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These lessons accompany and are based on Go Math textbook (4th Grade), with rich content and higher level questions. The lessons can stand on their own even if instructors do not use Go Math, where alternative practice exercises can be utilized.
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Chapter 1 Place Value, Addition, and Subtraction to One Million
Our place-value system provides many opportunities for students to look for and make use of structure. Students can use patterns in the place-value system to deepen their understanding of a number. This understanding leads students to expect structure.
Lesson 1.1 Model Place Value Relationships
Lesson 1.2 Read and Write Numbers
Lesson 1.3 Compare and Order Numbers
Lesson 1.4 Round Numbers
Lesson 1.5 Rename Numbers
Lesson 1.6 Add Whole Numbers
Lesson 1.7 Subtract Whole Numbers
Lesson 1.8 Comparing Problems with Addition and Subtraction
Chapter 2 Multiply by 1-Digit Numbers
Students should have opportunities to explore different strategies for multiplication. This builds meaning for the operation and contributes to their fluency in the operation. Further, discussing their strategies allows them to share ideas and build more understanding. These experiences help students make sense of problems and persevere in solving them.
Lesson 2.1 Multiplication Comparison
Lesson 2.2 Comparison Problems
Lesson 2.3 Multiply Tens, Hundreds, and Thousands
Lesson 2.4 Estimate Products
Lesson 4.5 Investigate ● Multiply Using the Distributive Property
Lesson 2.6 Multiply Using Expanded Form
Lesson 2.7 Multiply Using Partial Products
Lesson 2.8 Multiply Using Mental Math
Lesson 2.9 Problem Solving ● Multistep Multiplication Problems
Lesson 2.10 Multiply 2-Digit Numbers with Regrouping
Lesson 2.11 Multiply 3-Digit and 4-Digit Numbers with Regrouping
Lesson 2.12 Algebra ● Solve Multistep Problems Using Equations
Chapter 3 Multiply 2-Digit Numbers
When students connect the area representation of two-digit multiplication to place value within the partial products, they have an opportunity to reason abstractly and quantitatively. The sizes of the rectangles reflect the relative sizes of the partial products. Knowing this can be a quick way to check the reasonableness of their work.
Lesson 3.1 Multiply by Tens
Lesson 3.2 Estimate Products
Lesson 3.3 Investigate | Area Models and Partial Products
Lesson 3.4 Multiply Using Partial Products
Lesson 3.5 Multiply with Regrouping
Lesson 3.6 Choose a Multiplication Method
Lesson 3.7 Problem Solving | Multiply 2-Digit Numbers
Chapter 4 Divide by 1-Digit Numbers
Learning division concepts offers many opportunities for students to attend to precision. Placing the first digit in the quotient relies on their understanding of place value and number sense. They also need to understand the effect of the operation and the meaning of the remainder in order to give accurate solutions to problems.
Lesson 4.1 Estimate Quotients Using Multiples
Lesson 4.2 Investigate | Remainders
Lesson 4.3 Interpret the Remainder
Lesson 4.4 Divide Tens, Hundreds, and Thousands
Lesson 4.5 Estimate Quotients Using Compatible Numbers
Lesson 4.6 Investigate | Division and the Distributive Property
Lesson 4.7 Investigate | Divide Using Repeated Substractions
Lesson 4.8 Divide Using Partial Quotients
Lesson 4.9 Investigate | Model Division with Regrouping
Lesson 4.10 Place the First Digit
Lesson 4.11 Divide by 1-Digit Numbers
Lesson 4.12 Problem Solving | Multistep Division Problems
Chapter 5 Factors, Multiples, and Patterns
As students study factors and multiples, it will be beneficial for them to look for and express regularity in repeated reasoning. For instance, when examining factors of square numbers (e.g., 4, 9, 16) students will begin to notice that there will always be one factor repeated so that it does not have a “partner” like all of the other factors of the square number.
Lesson 5.1 Model Factors
Lesson 5.2 Factors and Divisibility
Lesson 5.3 Problem Solving | Common Factors
Lesson 5.4 Factors and Multiples
Lesson 5.5 Prime and Composite Numbers
Chapter 6 Fraction Equivalence and Comparison
Students will learn to reason about fractions to find equivalent fractions and to compare and order fractions. This improves their number sense as it relates to fractions, or fraction sense. For example, if only one fraction in a set of three fractions is less than12, then that leaves only two fractions left to compare. These experiences help students to look for and express regularity in repeated reasoning.
Lesson 6.1 Investigate • Equivalent Fractions
Lesson 6.2 Generate Equivalent Fractions
Lesson 6.3 Simplest Form
Lesson 6.4 Common Denominators
Lesson 6.5 Problem Solving • Find Equivalent Fractions
Lesson 6.6 Compare Fractions Using Benchmarks
Lesson 6.7 Compare Fractions
Lesson 6.8 Compare and Order Fractions
Chapter 7 Add and Subtract Fractions
When learning to add and subtract fractions and mixed number, students need many opportunities to make sense of problems and build meaning for the algorithms. This is facilitated by solving problems situated in real-world contexts by representing them with models and symbols. They also apply properties to solve problems and symbols. They also apply properties to solve problems and use proper language to explain solution processes. Students who use these methods to develop meaning will also find it east to attend to precision.
