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.

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.

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 :

[MA2019] (4) 3 :

[MA2019] (4) 11 :

1. Interpret and write equations for multiplicative comparisons.

[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 :

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).

View Standards
**Standard(s): **
[MA2019] (4) 3 :

[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.

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 :

Module 3 closes with Topic H as students multiply two-digit by two-digit numbers. Lesson 34 begins this topic by having students use the area model to represent and solve the multiplication of two-digit multiples of 10 by two-digit numbers using a place value chart. Practice with this model helps to prepare students for two-digit by two-digit multiplication and builds the understanding of multiplying units of 10. In Lesson 35, students extend their learning to represent and solve the same type of problems using area models and partial products. In Lesson 36, students make connections to the distributive property and use both the area model and four partial products to solve problems. Lesson 37 deepens students’ understanding of multi-digit multiplication by transitioning from four partial products with the representation of the area model to two partial products with the representation of the area model and finally to two partial products without representation of the area model. Topic H culminates at the most abstract level with Lesson 38 as students are introduced to the multiplication algorithm for two-digit by two-digit numbers. Knowledge from Lessons 34–37 provides a firm foundation for understanding the process of the algorithm as students make connections from the area model to partial products to the standard algorithm (4.NBT.5). Students see that partial products written vertically are the same as those obtained via the distributive property: 4 twenty-sixes + 30 twenty-sixes = 104 + 780 = 884.

View Standards
**Standard(s): **
[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.

This visual tool illustrates how to decompose numbers and find four different products. As students' skills improve, they will move from this pictorial model into a concrete method called partial products.

When first learning to multiply two 2-digit numbers, students will use the area model. To start, students will use their knowledge of place value to decompose into tens and ones. To decompose means to break apart. This video will introduce students to this strategy.