To work systematically means to work in an organised way, often according to a fixed plan or system.

Infinite means without an end. If something is unlimited, you could say it has an infinite number of things.

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

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

Solve problems with two unknowns in a range of contexts

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

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

If one of the unknowns is 50, what would the other unknown be? {{ }}

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?

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?

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

 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?

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

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? {{ }} $$cm^2$$

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

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

Lesson outcome