# Grades K 8. Scope and Sequence. Math K 4. Intermediate 3 5. Courses 1 3

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1 Grades K 8 Scope and Sequence 4 Intermediate 3 5 Courses 1 3

2 K 4 4 Scope and Sequence The Scope and Sequence for the K 4 mathematics series is intended to help educators view the progression of mathematical topics throughout the series. Topics are grouped into nine strands: Harcourt Achieve Inc. All rights reserved. 1. Numbers and Operations 2. Measurement 3. Geometry 4. Patterns, Algebra, and Functions 5. Statistics, Data Analysis, and Probability 6. Problem Solving 7. Communication 8. Mathematical Reasoning 9. Connections The locators in the Scope and Sequence identify lessons in which direct instruction of a topic is presented. The first lesson where the concept is taught is referenced, and subsequent lessons are referenced only when the concept is extended. Occasional references to spans of The Meetings are included to show the daily practice of expanding skills and concepts.

3 SCOPE AND SEQUENCE The locators in this Scope and Sequence indicate where direct instruction on each topic can be found. Locators refer to lessons and Meetings (M). In, every tenth lesson has two parts, and in, 2, 3, and 4 every fifth lesson has two parts; locators for these lessons are labeled -1 or -2. Numbers and Operations Number Sense and Numeration Counts by 1 s M1; 7, 41, 61 2, 20-1, 34, 99, 131 1, 76, Counts backward 109 4, 34, 43, 56 M5 M Counts by 2 s 125; M22 47, 51, 56, 64 M14 29, Counts by 5 s 91, 92; M18 Counts by 10 s 64, 65, 67, 68; M , 98 32, 46, 49, 78 43, 46, 85-1, 90-1, , 76, 77, , 23, 30-2, , 23, 64 22, 33 Counts by 100 s 93, 131, , 77, 95-2 M3 9, Counts by 25 s Counts by 3 s M78 M Counts by 4 s M106 M Counts by 6 s M Counts by 7 s M Counts by 8 s M Counts by 9 s M Counts by 12 s M Counts by 1,000 s Counts by ½ s Counts by ¼ s M Counts by 11 s 30-1 Matches sets and numbers 24, 42, 62, 73 Counts and groups numbers in tens and ones M4A; 13, 64, 65, 67, 68 2, 5, 9, 10-1, 19 46, 84, 93, 131, , 76, 113, , 52, 64, 67, 76 11, 13, 16, 41 Uses expanded form to represent 67, 81, 113 M , 104, numbers Writes digits , 5, 8 Writes numbers using words 63 68, 78, 103, , 52 Reads and writes whole numbers to 30 Reads and writes whole numbers to 100 (2-digit numbers above 30) Reads and writes whole numbers to 1,000 (3-digit numbers) 21, 74, 111, 120-1, , 5, 8, 1, 4 3, , 4 3, , 76 27, 34, 41,

