Scope and Sequence Grades Pre-K–8

SCOTT FORESMAN ADDISON WESLEYPRENTICE HALL

6-12 Version Also Available

Our scope and sequence across Grades Pre-K–8 is carefully developed to guarantee full coverage of important concepts and skills with no gaps to impede understanding. The curriculum outlined here reflects a sound instructional design based on scientific mathematics research and years of leadership in publishing mathematics materials.

See PHSchool.com/math to obtain the Grade 6-12 Scope and Sequence.

Scope and SequenceFor Scott Foresman - Addison Wesley Mathematics

and Prentice Hall Mathematics

Grade Pre–K

Grade 3

Grade 6 Grade 7 Grade 8

Grade 4 Grade 5 Grade 6

Grade K Grade 2Grade 1

Grade Pre-K

Unit 1Counting and Number

Unit 2Understanding ArithmeticOperations (Part 1)

Unit 3Spatial Sense and Geometry

Unit 4Patterns

Unit 5Understanding ArithmeticOperations (Part 2)

Unit 6Measurement and Data

Unit 7Logical Reasoning

Grade K

Chapter 1Position and Sorting

Chapter 2Graphing and Patterns

Chapter 3Numbers Through 5

Chapter 4Numbers Through 10

Chapter 5Numbers Through 31

Chapter 6Measurement

Chapter 7Time and Money

Chapter 8Geometry and Fractions

Chapter 9Readiness for Addition and Subtraction

Chapter 10Understanding Addition

Chapter 11Understanding Subtraction

Chapter 12Counting and Number Patterns to 100

Grade 1

Chapter 1Patterns and Readiness forAddition and Subtraction

Chapter 2Understanding Addition and Subtraction

Chapter 3Strategies for Addition Facts to 12

Chapter 4Strategies for Subtraction Facts to 12

Chapter 5Geometry and Fractions

Chapter 6Time

Chapter 7Counting to 100

Chapter 8Place Value, Data, and Graphs

Chapter 9Money

Chapter 10Measurement and Probability

Chapter 11Addition and Subtraction Factsto 18

Chapter 12Two-Digit Addition andSubtraction

Grade 2

Chapter 1Understanding Addition and Subtraction

Chapter 2Fact Strategies for Addition and Subtraction

Chapter 3Place Value to 100 and Money

Chapter 4Mental Math: Addition and Subtraction

Chapter 5Two-Digit Addition

Chapter 6Two-Digit Subtraction

Chapter 7Geometry and Fractions

Chapter 8Time, Data, and Graphs

Chapter 9Measurement and Probability

Chapter 10Numbers to 1,000

Chapter 11Addition and Subtraction ofThree-Digit Numbers

Chapter 12Understanding Multiplicationand Division

Scott Foresman - Addison Wesley Mathematics

2

Grade 3

Chapter 1Place Value and Money

Chapter 2Addition and SubtractionNumber Sense

Chapter 3Adding and Subtracting

Chapter 4Time, Data, and Graphs

Chapter 5Multiplication Concepts and Facts

Chapter 6More Multiplication Facts

Chapter 7Division Concepts and Facts

Chapter 8Geometry and Measurement

Chapter 9Fractions and Measurement

Chapter 10Decimals and Measurement

Chapter 11Multiplying and Dividing Greater Numbers

Chapter 12Measurement and Probability

Grade 4

Chapter 1Place Value and Money

Chapter 2Adding and Subtracting WholeNumbers and Money

Chapter 3Multiplication and DivisionConcepts and Facts

Chapter 4Time, Data, and Graphs

Chapter 5Multiplying by One-DigitNumbers

Chapter 6Multiplying by Two-DigitNumbers

Chapter 7Dividing

Chapter 8Geometry and Measurement

Chapter 9Fraction Concepts

Chapter 10Fraction Operations andCustomary Measurement

Chapter 11Decimals and MetricMeasurement

Chapter 12Graphing and Probability

Grade 5

Chapter 1Place Value, Adding, and Subtracting

Chapter 2Multiplying Whole Numbers and Decimals

Chapter 3Dividing with One-Digit Divisors

Chapter 4Dividing with Two-Digit Divisors

Chapter 5Data, Graphs, and Probability

Chapter 6Geometry

Chapter 7Fraction Concepts

Chapter 8Fraction Operations

