GRADE 6 ATHEMATICS CURRICULUM UIDE...of operations on real numbers. Identify the property of...

GRADE 6 MATHEMATICS

CURRICULUM GUIDE

Loudoun County Public Schools

2011-2012

Complete scope, sequence, pacing and resources are available on the LCPS Intranet.

INTRODUCTION TO LOUDOUN COUNTY’S MATHEMATICS CURRICULUM GUIDE

This CURRICULUM GUIDE is a merger of the Virginia Standards of Learning (SOL) and the Mathematics Achievement Standards for Loudoun

County Public Schools. The CURRICULUM GUIDE includes excerpts from documents published by the Virginia Department of Education. Other

statements, such as suggestions on the incorporation of technology and essential questions, represent the professional consensus of Loudoun’s teachers

concerning the implementation of these standards. In many instances the local expectations for achievement exceed state requirements. The GUIDE is

the lead document for planning, assessment and curriculum work. It is a summarized reference to the entire program that remains relatively

unchanged over several student generations. Other documents, called RESOURCES, are updated more frequently. These are published separately but

teachers can combine them with the GUIDE for ease in lesson planning.

Mathematics Internet Safety Procedures 1. Teachers should review all Internet sites and links prior to using it in the classroom.

During this review, teachers need to ensure the appropriateness of the content on the site,

checking for broken links, and paying attention to any

inappropriate pop-ups or solicitation of information.

2. Teachers should circulate throughout the classroom while students are on the

internet checking to make sure the students are on the appropriate site and

are not minimizing other inappropriate sites.

3. Teachers should periodically check and update any web addresses that they have on their

LCPS web pages.

4. Teachers should assure that the use of websites correlate with the objectives of

lesson and provide students with the appropriate challenge.

5. Teachers should assure that the use of websites correlate with the objectives

of the lesson and provide students with the appropriate challenge.

Grade 6 Mathematics Nine Weeks Overview

1st Quarter 2

nd Quarter 3

rd Quarter 4

th Quarter

Properties of Real Numbers 6.19

Rational Numbers 6.2

Sequences 6.17

Number 6.5

6.3

6.11

6.8

Equations and

Inequalities 6.20

Fractions 6.6 b

6.4

6.6

Benchmark

Decimals 6.7

Ratios 6.1

Rational Number

Relationships 6.2 c

Measurement 6.9

Geometry 6.13

6.12

6.10 c

Circles 6.10 a, b

Volume and Surface

Area 6.10 d

Probability and

Statistics 6.16

6.15

6.14

Grade 6 Quarter 1 School Year 2011-12

Number of

Blocks

Topics, Essential Questions, and Essential

Understandings

(Students should be able to answer essential

questions.)

Standard(s) of Learning

Essential Knowledge and Skills

Additional Instructional Resources

ESS: Grade 6 Enhanced

Scope and Sequence

Properties of Real Numbers

Introduce properties of real numbers in order to use

properties all year.

6.19 Essential Questions

What is the result of multiplying any real number

by zero?

Do all real numbers have a multiplicative inverse?

Compare and contrast the identity properties for

multiplication and addition.

How are the identity properties for multiplication

and addition the same? Different?

Create a real number equation and identify the

property of operations used to solve it.

6.19 Essential Understandings

How are the identity properties for

multiplication and addition the same?

Different? For each operation the

identity elements are numbers that combine

with other numbers without changing the

value of the other numbers. The additive

identity is zero (0). The multiplicative

identity is one (1).

What is the result of multiplying any real

number by zero? The product is always

zero.

Do all real numbers have a multiplicative

inverse? No. Zero has no multiplicative

inverse because there is no real number that

can be multiplied by zero resulting in a

product of one.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Rational Numbers

Introduction to rational numbers in decimal format


Create and justify representations in decimal format.

SOL 6.19 The student will investigate and recognize

a) the identity properties for addition and multiplication;

b) the multiplicative property of zero; and

c) the inverse property for multiplication.

6.19 Essential Knowledge and Skills

Identify a real number equation that represents each property of

operations with real numbers, when given several real number

equations.

Test the validity of properties by using examples of the properties

of operations on real numbers.

