Discover Mathematics P4: Term 1, Unit 8, Lessons 1–4
GoalUse a plan and a toolbox of strategies to solve a problem in steps.
New words
strategy · a plan or trick that helps us solve a problemguess and check · try a number, test it, and improve the guesswork backwards · start from the end and undo each step
Explanation
A good problem solver follows four steps: understand the problem, make a plan, solve it, and check the answer. Strategies are tools for the plan. In guess and check we try numbers that fit one clue and test the other clue: two numbers add to 20 and multiply to 91, so try 7 and 13: 7 + 13 = 20 and 7 × 13 = 91. When a story ends with the answer given, we work backwards and use the opposite operations. A table helps when two things change together. A diagram or bar model shows how the numbers are joined. Choose the tool that fits the problem, and always check that the answer matches every clue in the story.
Step
Ask yourself
1
What do I know? What must I find?
2
Which strategy fits: draw, table, guess and check, work backwards?
3
Do the calculations in order.
4
Does the answer fit every clue?
Worked examples
Guess
Sum
Product
Right?
8, 12
20
96
no, too big
7, 13
20
91
yes
Two numbers add to 20 and multiply to 91. Guess 8 and 12: the sum is 20 but 8 × 12 = 96, too big. Guess 7 and 13: 7 + 13 = 20 and 7 × 13 = 91. The numbers are 7 and 13.
Step in the story
Undo it
Money
end
90
got 40 LE
90 − 40
50
spent 25 LE
50 + 25
75
Youssef spent 25 LE on a book. His uncle then gave him 40 LE. Now he has 90 LE. How much did he have at first? Work backwards: 90 − 40 = 50, then 50 + 25 = 75. He had 75 LE. Check: 75 − 25 + 40 = 90.
Pens at 3 LE
Pens at 5 LE
Total cost
5
5
40
7
3
36
6
4
38
Mina buys 10 pens. Some cost 3 LE and the others 5 LE. He pays 38 LE. Make a table. With 6 pens at 3 LE and 4 pens at 5 LE: 6 × 3 + 4 × 5 = 18 + 20 = 38. So he bought 6 cheaper pens and 4 dearer pens.
Class activity
Mystery number. A grown-up thinks of a number, doubles it and adds 5. The result is 25. The child works backwards to find the number (10). Then swap places and invent your own mystery.
Practice
1
Two numbers add to 16 and multiply to 55. Find them with guess and check.
5 + 11 = 16 and 5 × 11 = 55. The numbers are 5 and 11.
2
Hana thinks of a number, doubles it and subtracts 6. The result is 20. What was her number?