Chapter 9Measurement

Chapter 10Measuring Solids

Chapter 11Ratio, Proportion, and Percent

Chapter 12Algebra: Integers, Equations,and Graphing

Grade 6

Chapter 1Numbers, Expressions, and Equations

Chapter 2Decimals

Chapter 3Number Theory and FractionConcepts

Chapter 4Adding and SubtractingFractions

Chapter 5Multiplying and DividingFractions

Chapter 6Ratio, Rates, and Proportion

Chapter 7Percent

Chapter 8Algebra: Integers and RationalNumbers

Chapter 9Geometry

Chapter 10Measurement

Chapter 11Data, Graphs, and Probability

Chapter 12Algebra: Inequalities, Equations,and Graphs

3

Course 1

Chapter 1Whole Numbers and Decimals

Chapter 2Data and Graphs

Chapter 3Patterns and Variables

Chapter 4Number Theory and Fractions

Chapter 5Adding and Subtracting Fractions

Chapter 6Multiplying and Dividing Fractions

Chapter 7Ratios, Proportions, and Percents

Chapter 8Tools of Geometry

Chapter 9Geometry and Measurement

Chapter 10Integers

Chapter 11Exploring Probability

Chapter 12Equations and Inequalities

Course 2

Chapter 1Decimals and Integers

Chapter 2Exponents, Factors, and Fractions

Chapter 3Operations with Fractions

Chapter 4Equations and Inequalities

Chapter 5Ratios, Rates, and Proportions

Chapter 6Percents

Chapter 7Geometry

Chapter 8Measurement

Chapter 9Algebra: Patterns and Rules

Chapter 10Graphing in the Coordinate Plane

Chapter 11Displaying and Analyzing Data

Chapter 12Using Probability

Course 3

Chapter 1Integers and Algebraic Expressions

Chapter 2Rational Numbers

Chapter 3Real Numbers and the Coordinate Plane

Chapter 4Applications of Proportions

Chapter 5Applications of Percent

Chapter 6Equations and Inequalities

Chapter 7Geometry

Chapter 8Measurement

Chapter 9Using Graphs to Analyze Data

Chapter 10Probability

Chapter 11Algebra: Functions

Chapter 12Polynomials and Properties of Exponents

Prentice Hall Mathematics Grades 6–8

4

Course Grade

◗

◗

◗

◗

5

● Early Experiences ● Introduce ● Develop ● Maintain and Apply

Numbers

Numeration Pre-K K 1 2 3 4 5 6 1 2 3

One-to-one correspondence ● ● ● ●

Relating sets of objects to numerals ● ● ● ●

Using ordinal numbers for position ● ● ● ● ●

Counting, reading, writing, renaming

Numbers to 10 ● ● ● ● ●

Numbers to 100 ● ● ● ● ● ● ●

Numbers to 1,000 ● ● ● ● ● ●

Numbers to 10,000 ● ● ● ●

Numbers to 1 million (through 999,999) ● ● ● ●

Numbers to 1 billion (through 999,999,999) ● ● ● ●

Greater numbers ● ● ● ●

Concrete/pictorial and number-line models ● ● ● ● ● ● ● ● ●

Comparing and ordering ● ● ● ● ● ● ● ● ● ● ●

Forms of numbers (standard form, words, expanded form) ● ● ● ● ● ● ● ●

Place value ● ● ● ● ● ● ● ● ●

Place-value relationships and patterns ● ● ● ● ● ● ● ● ●

Skip counting ● ● ● ●

Rounding ● ● ● ● ● ● ● ● ●

Powers and exponents ● ● ● ● ●

Negative exponents ● ●

Square numbers ● ● ● ● ● ●

Scientific notation ● ● ● ●

Number Theory

Even and odd numbers ● ● ● ● ● ● ●

Prime and composite numbers ● ● ● ● ● ●

Prime factorization ● ● ● ● ●

Factor trees ● ● ● ● ●

Divisibility ● ● ● ● ● ● ●

Scope and Sequence

◗

◗

6

● Early Experiences ● Introduce ● Develop ● Maintain and Apply

Course Grade

Number Theory (cont’d) Pre-K K 1 2 3 4 5 6 1 2 3

Factors and multiples ● ● ● ● ● ● ●

Greatest common factor (GCF) ● ● ● ● ●

Least common multiple (LCM) ● ● ● ● ●

Money

Counting and showing amounts

Penny, nickel, dime ● ● ● ● ●

Quarter, half dollar, dollar ● ● ● ● ●

Fives, tens, twenties ● ●

Combinations of coins and bills ● ●

Comparing amounts ● ● ● ● ● ● ● ●

Making change ● ● ● ●

Rounding to nearest dollar ● ● ● ● ●

Fraction Concepts (also see Number Theory)

