Response to Intervention. Grade 4
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1 Houghton Mifflin Harcourt Response to Intervention FOR THE COMMON CORE STATE STANDARDS FOR MATHEMATICS Grade 4 Math Expressions s Correlated to Tier s Tier s correlated to Tier Skills and Tier Examples Pages taken from: Houghton Mifflin Harcourt Response to Intervention Online Teacher Edition
2 Math Expressions 0 Place Value and Multidigit Addition and Subtraction BIG IDEA Place Value to One Million Tier Place Value to Thousands 5 Place Value Patterns 7 Round Numbers 9 4 Numbers to One Million 5, 7 5 Compare and Round Greater Numbers 8, 9 BIG IDEA Addition with Greater Numbers Tier 6 Make New Groups for Addition 0 7 Add Greater Numbers 0 8 Estimation and Mental Math 0 BIG IDEA Subtraction with Greater Numbers Tier 9 Subtract from Thousands 0 Subtraction Undoes Addition 0, Subtract Greater Numbers Practice Addition and Subtraction Problem Solving with Greater Numbers 4 Focus on Mathematical Practices 8, 0, Multiplication with Whole Numbers BIG IDEA Multiplication with Tens and Hundreds Tier Arrays and Area Models, 5 Connect Place Value and Multiplication Mental Math and Multiplication 8 MATH EXPRESSIONS 0 CORRELATION
3 Math Expressions 0 BIG IDEA Multiply by One-Digit Numbers Tier 4 Model One-Digit by Two-Digit Multiplication 5, 6 5 Estimate Products 4 6 Use Place Value to Multiply 6, 7 7 Algebraic Notation Method 5 8 Compare Methods of One-Digit by Two-Digit Multiplication 5, 6, 7 9 Discuss Different Methods 5, 6, 7 0 One-Digit by Three-Digit Multiplication, 6, 7 Multistep Word Problems BIG IDEA Multiplication with Two-Digit Numbers Tier Two-Digit by Two-Digit Multiplication Different Methods for Two-Digit Multiplication 4, 5 4 Check Products of Two-Digit Numbers 5 Practice Multiplication 4, 5 BIG IDEA 4 Multiplication with Thousands Tier 6 Multiply One-Digit and Four-Digit Numbers, 6 7 Use the Shortcut Method 0 8 Practice Multiplying 6 9 Focus on Mathematical Practices 9, 0 Division with Whole Numbers BIG IDEA Dividing Whole Numbers Tier Divide with Remainders 8, 9 Relate Three-Digit Multiplication to Division 4 Discuss Two-Digit and Four-Digit Quotients 4 4 Digit-by-Digit Method 45, 46 5 Relate Three Methods 4, 4 6 Divide by Any Method 46 MATH EXPRESSIONS 0 CORRELATION
4 Math Expressions 0 BIG IDEA Division Issues and Word Problems Tier 7 Just-Under Quotient Digits 45, 46 8 Estimate to Check Quotients 7, 40 9 Make Sense of Remainders 8, 4 0 Mixed Problem Solving 46 Focus on Mathematical Practices 45, 46 4 Equations and Word Problems BIG IDEA Reasoning and Solving Problems Tier Properties and Algebraic Notation 4 Situation and Solution Equations for Addition and Subtraction Situation and Solution Equations for Multiplication and Division 0,, BIG IDEA Comparison Word Problems Tier 4 Multiplication Comparisons 5 5 Discuss Comparison Problems 6 Graphs and Comparison Problems BIG IDEA Problems with More Than One Step Tier 7 Solve Two-Step Problems, 7 8 Solve Multistep Problems, 7 9 Practice with Multistep Problems, 7 BIG IDEA 4 Analyzing Patterns Tier 0 Factors and Prime Numbers, Analyze Patterns Focus on Mathematical Practices,, 7 MATH EXPRESSIONS 0 CORRELATION