Lesson 7.1 Investigate | Add and Subtract Parts of a Whole
Lesson 7.2 Write Fractions as Sums
Lesson 7.3 Add Fractions Using Models
Lesson 7.4 Subtract Fractions Using Models
Lesson 7.5 Add and Subtract Fractions
Lesson 7.6 Rename Fractions and Mixed Numbers
Lesson 7.7 Add and Subtract Mixed Numbers
Lesson 7.8 Subtract with Renaming
Lesson 7.9 Algebra | Fractions and Properties of Addition
Lesson 7.10 Problem Solving | Multistep Fraction Problems
Chapter 8 Multiply Fractions by Whole Numbers
As students explore different strategies to multiply a fraction by a whole number, they develop ways to explain their work and reasoning. Working with are representation, counters, and number line strategies gives students many opportunities to construct viable arguments and critique the reasoning of others.
Lesson 8.1 Multiples of Unit Fractions
Lesson 8.2 Multiples of Fractions
Lesson 8.3 Multiply a Fraction by a Whole Number Using Models
Lesson 8.4 Multiply a Fraction of Mixed Number by a Whole Number
Lesson 8.5 Problem Solving ● Comparison Problems with Fractions
Chapter 9 Relate Fractions and Decimals
Students model with mathematics as they explore, interpret, represent, and describe decimal fractions. Students use tools such as decimal squares and number lines to build relationships between decimal numbers and their corresponding fractions.
Lesson 9.1 Relate Tenths and Decimals
Lesson 9.2 Relate Hundredths and Decimals
Lesson 9.3 Equivalent Fractions and Decimals
Lesson 9.4 Relate Fractions, Decimals and Money
Lesson 9.5 Problem Solving | Money
Lesson 9.6 Add Fractional Parts of 10 and 100
Lesson 9.7 Compare Decimals
Chapter 10 Two-Dimensional Figures
To model with mathematics in geometry involves hands-on application of the concepts. For example, using the concept of line symmetry for polygons can be helpful when students are folding napkins to decorate a dinner table or folding paper for origami figures. Furthermore, students’ knowledge of polygons and their classifications can be applicable in other school subjects such as art.
Lesson 10.1 Lines, Rays and Angles
Lesson 10.2 Classify Triangles
Lesson 10.3 Parallel Lines and Perpendicular Lines
Lesson 10.4 Classify Quadrilaterals
Lesson 10.5 Line Symmetry
Lesson 10.6 Find and Draw Lines of Symmetry
Lesson 10.7 Problem Solving | Shape Patterns
Chapter 11 Angles
Using a protractor to measure angles calls for students to reason abstractly and quantitatively. Students are often confused about which of the two scales to read on a protractor. If they think about the definitions of acute and obtuse angles, they can always choose the correct number. Visual inspection of angles will help students decide whether to choose the measure less than 90 degrees or the measure greater than 90 degrees.
Lesson 11.1 Investigate | Angles and Fractional Parts of a Circle
Lesson 11.2 Degrees
Lesson 11.3 Measure and Draw Angles
Lesson 11.4 Investigate | Join and Separate Angles
Lesson 11.5 Problem Solving | Unknown Angle Measures
Chapter 12 Relative Sizes of Measurement Units
Working with measurement concepts gives students multiple opportunities to attend to precision. They may use the relative sizes of units to evaluate the reasonableness of their results. Or, they may use benchmark measures to estimate length, weight, and volume.
Lesson 12.1 Measurement Benchmarks
Lesson 12.2 Customary Units of Length
Lesson 12.3 Customary Units of Weights
Lesson 12.4 Customary Units of Liquid Volume
Lesson 12.5 Line Plots
Lesson 12.6 Investigate | Metric Units of Length
Lesson 12.7 Metric Units of Mass and Liquid Volume
Lesson 12.8 Units of Time
Lesson 12.9 Problem Solving | Elapsed Time
Lesson 12.10 Mixed Measures
Lesson 12.11 Algebra | Patterns in Measurement Units
Chapter 13 Algebra: Perimeter and Area
When students begin to explore measurement attributes such as perimeter and area of common polygons (e.g., rectangles and squares), they should look for and make use of structure. For instance, once students study the concepts or perimeter for squares, they should consider the similarity between squares and rectangles that are not squares. They should be able to make some conjectures about the perimeter of rectangles that are not squares.
Lesson 13.1 Perimeter
Lesson 13.2 Area
Lesson 13.3 Area of Combined Rectangles
Lesson 13.4 Find Unknown Measures
Lesson 13.5 Problem Solving | Find the Area