Concrete/pictorial models for part of a whole/part of a set ● ● ● ● ● ● ● ●

Reading and writing fractions ● ● ● ● ● ● ● ●

Rounding/estimating ● ● ● ● ● ● ● ●

Equivalent fractions ● ● ● ● ● ● ●

Lowest terms/simplest form ● ● ● ● ● ●

Mixed numbers, fractions greater than 1 ● ● ● ● ● ● ●

Fractions on a number line ● ● ● ● ● ● ●

Comparing and ordering ● ● ● ● ● ● ●

Common denominators ● ● ● ● ●

Reciprocals ● ● ● ●

Related to decimals ● ● ● ● ● ● ●

Related to percents ● ● ● ● ● ●

Decimal Concepts

Meaning ● ● ● ● ●

Decimal notation for money ● ● ● ● ● ●

Pictorial models ● ● ● ● ●

Tenths and hundredths ● ● ● ● ●

7

Course Grade

Decimal Concepts (cont’d) Pre-K K 1 2 3 4 5 6 1 2 3

Thousandths ● ● ● ●

Millionths ● ●

Equivalent decimals ● ● ● ● ● ●

Fractions as decimals ● ● ● ● ● ●

Related to measurement (metric system) ● ● ● ● ●

Decimals on a number line ● ● ● ● ● ●

Decimals and calculators ● ● ● ● ● ● ●

Comparing and ordering ● ● ● ● ● ● ●

Rounding ● ● ● ● ● ●

Related to percent ● ● ● ● ● ●

Terminating and repeating decimals ● ● ● ●

Non-repeating/irrational numbers ● ● ●

Scientific notation ● ● ● ●

Integers and Other Numbers

Integers

Meaning ● ● ● ● ●

Opposites ● ● ● ● ●

Absolute value ● ● ● ●

Comparing/ordering ● ● ● ● ●

Applications of integers ● ● ● ● ●

On a number line ● ● ● ● ●

Ordered pairs in four quadrants ● ● ● ● ●

Rational numbers ● ● ● ●

Squares and square roots ● ● ● ● ●

Comparing rational and irrational numbers ●

Real numbers ●

Operations

Estimation and Mental-Math Strategies

Deciding when to estimate ● ● ● ● ● ● ● ● ●

Underestimates and overestimates ● ● ● ● ● ● ●

◗

◗

◗

◗

8

Course Grade

Estimation and Mental-Math Strategies (cont’d) Pre-K K 1 2 3 4 5 6 1 2 3

Using a range ● ● ● ● ●

Adjusting an estimate ● ● ● ● ● ● ●

Using front-end digits ● ● ● ● ● ● ● ●

Rounding whole numbers and decimals ● ● ● ● ● ● ● ●

Rounding fractions and mixed numbers ● ● ● ● ● ● ● ●

Substituting compatible numbers ● ● ● ● ● ● ● ●

Using a reference point or benchmark ● ● ● ● ● ● ● ● ●

Clustering ● ● ●

Estimating quantities and measures ● ● ● ● ● ● ● ● ● ●

Counting on or back ● ● ● ●

Breaking apart numbers ● ● ● ● ● ●

Compensation ● ● ● ● ● ●

Using 10s or 100s to add or subtract ● ● ● ● ●

Using multiplication and division patterns ● ● ● ● ●

Using the distributive property ● ● ● ● ● ●

Determining reasonableness of results ● ● ● ● ● ● ●

Whole-Number Addition

Meanings of addition ● ● ● ● ● ● ● ● ●

Related to subtraction ● ● ● ● ● ● ● ● ●

Basic facts and fact strategies ● ● ● ● ● ● ●

Fact families ● ● ● ●

Properties ● ● ● ● ● ● ● ● ●

Using concrete/pictorial models ● ● ● ● ●

Adding 2-digit numbers ● ● ● ● ● ● ● ● ●

Adding numbers up to 3 digits ● ● ● ● ● ● ● ●

Adding numbers with 4 or more digits ● ● ● ● ● ●

Adding money ● ● ● ● ● ● ● ● ● ●

Three or more addends ● ● ● ● ● ● ● ● ●

Choosing a computation method ● ● ● ● ● ● ● ●

Addition expressions/sentences/equations ● ● ● ● ● ● ● ● ● ●

Estimation and mental math ● ● ● ● ● ● ● ●

Problem solving ● ● ● ● ● ● ● ● ● ● ●

● Early Experiences ● Introduce ● Develop ● Maintain and Apply

◗

◗

◗

◗

9

Course Grade

Whole-Number Subtraction Pre-K K 1 2 3 4 5 6 1 2 3

Meanings of subtraction ● ● ● ● ● ● ● ● ●

Related to addition ● ● ● ● ● ● ● ● ●

Basic facts and fact strategies ● ● ● ● ● ● ●

Properties ● ● ● ● ● ● ● ● ●

Using concrete/pictorial models ● ● ● ● ● ● ● ● ●

Subtracting 2-digit numbers ● ● ● ● ● ● ●

Subtracting 100s ● ●

Subtracting 3-digit numbers ● ● ● ● ● ●

Subtracting 4-digit numbers ● ● ● ●

Subtracting money ● ● ● ● ● ● ● ● ● ●

Choosing a computation method ● ● ● ● ● ● ● ●

Subtraction expressions/sentences/equations ● ● ● ● ● ● ● ● ● ●