Identify the property of operations with real numbers that is

illustrated by a real number equation.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Review material to prepare for SOL 6.2

SOL 6.2 The student will

a) investigate and describe fractions, decimals, and percents as

ratios;


Demonstrate and explain how benchmarks can be

used to compare and order decimals.

Prove a sequence of values in decimal format using

two different strategies.

Compare and contrast addition and subtraction of

whole numbers and decimals.

Compare and contrast multiplication and division of

whole numbers and decimals.

What is the role of estimation in solving problems?

How can the distributive property help with

computation involving decimals?

Prove that using the distributive property does not

change the value of an equation.


What is the relationship among fractions, decimals

and percents?

Fractions, decimals, and percents are three different

ways to express the same number. A ratio can be

written using fraction form ( 2

3 ), a colon (2:3), or the

word to (2 to 3). Any number that can be written as a

fraction can be expressed as a terminating or

repeating decimal or a percent.

b) identify a given fraction, decimal, or percent from

representations;

c) demonstrate equivalent relationships between fractions,

decimals, and percents; and

d) compare and order fractions, decimals, and percents.


Identify the decimal and percent equivalents for numbers

written in fraction form including repeating decimals.

Represent fractions, decimals, and percents on a number line.

Describe orally and in writing the equivalent relationships

among decimals, percents, and fractions.

Represent, by shading a grid, a fraction, decimal, and percent.

Represent rational numbers in fraction, decimal, and percent

form a given shaded region of a grid.

Compare two decimals using manipulatives, pictorial

representations, number lines, and symbols (<, ,, >, =).

Compare two fractions using manipulatives, pictorial

representations, number lines, and symbols (<, ,, >, =).

Compare two percents using pictorial representations and

symbols (<, ,, >, =).

Order fractions, decimals, and percents in ascending or

descending order.

Sequences

Geometric and Arithmetic Sequences

6.17 Essential Questions and Understandings

What is the difference between an arithmetic and a

geometric sequence?

Compare and contrast arithmetic and geometric

sequences.

How can numerical or algebraic symbols represent

change in a pattern? (Based on a pattern, a prediction

can be made of the nth

term.)

Create and explain the strategies used to recognize

and describe the change between terms in arithmetic

patterns.

Create and explain the strategies used to recognize

and describe geometric patterns.

Continue to discuss sequences in the context of

exponents and square root.

SOL 6.17 The student will identify and extend geometric and

arithmetic sequences.


Investigate and apply strategies to recognize and describe the

change between terms in arithmetic patterns.

Investigate and apply strategies to recognize and describe

geometric patterns.

Describe verbally and in writing the relationships between

consecutive terms in an arithmetic or geometric sequence.

Extend and apply arithmetic and geometric sequences to similar

situations.

Extend arithmetic and geometric sequences in a table by using a

given rule or mathematical relationship.

Compare and contrast arithmetic and geometric sequences.

Identify the common difference for a given arithmetic sequence.


Identify the common ratio for a given geometric sequence.

Number and Number Sense

Exponents, perfect squares, square roots, scientific

notation


What does exponential form represent?

Recognize and describe patterns in exponents and

perfect squares.

Prove the value of a perfect square using

representation.

What is the relationship between perfect squares and

a geometric square?

SOL 6.5 The student will investigate and describe concepts of

positive exponents and perfect squares.


Recognize and describe patterns with exponents that are natural

numbers, by using a calculator.

Recognize and describe patterns of perfect squares not to exceed

202

, by using grid paper, square tiles, tables, and calculators.

Recognize powers of ten by examining patterns in a place value

chart: 104 = 10,000, 10

3 = 1000, 10

2 = 100, 10

1 = 10, 10

0=1.

ESS

http://www.doe.virginia.gov/testing/sol/

standards_docs/mathematics/index.sht

ml

Squares and Square Roots

Order of Operations

6.8 Essential Question and Understanding

What is the significance of the order of operations?

SOL 6.8 The student will evaluate whole number numerical

expressions, using the order of operations.

Simplify expressions by using the order of operations in a

demonstrated step-by-step approach. The expressions should be

limited to positive values and not include braces { } or absolute

value | |.

