Complete these pairs of number sentences. Use multiplication to check your answers to the divisions:

2 and .3.

.2: Multiplication and division flow diagrams

1. a) Draw the two spidergrams. Then fill in each output number.

• Spidergram 1 (Rule: $\times 4$)

  • Input: 3 $$3 \times 4 = 12$$ Output: $\boxed{12}$
  • Input: 5 $$5 \times 4 = 20$$ Output: $\boxed{20}$
  • Input: 7 $$7 \times 4 = 28$$ Output: $\boxed{28}$
  • Input: 9 $$9 \times 4 = 36$$ Output: $\boxed{36}$

• Spidergram 2 (Rule: $\div 4$)

  • Input: 12 $$12 \div 4 = 3$$ Output: $\boxed{3}$
  • Input: 20 $$20 \div 4 = 5$$ Output: $\boxed{5}$
  • Input: 28 $$28 \div 4 = 7$$ Output: $\boxed{7}$
  • Input: 36 $$36 \div 4 = 9$$ Output: $\boxed{9}$

1. b) What do you notice in these diagrams?
The outputs of the first spidergram are the inputs of the second spidergram, and the inputs of the first spidergram are the outputs of the second spidergram. The rules ($\times 4$ and $\div 4$) are inverse operations.

2. a) Draw tables to show the inputs and outputs in question 1.

• Table for Spidergram 1 (Rule: $\times 4$)

  Input number	3	5	7	9
  Output number	12	20	28	36

• Table for Spidergram 2 (Rule: $\div 4$)

  Input number	12	20	28	36
  Output number	3	5	7	9

.3: Complete these pairs of number sentences. Use multiplication to check your answers to the divisions.

1.

• $18 \div 6 = \boxed{3}$
• $3 \times 6 = 18$

2.

• $28 \div 7 = \boxed{4}$
• $4 \times 7 = 28$

3.

• $15 \div 3 = \boxed{5}$
• $5 \times 3 = 15$

4.

• $36 \div 12 = \boxed{3}$
• $3 \times 12 = 36$