4 Numbers and Operations, continued Number Sense and Numeration, continued Reads and writes whole numbers to 10,000 (4-digit numbers) Reads and writes whole numbers to 100,000 (5-digit numbers) Reads and writes whole numbers to 1,000,000 (6-digit numbers) Reads and writes whole numbers to 1,000,000,000 (9-digit numbers) Identifies numbers before, after, and 48, 75 17, 52, 92 between Identifies numbers on a hundred number chart Compares 1- and/or 2-digit whole numbers Orders 1- and/or 2-digit whole numbers M3, 4A 16, 34, 43, 52 71, 99, 102 9, 40-1, 92, , 35, 74 4, 9, 17, 20-1, 32, 92 1, 2, 13, 36 3, 9, 14 64, , , , , , 52 51, 52 8, 81 8, , 94 8, , 33 Compares 3-digit or larger whole 81 34, , 33 numbers Orders 3-digit or larger whole 74, 77 34, , 33 numbers Rounds numbers to the nearest ten , 98 18, 19, 31, 52, 62 13, 33, 119 Rounds numbers to the nearest hundred or thousand Identifies place value for each digit in numbers to 100 Identifies place value for each digit in numbers to 1,000 Identifies place value for each digit in numbers to 1,000,000 Identifies place value for each digit in numbers to 100,000,000 Represents 2-digit whole numbers using concrete materials and/or pictures Represents 3-digit or larger whole numbers using concrete materials and/or pictures Identifies and describes equivalent sets Estimates and counts collections of objects Represents equivalent forms of the same number Compares sets of objects and identifies sets with more, fewer, and the same 85-1, 131, , , 85-1, 131, , 42, 76, 84 72, , , , , 84, , 41, 64, 76 51, , , 22, 37, 63, , , , 118 4, 9, ; M , 84, 85-1, , 92, , 94, , 41, 42 22, 76, 94, 119, , 71 9, 38, 76, 82, , , 128 8, 77, , 40-2, 55-2, A 5, 22, 26, 30-1, 36, 53, 97 12, 51 4 Scope and Sequence

5 Numbers and Operations, continued Number Sense and Numeration, continued Identifies sets with the greatest and least number of objects 58, 98 7, 9, 38 49, 74, , 40-2, 55-2, A Renames numbers using regrouping 85-2, 86 61, 63, 68, 73 Identifies multiples of a number 103, 130-1, Identifies factors of a number 115-1, 120-1, Identifies prime and composite numbers Identifies the least common multiple of two numbers Identifies the greatest common factor of two numbers 22, 52, 67, 76 11, 16 M , 6, 22, 26, 29, 30-1, , 61, 94, 107, , 96 M , 109 Squares numbers 63, , 122 Identifies perfect squares Identifies and simplifies expressions , 117, 128 with exponents Finds square roots of perfect 81, D 116 squares Identifies and approximates square 122 roots Identifies cube roots and perfect cubes 128 Identifies rational numbers from pictures and draws pictures to show rational numbers Locates rational numbers on a number line 17, 24, , 55-1, 87, 107, 122 Identifies even and odd numbers , 56, 58, 64, 68 Identifies ordinal position 28, 37, 46, 59 19, 23, 24, 34, 41, 83 11, 37, 40-1, 56, , 56, 94 51, 54, 55-2, 99, , 96, 97, , 22, , 14, 16, 20-1 Identifies and creates pairs 64 37, Identifies dozen and half dozen Reads and writes Roman numerals Identifies the approximate value of π Concepts of Whole Number Operations Shows the meaning of addition 18, 27, 50-2, 89, 119 Acts out to show addition situations 18, 27, 50-2, 89, , 15-1, 19, 21, 25-1, 36, 94, , 15-1, 19, , 10-1, 29, 44 5, 11, 15-1, 52, 53, , 68, 79, 91 27, 33, 88, 93, , Math 5

6 Numbers and Operations, continued Concepts of Whole Number Operations, continued Uses manipulatives to model and solve addition problems Draws pictures to model and solve addition problems 18, 27, 50-2, 89, , 121, 122, 126 Creates addition problem situations 27, 73, 89, , 32, 58, 76, , 21, , 61, 104, A 15-1, 73, 74, , , 22 11, 35-2, Writes number sentences to show , , 35-2, addition Identifies addends and sums 21, 40-1, , 15-1, Identifies and uses the commutative and associative properties of addition 94, , Shows the meaning of subtraction 18, 27, 80-2, 89, 127 Acts out to show subtraction situations Uses manipulatives to model and solve subtraction problems Draws pictures to model and solve subtraction problems 18, 27, 80-2, 89, , 27, 80-2, 89, , 128, , 15-1, 33, 34, 44, , 15-1, 33, , 68, 101, 121, , 22, 29, , 11, 20-1, 35-2, 91, 92, , 88, , 74, 91, , , Creates subtraction problem 27, 89, , 33 11, situations Writes number sentences to show 33, , 89, 91 11, subtraction Identifies differences , , 60-1, 65-1, , 21 Uses the inverse relationship between subtraction and addition to check answers Writes addition and subtraction fact families 101, 121, , 75-1, 80-1, , ; M50-1, 53 Shows the meaning of multiplication 46, 93 92, 110-1, 116, 121, Acts out to show multiplication situations Uses manipulatives to model and solve multiplication problems Draws pictures to model and solve multiplication problems Writes number sentences to show multiplication 10-1, 20-1, 67, , 20-1, 25-1, 30-1, 35-1, , 56, 57, 87, 116, , 66 46, , 31, 45-1, , , 87, , , , , 110-1, 117 Identifies factors and products 115-1, 120-1, , , Scope and Sequence

