B2.2 Recall and demonstrate multiplication facts from 0 × 0 to 12 × 12, and related division facts.
Activity 1: If it Falls Over? (Array)
Directions
Ask students to represent 5 × 8 and 8 × 5 using arrays.
Here are some possible representations:
Proceed in the same way with various multiplications of 2 numbers.
Prompts
Ask questions to help understand the commutative property of multiplication, such as :
- What do you see?
- How many counters are there? rows? columns?
- I rotate the array 90° (as if it falls over). How many are there now?
- What is the product of 5 and 8? What other multiplication fact resembles this?
- How could we create a division problem from this multiplication problem? Explain your reasoning.
- By rotating the arrays, what other pairs of numbers give the same product?
- How can these arrays allow us to solve other multiplication or division problems? How can you demonstrate this?
Source: Guide d'enseignement efficace des mathématiques de la 1re à la 3e année, p. 41-42.
Activity 2: Distributive Property and Associative Property
Present the following array to students:
\(8\; \times \;9\; = \;?\)
Ask students questions such as:
- What are some ways to determine the product of \(8\; \times \;9\) from this array? Explain your reasoning.
- How can this array help us determine the product? Demonstrate it.
- What other multiplication situations might the array help us solve? Explain your thinking.