After students have shared their multiplication stories with the class, ask them to look over their problems and the problems in the Student Guide.
- Are 3 groups of 4 the same as 4 groups of 3? Explain. (They both equal 12, but 3 plates of 4 cookies looks different than 4 plates of 3 cookies.)
- For Question 7B, did anyone use repeated addition to solve 7 × 8?
- What number would go in the box: 8 + 8 + 8 + 8 + 8 + 8 + 8 ×
× 8? (7)
- For Question 7D, can you explain an easy way to multiply by a ten? (Cover the zero and think 7 times 1 ten equals 7 tens, or 70.)
- What patterns do you see about the products in the multiplication problems? (Possible response: When both numbers are whole numbers, the product is larger than each of them; when one of the numbers is a fraction, then the product is smaller than the other number; when one of the numbers ends in zero, the product ends in zero.)
If students do not suggest these patterns themselves, you can encourage them by asking:
- Find all problems that multiply two whole numbers. Write down the number sentences. How does the size of the product compare with the size of the numbers that were multiplied? (The product is larger than each of them. For example, in the problem 7 × 8 = 56, the product 56 is larger than both 7 and 8.)
- Find all problems that involve a fraction and write the number sentences. What can you say about the size of the products in these problems? (The product is smaller than the whole number that is multiplied. For example, in the problem 5 × 1/2, the product, 2 1/2, is smaller than 5.)
- Find all problems that have a ten or a number you say when you skip count by tens. What can you say about the products in these problems? (The products are all numbers that you say when you skip count by tens. They all end in zero. For example, in the problem 7 × 10, the product 70 ends in zero.)
For students having trouble solving a multiplication problem or drawing a picture to show the problem, have them describe the problem to a partner first. The partner or the student can then write down the problem. In addition, students may use connecting cubes or other counters to first model the multiplication problem. For example, 3 × 4 could be modeled by making 3 piles of 4 cubes (or using 3 pieces of paper to show the distinct groups with 4 cubes on each paper, or with 3 cups filled with 4 cubes, and so on). Once the child has created a visual model of the problem, he or she can then more easily draw a picture to show the problem.