7 Numbers and Operations, continued Concepts of Whole Number Operations, continued Makes, labels, and writes number sentences for an array Identifies and uses the commutative and associative properties of multiplication Shows the meaning of division 70-1, 97, 102, 115, 125 Acts out to show division situations 70-1, 97, 102, 115, 125 Uses manipulatives to model and solve division problems Draws pictures to model and solve division problems Writes number sentences to show division Identifies the properties of 0 or 1 in multiplication and/or division Uses the inverse relationship between division and multiplication to check answers Writes multiplication and division fact families Identifies quotients, dividends, and/ or divisors Uses a calculator to explore mathematical operations Whole Number Computation Addition Uses concrete objects or pictures to model and solve addition problems 70-1, 97, 102, 115, , 27, 50-2, 89, , , , , 118, , 97, 120-1, , 94, 97 37, 107, , , , , , 97 37, , , , 59, , 105-1, , 76, 77, 83, 87, 101 B A D 90-1, 120-1, 122, 130-1, , 32, 58, 76, 94 Identifies one more than a number , 34, 36, 37 28, 61, , 73, 74, 76, 93 2, 10-1 Identifies ten more than a number 89, 90-1, , 36, 44 14, 31 Masters addition facts to 18 27, 36, 41, 76, 94, , 10-1, 35-1, , 20-1, 25-1, 30-1, 35-1, , 25-2, 30-2, 35-2, 40-2 Identifies missing addends , 66, , 63 Estimates a sum 111, , , 52, 53, 13, 33, Adds using mental computation M41, 45-2, , 36, 44, 98 14, 31, 33, 42, 69 6, 11, 16 Math 7

9 Numbers and Operations, continued Whole Number Computation, continued Subtraction, continued Subtracts using mental computation 71 14, 62, Subtracts 2-digit numbers without regrouping , 62 Subtracts 2- or 3-digit numbers 87 89, 91, , 69, 72, 91, 92 Subtracts 3-digit numbers and money amounts (decimals) Subtracts 4-digit or larger numbers 66 Solves problems involving subtraction Writes story problems for subtraction number sentences Multiplication 18, 27, 89, 127, , 15-1, 33 11, 22, 89 11, 35-2, 67, 86, 93, 96, , 67, , 55-1, 59, 63 Doubles a number Masters multiplying by 0, 1, 2, 3, 4, and 5 103, 110-1, 115-1, 120-1, 125-1, , 70-1, 85-1, 95-1, Masters multiplying by 6, 7, 8, and , 110-1, 115-1, Multiplies by 10, 100, 1,000, and/or 10,000 Multiplies by multiples of 10, 100, 1,000, and/or 10,000 Multiplies using mental computation 92, 103, 110-1, 115-1, 120-1, 125-1, Multiplies a 2-digit number by a 1-digit number Multiplies a 3-digit or larger number by a 1-digit number Multiplies a 2-digit or larger number by a 2-digit number Makes and uses a multiplication table Uses multiplication to check division problems Multiplies using the multiplication algorithm Solves problems involving multiplication , , , , , 60-1, 65-1, 105-2, , 60-1, 65-1, 105-2, , 38, 49, 73, , A , 49, , 103, 110-1, 116, , 124, , , 76, 77, 83, 87, , 54, 73, , 56, 57, 63, 88, 125-1, , 80-1, 123 Math 9

