# Forming factors

Purpose

The purpose of this activity is to support students to recognise multiplication as an efficient way to combine equal sets.

Achievement Objectives
NA2-1: Use simple additive strategies with whole numbers and fractions.
Required Resource Materials
• Pictures of eggs and other objects in arrays (PowerPoint) or real cardboard trays and items to act as eggs of fruit, such as fruit counters, small balls, cubes.
• Calculators
Activity
1. Pose problems that involve arrays of eggs, fruit, or other items, like ping pong balls.
Mere buys a tray of eggs for her whanau.
How many eggs does she buy?   (Slide One of PowerPoint on screen or printed on A3)
2. Let the students solve the problem in any way they prefer. Discuss their strategies.
How did you work out the number of eggs in Mere’s tray?
As students explain their strategies record those strategies using mathematical symbols, such as:
5 + 5 + 5 + 5 + 5 + 5 = 30
6 + 6 = 12, 12 + 12 = 24, 24 + 6 = 30
10 + 10 + 10 = 30
Which strategy is the easiest to use? Why? (Easiness is related to available knowledge)
3. Show the students how a calculator can be used to find the answer. Display the calculator on the screen or use a large display calculator that students can see easily.
How many rows does Mere’s tray have? (Students should say “Five.” Type 5 on the calculator)
How many eggs are in each row?  (Students should say “Six”. Type x 6 on the calculator.)
How do I get the answer? (Students should say “You need to press equals.” Type =.)
How do we say this equation in words? (Students might give various answers like “Five times six” or “Six multiplied by five”. If they do not have words, tell them.)
4. Mouse click on Slide One to animate a 90 degree turn of Mere’s tray. If you have a physical model turn it 90 degrees (a right turn).
Here’s a different way to look at Mere’s tray. How many eggs are in the tray now?
Students may agree that the number of eggs is still 30, some are likely to be less certain.
How many rows does Mere’s tray have when we look at it this way? (Students should say “Six.” Type 6 on the calculator)
How many eggs are in each row?  (Students should say “Five”. Type x 5 on the calculator.)
How do I get the answer? (Students should say “You need to press equals.” Type =.)
How do we say this equation in words? (Students might give various answers like “Six times five” or “Five multiplied by six”. If they do not have words, tell them.)
5. Let’s write down the equations we made on the calculator:
6 x 5 = 30
5 x 6 = 30
What do you notice?
6. Look at the other examples of trays in PowerPoint One. Develop contexts using students’ names. Ask students to find the total number of items in each array. Give them access to a calculator so they can form multiplication equations, so they create the factors themselves.
Record the strategies students use with equations, whether the strategies are additive or multiplicative. Read the equations in words.
Note that Slide Three shows a non-example, as the rows are a combination of four and five apples. Do students adjust their strategy to cope, such as 2 x 4 + 2 x 5 = 18.

Next steps

1. Increasing the level of abstraction by covering the materials, asking anticipatory questions, and working with more complex facts, such as 6 x 7 or 9 x 3. More complex examples are likely to ‘sell’ the idea of multiplication to students.
2. Reverse the task. Give students a multiplication fact, such as 4 x 8, and ask them to draw or make the corresponding array with materials. Find ways to work out the product.
Attachments
Arrays.pptx780.89 KB