Working systematically means to solve a problem in an ordered and methodical way to ensure all outcomes are recorded.

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

Represent the structure of a problem with two unknowns in context

Maths

Compare the structure of problems with one or two unknowns

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

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

An efficient strategy is a when a problem can be solved:

The bar model shows two values a and b. What is the value of a?

The bar model shows two values c and d. What is the value of c?

Calculate the size of e in the bar model.

A supermarket sells 90 burgers and sausages altogether. They sell 40 more sausages than burgers. How many sausages do they sell?

Andeep is travelling to see his relatives. The whole journey is 182 km. He travels by train for 36 km further than he does by bus. How far does he travel by train altogether? {{ }} km

Two rods are equivalent to the yellow rod. One of them is red. What is the missing rod?

Two rods are equivalent to the yellow rod. One of them is white. What is the missing rod?

Two rods are equivalent to the black rod. What could the missing rods be?

Two rods are equivalent to the brown rod. What could the missing rods be?

Two rods are equivalent to the brown rod. One rod is twice the size of the other. What rods could they be?

Two rods are equivalent to the yellow. One rod is four times the size of the other rod. What rods could they be?

Represent the structure of a problem with two unknowns in context

Lesson outcome