Inverse operations ● ● ● ● ● ● ● ●

Estimation and mental math ● ● ● ● ● ● ● ● ●

Problem solving ● ● ● ● ● ● ● ● ● ● ●

Whole-Number Multiplication

Meanings of multiplication ● ● ● ● ● ●

Related to addition ● ● ● ● ● ● ● ●

Basic facts and fact strategies ● ● ● ●

Fact families ● ● ●

Multiplication stories ● ●

Multiplication table (fact table) ● ●

Three factors ● ● ● ● ●

Properties ● ● ● ● ● ● ● ●

Using concrete/pictorial models ● ● ● ● ● ●

By a 1-digit number ● ● ● ● ● ●

Multiplying money ● ● ● ● ● ● ●

By multiples of 10 and 100 ● ● ● ● ● ● ●

Partial products ● ● ● ● ● ●

By a multi-digit number ● ● ● ● ● ●

Missing factors ● ● ● ● ● ● ●

Exponents in multiplication ● ● ● ●

Choosing a computation method ● ● ● ● ● ● ●

◗

◗

10

Course Grade

Whole-Number Multiplication (cont’d) Pre-K K 1 2 3 4 5 6 1 2 3

Multiplication expressions/sentences/equations ● ● ● ● ● ● ● ●

Inverse operations ● ● ● ● ● ● ●

Estimation and mental math ● ● ● ● ● ● ●

Problem solving ● ● ● ● ● ● ● ●

Whole-Number Division

Meanings of division ● ● ● ● ● ● ● ● ●

Related to subtraction and multiplication ● ● ● ● ● ● ●

Basic facts: 2, 3, 4, 5, 6, 7, 8, and 9 as divisors ● ● ● ● ●

Fact families ● ●

Division stories ● ● ● ● ●

1 and 0 in division ● ● ● ● ● ● ●

Using concrete/pictorial models ● ● ● ● ● ● ● ●

2-digit dividends ● ● ● ● ●

By a 1-digit divisor ● ● ● ● ●

Dividing money ● ● ● ● ● ●

By multiples of 10 and 100 ● ● ● ● ● ●

By a 2-digit divisor ● ● ● ● ● ●

By a multi-digit divisor ● ● ●

Average (mean) ● ● ● ● ● ●

Interpreting remainders ● ● ● ● ● ● ●

Choosing a computation method ● ● ● ● ● ●

Division expressions/sentences/equations ● ● ● ● ● ● ● ●

Estimation and mental math ● ● ● ● ● ● ●

Problem solving ● ● ● ● ● ● ● ● ●

Fraction Operations

Adding and subtracting, pictorial models ● ● ● ● ● ●

Adding and subtracting, like denominators ● ● ● ● ● ●

Adding and subtracting, unlike denominators ● ● ● ● ● ●

Adding and subtracting mixed numbers ● ● ● ● ●

Finding a fraction of a whole number ● ● ● ● ● ● ●

Multiplying and dividing fractions using models ● ● ● ● ● ●

● Early Experiences ● Introduce ● Develop ● Maintain and Apply

11

Course Grade

Fraction Operations (cont’d) Pre-K K 1 2 3 4 5 6 1 2 3

Multiplying fractions ● ● ● ● ●

Multiplying mixed numbers ● ● ● ● ●

Dividing whole numbers by fractions using models ● ● ● ●

Dividing whole numbers by fractions ● ● ● ● ●

Dividing fractions ● ● ● ●

Dividing mixed numbers ● ● ●

Expressions/sentences/equations ● ● ● ● ● ● ●

Estimation and mental math ● ● ● ● ● ●

Problem solving ● ● ● ● ● ● ●

Choosing a computation method ● ● ● ●

Checking for reasonableness of results ● ● ● ●

Decimal Operations

Adding and subtracting money ● ● ● ● ● ● ●

Multiplying and dividing money ● ● ● ● ● ● ●

Adding and subtracting with pictorial models ● ● ● ●

Adding and subtracting ● ● ● ● ● ● ●

Multiplying by a whole number ● ● ● ● ● ●

Multiplying by a power of 10 ● ● ● ● ●

Multiplying and dividing with pictorial models ● ● ● ● ● ●

Multiplying a decimal by a decimal ● ● ● ● ●

Dividing a decimal by a whole number ● ● ● ● ●

Dividing a decimal by a decimal ● ● ● ●

Expressions/sentences/equations ● ● ● ● ● ● ●

Estimation and mental math ● ● ● ● ● ●

Problem solving ● ● ● ● ● ● ●

Integer Operations

Adding and subtracting integers ● ● ● ● ●

Using a pictorial or number-line model ● ● ● ● ●

Multiplying and dividing integers ● ● ●

Expressions/sentences/equations ● ● ● ● ●

◗

◗

◗

◗

12

Course Grade

Integer Operations (cont’d) Pre-K K 1 2 3 4 5 6 1 2 3

Estimation and mental math ● ● ●

Problem solving ● ● ● ● ●

Ratio, Proportion, and PercentRatio and Proportion

Defining ratio ● ● ● ● ●