Find the value of numerical expressions, using order of operations,

mental mathematics, and appropriate tools. Exponents are limited

to positive values.

Interpret numerical expressions at a level necessary to calculate

their value using a calculator or spreadsheet. For expressions with

variables, use and interpret conventions of algebraic notion, such

as y/2 is y ÷ 2 or ½ × y; (3± y) ÷ 5 or 1/5 × (3± y); is a × a, a3 is a

× a × a, a2b is a × a × b

ESS

http://www.doe.virginia.gov/testing/sol/

standards_docs/mathematics/index.sht

ml

Toothpick Patterns

Integers


Represent and explain the value of an integer using a

number line.

Compare and justify order of a set of integers using a

number line.

Create, model, and solve a real life problem

situations using integers.


a) identify and represent integers;

b) order and compare integers; and

c) identify and describe absolute value of integers.


Identify an integer represented by a point on a number line.

ESS

http://www.doe.virginia.gov/testing/s

ol/standards_docs/mathematics/index.

shtml

Investigating Integers

http://www.doe.virginia.gov/testing/sol/standards_docs/mathematics/index.shtml










What role do negative integers play in practical

situations?

How does the absolute value of an integer compare

to the absolute value of its opposite?

Represent integers on a number line.

Order and compare integers using a number line.

Compare integers, using mathematical symbols

(<, >, =).

Identify and describe the absolute value of an integer.


Equations and Inequalities


What is a variable?

Compare and contrast expressions and equations.

When solving an equation, why is it necessary to perform

the same operation on both sides of an equal sign?

Create and explain a one-step linear equation using two

strategies.



In an inequality, does the order of the elements matter?

Yes, the order does matter. For example, x > 5 is not the

same relationship as 5 > x. However, x > 5 is the same

relationship as 5 < x.

SOL 6.18 -The student will solve one-step linear equations in one

variable….

Understand that an expression records operations with numbers or

with letters standing for numbers.

Describe the structure and elements of simple expressions using

correct terminology (sum, term, product, factor, quotient,

coefficient); describe an expression by viewing one or more of its

parts as a single entity.

Understand and generate equivalent expressions:

o Understand that two expressions are equivalent if they name the

same number regardless of which numbers the variables in them

stand for.

o Understand that applying the laws of arithmetic to an expression

results in an equivalent expression

o Generate equivalent expressions to reinterpret the meaning of an

expression.

Understand that an equation is a statement that two expressions are

equal, and a solution to an equation is a replacement value of the

variables (or replacement values for all the variables if there is more

than one) that makes the equation true.

Using the idea of maintaining equality between both sides of the

equation, solve equations of the form x + p = q and px = q for cases in

which, p, q, and x are all nonnegative rational numbers.

SOL 6.20 The student will graph inequalities on a number line.


o Given a simple inequality with integers, graph the relationship on

a number line.

Given the graph of a simple inequality with integers, represent the

inequality two different ways using symbols (<, >, <, >).

Hands-on Equations: Book

1

5th

Grade ESS

http://www.doe.virginia.g

ov/testing/sol/standards_d

ocs/mathematics/index.sh

tml

Writing Algebraic

Expressions

Variables in Open

Sentences

Algebra Balance Scales:

http://nlvm.usu.edu/en/nav/

frames_asid_201_g_4_t_2.

html?open=instructions&fr

om=category_g_4_t_2.html

Assessment, Enrichment, and Remediation





http://nlvm.usu.edu/en/nav/frames_asid_201_g_4_t_2.html?open=instructions&from=category_g_4_t_2.html





Number of

Blocks

Topics, Essential Questions, and

Essential Understandings


questions.)



Additional

Instructional

Resources

ESS: VDOE

Enhanced

Scope and Sequence

Fractions

Add and Subtract Fractions in Practical Problems

6.6 b Essential Questions

Justify the use of estimation with rational numbers in

fraction format?

Compare and contrast addition and subtraction of fractions

and addition and subtraction of whole numbers?

Why are common denominators required to add or subtract

fractions?

Justify that the sum or difference is in simplest form.

