Table of Contents
Introduction 1
Addition 7
Addition Using Base Ten Blocks 9
Addition Using Base Ten Blocks with Regrouping 10
Addition with Place Value Strips 11
Addition with Place Value Strips and Regrouping 12
Jumps on a Number Line 13
Compensation 14
Making Tens 15
Landmark Numbers 16
Doubles Plus 17
Doubles/Near Doubles 18
Rounding Up or Down 19
Decomposing Using Place Value 20
Adding Left to Right 21
Adding Smaller Numbers in Expanded Form 22
Adding Larger Numbers in Expanded Form 23
Adding Numbers Larger Than 1,000 in Expanded Form 24
Adding Numbers Over 100 on an Open Number Line 25
Adding Numbers Over 1,000 on an Open Number Line 26
Adding Based on Partial Sums 27
Finding Perimeter by Adding Lengths 28
Subtraction 29
Subtracting Using Base Ten Blocks 31
Subtracting Using Base Ten Blocks with Regrouping 32
Subtracting with Place Value Strips 33
Subtracting Using Place Value Strips and Whether to Use Regrouping 34
Adding Up to Subtract 35
Counting Back 36
Counting Back by Hundreds, Tens, and Ones 37
Decomposing Using Place Value 38
Compensation 39
Round the Subtrahend and Compensate 40
Place Value with Small Numbers 41
Place Value with Larger Numbers 42
Distance on a Number Line 43
Distance on a Number Line: Another Look 44
Subtracting in Expanded Form 45
Subtracting Smaller Numbers on a Number Line 46
Subtracting Larger Numbers on a Number Line 47
Part-Part-Whole 48
Finding Missing Angles 49
Multiplication 50
Repeated Addition 52
Looking for Doubles 53
Doubling on a Number Line 54
Doubles Plus (3 as a Factor) 55
Doubles Plus; Decomposition (Factors of 3) 56
Doubles Plus Doubles (4 as a Factor) 57
Doubles Plus Doubles: Decomposition (4 as a Factor) 58
Double, Double, and Double Again (8 as a Factor) 59
Double, Double, and Double Again: Decomposition (8 as a Factor) 60
Half of 10 (5 as a Factor) 61
Half of 10: Abstract (5 as a Factor) 62
Subtracting from 10 (9 as a Factor) 63
Subtracting from 10: Abstract (9 as a factor) 64
Landmark Numbers 65
Multiplying Using a Number Line 66
Doubling and Halving 67
Decomposition Using Partial Products 68
Factor and Factor Again (Associative Property) 69
Multiplication Using an Array 70
Multiplication Using an Area Model and Place Value 71
Multiplying 2-Digit Numbers Using an Area Model and Place Value 72
Finding Perimeter Using
P = 2l + 2w or P = 2(l + w) 73
Area: A = lw 74
Adding Areas: A = lw 75
Area and the Distribution Property 76
Volume 77
Division 78
Equal Shares 80
Repeated Subtraction 81
Using an Array 82
Relationship Between Multiplication and Division 83
Using a Number Line 84
Tape Diagrams (Strip Diagrams) 85
Halving 86
Doubling 87
Area Model with 1-Digit Divisors 88
Area Model with 2-Digit Divisors 89
Decomposition and Distributed Division 90
Partial Quotients with Smaller Numbers 91
Partial Quotients with Larger Numbers 92
Place Value Columns (1-digit divisor/2-digit dividend) 93
Place Value Columns (1-digit divisor/3-digit dividend) 94
Place Value Columns (1-digit divisor/4-digit dividend) 95
Finding the Missing Side of a Rectangle 96
Common Multiplication and Division Situations 97
Fractions 98
Fair Shares and Partitioning 101
Set Models 102
More, Less, or Equal to One Whole 103
Comparing Fractions 104
Ordering Fractions 105
Equivalent Fractions Using Fraction Tiles 106
Equivalent Fractions Using a Number Line 107
Decomposing Fractions 108
Decomposing Fractions Using Tape Diagrams and Number Bonds 109
Adding Fractions Using Fraction Tiles 110
Adding Fractions Using a Number Line: Like Denominators 111
Adding Fractions Using a Number Line: Unlike Denominators 112
Adding Fractions Using a Tape Diagram: Like Denominators 113
Adding Fractions Using an Area Model: Unlike Denominators 114
Adding Fractions Using Decomposition 115
Adding Fractions Using Equivalency 116
Adding Fractions Using Tape Diagrams 117
Finding Perimeter by Adding Lengths 118
Subtracting Fractions Using Fraction Tiles 119
Subtracting Fractions Using a Number Line: Like Denominators 120
Subtracting Fractions Using a Number Line: Unlike Denominators 121
Subtracting Fractions Using an Area Model: Like Denominators 122
Subtracting Fractions Using an Area Model: Unlike Denominators 123
Subtracting Fractions Using Decomposition 124
Subtracting Fractions Using Equivalency 125
Subtracting Fractions Using Tape Diagrams 126
Multiplying Fractions Using Repeated Addition 127
Using Fraction Tiles to Multiply a Whole Number by a Fraction 128
Multiplying a Fraction by a Whole Number 129
Multiplying Fractions Using Fraction Tiles and a Number Line 130
Multiplying Fractions by Whole Numbers Using an Area Model 131
Multiplying Fractions Using an Area Model (Fraction × Fraction) 132
Multiplying Fractions by Fractions Using Counters 133
Multiplying Fractions Using Tape Diagrams 134
Multiplying Fractions Using the Distributive Property 135
Finding Perimeter Using P = 2l + 2w or P = 2(l + w) 136
Area: A = lw 137
Dividing a Whole Number by a Unit Fraction Using Part-Part-Whole Model 138
Dividing a Whole Number by a Unit Fraction 139
Dividing a Unit Fraction by a Whole Number 140
Dividing a Unit Fraction by a Whole Number Using a Number Line 141
Dividing a Whole Number by a Unit Fraction Using a Number Line 142
Dividing a Whole Number by a Fraction 143
Decimals 144
Identifying Decimals 146
Decimal Place Value 147
Rounding Decimals to the Nearest Whole 148
Adding Decimals Using Decimal Squares 149
Adding Decimals by Decomposing (Partial Sums) 150
Adding Decimals Using a Place Value Strategy 151
Adding Decimals on an Open Number Line 152
Adding Decimals in Expanded Form 153
Subtracting Decimals by Counting Back by the Ones, Tenths, and Hundredths 154
Subtracting Decimals on an Open Number Line 155
Subtracting Decimals Using Decimal Squares 156
Subtracting Decimals Using a Place Value Strategy: No Regrouping 157
Multiplying Decimals Using Decimal Squares 158
Multiplying Decimals Using Decimal Squares with an Array 159
Multiplying Decimals Using an Area Model 160
Dividing Decimals Using Decimal Squares 161
Dividing Decimals Based on Multiplication 162
Further Reading Opportunities 163
References 165
About the Author 166