# Lesson 31: Applying Addition and Multiplication

## Lesson Objectives

- Use objects, pictures, drawings, and number lines to understand multiplication
- See multiplication as repeated addition
- Apply skip counting and the TouchMath approach for finding products

- Apply understanding in making comparisons of pairs of factors
- Skip count up and down by 5’s using concrete objects and pictures
- Use arrays as a strategy for skip counting

## Materials

- Extend Workbook (Page 31)
- Counters or manipulatives
- Graph paper
- Highlighters, markers, or crayons
- TouchMath’s Foam Numerals and TouchPoints (for more concrete)

## Step 1: Warm Up (5 min)

Draw a few multiplication arrays with multiples of 5 (5x1, 5x2, 5x3), using stars, dots, or another symbol (e.g. 5 dots in one row, 5 dots in two rots, 5 dots in three rows). Draw boxes around each group of 5 in the array drawings. Within each array, write the multiplication sentence next to each group of 5. You can break down each group to simplify things or show the skip counting sequence on one side of the box (5, 10, 15). Play around with different ways to visually illustrate arrays using multiples of 5 to start.

## Step 2: Vocab Review (5 min)

Review prior vocabulary: arrays (an arrangement of a set of numbers or objects in rows and columns) products of multiplication problems, rows, and groups.

## Step 3: Model (5 min)

Review various use real-life connections to help build stronger connections to the concept, using multiples of 5: Ask students how much it would cost if each member of their family went out to dinner and had $5 each to spend; Ask the class, how many total problems would be done if each student were assigned 5 problems (can ask a group of students if class is large); or, another relevant example. Model making arrays with multiples of 5’s. Review skip counting by 5’s song for further support. 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 3 by 5’s in 5×3: 5, 10, 15; if skip counting by 5’s, skip count on the 4 by 5’s in 5×4: 5, 10, 15, 20).

## Step 4: Guided Practice (5 min)

Pull out 100s Chart and multiples of 5 resource page made in prior lesson. In groups, ask students to draw 1-2 arrays with multiples of 5 (5×2, 5×3, 5×4, etc.). Have students circle each group of 5. 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 3 groups of dots and there are 5 dots in each group. Therefore, my multiplication sentence is 5×3=15 OR 3×5=15. There are 15 total dots altogether. This means the product of 5×3 is 15.”). Ask what the repeated addition statements would look like (e.g. 3+3+3+3+3 OR 5+5+5). Have students practice skip counting by one number while touching the TouchPoints on the other number.

## Step 5: Student Practice (5 min)

Go to Student Workbook Page (31). Read the directions at the top of the page. Tell students they will be practicing working with arrays to understand groups of items. Remind students that they can use any supports from today or previous lessons. Count the dots in each row with the first problem, reminding them to circle or box each row, and then write how many are in each row on the line provided. Solve 5+5 and 2×5 (remind students the answer is the same, as multiplication is repeated addition). Remind students to skip count by one number while touching the TouchPoints on the other number, as well. Complete the same steps for the next array. For the third problem, have students count the number of dots in each of the four circles, and remind students to circle each group of 6. Answer the questions to the right of the array: There are 4 groups of 6: 6+6+6+6 = 24. 6×4=24. Follow the same steps with the last array.

## 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.