# Lesson 34: Expanded Multiplication

## Lesson Objectives

- Use objects, pictures, drawings, and number lines to understand multiplication
- See multiplication as repeated addition
- Use addition to find the total number of objects and dots in arrays
- Write equations of repeated addition and multiplication
- Apply skip counting and the TouchMath approach for finding products
- Apply vocabulary (factors and products) in explaining multiplication
- Apply the commutative property to multiplication
- Use arrays as a strategy for skip counting
- Use strategies, including repeated addition and skip counting, to find products

## Materials

- Extend Workbook (Page 34)
- Counters or manipulatives
- Highlighters, markers, or crayons
- TouchMath’s Foam Numerals and TouchPoints (for more concrete)
- Skip counting multiplication songs (multiples of 5) (as needed)

## Step 1: Warm Up (5 min)

Review prior vocabulary showing a few multiplication problems with visuals (e.g. arrays) and going through each part (factor x factor = product), look at the groups of dots and circle/ring, count the number of items in each group to determine the factors (3 groups of 5 = 15 total items). Review that multiplication is repeated addition (5+5+5, but also if factors are reversed, the result is same product (3+3+3+3+3). Optional: review skip counting songs for multiples of 5.

## Step 2: Vocab Review (5 min)

Review prior vocabulary: repeated addition, arrays (an arrangement of a set of numbers or objects in rows and columns) products of multiplication problems, and factors (a number that you multiply with another number to get a product).

## Step 3: Model (5 min)

Expanding on the warm-up, review several examples of commutative property of multiplication with visuals underneath both examples (5×4 and 4x5) and illustrating the separate repeated addition problems, with the same products. Use counters and the whiteboard to physically break down this concept in the concrete and then representational. Show a few multiplication problems with multiples of 5 and teach skip counting by one number while touching the TouchPoints on the other number (e.g. if skip counting by 5’s, skip count on the 4 by 5’s in 5x4: 5, 10, 15, 20). Using TouchMath’s Foam Numerals, show how to skip count on one number (place visual examples with counters underneath, as well).

## Step 4: Guided Practice (5 min)

Pull out 100s Chart and multiples of 5 resource pages made in prior lessons, or make a resource page prior to this lesson. In groups, ask students to draw arrays with dots/circles/dots with multiples of 2’s and 5’s for review (5×4, 6×2, 5×8, 2x9, etc.). Have students circle each group. Ask them, “how many groups of dots/stars did you circle? How many dots/stars are in each group?” Then have them write down their multiplication sentences/problems next to their arrays (e.g. “We circled 8 groups of dots and there are 5 dots in each group. Therefore, my multiplication sentence is 8×5=42. There are 42 total dots altogether. This means the product of 5+5+5+5+5+5+5+5 is 40”). Ask what the repeated addition statements would look like (e.g. 5+5+5+5+5+5+5+5 OR 8+8+8+8+8). Have students practice skip counting by one number while touching the TouchPoints on the other number using TouchMath’s Foam Numerals.

## Step 5: Student Practice (5 min)

Go to Student Workbook Page (34). Read the directions at the top of the page. Tell students they will be practicing repeated addition, skip counting, and creating multiplication problems based on the repeated addition statements. For the first problem, ask students to count how many boxes of 5’s there are at the top of the page or how many 5’s there are in the repeated addition equation right below it (4). Ask students to skip count 5 four times (5, 10, 15, 20) and then write 20 on the line provided. Next, have students fill out the statements below: There are 4 groups of 5. Then, remind them this means 4×5, which is the same thing as 5+5+5+5, and the sum of 5+5+5+5 is the same as the product of 4×5 (20). Have students write 20 on the line provided. Repeat these steps for the next two problems.

## Step 6: Wrap Up (5 min)

To wrap up the lesson, review the learning objectives and core vocabulary words again and ask your students about their experience.