
6.DS.1: Put a data set in
order from least to greatest.
6.DS.1: Find the largest or
smallest number in a data set.
It Is Essential for Students to Know: Students need to be able to order numbers from least to greatest. Students need to be able to identify the
smallest and largest number within a data set.
Applications to Daily Tasks, Activities, Routines, or Life Experiences
• The students can collect data within the classroom such as shoes sizes. For example, the students can collect information on each person’s
shoe size and plot the information on a large number line on the board or interactive whiteboard. Discuss with students what the range,
median, and mode of the shoe sizes are in the classroom. This can be expanded to collecting data across people or classrooms in the school
building.
Standard Vocabulary Skills Daily Activities Functional Activities
6DS Mean
Median
Mode
Range
Determine
smallest and
largest
Order (by
attribute)
Order common objects by attribute (size)
With popcorn activity (from 4th MDA), order
distance data to find mean, median, mode
Using bags of colored candy, have students sort
candy by color, collect data, and find mean,
median, mode
Make a rock collection and weigh rocks to find
mean, median, mode
Locating the middle step of a list of steps
Planning a schedule and managing time
Using a calendar to find the middle day of week or middle
day of the month
Using a pay schedule to calculate dates of pay during the
month
Calculating a median salary using a list
Practicing comparison shopping by putting prices in order
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7th Grade
Key Concept: Data Analysis, Statistics, and Probability
SCCCR Standards: Investigate concepts of random sampling. a. Understand that a sample is a subset of a population and both possess the same
characteristics. b. Differentiate between random and non-random sampling. c. Understand that generalizations from a sample are valid only if the
sample is representative of the population. d. Understand that random sampling is used to gather a representative sample and supports valid
inferences about the population (7.DSP.1). Draw inferences about a population by collecting multiple random samples of the same size to
investigate variability in estimates of the characteristic of interest (7.DSP.2). Compare the numerical measures of center (mean, median, mode)
and variability (range, interquartile range, mean absolute deviation) from two random samples to draw inferences about the populations (7.DSP.4).
Investigate the concept of probability of chance events. a. Determine probabilities of simple events. b. Understand that probability measures
likelihood of a chance event occurring. c. Understand that the probability of a chance event is a number between 0 and 1. d. Understand that a
probability closer to 1 indicates a likely chance event. e. Understand that a probability close to 12 indicates that a chance event is neither likely nor
unlikely. f. Understand that a probability closer to 0 indicates an unlikely chance event (7.DSP.5).
Prioritized Standard Level 4: Exceeds Standard Level 3: Meets Standard Level 2: Emerging Level 1: Foundational
7.DSP.1: Understand that a
sample is a subset of a
population. Distinguish between
populations and samples.
Distinguish between random and
nonrandom samples.
7.DSP.1: Understand that a
sample is a subset of a
population. Distinguish between
populations and samples.
Distinguish between random and
nonrandom samples.
7.DSP.1: Understand that a
sample is a subset of a
population. Identify populations
and samples. Identify random
and nonrandom samples.
7.DSP.1: Distinguish
between a population
or a sample.
7.DSP.1: Distinguish
between a whole and a
part.
7.DS.2: Draw inferences about a
population by collecting random
samples.
7.DS.2: Draw inferences about a
population by collecting random
samples.
7.DS.2: Draw inferences about a
population when given random
samples.
7.DS.2: Identify a
statement about a
given random
sample.
7.DS.2: Determine if a
sample is random.
7.DSP.4: Use the numerical
measures of center (mean,
median, mode, and range).
7.DSP.4: Use the numerical
measures of center (mean,
median, mode, and range).
7.DSP.4: Use the numerical
measures of center (mean and
median).
7.DSP.4: Identify the
median of a data set.
7.DSP.4: Determine the
middle point of a
collection of objects.
7.DSP.5: Understand that
probability measures likelihood
of a chance event occurring.
7.DSP.5: Determine the
probability of simple events.
7.DSP.5: Understand that
probability measures likelihood
of a chance event occurring.
