8 SCOTT FORESMAN ADDISON WESLEY PRENTICE HALL

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1 Scope and Sequence Grades Pre-K 8 SCOTT FORESMAN PRENTICE HALL ADDISON WESLEY

2 Scope and Sequence For Scott Foresman - Addison Wesley Mathematics and Prentice Hall Mathematics Grade Pre K Grade K Grade 1 Grade 2 Grade 3 Grade 4 Grade 5 Grade 6 Grade 6 Grade 7 Grade 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.

3 Scott Foresman - Addison Wesley Mathematics Grade Pre-K Grade K Grade 1 Grade 2 Unit 1 Counting and Number Unit 2 Understanding Arithmetic Operations (Part 1) Unit 3 Spatial Sense and Geometry Unit 4 Patterns Unit 5 Understanding Arithmetic Operations (Part 2) Unit 6 Measurement and Data Unit 7 Logical Reasoning Chapter 1 Position and Sorting Chapter 2 Graphing and Patterns Chapter 3 Numbers Through 5 Chapter 4 Numbers Through 10 Chapter 5 Numbers Through 31 Chapter 6 Measurement Chapter 7 Time and Money Chapter 8 Geometry and Fractions Chapter 9 Readiness for Addition and Subtraction Chapter 10 Understanding Addition Chapter 11 Understanding Subtraction Chapter 12 Counting and Number Patterns to 100 Chapter 1 Patterns and Readiness for Addition and Subtraction Chapter 2 Understanding Addition and Subtraction Chapter 3 Strategies for Addition Facts to 12 Chapter 4 Strategies for Subtraction Facts to 12 Chapter 5 Geometry and Fractions Chapter 6 Time Chapter 7 Counting to 100 Chapter 8 Place Value, Data, and Graphs Chapter 9 Money Chapter 10 Measurement and Probability Chapter 11 Addition and Subtraction Facts to 18 Chapter 12 Two-Digit Addition and Subtraction Chapter 1 Understanding Addition and Subtraction Chapter 2 Fact Strategies for Addition and Subtraction Chapter 3 Place Value to 100 and Money Chapter 4 Mental Math: Addition and Subtraction Chapter 5 Two-Digit Addition Chapter 6 Two-Digit Subtraction Chapter 7 Geometry and Fractions Chapter 8 Time, Data, and Graphs Chapter 9 Measurement and Probability Chapter 10 Numbers to 1,000 Chapter 11 Addition and Subtraction of Three-Digit Numbers Chapter 12 Understanding Multiplication and Division 2

4 3 Grade 4 Grade 5 Grade 6 Chapter 1 Place Value and Money Chapter 2 Addition and Subtraction Number Sense Chapter 3 Adding and Subtracting Chapter 4 Time, Data, and Graphs Chapter 5 Multiplication Concepts and Facts Chapter 6 More Multiplication Facts Chapter 7 Division Concepts and Facts Chapter 8 Geometry and Measurement Chapter 9 Fractions and Measurement Chapter 10 Decimals and Measurement Chapter 11 Multiplying and Dividing Greater Numbers Chapter 12 Measurement and Probability Chapter 1 Place Value and Money Chapter 2 Adding and Subtracting Whole Numbers and Money Chapter 3 Multiplication and Division Concepts and Facts Chapter 4 Time, Data, and Graphs Chapter 5 Multiplying by One-Digit Numbers Chapter 6 Multiplying by Two-Digit Numbers Chapter 7 Dividing Chapter 8 Geometry and Measurement Chapter 9 Fraction Concepts Chapter 10 Fraction Operations and Customary Measurement Chapter 11 Decimals and Metric Measurement Chapter 12 Graphing and Probability Chapter 1 Place Value, Adding, and Subtracting Chapter 2 Multiplying Whole Numbers and Decimals Chapter 3 Dividing with One-Digit Divisors Chapter 4 Dividing with Two-Digit Divisors Chapter 5 Data, Graphs, and Probability Chapter 6 Geometry Chapter 7 Fraction Concepts Chapter 8 Fraction Operations Chapter 9 Measurement Chapter 10 Measuring Solids Chapter 11 Ratio, Proportion, and Percent Chapter 12 Algebra: Integers, Equations, and Graphing Chapter 1 Numbers, Expressions, and Equations Chapter 2 Decimals Chapter 3 Number Theory and Fraction Concepts Chapter 4 Adding and Subtracting Fractions Chapter 5 Multiplying and Dividing Fractions Chapter 6 Ratio, Rates, and Proportion Chapter 7 Percent Chapter 8 Algebra: Integers and Rational Numbers Chapter 9 Geometry Chapter 10 Measurement Chapter 11 Data, Graphs, and Probability Chapter 12 Algebra: Inequalities, Equations, and Graphs 3

