This is a level 2 number activity from the Figure It Out series. It relates to Stage 5 of the Number Framework.
A PDF of the student activity is included.
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use arrays to solve multiplication and division
36 counters
A classmate
This page builds on the arrays used in the previous three pages but this time uses them to investigate division. The students need prior knowledge of arrays and skip-counting for these activities.
Give the students a total number of objects and a number of rows and ask them to find out how many objects there will be in each row. Using counters to represent dinosaurs and a blank grid to keep arrays organised is a good idea. Emphasise that to divide in this context means to equally share the total number between a predetermined number of rows. Use everyday language such as “split between” or “shared between” to help develop their understanding, for example:
“There are 12 dinosaurs sharing two waterholes. How many dinosaurs at each waterhole?”
“There are 12 dinosaurs sheltering under three trees. How many under each tree?”
“If there were six zoos and 12 crocodiles, how many crocodiles would each zoo get?”
Activity One
After the students have done question 1, discuss with them the counting strategies they used and record their responses on a chart or board. Accept all counting strategies and discuss which ones are the most efficient. Some students may count in fives and others group two sets of five as 10.
Ask the students “Is 5, 10, 15, 20, 25 more efficient than 10, 20, 25?”
Ensure that the students understand what is being asked in questions 2 to 4. Modelling or drawing the array will help them to clarify their thinking. You could also ask the students to write number sentences for the arrays once they are completed, that is, 18 ÷ 6 = 3 or, in words, “18 dinosaurs shared between six watering holes means three dinosaurs at each watering hole”.
Activity Two
Encourage the students to share their results and discuss systematic ways to find all the solutions. As an extension, the students could explore square numbers further. Ask them: “If there were 49 pebbles, how many rows would there be?” “What other numbers of pebbles could be put into perfect squares?”
Answers to Activities
Activity One
1. a. 25
b. 16
2. 6
3. 3
4. 6 rows with 6 in each row
Activity Two
2. 1 x 36
2 x 18
3 x 12
4 x 9
6 x 6
9 x 4
12 x 3
18 x 2
36 x 1