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**Standard(s): **
[MA2019] (4) 2 :

2. Solve word problems involving multiplicative comparison using drawings and write equations to represent the problem, using a symbol for the unknown number.

Students will review the commutative property of multiplication. They will complete word problems using musical instrument references.

View Standards
**Standard(s): **
[MA2019] (4) 2 :

[MA2019] (4) 23 :

2. Solve word problems involving multiplicative comparison using drawings and write equations to represent the problem, using a symbol for the unknown number.

[MA2019] (4) 23 :

23. Apply area and perimeter formulas for rectangles in real-world and mathematical situations.

Students begin Topic A by investigating the formulas for area and perimeter. In Lesson 1, they use those formulas to solve for area and perimeter and to find the measurements of unknown lengths and widths. In Lessons 2 and 3, students use their understanding of the area and perimeter formulas to solve multiplicative comparison problems including the language of times as much as with a focus on problems using area and perimeter as a context (e.g., A field is 9 feet wide. It is 4 times as long as it is wide. What is the perimeter of the

field?) (4.OA.2, 4.MD.3). Students create diagrams to represent these problems as well as write equations with symbols for the unknown quantities.

View Standards
**Standard(s): **
[MA2019] (4) 2 :

[MA2019] (4) 11 :

2. Solve word problems involving multiplicative comparison using drawings and write equations to represent the problem, using a symbol for the unknown number.

[MA2019] (4) 11 :

11. Find the product of two factors (up to four digits by a one-digit number and two two-digit numbers), using strategies based on place value and the properties of operations.

a. Illustrate and explain the product of two factors using equations, rectangular arrays, and area models.

In Module 3, Topic B, students examine multiplication patterns when multiplying by 10, 100, and 1,000. Reasoning between arrays and written numerical work allows students to see the role of place value units in multiplication. Students also practice the language of units to prepare them for multiplication of a single-digit factor by a factor with up to four digits. Teachers also continue using the phrase “____ is ____ times as much as ____” (e.g., 120 is 3 times as much as 40). This carries forward multiplicative comparison from Topic A, in the context of area, to Topic B, in the context of both calculations and word problems.

[MA2019] (4) 11 :

11. Find the product of two factors (up to four digits by a one-digit number and two two-digit numbers), using strategies based on place value and the properties of operations.

a. Illustrate and explain the product of two factors using equations, rectangular arrays, and area models.

Building on their work in Module 3, Topic B, students begin in Topic C decomposing numbers into base ten units in order to find products of single-digit by multi-digit numbers. Students practice multiplying by using models before being introduced to the standard algorithm. Throughout the topic, students practice multiplication in the context of word problems, including multiplicative comparison problems. In Lessons 7 and 8, students use place value disks to represent the multiplication of two-, three-, and four-digit numbers by a one-digit whole number. Lessons 9 and 10 move students to the abstract level as they multiply three- and four-digit numbers by one-digit numbers using the standard algorithm. Finally, in Lesson 11, partial products, the standard algorithm, and the area model are compared and connected via the distributive property (4.NBT.5).

View Standards
**Standard(s): **
[MA2019] (4) 1 :

[MA2019] (4) 2 :2. Solve word problems involving multiplicative comparison using drawings and write equations to represent the problem, using a symbol for the unknown number.

[MA2019] (4) 3 :

[MA2019] (4) 11 :

1. Interpret and write equations for multiplicative comparisons.

[MA2019] (4) 2 :

[MA2019] (4) 3 :

3. Determine and justify solutions for multi-step word problems, including problems where remainders must be interpreted.

a. Write equations to show solutions for multi-step word problems with a letter standing for the unknown quantity.

b. Determine reasonableness of answers for multi-step word problems, using mental computation and estimation strategies including rounding.

[MA2019] (4) 11 :

11. Find the product of two factors (up to four digits by a one-digit number and two two-digit numbers), using strategies based on place value and the properties of operations.

a. Illustrate and explain the product of two factors using equations, rectangular arrays, and area models.

Module 3, Topic D gives students the opportunity to apply their new multiplication skills (4.NBT.5). In Lesson 12, students extend their work with multiplicative comparison from Topic A to solve real-world problems (4.OA.2). As shown on the next page, students use a combination of addition, subtraction, and multiplication to solve multi-step problems in Lesson 13 (4.OA.3).