# Using the distributive property

Purpose

The purpose of this activity is to support students to apply the distributive property to derive ‘new-to-them’ facts from facts they know. It is expected that students at this point will recall their x 2, x 5 and x 10 facts fluently.

Achievement Objectives
NA2-1: Use simple additive strategies with whole numbers and fractions.
Required Resource Materials
• Slavonic Abacus
• Calculator
Activity
1. Push across five rows of two beads, as shown. What multiplication facts am I showing? (5 x 2)
Where are the “five” and “two’ in what I have done?
Students should identify that there are “five rows of two.”
What should I do to make the abacus show 5 x 3?
Students should suggest the one needs to be added to each row.
What is the product of 5 x 3?
How do you know?
2. Record the connected equations vertically to look for pattern.
5 x 2 = 10
5 x 3 = 15
Why is the answer to 5 x 3 “five more” than the answer to 5 x 2?
3. Provide other examples to develop the idea of deriving from known facts using the distributive property. Ask for the action required to change the Slavonic Abacus model of one fact into the model for a related fact. Record the pairs of equations vertically and look for pattern. Good examples are:

• 10 x 5 = 50 so 10 x 6 = [ ] • 9 x 2 = 18 so 9 x 3 = [ ] • 6 x 5 = 30 so 6 x 6 = [ ] • 4 x 5 = 20 so 4 x 7 = [ ] 1. Progress to providing students with paired equations without the visual support of the Slavonic Abacus. Ask students to anticipate the product of the second equation and explain their prediction. Students can manipulate beads of the Abacus to confirm their prediction.
• 7 x 2 = 14 so 7 x 3 = [ ]
• 8 x 5 = 40 so 8 x 6 = [ ]
• 6 x 5 = 30 so 6 x 7 = [ ]
• 4 x 10 = 40 so 4 x 11 = [ ]
• 6 x 6 = 36 so 6 x 8 = [ ]

Next steps

• Build on the x 2 facts to learn the x 3 facts.
• Build on the x 5 facts to learn the x 6 and x 7 facts.
• Build on the x 10 facts anticipate the result of facts for x 11, x 12, etc.