Reading and writing ratios ● ● ● ● ●

Equivalent ratios in tables, graphs ● ● ● ● ●

Rates and unit prices ● ● ● ● ●

Solving proportions ● ● ● ● ●

Distance, rate, time ● ● ● ●

Reasoning with proportions ● ● ● ●

Related to maps and scale drawings ● ● ● ● ●

Related to similar figures ● ● ● ●

Related to scale models ● ● ●

Estimation and mental math ● ● ● ●

Percent

Meaning of percent ● ● ● ● ●

Using percent models ● ● ●

Reading and writing ● ● ● ● ●

Related to fractions and decimals ● ● ● ● ●

Comparing and ordering fractions, decimals, and percents ● ● ● ●

Finding a percent of a number ● ● ● ● ●

Greater than 100%, less than 1% ● ●

Finding what percent one number is of another ● ● ●

Finding a number when a percent is known ● ●

Using equations with percent ● ● ●

Using proportions with percent ● ● ●

Discount, sales tax, tipping ● ● ● ●

Interest, commission ● ● ● ●

Related to circle graphs ● ● ● ●

● Early Experiences ● Introduce ● Develop ● Maintain and Apply

◗

◗

◗

◗◗

◗

◗

◗

◗

◗

◗

◗

◗

◗

◗

◗

◗

◗

◗

◗

◗

◗

◗

◗

13

Course Grade

Percent (cont’d) Pre-K K 1 2 3 4 5 6 1 2 3

Estimation and mental math ● ● ● ● ●

Percent increase and decrease ● ● ●

Geometry

Plane and Solid Figures

Identifying polygons ● ● ● ● ● ● ● ● ● ● ●

Sides and corners/vertices ● ● ● ● ● ● ● ● ● ● ●

Identifying solid figures ● ● ● ● ● ● ● ● ● ● ●

Points, lines, line segments, rays, angles ● ● ● ● ● ● ●

Measuring angles ● ● ● ● ● ●

Sum of the interior angles of a polygon ● ● ● ● ●

Circles, parts of ● ● ● ● ● ● ●

Faces, edges, vertices ● ● ● ● ● ● ● ● ● ● ●

Combining shapes ● ● ● ● ● ● ● ● ● ● ●

Subdividing shapes ● ● ● ● ● ● ● ●

Relating plane and solid figures ● ● ● ● ● ● ● ● ● ● ●

Symmetry ● ● ● ● ● ● ● ● ● ●

Rotational symmetry ● ●

Identifying and drawing patterns for solids (nets) ● ● ● ● ● ● ● ●

Tessellations ● ● ● ●

Drawing figures from descriptions ● ● ● ● ● ● ● ● ● ● ●

Drawing/constructing/building ● ● ● ● ● ● ● ●

Visual thinking ● ● ● ● ● ● ● ● ● ●

Reflections, translations, rotations on coordinate grids ● ● ● ●

Enlargements, reductions, dilations

Trigonometric ratios (sine, cosine, tangent)

Geometric models for real-world situations ● ● ● ● ● ● ● ● ● ●

Geometric figures on coordinate system ● ● ● ●

Making conjectures about geometric relationships ● ● ●

Pythagorean Theorem ● ● ●

Classifying Figures

Congruent figures ● ● ● ● ● ● ● ● ●

Congruent angles ● ● ● ●

◗

◗

◗

◗

◗

◗

◗

◗

14

Course Grade

Classifying Figures (cont’d) Pre-K K 1 2 3 4 5 6 1 2 3

Transformations (slides, flips, turns) ● ● ● ● ● ● ● ● ●

Similar figures ● ● ● ● ● ●

Pairs of lines/line segments (parallel, perpendicular, skew) ● ● ● ● ●

Angles, compared to right angle ● ● ● ● ● ● ●

Polygons ● ● ● ● ● ● ● ● ● ● ●

Triangles ● ● ● ● ● ● ●

Quadrilaterals ● ● ● ● ● ● ●

Polyhedrons/solid shapes ● ● ● ● ● ● ● ● ●

Measurement

Length, Weight/Mass, Capacity, and Temperature

Comparing and ordering using direct comparison ● ● ● ● ● ● ● ● ●

Nonstandard units ● ● ● ● ●

Customary units

Length: inches, feet ● ● ● ● ● ● ● ● ●

Length: fraction of an inch ● ● ● ● ● ● ● ●

Length: yards ● ● ● ● ● ● ● ●

Length: miles ● ● ● ● ● ● ●

Capacity: fluid ounces, teaspoons, tablespoons ● ● ● ● ● ●

Capacity: cups ● ● ● ● ● ● ● ● ●

Capacity: pints, quarts ● ● ● ● ● ● ● ● ●

Capacity: gallons ● ● ● ● ● ● ● ●

Weight: ounces ● ● ● ● ● ● ● ●

Weight: pounds ● ● ● ● ● ● ● ● ●

Weight: tons ● ● ● ● ● ●

Temperature: degrees Fahrenheit ● ● ● ● ● ● ● ● ●

Metric units

Length: millimeters ● ● ● ● ● ●

● Early Experiences ● Introduce ● Develop ● Maintain and Apply

15

Course Grade

Length, Weight/Mass, Capacity, and Temperature (cont’d) Pre-K K 1 2 3 4 5 6 1 2 3

