Step 7 Objective

Construct and solve linear equations with integer coefficients (with and without brackets, negative signs anywhere in the equation, positive or negative solution) using an appropriate method.

Examples of what pupils should know and be able to do

Solve linear equations such as:

3c – 7 = –13
4(z + 5) = 8
4(b – 1) – 5(b + 1) = 0

Construct linear equations, e.g.

the length of a rectangle is three times its width. Its perimeter is 24 cm. Find its area.

I think of a number, multiply it by 7 and add 3 to the result. The answer I get is the same when I add 23 to twice the number I thought of. Construct an equation to help you to find the number I'm thinking of.

Probing questions

The area of this rectangle is 10 cm². What is its width? What do we need to find?

2x + 7 = 13. What is the question?

How do you decide where to start when solving a linear equation?

Having given the pupils a list of linear equations, ask:

6 = 2p – 8. How many solutions does this equation have? Give me other equations with the same solution. Why? How do you know?

How do you go about constructing equations from information given in a problem? How do you check whether it works?

What if pupils find this a barrier?

Refer to Step 6.

Choose some equations that are typically causing problems. Ask pupils to 'read' the information given to them in the equation. Use dialogue to expose the nature of the misconception.

Provide a range of equations for pupils to classify and solve in pairs.

This kind of activity can usefully be followed up with approaches like annotate written solutions from TMM from L5 - Acrobat pdf document (32Kb).

A useful resource is the Learning from mistakes, misunderstandings and misconceptions in mathematics video.