Chapter 4.5, Problem 2P

Demarcus knows his $\text{1 ×, 2 ×, and 3 ×}$ multiplication tables. He also knows $4\text{ × }1,4\text{ × }2,4\text{ × }3,4\text{ × }4,\text{ and }4\text{ × }5$ .

a. Describe how the three arrays in Figure 4.36 1 provide Demarcus with three different ways to determine $4\text{ × }6$ from multiplication facts that he already knows. In each case, write an equation that corresponds to the array and that shows how $4\text{ × }6$ is related to other multiplication facts.

 
Figure 4.36 Different ways to think about $4\text{ × }6$ .

b. Draw arrays showing two different ways that Demarcus could use the multiplication facts he already knows to determine $4\text{ × }7$ . In each case, write an equation that corresponds to the array and that shows how $4\text{ × }7$ is related to other multiplication facts.

c. Draw arrays showing two different ways that Demarcus could use the multiplication facts he already knows to determine $4\text{ × }8$ . In each case, write an equation that corresponds to the array and that shows how $4\text{ × }8$ is related to other multiplication facts.