To represent something means to show something in a different way.

Solve problems with two unknowns in a range of contexts

Maths

Compare the structure of problems with one or two unknowns

Represent the structure of a problem with two unknowns in context

Explain why there is sometimes only one solution to a problem

Represent and solve problems with two unknowns efficiently

Use a bar model to represent spatial problems with two unknowns

Explain how to represent an equation with a bar model

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

Explain how to balance an equation with two unknowns

Solve problems with two unknowns with one, several and infinite solutions

In this unit pupils will compare and represent the structure of problems with two unknowns using a bar model. They will systematically solve problems with two unknowns using trial and improvement. In the future unit this understanding is formalised through the use of algebraic notation. 

In the prior unit pupils explained how to balance equations with addition or subtraction expressions and used knowledge of balancing equations to solve problems. In this unit pupils will compare and represent the structure of problems with two unknowns using a bar model. They will systematically solve problems with two unknowns using trial and improvement.

In this unit pupils will compare and represent the structure of problems with two unknowns using a bar model. They will systematically solve problems with two unknowns using trial and improvement.

Solving problems with two unknowns

The difference in cost is equal to 3 erasers.

The difference in cost is equal to 3 pencils.

1 eraser (a) and 3 pencils (3b) cost £1.75     4 erasers (4a) and 3 pencils (3b) cost £2.50     Which statements are true?

1 eraser (a) and 3 pencils (3b) cost £1.75     4 erasers (4a) and 3 pencils (3b) cost £2.50     Find the cost of one eraser. {{ }} p

The masses of some groups of large and small bags of potatoes are shown here. What is the mass of the large bag? {{ }} kg

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 triangular tile? {{ }} $$cm^2$$

Lucas knows that the cost of 1 lemon is 30 p. What is the missing total highlighted? Give your answer in pounds. £{{ }}

Lucas knows that the cost of 1 lemon is 30 p and the cost of 1 pear is 50 p. What is the missing total highlighted? Give your answer in pounds. £{{ }}

1 apple and 2 bananas cost £1.85     3 apples and 2 bananas cost £2.75    Complete the equations to represent this. a + 2b = £1.85 and {{ }} + 2b = £2.75

Which pair of equations represent the image?

Match the mass in kilograms to its equivalent mass in grams.

£10 is shared between 8 people. How much does each person get? Write your answer in pounds. £{{ }}

If four peaches cost £3.40, what is the cost of one peach? Give your answer in pence. {{ }} p

1 apple and 2 bananas cost £1.85     3 apples and 2 bananas cost £2.75    What is the cost of one banana? Give your answer in pence.

This lesson was made for home learning during the pandemic.

Solve problems with two unknowns in a range of contexts

Lesson outcome

This lesson was made for home learning during the pandemic.