Length: centimeters ● ● ● ● ● ● ● ● ●

Length: meters ● ● ● ● ● ● ● ●

Length: decimeters, kilometers ● ● ● ● ● ● ●

Length: dekameters, hectometers ● ● ● ●

Capacity: liters ● ● ● ● ● ● ● ● ●

Capacity: milliliters ● ● ● ● ● ● ●

Capacity: kiloliters ● ● ● ●

Mass: grams ● ● ● ● ● ● ● ● ●

Mass: kilograms ● ● ● ● ● ● ● ● ●

Temperature: degrees Celsius ● ● ● ● ● ● ● ● ●

Length, estimating using benchmarks ● ● ● ● ● ● ● ● ● ●

Capacity, estimating using benchmarks ● ● ● ● ● ● ● ● ● ●

Weight/mass, estimating using benchmarks ● ● ● ● ● ● ● ● ● ●

Choosing appropriate measuring units ● ● ● ● ● ● ● ● ●

Choosing appropriate measuring instruments ● ● ● ● ● ● ● ●

Compass ● ● ● ●

Graph paper ● ● ● ● ●

Protractor ● ● ● ● ● ●

Ruler ● ● ● ● ● ● ● ● ●

Time

Nearest hour/half hour ● ● ● ● ●

Minutes before/after the hour ● ● ●

Reading schedules ● ● ● ●

Elapsed time ● ● ● ● ● ● ●

Calendar ● ● ● ● ●

Estimating time ● ● ● ● ● ● ● ●

Relationships between units of time ● ● ● ● ● ● ● ●

A.M. and P.M. ● ● ●

◗

◗

16

Course Grade

Perimeter, Area, and Volume Pre-K K 1 2 3 4 5 6 1 2 3

Perimeter, estimating and counting units ● ● ● ● ● ● ●

Perimeter formulas ● ● ● ● ● ●

Circumference ● ● ● ● ● ● ●

Area, estimating and counting square units ● ● ● ● ● ● ● ● ● ●

Area of a rectangle ● ● ● ● ● ●

Area of a parallelogram ● ● ● ● ●

Area of a triangle ● ● ● ● ●

Area of a trapezoid ● ● ● ● ●

Area of a circle ● ● ● ●

Area of composite figures ● ● ● ● ●

Surface area of a prism ● ● ● ● ● ●

Surface area of a cylinder ● ● ● ●

Volume, estimating and counting cubic units ● ● ● ● ● ● ●

Volume formulas ● ● ● ● ● ●

Volume of a prism ● ● ● ● ● ●

Volume of a cylinder ● ● ● ●

Volume of cone/pyramid/sphere ●

Length/perimeter/area relationships ● ● ● ● ● ●

Length/perimeter/area/volume relationships ● ● ● ●

Irregular figures ● ● ● ●

Estimate by attribute: dimensional analysis ● ●

Choosing appropriate type of unit: length, area, volume ● ● ● ● ● ●

Converting Units

Length, converting units ● ● ● ● ● ● ●

Capacity, converting units ● ● ● ● ● ● ●

Weight/mass, converting units ● ● ● ● ● ● ●

Converting units between systems ● ● ● ● ● ●

Adding and subtracting measures ● ● ● ● ● ●

Connecting volume, mass, and capacity ● ● ● ● ● ●

Precision and error in measurement ● ● ● ●

Significant digits ●

● Early Experiences ● Introduce ● Develop ● Maintain and Apply

17

Course Grade Data Analysis and Probability

Graphs Pre-K K 1 2 3 4 5 6 1 2 3

Reading and making graphs

Pictographs/real graphs ● ● ● ● ● ● ● ●

Bar graphs ● ● ● ● ● ● ● ● ● ●

Double bar graphs ● ● ● ●

Stacked/sliding bar graphs

Line graphs ● ● ● ● ● ● ●

Multiple line graphs ● ● ● ●

Line plots ● ● ● ● ● ● ● ●

Circle graphs ● ● ● ● ● ●

Stem-and-leaf plots ● ● ● ● ● ●

Box-and-whisker plots ● ● ● ●

Histograms ● ● ● ● ● ●

Scatterplots ● ● ● ●

Misleading graphs ● ● ● ● ● ●

Naming ordered pairs ● ● ● ● ● ● ● ● ●

Graphing ordered pairs ● ● ● ● ● ● ●

Graphing equations ● ● ● ● ●

Identifying trend line and line of best fit ●

Choosing appropriate graphs ● ● ●

Making predictions from graphs ● ● ● ● ● ● ●

Drawing and comparing different representations ● ● ●

Data Collection and Analysis

Reading charts/tables ● ● ● ● ● ● ● ● ● ●

Collecting and organizing data ● ● ● ● ● ● ● ● ● ● ●

Making charts/tables ● ● ● ● ● ● ● ● ● ●

Tally charts ● ● ● ● ● ● ●

Taking a survey ● ● ● ● ● ● ●

Writing a survey ● ● ● ● ●

Identifying bias in surveys ●

Interpreting data ● ● ● ● ● ● ● ● ●

Making predictions, interpolations, extrapolations ● ● ● ● ● ● ● ●

Sampling techniques ● ● ● ●

◗

◗

◗

◗

◗

◗

◗

◗

◗

◗

◗

◗

◗

◗

◗

◗

18

Course Grade

Data Collection and Analysis (cont’d) Pre-K K 1 2 3 4 5 6 1 2 3

Frequency distribution ● ● ●

Mean/mode/range ● ● ● ● ● ● ●

Median ● ● ● ● ● ● ●

Describing sets of data ● ● ● ● ● ● ●

Outliers and quartiles ● ● ● ● ●

Determining trends from data ● ●

Comparing related sets of data ● ● ● ● ● ● ●

Misleading statistics ● ● ● ●

Using data in problem solving ● ● ● ● ● ● ● ● ● ●

Probability

Probability experiments ● ● ● ● ● ● ● ● ●

Conducting simulations ● ● ●

Outcomes ● ● ● ● ● ● ● ● ●

Tree diagrams ● ● ● ● ● ● ●

Writing probability as a fraction ● ● ● ● ● ● ●

