Solve multiplication and division problems by using proportional adjustment.
Number Framework Stage 7
Using Number Properties
Problem: Write 24 on a card and stick it on the board. Write ÷ 2 beside it and ask the answer. Write x 2 beside it and ask the answer. So 24 ÷ 2 x 2 = 24 is on the board.
Examples: Repeat for 10 x 2 ÷ 2, 100 x 2 ÷ 2, 6 ÷ 3 x 3 ...
Understanding Number Properties:
Make up an example that shows the effect of multiplying and dividing by the same number. (Answer: The original number stays the same.)
Problem: Write 5 x 468 024 806 642 = 2 340 124 033 210 on the board. Ask the students how this works.
(Answer: Multiplying 5 by 2 gives 10 and dividing 468 024 806 642 by 2 gives 234 012 403 321. And 10 x 234 012 403 321 = 2 340 124 033 210.)
Problem: “Find 3 1/3 x 3 636.”Write 3 x 3 1/3 on the board and discuss the answer. (Answer: 10.)
Discuss why 3 1/3 x 3 636 = 10 x 1 212 = 12 120.
Problem: “Which is larger 30 ÷ 5 or 60 ÷ 10 or are they both the same?” Discuss why they are the same.
Problem: “Does 340 ÷ 0.5 = 680 ÷ 1? How does this help to find 340 ÷ 0.5?”
Examples: Worksheet (Material Master 8–6).
Understanding Number Properties:
Does 25 x 36 = (25 x 89) x (36 ÷ 89)? Explain.
(Answer: Yes. Multiplying and dividing by the same number balances out and leaves the original problem the same.)