10 Numbers and Operations, continued Whole Number Computation, continued Division Divides sets of objects into equal groups Divides by , 125, , 102, , 125-1, 133 9, 56, 57 18, Masters division facts 59, , 110-1, 115-2, 120-2, 135 Writes division problems in three ways 59, 90-1, , 76 Divides using mental computation Divides 2- and/or 3-digit multiples , 101 of 10 by a 1-digit number Divides a 2-, 3-, and/or 4-digit number by a 1-digit number Checks division answers using multipication 122, 124, , 77, 83, 84, 87, 90-1, 101, , 124, , 76, 77, 83, 87, 101 Divides using the division algorithm , 87, 101 Solves problems involving division 70-1, 97, 115, 132, 134 Fractions and Decimals Identifies one half and/or one fourth of a whole Identifies a fractional part of a whole Writes a fraction to show a part of a whole Represents and writes mixed numbers 70-1, 115, 132, , 115, 132, , , 107, 108, 124, , 55-1, 67, 88 18, 55-1, 67, 88, 107, , 23, 24, 34, 39, 41 19, 23, 24, , 76, 83, , 24, , , 21, 24, 25-2, 93, 94 17, , 83 24, 25-2, 74, 17, , , , 99, , 79, 84 Finds half of a set of objects , 96, 97 37, Indentifies a fractional part of a set , 83, 96, 26, 61, , 128 Writes a fraction to show a part of a set 59, 83 26, Compares fractions , , 41 73, 74, 93, 94 Recognizes and identifies equivalent fractions Orders fractions 73, 74, 93, 94 27, 28, 68, 69, , 96 27, 28, 68, 69, 88 Simplifies fractions 98, 109 Writes fraction number sentences 25-2 that equal 1 10 Scope and Sequence

11 Numbers and Operations, continued Fractions and Decimals, continued Adds and subtracts fractions 73, 74, 93, 94 Uses pictures to represent decimal fractions Writes tenths or hundredths using common and decimal fractions Identifies fraction, decimal, and/or percent equivalents 91, 95-1, 102, , , 119, , 95-1, , 119, Finds the percent of a number Adds money amounts (decimals) 53, 54, 61, 62, , 89, 106 6, 8, 12, 13, 41, 95-1 Subtracts money amounts (decimals) 87, 88, , 95-1 Multiplies and/or divides money amounts (decimals) Money Identifies and counts pennies 41, 42, 44, 51, Identifies and counts dimes 65, 67, 68, 113 Identifies and counts nickels 91, 92, 94, 96, , 51, 53, 85-1, , 53, 66, 85-1, , 99, 116, 126 M127 38, 54, 77, 87, 101, 120-1, , 51, , , 51, , 23, , 51, , 23, Identifies and/or counts quarters 113, , Identifies one-dollar bills , Finds the value of a set of coins 51, 67, 92, 113, , 66, 99, 116, 126 Trades pennies for dimes and nickels 65, 91 53, 85-2, 86, , 23, , 61 63, , Compares the values of sets of coins Finds the value of a set of coins and 63 bills Reads and writes money amounts to \$1.00 using dollar and cent symbols 49, 51 16, 66, 105-2, , 109, , Reads and writes money amounts to 86, 109, , 36 14, 123 \$10.00 Reads and writes money amounts to 78, \$99, Selects coins for a given amount , , Pays for items and/or makes change using coins Makes change from \$1.00, \$5.00, and/or \$ , 68, 94, , , , ; M Counts bills 105-2, , Pays for items using bills , , 63 1