Writing probability as a decimal or percent ● ● ● ●

Certain/possible/impossible events ● ● ● ● ● ● ● ● ●

Compound events ● ● ●

Complementary events ● ● ●

Experimental/theoretical probability ● ● ● ● ●

Independent and dependent events ● ● ●

Making predictions ● ● ● ● ● ● ● ● ●

Estimating probability of simple and compound events ● ● ● ●

Fair and unfair games ● ● ● ● ● ● ●

Fundamental counting principle ● ● ● ●

Permutations and combinations ● ● ● ●

● Early Experiences ● Introduce ● Develop ● Maintain and Apply

◗

◗

◗

◗

◗

◗

◗

◗

◗

◗

◗

◗

19

Course Grade Algebra

Patterns, Properties, and Expressions Pre-K K 1 2 3 4 5 6 1 2 3

Patterns with objects/geometric figures ● ● ● ● ● ● ● ● ● ● ●

Number patterns ● ● ● ● ● ● ● ● ● ●

Making generalizations and predictions ● ● ● ● ● ● ● ● ●

Patterns using words, tables, and graphs ● ● ● ● ● ● ● ● ●

Skip counting ● ● ● ● ●

Sequences

In tables, charts, and graphs ● ● ● ● ● ● ● ● ●

Used to make predictions ● ● ● ● ● ● ● ● ●

Arithmetic and geometric ● ●

Fibonacci sequence ● ● ●

Logical reasoning ● ● ● ● ● ● ● ● ● ●

Venn diagrams ● ● ● ● ● ●

Addition properties

Commutative and associative properties ● ● ● ● ● ● ● ● ●

Adding zero (identity property) ● ● ● ● ● ● ● ● ●

Opposites (additive inverse property) ● ● ●

Multiplication properties

Commutative property ● ● ● ● ● ● ● ●

Associative property ● ● ● ● ● ● ●

Multiplying by 1 (identity property) ● ● ● ● ● ● ●

Multiplying by 0 (zero property) ● ● ● ● ● ● ●

Reciprocals (multiplicative inverse property) ● ●

Distributive property ● ● ● ● ● ●

Writing/evaluating numerical expressions ● ● ● ● ● ● ● ● ● ●

Order of operations ● ● ● ● ●

Expressions with parentheses ● ● ● ● ● ●

Expressions with exponents ● ● ● ●

Writing/evaluating expressions with variables ● ● ● ● ● ● ●

Writing inequalities ● ●

Simplifying expressions with variables ● ● ● ●

◗

◗

◗

◗

20

Course Grade

Patterns, Properties, and Expressions (cont’d) Pre-K K 1 2 3 4 5 6 1 2 3

Applying properties to expressions with variables ● ● ●

Explaining properties and relationships ● ● ● ● ● ●

Integers (see Numbers: Integers and other Numbers) ● ● ● ● ● ●

Relationships

Sorting and classifying ● ● ● ● ● ● ●

Function tables (input/output tables) ● ● ● ● ● ● ● ● ●

Function tables, rules stated using variables ● ● ● ● ● ●

Graphing functions ● ● ● ●

Modeling problem situations with objects ● ● ● ● ● ● ●

Using symbols to show relationships ● ● ● ● ● ● ● ● ●

Relating addition and subtraction ● ● ● ● ● ● ● ● ●

Relating multiplication and division ● ● ● ● ● ● ●

Ordered pairs ● ● ● ● ● ● ●

Finding rate of change and slope ● ● ● ●

Identifying linear functions ● ● ● ●

Analyzing and interpreting linear relationships ● ● ● ●

Making generalizations about linear relationships ● ● ●

Identifying quadratic functions ●

Identifying other nonlinear functions ● ●

Equations and Inequalities

Completing number sentences ● ● ● ● ● ● ● ●

Finding missing addends, subtrahends, minuends ● ● ● ● ● ● ●

Finding missing factors ● ● ● ● ● ● ●

Equations that use letters as variables ● ● ● ● ● ● ●

Expressing relationships using equations ● ● ● ● ● ● ●

Solving equations using tables, graphs, and models ● ● ● ● ● ●

Equations with decimals, fractions, integers ● ● ● ● ●

Solving equations by substitution ● ● ● ● ● ●

Solving one-step equations ● ● ● ● ● ●

Solving two-step equations ● ● ● ●

● Early Experiences ● Introduce ● Develop ● Maintain and Apply

◗

◗

◗

◗

◗

◗

◗

◗

21

Course Grade

Equations and Inequalities (cont’d) Pre-K K 1 2 3 4 5 6 1 2 3

Solving multi-step equations ●

Graphing linear equations ● ● ● ● ● ●

Identifying slope and intercepts ●

Graphing equations using slope and intercepts ●

Solving systems of linear equations

Non-linear relations ● ● ● ●

Inequalities ● ● ● ● ● ● ●

Using inequality symbols to compare numbers ● ● ● ● ● ● ● ● ●

Solving one-step inequalities ● ● ● ●

Solving two-step inequalities ● ●

Solving problems using formulas ● ● ● ● ● ●

Formulas ● ● ●

Properties of equality and inequality ● ● ● ● ● ●

Solving problems using equations and inequalities ● ●

Mathematical Processes

Problem-Solving Skills

Using a problem-solving plan ● ● ● ● ● ● ●

Use data from a picture, graph, table ● ● ● ● ● ● ● ● ● ●