7.DSP.5: Identify if
an event is possible
or impossible.
7.DSP.5: Recognize the
outcome of an event.
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It Is Essential for Students to Know: Students need to be able to determine if an event is possible or likely. Students need to be able to
differentiate between a population and a sample. Students need to be able to make statements about a data set (e.g., lunch choices). Students also
need to be able to determine the median of a data set.
Applications to Daily Tasks, Activities, Routines, or Life Experiences
• Collect data in the classroom by asking everyone on the basketball team their shoe size, then find the mode of the data to help the coach
determine how many different sized shoes should be ordered for the team.
Standard Vocabulary Skills Daily Activities Functional Activities
7DSP Sample
Subset
Population
Random
Nonrandom
Median
Center
Mean
Probability
(univariate)
Find middle
Identify population
Determine probability
Practice using probability; put items in a bag and calculate
chances of pulling specific item out
Determine probability by flipping a coin
Determine future predictions by shooting basketball and
collecting and analyzing data
Make predictions and understand probability by reviewing
classroom attendance data
Analyze school menu to make predictions
Determining probability by
analyzing the weather
Maintaining stock for school store;
determining buying trends to
predict future buying trends
Sampling students at random on
transportation mode to school
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8th Grade
Key Concept: Functions
SCCCR Standards: Explore the concept of functions. a. Understand that a function assigns to each input exactly one output. b. Relate inputs
(𝑥-values or domain) and outputs (𝑦-values or range) to independent and dependent variables. c. Translate among the multiple representations of a
function, including mappings, tables, graphs, equations, and verbal descriptions. d. Determine if a relation is a function using multiple
representations, including mappings, tables, graphs, equations, and verbal descriptions. e. Graph a function from a table of values. Understand that
the graph and table both represent a set of ordered pairs of that function (8.F.1). Compare multiple representations of two functions, including
mappings, tables, graphs, equations, and verbal descriptions, in order to draw conclusions (8.F.2). Apply the concepts of linear functions to real-
world and mathematical situations. a. Understand that the slope is the constant rate of change and the 𝑦-intercept is the point where 𝑥 = 0.
b. Determine the slope and the 𝑦-intercept of a linear function given multiple representations, including two points, tables, graphs, equations, and
verbal descriptions. c. Construct a function in slope-intercept form that models a linear relationship between two quantities. d. Interpret the
meaning of the slope and the 𝑦-intercept of a linear function in the context of the situation. e. Explore the relationship between linear functions and
arithmetic sequences (8.F.4).
Prioritized Standard Level 4: Exceeds Standard Level 3: Meets Standard Level 2: Emerging Level 1: Foundational
8.F.1: Understand that a function
assigns to each input exactly one
output. Determine if a relation is a
function using multiple representations,
including tables, graphs, and equations.
Graph a function from a table of x and y
values. Extend the knowledge of the
coordinate plane to use the set of
ordered pairs of that function.
8.F.1: Generate ordered pairs
from two distinct numerical
patterns. Extend a symbolic
pattern by applying the rule.
8.F.1: Graph a function
from a table of x and y
values.
8.F.1: Graph a point
when given an
ordered pair of
numbers.
8.F.1: Identify a point.
8.F.2: Compare two functions,
including tables, graphs, and equations,
in order to draw conclusions.
8.F.2: Compare two functions,
including tables, graphs, and
equations, to draw conclusions.
8.F.2: Compare the slopes
of two functions given in
equation form (slope-
intercept form).
8.F.2: Identify the
slope and intercepts
of a function given
in equation form.
8.F.2: Identify the
slope or intercepts of a
function in graph form.
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Prioritized Standard Level 4: Exceeds Standard Level 3: Meets Standard Level 2: Emerging Level 1: Foundational
8.F.4: Understand that the slope is the
constant rate of change and the y-
intercept is the point where x = 0.
Interpret the meaning of the slope and
the y-intercept of a linear function in the
context of the situation.
8.F.4: Understand that the slope
is the constant rate of change,
and the y-intercept is the point
where x = 0. Interpret the
meaning of the slope and the y-
intercept of a linear function in
the context of the situation.