12 Numbers and Operations, continued Money, continued Adds and subtracts money amounts (decimals) , 86, , 54, 61 64, 109, , 89, 96, , 41, 95-1, 66, 67 Writes checks 78, , 42 Balances a checkbook register 67 Completes a catalog order form 42 Determines unit cost Estimates and finds amount of sales tax M Measurement Calendar and Time Identifies seasons 82, Identifies today s date M M1 135 M Identifies dates on a calendar M1 25 M1 135 M , 2, 24 Solves problems using a calendar M19, 21, 23, 25 M M ; M1 135 Writes the date using digits 47; M48, Identifies yesterday, today, and M19 M1 135 M1 M1 5 tomorrow Identifies days of the week and/or M1 25 M M1 35 1, 24 months of the year Identifies weekdays and days of the 16 M1 11 weekend Identifies morning, afternoon, , evening, and night Identifies a.m., p.m., noon, and midnight Uses digital and analog clocks to tell and show time 45, 47 48, 57, 87 3, 12, 26, 78, 106, 123 1, 4, 39, 71, 97 Tells and shows time to the hour 45, 47 48, 57 3, 12; M Tells and shows time to the half hour Tells and shows time to the quarter hour Tells and shows time to the 78 39, minute interval and/or minute Tells and shows time to the second 7, 34 Estimates time to the nearest half hour 4 Identifies days of the week when 40-1 regularly scheduled events occur Sequences daily events 30-1, , 35-1 Compares events according to duration 65, 91, Scope and Sequence

13 Measurement, continued Calendar and Time, continued Orders events by time 11, 35-1, Identifies activities that take one 106 hour, one minute, and one second Identifies equivalent units of time , 84 7, 22, 24, 36 Finds elapsed time 12 1, 4, Identifies United States time zones 37 Temperature Identifies cold, cool, warm, and/or , C M1 14 hot Compares differences in hourly, 82, 124, ; M2 135 M daily, and/or seasonal temperature Compares situations and objects by relative temperature C 46 Reads a Fahrenheit thermometer 128, C 27, 69 18, 29, 46 74, 75-1 Estimates temperature 27 46, Identifies common temperatures 69 18, 29, Reads a Celsius thermometer 83 74, 75-1 Linear Measure Compares the length or height of objects 83, 120-2, 131 4, 7, 62, 104 8, 55-2, 99, 102 Orders objects by length or height 84, 87, 93 9, Creates a measuring tool Estimates and measures length or distance using nonstandard units 87, 106, , 62, 95-2 Estimates length or distance , 95-2, 104 Selects and/or uses appropriate tools for measuring length Measures length using customary units (inch, foot, and yard) Draws line segments using customary units (inch) Measures length using metric units (centimeter, millimeter, and meter) Draws line segments using metric units (centimeter and millimeter) Compares the size of the unit and the number of units used to measure an object Identifies equivalent units of linear measure Uses a scale to find distance on a map , 97, 104, , , 43, 55-2, 72, 99, 102, , 19, 43, 88, , 32, , 88, , 54, , , 15-1, 18, 28, 39, 69, 103, , , 19, 28, 69, , , 85-2, , 15-1, 39, , 43, 114, , , 22, 28, ,

14 Measurement, continued Weight (Mass) Compares and orders objects by weight (mass) Weighs objects using nonstandard units 53, 72 29, , 110-2, , , Estimates weight (mass) 72, , 39, , Selects and/or uses appropriate 53, tools for measuring weight Identifies customary and/or metric , units of mass Weighs objects using customary or 110-2, metric units Capacity (Volume) Compares and/or orders containers by capacity 90-1, , Identifies customary and/or metric units of capacity (cup, quart, gallon, and liter) Selects and/or uses appropriate tools for measuring capacity Estimates capacity 78, 90-1, Measures capacity 77, 78, 90-1, , , 50-2, , , 55-2, , 55-2, , 55-2, , 60-2, , , , , , 50-2, 75-2 Identifies and uses measuring cups , , 50-2, 75-2 Identifies and uses measuring spoons (tablespoon, teaspoon, and ½ teaspoon) Follows a recipe and measures ingredients Identifies equivalent units of capacity Area, Perimeter, and Volume Compares and orders objects by size (area) 45-2, , 60-2, , , , 112, , , 15-2, 63 Finds area using nonstandard units , 115-2, Estimates area Finds area of a rectangle 115-2, , 57 Finds the length of a side of a 81 square given the area Finds perimeter of a polygon , Uses perimeter formulas , 50-2, Compares, estimates, and measures circumference Scope and Sequence

