Planting with the Whānau

The gardens used in the activity are set out as multiplication arrays. The students will use a range of strategies and a range of operations as they answer the questions.
Discuss with your students the strategies that Māni, Ruawai, and Huia have used. Ask them what facts the characters would have to know to choose the strategies they did. (Māni saw 19 as 10 and 9, Ruawai saw 19 as 20 – 1, and Huia saw 5 as 10 ÷ 2.) Point out that all the characters were looking for an easy way to find a solution, and this is what your students should do as well. Asking them to mentally solve questions such as “If 8 x 5 = 40, then 16 x 5 =  ” will help them to see easier ways to find the solution. Initially, they may find this difficult because they may not be used to this type of question, but encouragement and regular practice will improve their thinking dramatically.

Answers to Activity

1. You should find that each method gives an answer of 95 kūmara plants.
Māni’s method:
10 x 5 = 50
9 x 5 = 45
50 + 45 = 95
Ruawai’s method:
5 x 20 = 100
100 – 5 = 95
Huia’s method:
19 x 10 = 190
190 ÷ 2 = 95
2. a. There are 234 potato plants.
Māni’s method:
9 x 20 = 180
9 x 6 = 54
180 + 54 = 234
Ruawai’s method:
8 x 25 = 200
200 + 25 = 225
225 + 9 = 234
Huia’s method:
10 x 26 = 260
260 – 26 = 234
b. Answers will vary. With these numbers, each method is equally efficient.
3. Answers will vary. Some possible ways to find 4 x 18 are:
i. (4 x 10) + (4 x 8)
= 40 + 32
= 72
ii. 4 x 20 = 80, 4 x 2 = 8, 80 – 8 = 72
iii. 4 x 18 = 8 x 9 (double one factor, halve the other)
= 72
iv. 5 x 18 = 90, 90 – 18 = 72
v. 3 x 4 = 12, so 6 x 4 = 24 and 12 x 4 = 48.
48 + 24 = 72
vi. 9 x 4 = 36, so 18 x 4 = 72.