A coefficient is number used to multiply an unknown value.

To solve something efficiently means to solve a problem quickly whilst also maintaining accuracy.

Represent and solve problems with two unknowns efficiently

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

Use a bar model to represent spatial problems with two unknowns

Explain how to represent an equation with a bar model

Solve problems with two unknowns in a range of contexts

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

5 apples and 3 pears cost £3.10; 4 apples and 3 pears cost £3.60 

3 apples and 3 pears cost £2.50; 4 apples and 5 pears cost £3.80 

2 apples and 2 pears cost £3.00; 1 apple and 3 pears cost £3.60

Tick the problems that, when written as a pair of equations, would share the same coefficient.

What is the value of the gap marked ? in the bar model? Give your answer in pence. {{ }} p

What is the value of b in the bar model? Give your answer in pence. {{ }} p

What is the value of k? Give your answer in pence. {{ }} p

Cereal is sold in big boxes and small boxes. 3 big boxes and 2 small boxes costs £9.50. 2 big boxes and 3 small boxes costs £8.00
What is the cost of the big box of cereal?

When the sum and the multiplicative relationship between two unknown numbers is known, how many possible solutions are there?

What is the value of a in this equation? a × 6 = 42

a represents a larger numbers and b represent a smaller number. 
The sum of a and b is 340, and the difference between them is 40
What number does b represent?

Grace is 32 years younger than her father. The sum of their ages is 64 years. How old is Grace’s father? {{ }} years old.

The sum of two numbers is 240
One number is five times the size of the other number. What are the two numbers?

The sum of two numbers is 500
One number is one-third times the size of the other number. What is the value of the largest number?

Starter Quiz

When the sum and the multiplicative relationship between two unknown numbers is known, how many possible solutions are there?