6.6 b Essential Understandings


o Estimation helps determine the reasonableness of

answers.

SOL 6.6 b Estimate solutions and then solve single-step

and multistep practical problems involving addition,

subtraction, multiplication, and division of fractions.

6.6 b Essential Knowledge and Skills

Solve single-step and multistep practical problems that

involve addition and subtraction with fractions and

mixed numbers, with and without regrouping, that

include like and unlike denominators of 12 or less.

Answers are expressed in simplest form.


Multiplication and Division of Fractions



Justify multiple representations of multiplication and

division of fractions.

Create, demonstrate, and explain a model using

multiplication and/or division of fractions.

Justify that a fraction is in simplest form.


When multiplying fractions, what is the meaning of the

operation?

o When multiplying a whole by a fraction such as 3 x 1

2 ,

the meaning is the same as with multiplication of whole

numbers: 3 groups the size of 1

2 of the whole.

o When multiplying a fraction by a fraction such as2 3

3 4,

we are asking for part of a part.

o When multiplying a fraction by a whole number such as

1

2 x 6, we are trying to find a part of the whole.

What does it mean to divide with fractions?

o For measurement division, the divisor is the number of

groups and the quotient will be the number of groups in

the dividend. Division of fractions can be explained as

how many of a given divisor are needed to equal the

given dividend. In other words, for 1 2

4 3 the question

is, “How many 2

3 make

1

4?”

o For partition division the divisor is the size of the group,

so the quotient answers the question, “How much is the

whole?” or “How much for one?”

SOL 6.4 The student will demonstrate multiple representations of multiplication and division of fractions.


Demonstrate multiplication and division of fractions using

multiple representations.

Model algorithms for multiplying and dividing with

fractions using appropriate representations.

ESS

http://www.doe.virgi

nia.gov/testing/sol/sta

ndards_docs/mathem

atics/index.shtml

Area Model of

Multiplication

Dividing Fractions,

Using Pattern Blocks

Decimal Division

Estimation Strategies

Estimation in

Problem Solving






Multiplication and Division of Fractions in Practical

Situations


Justify that product or quotient is in simplest form.

How are multiplication and division of fractions and

multiplication and division of whole numbers alike?

Create and solve a practical problems using estimation of

fractions.

How could the distributive property be used in computation

strategies for fractions?

Prove that the use of the distributive property does not

change the value of the product.

Create and explain single-step practical problems using

fractions.

Create and explain multistep practical problems using

fractions.


How are multiplication and division of fractions and

multiplication and division of whole numbers alike?

o Fraction computation can be approached in the same

way as whole number computation, applying those

concepts to fractional parts.


o Estimation helps determine the reasonableness of

answers.


a) multiply and divide fractions and mixed numbers;

and

b) estimate solutions and then solve single-step and

multistep practical problems involving addition,

subtraction, multiplication, and division of fractions.

Essential Knowledge and Skills Multiply and divide with fractions and mixed numbers.


Solve single-step and multistep practical problems that

involve multiplication and division with fractions and

mixed numbers that include denominators of 12 or less.


Decimals

Solve multi-step problems involving decimals



Create and solve a practical problem using estimation of

decimals.

Justify estimation strategies for the sum, difference,

product, or quotient of two quantities.

How could the distributive property be used in computation

strategies for decimals?

Prove that the use of the distributive property does not

SOL 6.7 The student will solve single-step and multistep

practical problems involving addition, subtraction,

multiplication, and division of decimals.


Solve single-step and multistep practical problems

involving addition, subtraction, multiplication and division

with decimals expressed to thousandths with no more than

two operations.

ESS



ndards_docs/mathem

atics/index.shtml

Pizza Your Way

Getting the Most for

Your Money!






change the value of the product.

Create and explain single-step practical problems using

decimals.

Create and explain multistep practical problems using

decimals.



o Estimation gives a reasonable solution to a problem

when an exact answer is not required. If an exact

answer is required, estimation allows you to know if

the calculated answer is reasonable.

Ratios


Create real life problem situations comparing data using a

variety of ratios relationships.

Justify the relationship between the two values in a ratio?