8.F.4: Understand that the
slope is the constant rate of
change, and the y-intercept
is the point where x = 0.
8.F.4: Understand
that slope is related
to the direction of
the line.
8.F.4: Identify a line on
a graph.
It Is Essential for Students to Know: Students need to be able to graph ordered pairs on a coordinate plane. Students need to be able to identify
the rise and run of a line on a graph. Students also need to be able to identify if a line has a positive or negative slope.
Applications to Daily Tasks, Activities, Routines, or Life Experiences
• Using a wooden plank and a toy car, explore the concept of steepness.
• Graph real-life situations and explore the meaning of slope and y-intercept within a real-world context. For example, the students can
analyze the following graph that shows the number of hours Mike works and the amount of cash he has. The y-intercept of the graph
shows that before he started working he had already saved $10, and the slope shows that as he works more his cash is increasing, which is
why the slope of the line is positive.
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Standard Vocabulary Skills Daily Activities Functional Activities
8F Function
x value
y value
Slope
Intercept
Point
Line
Identify a point
Graph point
Identify slope
Compare slopes
Identify line
Understand slope
Practice using concept of slope using skiing, cars on different
ramps, etc.
Make sundials and measure shadows at different times of day
Plotting data from plant growth over time
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11th Grade
Key Concept: Interpreting Functions
SCCCR Standards: Extend previous knowledge of a function to apply to general behavior and features of a function. a. Understand that a
function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range.
b. Represent a function using function notation and explain that f (𝑥) denotes the output of function 𝑓 that corresponds to the input 𝑥. c.
Understand that the graph of a function labeled as 𝑓 is the set of all ordered pairs (𝑥, y) that satisfy the equation 𝑦 = f (𝑥) (A1.FIF.1). Interpret key
features of a function that models the relationship between two quantities when given in graphical or tabular form. Sketch the graph of a function
from a verbal description showing key features. Key features include intercepts; intervals where the function is increasing, decreasing, constant,
positive, or negative; relative maximums and minimums; symmetries; end behavior and periodicity (A1.FIF.4). Graph functions from their
symbolic representations. Indicate key features including intercepts; intervals where the function is increasing, decreasing, positive, or negative;
relative maximums and minimums; symmetries; end behavior and periodicity. Graph simple cases by hand and use technology for complicated
cases. (Note: FIF.7a–d are not Graduation Standards.) a. Graph rational functions, identifying zeros and asymptotes when suitable factorizations
are available, and showing end behavior. b. Graph radical functions over their domain show end behavior. c. Graph exponential and logarithmic
functions, showing intercepts and end behavior. d. Graph trigonometric functions, showing period, midline, and amplitude (A1.FIF.7).
Prioritized Standard Level 4: Exceeds Standard Level 3: Meets Standard Level 2: Emerging Level 1: Foundational
A1.FIF.1: Understand that a function
from one set (called the domain) to
another set (called the range) assigns
to each element of the domain exactly
one element of the range.
A1.FIF.1: Identify the
domain and range of a given
function.
A1.FIF.1: Identify if a
relation given in table form
is a function.
A1.FIF.1: Given a table
of values, identify a
possible missing x value
(so that an x value does
not repeat).
A1.FIF.1: Given a set
of table values, identify
the set of x values.
A1.FIF.4: Recognize features of a
linear function in graphical form (e.g.,
slope, intercepts; if the function is
increasing, decreasing, constant,
positive, or negative).
A1.FIF.4: Given the slope
and intercept of a function,
identify its graph.
A1.FIF.4: Given a
description of a function,
identify the graph (positive
slope, negative slope,
constant, given y-intercept;
limit to first quadrant).
A1.FIF.4: Given an
intercept of the graph,
identify the graph.
A1.FIF.4: Given a key
feature (increasing,
decreasing, or
constant), identify the
graph.
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Prioritized Standard Level 4: Exceeds Standard Level 3: Meets Standard Level 2: Emerging Level 1: Foundational
A1.FIF.7: Graph linear functions
using their key features.