15 Measurement, continued Area, Perimeter, and Volume, continued Finds volume of a rectangular prism Finds volume of a cube Geometry Spatial Relationships and Geometric Shapes Identifies right and left , 2 Identifies first, last, between, and middle Describes, compares, and orders concrete objects by relative position and attributes Gives and follows directions about location Arranges and describes objects in relative space Makes and covers designs with pattern blocks or tangrams Makes and copies designs on a geoboard Creates, identifies, and/or draws congruent shapes, designs, and/or line segments Creates and/or identifies similar shapes Combines geometric shapes to make new shapes Identifies, describes, sorts, and/ or compares two-dimensional geometric shapes Identifies, describes, and classifies polygons 28, 37, 46, 48, 75 12, 23, 32, 43, 53, 72, 83, 84, 87, 93 2, 3, 5, 8, 11 7, 16 7, 11, 14, 17, 52 6, 9, 21, 25-2, , 48, 75 7, 19, 38 1, 2, , 19, , 15, 29, 79, 105, 108, , 57, 63, 86, , 42, 60-1, , 10-2, 15-2, 85-2, 90-2, , 83, 96 57, 60-2, 65-2, , , 83, , 65-2, 108, , , 12, 17, 32, , , 23, 31, 57 19, 23, 31, 54, 85, , 70-2, , 13, 24, 26, 124 6, 13, 24, 26, , 60-2, , 18, 21, 25-2, 30-2, 57 Identifies angles and sides 6, 13, 14, 24 57, 114, 118, C Identifies parallel lines and line segments Identifies intersecting and perpendicular lines and line segments Identifies horizontal, vertical, and oblique line segments 65-1, 81, 85-1, , 10-2, 100-2, , 10-2, 20-2, 50-2, , 20-2, 43, , 71, 81, 82, 85-1, 86 64, 71, 81, 82, 85-1, 86 81, , , 100-2, , , 43, , Names line segments 43 14, 15-1, 28, 69, 126 5

16 Geometry, continued Spatial Relationships and Geometric Shapes, continued Identifies right angles 114, 118, C 7, 100-2, , 85-1, 108, 111, 121, 124 Identifies acute and obtuse angles C , 131, 135 Identifies straight angles 108, 111 Identifies supplementary angles 135 Identifies right triangles , 124, 135 Names triangles by angle size C , 131 (acute, obtuse, or right) Identifies and classifies triangles by lengths of sides (scalene, isosceles, and equilateral) Constructs scalene, isosceles, and equilateral triangles Identifies and sorts concrete objects by attribute Identifies, describes, sorts, compares, and/or constructs threedimensional geometric solids Identifies faces, vertices, and edges of a geometric solid Transformations and Symmetry Identifies and draws a line of symmetry and/or creates symmetrical designs Explores, identifies, and/or shows transformations: translations (slides), rotations (turns), and reflections (flips) 23, 32, 43, 54 Patterns, Algebra, and Functions Patterns and Sequences Identifies, reads, and extends patterns in shapes, colors, designs, and/or numbers 93, 112, , 120-1, , 13, 24, 26 6, 9, 21, 25-2, , , , , 114 D , 89 9, 25, 33, 52, 55, 66, 88, , 58, 59 7, 15-2, 20-2, 30-1 M Identifies the missing shape or M , 20-2 M design in a repeating pattern Identifies the missing number in a 21, 35, M sequence Identifies the missing item(s) in an 23, 32, M array or matrix Makes, labels, and writes number 121, , 61 sentences for an array Readiness for Algebraic Reasoning Constructs a number line and/or locates points on a number line 48, 75, , 80-1, 92 56, 94 51, 54, 55-2, , 33, Scope and Sequence