What is a ratio?

o A ratio is a comparison of any two quantities. A ratio is

used to represent relationships within a set and between

two sets. A ratio can be written using fraction form

( 2

3 ), a colon (2:3), or the word to (2 to 3).

SOL 6.1 The student will describe and compare data,

using ratios, and will use appropriate notations, such

as a

b , a to b, and a:b.


Describe a relationship within a set by comparing part of

the set to the entire set.

Describe a relationship between two sets by comparing

part of one set to a corresponding part of the other set.

Describe a relationship between two sets by comparing

all of one set to all of the other set.

Describe a relationship within a set by comparing one

part of the set to another part of the same set.

Represent a relationship in words that makes a

comparison by using the notations a

b, a:b, and a to b.

Create a relationship in words for a given ratio expressed

symbolically.

ESS



ndards_docs/mathem

atics/index.shtml

Exploring Ratio

Paper Chains and

Countries







Number of

Blocks




questions.)



Additional

Instructional

Resources

ESS: VDOE

Enhanced

Scope and Sequence

Rational Number Relationships


What is the relationship among fractions, decimals,

and percents?

Justify that fractions, decimals, and percents are ratios.

Compare and prove order of a set of fractions,

decimals, and percents using two strategies.

Compare and contrast fractions, decimals, and

percents.

6.2 Essential Understanding

What is the relationship among fractions, decimals

and percents?

o Fractions, decimals, and percents are three

different ways to express the same number. A

ratio can be written using fraction form ( 2

3 ), a

colon (2:3), or the word to (2 to 3). Any number

that can be written as a fraction can be expressed

as a terminating or repeating decimal or a percent.

SOL 6.2 The student will a) investigate and describe fractions, decimals and percents

as ratios;

b) identify a given fraction, decimal or percent from a

representation;

c) demonstrate equivalent relationships among fractions,

decimals, and percents; and

d) compare and order fractions, decimals, and percents. 6.2 Essential Knowledge and Skills

Identify the decimal and percent equivalents for numbers

written in fraction form including repeating decimals.

Represent fractions, decimals, and percents on a number line.

Describe orally and in writing the equivalent relationships

among decimals, percents, and fractions that have

denominators that are factors of 100.

Represent, by shading a grid, a fraction, decimal, and percent.

Represent in fraction, decimal, and percent form a given

shaded region of a grid.

Compare two decimals through thousandths using

manipulatives, pictorial representations, number lines, and

symbols (<, ,, >, =).

Compare two fractions with denominators of 12 or less using

manipulatives, pictorial representations, number lines, and

symbols (<, ,, >, =).

Compare two percents using pictorial representations and

symbols (<, ,, >, =).

Order no more than 3 fractions, decimals, and percents

(decimals through thousandths, fractions with denominators of

12 or less), in ascending or descending order.

ESS



ndards_docs/mathem

atics/index.shtml

Percent Grid Patterns

Who Has 100

Things?






Measurement

Comparisons between metric and U.S. Customary

systems


Why are there two different measurement

systems?

How do you determine which units to use at

different times?

Create scenarios and justify the unit of

measurement used to solve each problem.

Compare and justify measurements in U.S.

Customary with ballpark measurements in the

metric systems.

Compare and justify measurements in the metric

system with ballpark measurements in U.S.

Customary system.

Compare and contrast ballpark measurements

between U.S. Customary and metric systems.

Create scenarios in which benchmark

measurements are justified. Compare and contrast weight and mass.

SOL 6.9 The student will make ballpark comparisons between

measurements in the U.S. Customary System of measurement

and measurements in the metric system.


Estimate the conversion of units of length, weight/mass,

volume, and temperature between the U.S. Customary

system and the metric system by using ballpark

comparisons. Ex: 1 L 1qt. Ex: 4L 4 qts.

Estimate measurements by comparing the object to be

measured against a benchmark.

ESS



ndards_docs/mathem

atics/index.shtml

Measuring Mania

Geometry

Classify Quadrilaterals


Compare and contrast characteristics of

quadrilaterals.

Justify how a quadrilateral can belong to more

than one subset.

Prove the sum of the angles of any quadrilateral

using two strategies.

