Problem Solving Skills 31
Locate Objects 31
Make Comparisons 32
Classify and Sort 33
Recognizing Colors 33
Recognizing Size 34
Recognizing Shapes 35
Using Sets 35
Identify and Use Patterns 36
Make and Check an Estimate 37
Estimation strategies 38
Use of a Reference 38
Chunking 38
Front-end Estimation 39
Solve One-step Word Problems 39
How to Approach a Problem 39
Collect, Record, Interpret Information 40
Create Problems 41
Use a Calculator 41
Use a Computer 41
Probability and Statistics 41
Understanding Numbers 0 - 20 43
Counting 43
Understanding Quantity 43
Compare and Order Sets and Numbers 44
Identify the Next Number 46
Understanding Numbers 20 - 999 49
Recognize, name, and write numbers 20 - 999 49
Place Value 49
Order three and four numbers 51
Compare Two Numbers Using Place Value 52
Computation With Whole Numbers 52
Teaching Tips 52
Addition 53
Properties of Addition 53
Addition: Renaming Ones 54
Addition Fact Strategies 54
Subtraction 55
Subtraction Fact Strategies 56
Subtraction: Renaming Ones and Tens 57
Multiplication 57
Division 59
Money 60
Measurement 62
Concepts 62
Estimate and Measure Temperature, Length, Weight and Capacity 63
Practice 65
Time 66
Activities to practice concepts 67
Days and Months 68
Reading a Clock 69
Geometry and Spatial Sense 70
Identifying Shapes and Solids 70
Analyzing Shapes and Solids 72
Symmetry 73
Congruent Figures 74
Making Solids Using Patterns 74
Fractions 74
the Concept 74
Equal Parts of a Region 75
Equal Parts of a Group 76
GRADES 3 – 4 OBJECTIVES
Problem Solving 77
Probablitity and Statistics
Whole Number Concepts and Computation
Fractions
Roman Numerals 81
Decimals 81
Money
Time
Geometry
Measurement
TEACHING GRADES 3 - 4
Problem Solving 84
Types of Problems 84
Reasoning 84
Computation 84
Collect, Record, and Analyze Information 85
Word Problems 85
Solving One- and Two-step Problems 86
Problem Solving Strategies 87
Probability and Statistics 88
Finding Probability 88
Finding Range, Average, Median and Mode 88
Number Concepts and Computation 90
Teaching Tips 90
Place Value 90
Compare and Order Numbers 91
Round to 10, 100, 1,000 92
Addition 94
Properties 94
Estimation 94
Missing Addends 95
Adding 3- and 4-Digit Numbers 95
Procedure for Addition 96
Procedure for Addition With Renaming 96
Practice 97
Subtraction 97
Renaming: Step-by-Step 98
Checking Subtraction 98
Multiplication 98
Multiplication and Division as Inverse Operations 99
Commutative Property of Multiplication 99
Multiples of a Number 99
Multiplication Facts 99
Multiply 1-Digit Numbers by Ten and Multiples of Ten 100
Multiply 1- to 4-Digit Numbers 101
The Procedure (Algorithm) 101
Multiply 2-Digit Numbers by Multiples of Ten 104
Esitmating Products 104
Common Multiples 104
Division 105
Concepts 105
The Procedure (Algorithm) 107
Divide by 10, 100, 1,000 109
Fractions 109
Teaching Sequence 109
Concepts 110
Practice 110
Compare and Order 111
Equivalent Fractions 111
Mixed Numbers 112
Lowest Terms 112
Add and Subtract 113
Convert to Decimals 114
Roman Numerals 114
Decimals 115
Compare and Order 116
Add and Subtract 116
Rounding 117
Money 118
Recognize and Count 118
Make Change 118
Add and Subtract 119
Multiply and Divide Dollars by 0-9 120
Time 120
Units of Time 120
Telling Time to the Minute 120
Finding Elapsed Time 121
Word Problems 121
Geometry 123
Lines 123
Shapes (plane figures) 123
Angles 124
Slides, Flips, and Turns of Figures 124
Congruent and Similar Figures 125
Parts of a Circle 125
Measuring Perimeter and Area 126
Solids (space figures) 127
Measuring Volume 127
Measurement 128
Symbols and Abbreviations 128
Converting Units Within a System 128
Choosing Appropriate Units 128
Estimating Measures 129
Addition and Subtraction 129
GRADES 5 - 6 OBJECTIVES
Problem Solving
Probability and Statistics
Ratio, Proportion and Percent
Whole Number Concepts and Computation 132
Fractions 134
Roman Numerals 134
Number Base Systems 134
Decimals 134
Positive and Negative Integers 135
Algebra 135
Money 135
Time 135
Geometry 136
Measurement 137
TEACHING GRADES 5-6
Problem Solving 138
Types of Problems 138
Analyzing Data 139
Solving Multi-Step Problems 141
Strategies 142
Probability and Statistics 143
Range, Mean, Median and Mode 143
Determining Probability 143
Probability as a Fraction 143
Drawing a Tree Diagram of Possible Outcomes 144
Ratio 144
The Concept 144
Equal Ratios 145
Proportion 145
The Concept 145
Solving Problems 146
Percent 147
The Concept 147
Converting to and from Decimals 148