A1.FIF.7: Given a graph of a
linear function, identify the
slope and intercepts.
A1.FIF.7: Given a graph of
a linear function in the first
quadrant, identify features
of the graph (positive slope,
negative slope, constant,
intercepts).
A1.FIF.7: Given a graph
of a linear function,
identify the x-intercept.
A1.FIF.7: Identify
whether a given graph
is increasing,
decreasing, or constant.
It Is Essential for Students to Know: Students need to be able to identify if a graph is increasing, decreasing, or constant. Students need to be
able to identify the domain and the range of a function.
Applications to Daily Tasks, Activities, Routines, or Life Experiences
• Identify the domain and range of a function in a real-world context. For example, the following function is used to find the temperature, F,
in degrees Fahrenheit for any given temperature C, given in Celsius. The domain of the function is the temperature given in Celsius and
the range is the temperature given in Fahrenheit.
• Another example would be the function y = 10x + 40, where y represents the total money Erika needs for a school trip. She is saving $10
per week and has already saved $40. She has 5 weeks to save the money. What are possible domains for the function? In this case, because
she has only 5 weeks to save the money, the only domains for this function would be {1, 2, 3, 4, 5}.
Standard Vocabulary Skills Daily Activities Functional Activities
11FIF Increasing
Decreasing
Constant
Identify positive, negative
or constant slopes
Identify x-intercept
Use stairs to identify slopes and compare increasing
or decreasing quantities (1 step = 5 inches,
2 steps = 10 inches, etc.)
Calculate the total cost of items in the school store
(1 pencil, 2 pencils, 3 pencils)
Using a recipe – If 3 cakes need x eggs, how
many eggs are needed to make 2 cakes?
Estimating the materials needed for projects
– make 1 item; make 2 items; make 3 items
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8th Grade
Key Concept: Data Analysis, Statistics, and Probability
SCCCR Standards: Investigate bivariate data. a. Collect bivariate data. b. Graph the bivariate data on a scatter plot. c. Describe patterns observed
on a scatter plot, including clustering, outliers, and association (positive, negative, no correlation, linear, nonlinear) (8.DSP.1).
Prioritized Standard Level 4: Exceeds Standard Level 3: Meets Standard Level 2: Emerging Level 1: Foundational
8.DSP.1: Recognize patterns
observed on a scatter plot,
including clustering, outliers,
and association (positive,
negative, or no correlation).
8.DSP.1: Recognize patterns
observed on a scatter plot,
including clustering, outliers,
and association (positive,
negative, or no correlation).
8.DSP.1: Recognize patterns
observed on a scatter plot,
including clustering and outliers.
8.DSP.1: Graph points
when given an ordered
pair of numbers.
8.DSP.1: Identify
a point.
It Is Essential for Students to Know: Students need to be able to identify a point on a scatterplot.
Applications to Daily Tasks, Activities, Routines, or Life Experiences
• Analyze patterns on scatter plots from articles and magazines. This article is looking at which states have the happiest people in the
United States.
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Standard Vocabulary Skills Daily Activities Functional Activities
8DSP Scatter plot
Pattern
Clustering and outliers
Ordered pair
(bivariate)
Identify a point
Graph point given an ordered pair
Recognize patterns
Find outliers
Put multicolored objects in bag and chart the
number of objects of each color
Create art using splatter paint, place a grid
over the paint, and identify ordered pairs
Charting the number of times that
certain foods are served in cafeteria
Gathering temperatures over time
and plotting the weather (i.e., dates
vs. temperatures)
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11th Grade
Key Concept: Interpreting Data
SCCCR Standards: Using technology, create scatterplots and analyze those plots to compare the fit of linear, quadratic, or exponential models to
a given data set. Select the appropriate model, fit a function to the data set, and use the function to solve problems in the context of the data
(A1.SPID.6).
Prioritized Standard Level 4: Exceeds Standard Level 3: Meets Standard Level 2: Emerging Level 1: Foundational
A1.SPID.6: Identify the
general form of a given data
set as linear or non-linear.