Choose an operation ● ● ● ● ● ● ● ● ● ●

Multiple-step problems ● ● ● ● ● ● ● ● ●

Extra or missing information ● ● ● ● ● ● ● ● ●

Exact answer or estimate ● ● ● ● ● ● ● ● ●

Interpreting remainders ● ● ● ● ● ● ●

Translating words to expressions ● ● ● ● ● ● ● ●

Writing to explain ● ● ● ● ● ● ●

Writing to describe ● ● ● ● ● ● ●

Writing to compare ● ● ● ● ● ● ●

Writing to persuade ● ● ●

Using a calculator or computer ● ● ● ● ● ● ● ● ●

◗

◗

◗

◗

◗

◗

◗

◗

22

Course Grade

Problem-Solving Strategies Pre-K K 1 2 3 4 5 6 1 2 3

Act it out, use objects, do simulations ● ● ● ● ● ● ● ● ● ● ●

Draw a picture ● ● ● ● ● ● ● ● ● ●

Use logical reasoning ● ● ● ● ● ● ● ● ● ●

Try, check, and revise ● ● ● ● ● ● ● ● ● ●

Look for a pattern ● ● ● ● ● ● ● ● ● ● ●

Make an organized list ● ● ● ● ● ● ● ● ● ●

Make a table ● ● ● ● ● ● ● ● ● ●

Make a graph ● ● ● ● ● ● ● ● ● ●

Solve a simpler problem ● ● ● ● ● ● ●

Work backward ● ● ● ● ● ● ●

Write a number sentence/equation/proportion ● ● ● ● ● ● ● ● ● ●

Choose a strategy ● ● ● ● ● ● ●

Compare strategies ● ● ●

Using multiple strategies ● ● ● ● ● ● ●

Reasoning and Proof

Logical reasoning

Comparing/contrasting ● ● ● ● ● ● ● ● ● ● ●

Classifying/sorting/Venn diagrams ● ● ● ● ● ● ● ● ● ● ●

Finding/extending/using patterns ● ● ● ● ● ● ● ● ● ● ●

Making connections ● ● ● ● ● ● ● ● ● ● ●

Making generalizations ● ● ● ● ● ● ● ● ●

Drawing conclusions and evaluating arguments ● ● ● ● ● ● ● ● ● ●

Making/testing conjectures ● ● ● ● ● ● ● ● ●

Explaining/justifying answers/checking for reasonableness ● ● ● ● ● ● ● ● ●

Visual and creative thinking

Visual patterns/spatial reasoning ● ● ● ● ● ● ● ● ● ● ●

Solving non-routine problems ● ● ● ● ● ● ● ● ● ●

Generating problems ● ● ● ● ● ● ● ● ●

● Early Experiences ● Introduce ● Develop ● Maintain and Apply

23

Course Grade

Connections Pre-K K 1 2 3 4 5 6 1 2 3

Curriculum connections to other subjects ● ● ● ● ● ● ● ● ● ●

Connections among mathematical ideas ● ● ● ● ● ● ● ● ●

Real-world connections

Students’ daily lives ● ● ● ● ● ● ● ● ● ● ●

Consumer ● ● ● ● ● ●

Career ● ● ● ● ● ●

Multicultural connections ● ● ● ● ● ● ● ● ● ●

Connections using technology ● ● ● ● ● ● ● ● ●

Communication

Writing to explain ● ● ● ● ● ● ●

Writing to compare ● ● ● ● ● ● ●

Writing to describe ● ● ● ● ● ● ●

Writing to persuade ● ● ●

Reading for math success/reading assists/math language ● ● ● ● ● ● ● ● ● ●

Write about it/journal ● ● ● ● ● ● ●

Talk about it/share ● ● ● ● ● ● ● ● ● ● ●

Working in groups ● ● ● ● ● ● ● ● ● ● ●

Writing convincing arguments using mathematical ideas ● ● ● ● ● ● ● ● ●

Representation

Concrete/pictorial and number-line models for whole numbers ● ● ● ● ● ● ●

Integers on a number line ● ● ● ● ●

Whole-number addition/subtraction using concrete/pictorial models ● ● ● ● ●

Whole-number multiplication/division using concrete/pictorial models ● ● ● ●

◗

◗

◗

◗

24

Course Grade

Representation (cont’d) Pre-K K 1 2 3 4 5 6 1 2 3

Integer computation using pictorial or number-line models ● ● ● ● ●

Concrete/pictorial models for part of a whole/set ● ● ● ● ● ● ● ●

Fractions on a number line ● ● ● ● ● ● ●

Fraction operations using pictorial models ● ● ● ● ● ● ●

Dividing whole numbers by fractions using pictorial models ● ● ● ● ●

Pictorial models for decimals ● ● ● ● ● ● ●

Decimals on a number line ● ● ● ● ● ●

Decimal operations using pictorial models ● ● ● ● ● ● ●

Integers on a number line ● ● ● ● ●

Integer operations using pictorial or number-line models ● ● ● ● ●

Ratio, proportion, percent models ● ● ● ● ●

Proportions related to maps and scale drawings ● ● ● ● ●

Counting units to find length, area, volume ● ● ● ● ● ● ● ● ● ●

Geometric models for real-world situations ● ● ● ● ● ● ● ● ● ●

Making graphs/charts/tables/diagrams ● ● ● ● ● ● ● ● ● ● ●

Models for equations (algebra tiles, two-color counters) ● ● ● ● ● ●

Solving problems by drawing a picture/diagram ● ● ● ● ● ● ● ● ● ●

Number sentences and equations to model real situations ● ● ● ● ● ● ● ● ● ●

● Early Experiences ● Introduce ● Develop ● Maintain and Apply

0-13-350163-9 3M.V1.1106.AV.JC.RG

Grade 3 Grade 4 Grade 5 Grade 6

Grade Pre-K Grade K Grade 1 Grade 2

Grade 6 Grade 7 Grade 8