17 Patterns, Algebra, and Functions, continued Readiness for Algebraic Reasoning, continued Graphs large numbers on a number line Shows addition, subtraction, and/or multiplication on a number line Locates and graphs points (ordered , , 133 pairs) on a coordinate graph Graphs linear functions on a 133 coordinate plane Simplifies expressions containing 118, addition, subtraction, multiplication, and division Uses the order of operations to 38, 118, simplify expressions Simplifies expressions containing 38, 118, , 134 parentheses Simplifies expressions containing , 117, 128 exponents Adds positive and negative numbers , 99 Relations and Functions Writes and solves number sentences for problems involving addition or subtraction Creates problems for addition and subtraction number sentences Writes and solves number sentences for problems involving multiplication or division Creates problems for multiplication and division number sentences Uses comparison symbols (>, <, and =) Represents an unknown using a symbol 21, 25-1, 33, 132, , 89 11, 35-2, 52, 53, 66, 93, , , , , 57, 107, , , , 25-1, , 35-1, 40-1, 45-1, 50-1, Identifies and writes a function rule , 133 Uses a function rule to complete a , 133 table Graphs linear functions on a coordinate plane 133 Statistics, Data Analysis, and Probability Data and Statistics Identifies an object that doesn t belong to a group Sorts and classifies objects by common attributes , 32, 43, 54, 85 13, 15-2, 38, 60-1, , 25-2, 30-2, 46, 65-2,

18 Statistics, Data Analysis, and Probability, continued Data and Statistics, continued Identifies a sorting rule 34, , 15-2, 38, 60-1, , 25-2, 30-2, 46, 85-2 Determines questions for a survey , 35-1 Conducts a survey and/or records , 35-1 data Tallies data 70-1, 72, 98 32, 113, Collects and sorts data , 38, 60-1, 72, 118 2, 17, 31, 32, 39, 48, 66, 82, 105-2, 113, 120-2, 125-2, 134, , 40-2, , 30-2, 40-2, 70-2, , 100-1, , 3, 35-1, 90-1, 104 Finds the range and mode of a set 69, A, E 20-1 of data Finds the median of a set of data 77 A 112 Finds the mean (average) of a set of data B, E 90-1, 104, 112 Uses a calculator to compare data A, B E 90-1, 104, 120-1, 122, 130-1, 132 Graphing Makes a real graph 11, 17, 22, 58, 69 5, 38, 65-1 Graphs a picture on a pictograph 5, 82, 107, 135 Graphs data on a bar graph 11, 22, 58, 90-2 Identifies most, more, fewest, less, and/or same on a graph Draws conclusions, answers questions, and writes observations about a graph 7, 9, 38, 82 17, 82, , , 7, 10-1, 19, 38, 40-1, 65-1, 82, , 17, 22 7, 9, 38, 65-1, 82, , 19, 40-1, 65-1, 82, 118 2, 31, 39, 48, 134, 135 2, 31, 39, 48, 135 2, 17, 31, 39, 48, 105-2, 125-2, 134, 135 2, 40-2, 55-2, 70-2, 80-2, , 40-2, , 40-2, 55-2, 70-2, 80-2, , , 10-1, 20-1 Draws and reads a pictograph 17, 82, , , 50-1 Draws and reads a bar graph 2, 31, 39, 48, 113 Draws and reads a bar graph with a scale greater than 1 2, , 10-1, , 10-1, 50-1, 104 Draws and reads a line graph M Creates and reads a Venn diagram 48, Makes and reads a line plot A 20-1 Draws and reads a circle (pie) graph 40-1 Makes a stem-and-leaf plot Scope and Sequence