A1.SPID.6: Identify the
general form of a given data
set as linear or non-linear.
A1.SPID.6: Identify a data
set that is linear.
A1.SPID.6: Identify a data
set that can be modeled as a
straight line.
A1.SPID.6: Identify a graph
that is a straight line.
It Is Essential for Students to Know: Students need to be able to recognize a pattern in scatterplots, such as positive association, negative
association, and no association.
-80-
Applications to Daily Tasks, Activities, Routines, or Life Experiences
• Analyze data from articles, and determine if the data is linear or non-linear.
Standard Vocabulary Skills Daily Activities Functional Activities
11SPID Graph
Linear
Straight line
Non-linear
Data set
Identify graphs that are
linear (straight line)
Measure anything that grows
Measure the depth of trash in a
trash can throughout the day
Calculating used and remaining cell phone minutes
Measuring the amount of water in glass set in the window over time
(evaporation)
Counting the laundry washed over time
Recording the amount of formula that a student is tube-fed over time
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11th Grade
Key Concept: Quantities
SCCCR Standards: Use units of measurement to guide the solution of multi-step tasks. Choose and interpret appropriate labels, units, and scales
when constructing graphs and other data displays (A1.NQ.1).
Prioritized Standard Level 4: Exceeds Standard Level 3: Meets Standard Level 2: Emerging Level 1: Foundational
A1.NQ.1: Choose the
appropriate labels, units, and
scales when constructing
graphs.
A1.NQ.1: Given a data set,
identify an appropriate scale
for a graph of the data.
A1.NQ.1: Given a data set,
identify the appropriate units
for a graph of the data.
A1.NQ.1: Given context,
identify a graph with correct
labels.
A1.NQ.1: Given data and a
context, identify an
appropriate title for a graph
of the data.
It Is Essential for Students to Know: Students need to be able to identify the different parts of the graph (such as the title and axis labels).
Applications to Daily Tasks, Activities, Routines, or Life Experiences
• Explore scale of graphs using Excel, where you can create graphs using data. Play around with the scale to show how you can manipulate
data to prove a point. For example, the graph below shows the average house prices for 1998 and 1999 in a certain city. See how the scale
of the vertical axes can make it look like the average price of the houses increased dramatically or barely.
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Standard Vocabulary Skills Daily Activities Functional Activities
11NQ Data set
Unit
Title
Graph
Identify unit
Identify graph
Identify title of the graph
Conduct school polls and graph the results,
such as how many students recycle, prefer a
sports team, wear an article of clothing, etc.
Locating graphs in newspapers or magazines and then
discussing the information presented in the graphs
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11th Grade
Key Concept: Real Number System
SCCCR Standards: Rewrite expressions involving simple radicals and rational exponents in different forms (A1.NRNS.1).
Prioritized Standard Level 4: Exceeds Standard Level 3: Meets Standard Level 2: Emerging Level 1: Foundational
A1.NRNS.1: Evaluate
square roots of perfect
squares.
A1.NRNS.1: Evaluate
square roots of perfect
squares.
A1.NRNS.1: Understand
that the square root is the
inverse of squaring a
number.
A1.NRNS.1: Understand
how to square a number.
A1.NRNS.1: Understand
multiplication facts of whole
numbers with products up to
100.
It Is Essential for Students to Know: Students need to be able to recognize perfect squares.
Applications to Daily Tasks, Activities, Routines, or Life Experiences
• Evaluating square roots is used when using the Pythagorean theorem. For example, “Simon leans a 10 ft. ladder against the wall. The
distance from the bottom of the ladder to the wall is 8 ft. How far up on the wall is the ladder placed?”
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Standard Vocabulary Skills Daily Activities Functional Activities
11NRNS Square root
Inverse
Squaring
Square numbers
(multiply)
Determine square
root
Use cubes or tiles to form squares and count the number
of cubes or tiles
Use a checker board to illustrate the concept of “square”
Baking a cake in a square pan and cutting into
equal parts to demonstrate the concept of
“square”
Planting a garden in square shape