5 Prentice Hall Mathematics Grades Chapter 1 Whole Numbers and Decimals Chapter 2 Data and Graphs Chapter 3 Patterns and Variables Chapter 4 Number Theory and Fractions Chapter 5 Adding and Subtracting Fractions Chapter 6 Multiplying and Dividing Fractions Chapter 7 Ratios, Proportions, and Percents Chapter 8 Tools of Geometry Chapter 9 Geometry and Measurement Chapter 10 Integers Chapter 11 Exploring Probability Chapter 12 Equations and Inequalities Chapter 1 Decimals and Integers Chapter 2 Exponents, Factors, and Fractions Chapter 3 Operations with Fractions Chapter 4 Equations and Inequalities Chapter 5 Ratios, Rates, and Proportions Chapter 6 Percents Chapter 7 Geometry Chapter 8 Measurement Chapter 9 Algebra: Patterns and Rules Chapter 10 Graphing in the Coordinate Plane Chapter 11 Displaying and Analyzing Data Chapter 12 Using Probability Chapter 1 Integers and Algebraic Expressions Chapter 2 Rational Numbers Chapter 3 Real Numbers and the Coordinate Plane Chapter 4 Applications of Proportions Chapter 5 Applications of Percent Chapter 6 Equations and Inequalities Chapter 7 Geometry Chapter 8 Measurement Chapter 9 Using Graphs to Analyze Data Chapter 10 Probability Chapter 11 Algebra: Functions Chapter 12 Polynomials and Properties of Exponents 4

6 Scope and Sequence Numbers Grade Numeration Pre-K K 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 Early Experiences Introduce Develop Maintain and Apply 5

7 Number Theory (cont d) Pre-K K 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 6 Early Experiences Introduce Develop Maintain and Apply

8 Decimal Concepts (cont d) Pre-K K 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 7

9 Estimation and Mental-Math Strategies (cont d) Pre-K K 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 8 Early Experiences Introduce Develop Maintain and Apply

10 Whole-Number Subtraction Pre-K K 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 9

11 Whole-Number Multiplication (cont d) Pre-K K 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 10 Early Experiences Introduce Develop Maintain and Apply

12 Fraction Operations (cont d) Pre-K K 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 11

13 Integer Operations (cont d) Pre-K K Estimation and mental math Problem solving Ratio, Proportion, and Percent Ratio 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 12 Early Experiences Introduce Develop Maintain and Apply

14 Percent (cont d) Pre-K K 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 13

15 Classifying Figures (cont d) Pre-K K 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 14 Early Experiences Introduce Develop Maintain and Apply

16 Length, Weight/Mass, Capacity, and Temperature (cont d) Pre-K K 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 Time Compass Graph paper Protractor Ruler 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. 15

17 Perimeter, Area, and Volume Pre-K K 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 16 Early Experiences Introduce Develop Maintain and Apply

18 Data Analysis and Probability Grade Graphs Pre-K K 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 17

19 Data Collection and Analysis (cont d) Pre-K K 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 18 Early Experiences Introduce Develop Maintain and Apply

20 Algebra Grade Patterns, Properties, and Expressions Pre-K K 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 19

21 Patterns, Properties, and Expressions (cont d) Pre-K K 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 20 Early Experiences Introduce Develop Maintain and Apply

22 Equations and Inequalities (cont d) Pre-K K 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 21

23 Problem-Solving Strategies Pre-K K 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 22 Early Experiences Introduce Develop Maintain and Apply

24 Connections Pre-K K 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 23

25 Representation (cont d) Pre-K K 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 24 Early Experiences Introduce Develop Maintain and Apply

26 Pre-K Grade K Grade 1 Grade 2 Grade 3 Grade 4 Grade 5 Grade 6 Grade 6 Grade 7 Grade M.V AV.JC.RG

SCOPE AND SEQUENCE. Grade Level: 7 th Curriculum: Saxon Math 8/7 Publisher: 2004 by Saxon Publishers, Inc.

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