19 Statistics, Data Analysis, and Probability, continued Probability Describes the likelihood of an event , , 90-2, C 100-1, Conducts a probability experiment , , 90-2, C 100-1, Predicts the outcome of a , , 90-2, C 100-1, probability experiment Determines the fairness of a game 90-2 Problem Solving Developing Skills for Problem Solving Identifies steps in a process 30-1, ; M1 Classifies and categorizes information 19, 23, 31, 32, 34, 43, 50-1, 85, , 35-1, 112, Identifies important/unimportant information Looks for a pattern 40-2, M7; 30-2, 60-2 Makes predictions , 100-1, Chooses appropriate methods for finding the answers to problems Strategies for Problem Solving Acts out a problem or makes a model 18, 50-2, 60-2, 80-2, 89, 119 Draws a picture 50-2, 80-2, 100-2, 110-2, 121, 128, Guesses, checks, and revises 70-2, 90-2, , 17, 31, 32, 48, 82, 113, 120-2, 125-2, 134, M , 15-2, 30-1, 60-1, , , 70-1, 100-1, B 12, 15-1, 80-2, 110-2, , 25-1, 50-2, 90-2, Looks for a pattern 40-2, M7; 30-2, , 12, 20-2, 100-2, 113, , 3, 35-1, 90-1, , , , , D 100-1, , 11, 40-1, 77, , 23, 76, 96, , 70-1, 80-1, E 11, 30-1, 56, 64, , 40-1, 56, 57, 70-1, 80-1, , , 60-1, , 15-2, 30-1, 60-1, , 23, 50-2, , 70-2, 74, , , 30-2, 50-2, Uses logical reasoning 10-2, , , 80-2, 90-2, 100-2, Writes a number sentence 25-1, 33, , 89, 91, 92 11, 35-2, 66, 93, 107, 108, 126 Makes an organized list 20-2, , 22, 34, 50-1, Makes a table or chart , 32, 48, 82, , 70-1, 80-1, 110-1, , 45-1, , , 40-2, 43 9

20 Problem Solving, continued Strategies for Problem Solving, continued Simplifies the problem 40-1, 80-1, , 52, 60-1, 80-1, 110-1, Works backward to solve a problem 20-1, 90-1, Communication 11, 16, 38, 119, Questions and responds Works with partners or in groups 21, 52, 73, , , 118 Communicates mathematical ideas M1 25 B; M1 135 M1 135 M1 135 M1 135 through objects, words, pictures, numbers, technology, and symbols Writes about math 118 4, 22, 29, 47, 84, 86, 92, 105-2, 111, , Mathematical Reasoning Recognizes patterns 23, 33, 66, 95 Classifies and sorts 16, 19, 23, 31, 57, 105, , 30-2, , 24, 38, 60-1, 72, 122 Solves spatial problems 15, 63, , 31, 42, 60-1, 65-1 Estimates 64, 90-1, 106, Explains an answer 40-2, 50-2, 60-2, 70-2, 80-2, 90-2, Connections Connects math to everyday life 45, 47, 49, 51, 68, 81, 94, 96, 116, , 50-1, 62, 111, , 15-2, 20-2, , 9, 18, 21, 25-2, 30-2, 60-2, 65-2, 101 M , 12, 20-2, 100-2, , 2, 7, , 15-2, , 55-2, 75-2, 95-2, 98, , 6, 32, 46, 52, 62, 72, 85-2, , 71, 81, 85-1, , 86 M , 66, 72, 87, 118, 128 Connects math to science 77, , 39, 50-1, 128, 130-1, C 17, 18, 37, 83, 86 2, 17, 31, 50-2, 120-2, 134, 135, B 1, 4, 28, 39, 65-2, 78, 84, , 40-2, 46, 65-2, Connects math to social studies , 125-2, , 90-1, 103, 122, , 32, 41, 44, , 74, 75-1, 112, , 43, Scope and Sequence

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