Explain how you know you have found all the possible solutions to a problem with two unknowns | Maths

Starter quiz

1 eraser (a) and 4 pencils (4b) cost £3; 3 erasers (3a) and 4 pencils (4b) cost £3.80; Find the cost of one eraser. ______ p

'40' ✓
Two different designs are made with the same square and triangular tiles. The area of the whole design is given. What is the area of one square tile? ______ $cm^2$

'26' ✓
The masses of some groups of large and small bags of potatoes are shown here. What is the mass of the small bag? ______ kg

'1.6' ✓
What is the value of a? a = ______

'120' ✓
What is the value of b? b = ______

'550' ✓
What is the value of c? c = ______

'80' ✓

Exit quiz

Match the pairs of missing unknown numbers to find possible solutions.

5

⇔

20 ✓

1

⇔

16 ✓

3

⇔

18 ✓

2

⇔

17 ✓

4

⇔

19 ✓
If one of the unknowns is 50, what would the other unknown be? ______

'65' ✓
Laura has some triangles and pentagons. She chooses some of the shapes and when she counts the number of sides, she finds that the total is 35 How many of each shape could she have?

5 triangles and 4 pentagons ✓

4 triangles and 5 pentagons

10 triangles and 2 pentagons

10 triangles and 1 pentagon ✓
Laura has some squares and pentagons. She chooses some of the shapes and when she counts the number of sides, she finds that the total is 52 How many of each shape could she have?

8 squares and 4 pentagons ✓

8 pentagons and 4 squares

8 pentagons and 3 squares ✓

3 pentagons and 9 squares
I use two different lengths of wood to make a fence 10.4 m long. One length of wood is 80 cm and the other is 1.20 m. If four 80 cm planks were used, how many of length 1.20 m were used? ______ planks

'6' ✓
In one month, Jun spends 9.5 hours in maths and science lessons. One Maths lesson is 50 minutes and one science lesson is 70 minutes. Jun had 3 maths lessons, how many science lessons did he have?

'6' ✓

Worksheet

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Lesson Details

Key learning points

A trial and improvement approach can be used if a model can't easily be drawn.
A table can be used to record and check all possible solutions have been found.
Some problems with two unknowns have an infinite number of solutions.

Common misconception

Pupils attempt to represent the problems with bar models rather than take a systematic, trial and improvement approach.

Encourage pupils to represent each problem how they would like. Pupils should take time to notice why it is that the bar model if not appropriate to help solve these problems and identify these clues within the questions.

Keywords

Systematically - To work systematically means to work in an organised way, often according to a fixed plan or system.
Infinite - Infinite means without an end. If something is unlimited, you could say it has an infinite number of things.