Converting to and from Fractions 148
Finding the Percent of a Number 149
Estimating Percent 150
Finding Simple Interest 150
Number Concepts and Computation 151
Number Expressions 152
Order of Operations 152
Prime and Composite Numbers 153
Place Value 155
Comparing and Ordering Numbers 157
Rounding to the Nearest Million 157
Writing Exponents 158
Computation 158
Addition 158
Subtraction 159
Multiplication 160
Factors: Prime, Common, and Greatest Common Factors 160
Using Exponents 160
Multiples, Least Common Multiple 161
Mental Multiplication 161
Estimate Products by Rounding 162
Multiply by Multiples of Ten 162
Multiplication and Possible Errors in Procedure 162
Division 163
Divisibility Rules 164
Division and Errors in Procedure 164
Estimating Quotients 165
Fractions 166
Equivalent Fractions 167
Lowest Terms 167
Compare and Order 168
Plot on a Number Line 168
Add and Subtract 168
Multiply by a Whole Number 170
Multiply Fractions 170
Divide Fractions 171
Reciprocals 171
Word Problems 172
Write as a Decimal 172
Roman Numerals 173
Number Base Systems 174
Decimals 175
Write in Various Forms 175
Compare and Order 175
Rounding 176
Estimate by rounding 176
Add and Subtract 177
Multiplication 178
Mentally Multiply by Powers of Ten 180
Division 181
Divide by a Whole Number 181
Repeating and Terminating Decimals 181
Divide by 10, 100, 1,000 182
Divide by a Decimal 182
Round Quotients 183
Positive and Negative Integers 184
Compare and Order 184
Add and Subtract 185
Algebra 186
Solve Expressions 186
Graph Ordered Pairs 187
Money 188
Add, Subtract, Multiply, Divide 188
Count and Make Change 188
Unit Pricing 189
Estimating Prices 189
Time 189
Calculate Elapsed Time 189
Problem Solving 190
Geometry 191
Lines 191
Classifying Solids 191
Classifying Shapes 193
Slides, Flips, Turns of Figures 194
Congruent, Similar, Symmetrical Figures 195
Draw and Measure Angles 195
Construct and Bisect angles 197
Polygons 197
Perimeter 197
Area Using a Formula 198
Rectangular Prisms 201
Volume 201
Surface Area 201
Volume of Cylinders 201
Circles 202
Parts of a Circle 202
Measuring Circumference 203
Measuring Area 204
Measurement 204
Choosing Units 204
Converting Measurements Within a System 204
Estimating, Measuring, and Solving problems 207
Using Scale Drawings 207
GRADES 7 - 8 OBJECTIVES
Problem Solving
Probability
Statistics
Ratio, Proportion, Percent
Whole Number Concepts and Computation
Fractions
Number Base Systems
Decimals
Integers, Rationals, Irrationals
Algebra
Money / Consumer Math
Time 212
Geometry
Measurement
TEACHING GRADES 7 - 8
Problem Solving 215
Probability 216
Probability of Independent Events 216
Probability of Dependent Events 217
Determining Odds 217
Sampling 217
Statistics 218
Range, Mean, Median, Mode 218
Frequency Tables 218
Histograms 218
Analyzing Data 219
Ratio, Proportion, Percent 219
Ratio 219
Rate 219
Proportion 220
Using Cross Products to Find Proportion 220
Percent 220
Converting Percents 220
Finding the Percent of a Number 221
Finding the Original Number of a Given Percent 221
Finding the Percent One Number is of Another 222
Finding the Percent of Increase or Decrease 223
Finding Simple Interest 223
Whole Number Concepts and Computation 223
Prime Factors and Greatest Common Factors 224
Negative and Zero Exponents 224
Order of Operations 224
Fractions 225
Number Base Systems 225
Decimals 225
Compare and Order 225
Expanded Notation 225
Add, Subtract, Multiply, Divide 225
Scientific Notation 226
Integers, Rationals, Irrationals 226
Integers 226
Additive Inverse 226
Absolute Value 227
Rules for Operations 227
Rationals, and Irrationals 227
Definitions 227
Squares and Square Roots 228
Algebra 229
Expressions 229
Multi-Step Equations 229
Functions 230
Solve and Graph Equations 231
Solve and Graph Inequalities 232
Simply Expressions 233
Money / Consumer Math 233
Time 234
Geometry 234
Angles and Angle Relationships 234
Shapes 235
Transformations: translation, reflection, rotation 235
Congruent lines, angles, and figures 235
Triangles 236
Similar triangles: corresponding sides 236
Rules for Congruent Triangles 236
Tangent Ratios 237
Pythagorean Theorem 237
Solids 238
Cross Sections 238
Surface Area 238
Cylinders 238
Volume 239
Cones and Pyramids 239
Prisms 239
Cylinders 239
Measurement 239
Precision in Measurement 239
Greatest Possible Error 239
Converting Metric Units of Measurement 240
Solving Problems 240
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