Solve multiplication and division problems by using proportional adjustment.
Number Framework Stage 7
Using Materials
Problem: “Tana collects $25 from each person in a group of 9 people to buy concert tickets. How much money does he have?”
Get the students to lay out 9 piles of $25 in play money. The students look at the first 4 piles.
How much money is in the piles? (Answer: $100.)
“Could you make another pile of $100?”
(Answer: Yes, because there are 5 piles left, and we need only 4 to make $100.)
Discuss why the answer is $225.
Examples: Word stories and recording for: 7 x 25, 5 x 25, 12 x 25, 10 x 25,14 x 25 ...
Using Imaging
Problem: “Tana collects $25 from each person in a group of 11 people to buy concert tickets. How much money does he have?”
Shield 11 piles of $25 from the students. Ask them to imagine how the bundles will be combined to form $100 piles. If necessary, revert to materials by showing the piles.
Examples: Word stories and recording for:
21 x 25
24 x 25
16 x 25
15 x 25
13 x 25 ...
Using Number Properties
Discuss reversing the problem to 35 x 25.
Discuss how many groups of 4 are in 35.(Answer: 8.)
“What is the remainder?” (Answer: 3.)
Discuss how this leads to the answer being 875.
Examples: Work out: 40 x 25, 25 x 25, 25 x 41, 80 x 25, 25 x 45
Make up your own problem of 25 times a two digit number and explain how to solve it.