Hard Times

This activity uses a physical model to help students explore ways to multiply a two-digit number by a one-digit number. This activity will help them to develop and use mental strategies to solve multiplication problems.
Using the place value blocks, the students should see that an easy way to solve the problem is to collect all the tens blocks and then collect the ones blocks. They get the answer by adding the two totals together. For example, for question 1,
4 x 30 = 120
4 x 6 = 24
Total = 144
You can write this as:
36 = 30 + 6
4 x 36 = 4(30 + 6).
The brackets show that both the 30 and the 6 are multiplied by 4:
= 4 x 30 + 4 x 6
= 120 + 24
= 144.
When the students have become familiar with this method using place value blocks, they may be able to solve the problems without using them, but let them use the blocks for as long as they need them. Students who are not using the blocks might approach question 4 like this:
Steven 3 x 40 = $120
3 x 6 = $18
Total = $138
or alternatively:
3 x 46 = 3(40 + 6)
= 3 x 40 + 3 x 6
= 120 + 18
= $138
Tama 4 x 30 = $120
4 x 4 = $16
Total = $136
Karla 5 x 20 = $100
5 x 8 = $40
Total = $140
Note that the setting out is different from the usual vertical form. This setting out shows the usual way that students think through the problem and leads to a better understanding of multiplication and finding estimates.

Answers to Activity

1. 4 x 30 = 120
4 x 6 = 24
so 4 x 36 = 144
2. a. 3 x 53
b. 3 x 50 = 150
3 x 3 = 9
3 x 53 = 159

3a.

b. i. 150
ii. 180
iii. 141
iv. 112
4. a. $138
b. $136
c. $140