5 Math Expressions 0 5 Measurement BIG IDEA Converting Measurements Tier Measure Length 80 Metric Measures of Liquid Volume and Mass 8 Units of Time 8 4 Customary Measures of Length 77 5 Customary Measures of Weight and Liquid Volume 78, 79 BIG IDEA Perimeter and Area Tier 6 Perimeter and Area of Rectangles 87, 88 7 Solve Measurement Problems 86, 90 8 Focus on Mathematical Practices 87, 88 6 Fraction Concepts and Operations BIG IDEA Fractions with Like Denominators Tier Understand Fractions 56 Fraction Addends of One Whole 55, 56 Add and Subtract Fractions with Like Denominators 6, 6, 6 BIG IDEA Mixed Numbers with Like Denominators Tier 4 Mixed Numbers and Fractions Greater Than 57 5 Add and Subtract Mixed Numbers with Like Denominators 58, 59, 60 6 Practice with Fractions and Mixed Numbers 58, 6 4 MATH EXPRESSIONS 0 CORRELATION
6 Math Expressions 0 BIG IDEA Multiply Fractions and Whole Numbers Tier 7 Multiply a Fraction by a Whole Number 65, 67 8 Practice with Fractions 65, 67 9 Mixed Practice 58, 6, 67 0 Focus on Mathematical Practices 58, 6, 67 7 Fractions and Decimals BIG IDEA Comparing Fractions Tier Compare Fractions 5 Fractions on the Number Line 54 Fractions of Different-Size Wholes 5 BIG IDEA Equivalent Fractions Tier 4 Equivalent Fractions Using Multiplication 48 5 Equivalent Fractions Using Division 49 6 Compare Fractions with Unlike Denominators 5, 54 7 Fractions and Line Plots 9 BIG IDEA Understanding Decimals Tier 8 Relate Fractions and Decimals 70 9 Explore Decimal Numbers 7, 7 0 Compare Decimals to Hundredths 75 Decimals Greater Than 7, 7 Compare Decimals Greater Than 75 Focus on Mathematical Practices 48, 5, 70 MATH EXPRESSIONS 0 CORRELATION 5
7 Math Expressions 0 8 Geometry BIG IDEA Measuring and Drawing Angles Tier Points, Rays, and Angles 98 Measuring Angles 95 Circles and Angles 9, 94 BIG IDEA Triangles and Angle Measurements Tier 4 Name Triangles 00 5 Compose and Decompose Angles 96 6 Real World Problems 97 BIG IDEA Analyzing Quadrilaterals Tier 7 Parallel and Perpendicular Lines and Line Segments 99 8 Classify Quadrilaterals 0 9 Decompose Quadrilaterals and Triangles 00 BIG IDEA 4 Analyzing Polygons Tier 0 Classify Polygons 00, 0 Line Symmetry 0, 0 Focus on Mathematical Practices 99, 0, 0 6 MATH EXPRESSIONS 0 CORRELATION
8 Tier and Tier Intervention for Tier s If students need additional support for Tier lessons, use the prerequisite skills and scaffolded examples listed below. Tier Tier Skills and Tier Examples Tier Tier Skills and Tier Examples S4, S5, E4, E5 S4, S5, S4, E4, E5, E4 S8, S6, S4, S6, S47, S64, E8, E6, E4, E6, E47, E64 4 S9, S9, S48, S64, S65, E9, E9, E48, E64, E65 5 S4, S8, S9, S54, E4, E8, E9, E54 6 S59, S7, E59, E7 7 S, S8, S, S6, S5, S44, S49, S56, S6, S64, E, E8, E, E6, E5, E44, E49, E56, E6, E64 8 S6, S9, E6, E9 9 S6, S66, E6, E66 0 S6, S9, S66, E6, E9, E66 S0, S, S, S66, S68, E0, E, E, E66, E68 S6, S66, E6, E66 7 S6, S0, S45, S46, E6, E0, E45, E46 8 S6, S0, S7, S8, S45, E6, E0, E7, E8, E45 9 S4, S6, S45, S46, E4, E6, E45, E46 0 S4, S6, S46, S49, E4, E6, E46, E49 S6, S, S44, E6, E, E44 S0, S5, E0, E5 S9, S8, S44, S5, E9, E8, E44, E5 4 S6, S9, S9, S44, S5, S5, E6, E9, E9, E44, E5, E5 5 S6, S0, S46, S49, E6, E0, E46, E49 6 S46, S5, S54, E46, E5, E54 7 S, S, S44, S49, S68, E, E, E44, E49, E68 8 S55, S58, E55, E58 S0, S, S, S9, S4, S55, S68, E0, E, E, E9, E4, E55, E68 