Multiplication and Rectangles

Explore Prime Numbers. For Part 4, students will need 25 tiles and their partially completed My Multiplication Table from Lesson 3. Direct students' attention to the Finding More Rectangles pages in the Student Activity Book. Assign Questions 1–3 to student pairs.

Questions 1 and 2 ask students to build as many rectangles as they can with 5 and 7 tiles, respectively. They find that they can only build rectangles with one row or one column. For example, there are only two rectangles that can be built with 5 tiles (5 × 1 = 5 and 1 × 5 = 5). The same is true for 7 tiles.

Numbers that have only two factors (themselves and 1) are called prime numbers.

Encourage students to take some time to find all the rectangles that can be made with both numbers of tiles and to write number sentences for them. Students should be able to justify their responses using the tiles. Since they can make only two rectangles with the tiles for 11 (11 × 1 and 1 × 11) and can make more rectangles for 10 (10 × 1, 1 × 10, 5 × 2, and 2 × 5), then 11 is prime and 10 is not.

Explore Square Numbers. Assign Questions 4–6 on the Finding More Rectangles pages in the Student Activity Book to student pairs.

For Question 4, students build squares with tiles that have side lengths of 1 to 10 to find the square numbers from 1 to 100. They record their work in a table. Question 5 defines square numbers and asks students to add the square numbers to their multiplication tables as shown in Figure 6. Question 6 asks students to look for patterns.

Update Patterns Chart. Ask students to refer to and update the Patterns for Remembering the Facts chart that was created in Lesson 3. Add the patterns they discovered for square numbers. See Figures 6 and 7.