SOL 6.13 The student will describe and identify properties of

quadrilaterals.


Understand that properties belonging to a category of

quadrilaterals also belong to all subcategories of that

category.

Classify quadrilaterals in a hierarchy based on properties.

o Quadrilaterals include quadrilaterals, parallelograms,

rectangles, trapezoids, kites, rhombi, and squares.

o Properties include number of parallel sides, angle

measures and number of congruent sides.

Identify the sum of the measures of the angles of a

quadrilateral as 360°.

ESS



ndards_docs/mathem

atics/index.shtml

Exploring

Quadrilaterals

Quadrilaterals










Congruence


Create and justify congruent and noncongruent

segments, angles, and polygons using two

strategies.

Given two congruent figures, what inferences can

be drawn about how the figures are related?

Given two congruent polygons, what inferences

can be drawn about how the polygons are related?

SOL 6.12 The student will determine congruence of segments,

angles, and polygons.


Characterize polygons as congruent and noncongruent

according to the measures of their sides and angles.

Determine the congruence of segments, angles, and

polygons given their attributes.

Draw polygons in the coordinate plane given coordinates for

the vertices; use coordinates to find the length of a side joining

points with the same first coordinate or the same second

coordinate. Apply these techniques in the context of solving

practical and mathematical problems.†

ESS

http://www.doe.virgini

a.gov/testing/sol/stand

ards_docs/mathematics

/index.shtml

Congruence

Perimeter and Area in Practical Problems

6.10 c Essential Questions and Understandings

Why is area expressed in square units?

Compare and contrast perimeter and area.

How is perimeter used?

How might the distributive property help to find

perimeter?

Create and explain a practical problem involving

area and/or perimeter.

SOL 6.10 c The student will …

c) solve practical problems involving area and perimeter;

and ….

Understand that plane figures can be decomposed,

reassembled, and completed into new figures.

Apply formulas to solve practical problems involving

area and perimeter of triangles and rectangles.

Determine if a problem situation involving polygons of

four or fewer sides represents the application of

perimeter or area.

ESS



ndards_docs/mathem

atics/index.shtml

Measuring Mania

Areas with

Pentominoes/

Graph Paper/

Geoboards











Number

of

Blocks




questions.)



Additional

Instructional

Resources

ESS: VDOE Enhanced

Scope and Sequence

Geometry

Circles

6.10 a, b Essential Questions and Understandings

Create and solve problems that involve finding the

circumference and area of a circle when given the diameter

or radius.

SOL 6.10 a, b The student will

a) define pi (π) as the ratio of the circumference of a circle

to its diameter;

b) solve practical problems involving circumference and

area of a circle, given the diameter or radius; ….

6.10 a, b Essential Knowledge and Skills

Derive an approximation for pi (3.14 or 22

7 ) by

gathering data and comparing the circumference to the diameter

of various circles, using concrete materials or computer models.

Find the circumference of a circle by substituting a

value for the diameter or the radius into the formula C = d or

C = 2 r.

Find the area of a circle by using the formula

A = r2.

Create and solve problems that involve finding the

circumference and area of a circle when given the diameter or

radius.

Geometry

Volume and Surface area of a Rectangular Prism

6.10 d Essential Questions and Understandings

Why is volume expressed in cubic units?

Prove volume of a three-dimensional figure using

multiple strategies.

Compare and contrast surface area and volume.

What is the relationship between area and surface

area?

SOL 6.10 d The student will …

d) describe and determine the volume and surface area of a

rectangular prism.

6.10 d Essential Knowledge and Skills

Understand concepts of volume measurement:

The volume of a right rectangular prism with whole-unit side

lengths can be found by packing it with unit cubes and using


multiplication to count their number.

Decompose right rectangular prisms into layers of arrays of

cubes; determine and compare volumes or right rectangular

prisms, and objects well described as right rectangular prisms,

by counting cubic units.

Understand that three-dimensional figures can be formed by

joining rectangles and triangles along their edges to enclose a

solid region with no gaps or overlaps. The surface area is the

sum of the areas of the enclosing rectangles and triangles.

Find the surface area of cubes, prisms and pyramids (include

the use of nets to represent these figures.)