4 S4, S0, E4, E0 5 S, S4, E, E4 6 S, S, E, E 7 S, E 8 S6, S8, E6, E8 9 S6, S0, E6, E0 0 S4, S6, S7, S9, E4, E6, E7, E9 S5, S6, S5, S7, E5, E6, E5, E7 S0, S4, S9, E0, E4, E9 S6, S9, S44, E6, E9, E44 4 S6, S0, S9, S45, E6, E0, E9, E45 5 S8, S8, S9, E8, E8, E9 9 S6, S55, S58, E6, E55, E58 40 S6, S58, S60, S68, E6, E58, E60, E68 4 S6, S9, S8, S58, E6, E9, E8, E58 4 S8, S6, S57, S59, S68, E8, E6, E57, E59, E68 4 S9, S8, S9, S45, S57, S58, E9, E8, E9, E45, E57, E58 44 S, S5, S6, S55, S59, E, E5, E6, E55, E59 45 S, S5, S7, S45, S59, S6, S6, E, E5, E7, E45, E59, E6, E6 46 S, S5, S9, S45, S50, S59, S6, S6, E, E5, E9, E45, E50, E59, E6, E6 47 S7, S74, E7, E74 6 S6, S0, S8, S45, E6, E0, E8, E45 48 S9, S7, S74, S79, E9, E7, E74, E79 vi TIER TIER TIER CORRELATIONS
9 Tier and Tier Intervention for Tier s If students need additional support for Tier lessons, use the prerequisite skills and scaffolded examples listed below. Tier Tier Skills and Tier Examples Tier Tier Skills and Tier Examples 49 S58, S66, S67, S75, S79, E58, E66, E67, E75, E79 50 S69, S75, S76, S79, E69, E75, E76, E79 5 S7, S7, S75, S76, E7, E7, E75, E76 5 S8, S7, S7, E8, E7, E7 5 S75, S76, S77, S78, S79, S80, E75, E76, E77, E78, E79, E80 54 S75, S76, S77, S78, S79, S80, E75, E76, E77, E78, E79, E80 55 S, S, S7, E, E, E7 56 S7, S7, E7, E7 57 S8, S9, S59, S7, S7, S8, E8, E9, E59, E7, E7, E8 58 S8, S84, S85, E8, E84, E85 59 S8, S8, S84, S85, E8, E8, E84, E85 60 S4, S5, S8, S85, S86, E4, E5, E8, E85, E86 7 S7, S7, S85, E7, E7, E85 74 S89, S90, E89, E90 75 S8, S89, E8, E89 76 S94, S95, E94, E95 77 S9, S9, S40, S49, S94, E9, E9, E40, E49, E94 78 S9, S40, S45, S49, S94, E9, E40, E45, E49, E94 79 S9, S9, S40, S94, E9, E9, E40, E94 80 S9, S40, S45, S89, S95, E9, E40, E45, E89, E95 8 S9, S45, S95, E9, E45, E95 8 S7, S9, S9, S49, S9, E7, E9, E9, E49, E9 8 S40, S4, S96, S97, S98, E40, E4, E96, E97, E98 84 S55, S90, E55, E90 85 S7, S, S9, S9, E7, E, E9, E9 6 S, S7, S7, S8, E, E7, E7, E8 6 S, S7, S7, S8, E, E7, E7, E8 6 S, S, S7, S7, S8, S84, E, E, E7, E7, E8, E84 64 S8, S84, S86, E8, E84, E86 65 S, S68, S7, S8, S8, E, E68, E7, E8, E8 66 S, S9, S68, S7, S8, S8, E, E9, E68, E7, E8, E8 67 S9, S87, E9, E87 68 S9, S8, S85, S87, E9, E8, E85, E87 69 S9, S40, S85, S87, S88, E9, E40, E85, E87, E88 70 S, S45, S60, S76, S89, E, E45, E60, E76, E89 7 S8, S8, S89, E8, E8, E89 86 S8, S6, S9, S96, S97, S98, E8, E6, E9, E96, E97, E98 87 S8, S99, E8, E99 88 S49, S00, E49, E00 89 S9, S7, S49, S0, S0, E9, E7, E49, E0, E0 90 S6, S8, S6, S4, S49, S0, E6, E8, E6, E4, E49, E0 9 S9, S7, S49, S64, S0, S0, E9, E7, E49, E64, E0, E0 9 S7, S8, S84, S0, S04, E7, E8, E84, E0, E04 9 S7, S75, S76, S06, E7, E75, E76, E06 94 S49, S7, S75, S76, S06, E49, E7, E75, E76, E06 7 S7, S7, S85, E7, E7, E85 95 S08, E08 TIER TIER TIER CORRELATIONS vii
10 Tier and Tier Intervention for Tier s If students need additional support for Tier lessons, use the prerequisite skills and scaffolded examples listed below. Tier Tier Skills and Tier Examples Tier Tier Skills and Tier Examples 96 S8, S08, S09, E8, E08, E09 97 S, S8, S, S6, S08, E, E8, E, E6, E08 98 S05, E05 99 S05, S07, E05, E07 00 S07, S0, E07, E0 0 S07, S0, S, E07, E0, E 0 S70, E70 0 S70, E70 viii TIER TIER TIER CORRELATIONS
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