Solve problems that require finding the surface area of a

rectangular prism, given a diagram of the prism with the

necessary dimensions labeled.

Solve problems that require finding the volume of a rectangular

prism given a diagram of the prism with the necessary

dimensions labeled.

Probability

6.16 b Essential Questions and Understandings

Compare and contrast experimental or theoretical

probability to predict an outcome in an event.

Determine the probability of two dependent events.

Determine the probability of two independent

events.

Determine whether two events are dependent or

independent.

Compare and contrast dependent and independent

events.

Determine the probability of two dependent

events.

Determine the probability of two independent events.

SOL 6.16 b The student will …

b) determine probabilities for dependent and independent

events.

6.16 b Essential Knowledge and Skills

Determine the probability of two dependent events.

Determine the probability of two independent events.

ESS


a.gov/testing/sol/standa

rds_docs/mathematics/i

ndex.shtml

Fair or Not Fair

Statistics

Measures of Center


What does the phrase “measure of center” mean?

This is a collective term for the 3 types of averages for a


a) describe mean as balance point; and

b) decide which measure of center is appropriate for a

given purpose.


ESS




ndex.shtml

Measures of Central










set of data – mean, median, and mode.

Compare and contrast the measures of center.

What is meant by mean as balance point?

Mean can be defined as the point on a number line where

the data distribution is balanced. This means that the sum

of the distances from the mean of all the points above the

mean is equal to the sum of the distances of all the data

points below the mean. This is the concept of mean as the

balance point.

Create and explain a scenario depicting mean as a balance

point.

Find the mean for a set of data.

Describe the three measures of center and a situation in which

each would best represent a set of data.

Identify and draw a number line that demonstrates the concept

of mean as balance point for a set of data.

Tendency

Circle Graphs


What types of data are best presented in a circle graph?

Circle graphs are best used for data showing a relationship

of the parts to the whole.

Predict and draw conclusions based on data presented in a

graph.

Create and explain a circle graph based on a problem

situation.

Compare and contrast data presented in a circle graph

with the same data represented in other graphical forms.

SOL 6.14 The student, given a problem situation, will

a) construct circle graphs;

b) draw conclusions and make predictions, using circle graphs;

and

c) compare and contrast graphs that present information from

the same data set.


Collect, organize and display data in circle graphs by depicting

information as fractional.

Draw conclusions and make predictions about data presented in

a circle graph.

Compare and contrast data presented in a circle graph with the

same data represented in other graphical forms.

ESS




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Movie Data

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The Coordinate System


Can any given point be represented by more than one

ordered pair?

The coordinates of a point define its unique location in a

coordinate plane. Any given point is defined by only one

ordered pair.

In naming a point in the plane, does the order of the two

coordinates matter?

Yes. The first coordinate tells the location of the point to

the left or right of the y-axis and the second point tells

the location of the point above or below the x-axis. Point

(0, 0) is at the origin.


a) identify the coordinates of a point in a coordinate plane; and

b) graph ordered pairs in a coordinate plane.


A given point in the plane can be located by using an ordered

pair of numbers, called its coordinates. The first number

indicates how far to travel from the origin in the direction of

one axis, the second number indicates how far to travel in the

direction of the second axis.

Identify and label the axes of a coordinate plane.

Identify and label the quadrants of a coordinate plane.

Identify the quadrant or the axis on which a point is positioned

by examining the coordinates (ordered pair) of the point.






Justify ordered pairs represented by points in the four

quadrants and on the axes of the coordinate plane.

Create and interpret the coordinate values in the context

of a problem situation.

Graph ordered pairs in the four quadrants and on the axes of a

coordinate plane.

Identify ordered pairs represented by points in the four

quadrants and on the axes of the coordinate plane.

Where ordered pairs arise in a problem situation, interpret the

coordinate values in the context of the situation.

Make tables of equivalent ratios relating quantities with whole-

number measurements, finding missing values in the tables,

and plot the pairs of a values on the coordinate plane.

Enrichment, Assessment, and Remediation

GRADE 6 ATHEMATICS CURRICULUM UIDE...of operations on real numbers. Identify the property of...

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