Tag Archives: equations

335. The power of colour

As Mathematicians we appreciate the importance of getting the basics right and building a firm foundation. With this in mind I’ve been an absolute harridan with my Y8 students regarding presentation and technique for solving equations. If they can nail good algebraic presentation now, their future studies will be be much easier.

When we started there were students doing everything in their head, not always correctly. Some insisted on working backwards, which is great for basic cases but not for unknowns on both sides. Most frustratingly some students were breaking up the logic by putting extra working out between steps and losing track of what they were doing.

For example:

2x – 10 = 5x + 8

5x – 2x = 3x

3x – 10 = 8

So we had a really good discussion about logical presentation. We decided to write down what we were doing in the margin, try and keep the = sign lined up in the working and put any extra working out on the right.

This worked really well for most of the class, but I had a small group of students who just lost track of what they were doing and why. They knew things had to balance, but struggled to cope with equations with an unknown on both sides.

While I was talking things over with them using a mini whiteboard, I noticed they had a profusion of coloured pens and highlighters. Bring on the colour!

By highlighting the key point of each line of algebra and matching it with the balancing step they started to build the structure of good solutions. It was slow work to start with, but a couple of lessons later and these same struggling students are now hitting the extension work every time. And most of them no longer feel the need to highlight key information.

283. Splitting the steps – Rearranging Equations

Last year I put together some resources using the ‘Splitting the steps’ model which was introduced to me at a talk by Bruno Reddy (@mrreddymaths). I’ve realised I didn’t upload this one at the time!

This worksheet takes you through rearranging equations through two sets of questions, plus extension. The helpful hints and structure are gradually removed. You’ll notice that the + sign is left in, even when a – is required. This was specifically done to ensure my students focussed on opposite operations and writing in negative numbers. If you’d rather not have that, there is an editable version too.

Splitting the steps Rearranging equations (PDF)

Splitting the steps Rearranging equations (Word)

If you would like a starter activity relating to this, then go to this blog post on simple rearrangements: 224. No Nonsense Negatives

If you like this splitting the steps activity, try these out:

Splitting the Steps estimated mean

Splitting the steps Rationalising the denominator V2

188. Top Teachmeet Trumps Resource


I’m currently trying out ideas from the #mathsmeetnorthwest TeachMeet. Emma Weston did an excellent presentation on ‘Marking for motivation and progress’. She inspired me to look for a Top Trumps activity for my class – they needed some consolidation of solving equations with an unknown on each side and with brackets. I found this brilliant solving equations Top Trumps by Dusher on TES resources.

The Marvel comic themed algebra cards have three tiers of difficulty and went down a storm. My class would have happily played all lesson, if I had let them.


Who would have thought that equations could be so engaging?

186. Fantastical algebra

Have you ever played the parlour game ‘Fantastical Creatures’? Click for a lovely description and example of it by Little Cotton Rabbits.

I’ve adapted this concept for teaching aspects of number and algebra.

Basic arithmetic
Inverse operations
Order of operations
Setting up simple equations
Using brackets with numbers/letters
Solving single sided equations

Strips of paper – one sheet of A4 makes about 6 strips
Coloured pens (optional)

Basic instructions
1. Write an instruction on the top of the strip (portrait orientation). Label it (a).


2. Fold over the strip twice to hide the writing. Write (b).


3. Pass on the strip, do not unfold it.
4. By the ‘(letter label)’, write the next instruction. The letters help you keep track of how many times it has been passed on.
5. Fold over the strip twice and put a label for the next letter of the alphabet.
6. Repeat steps 3 – 5 as required.

The beauty of this activity is that each problem is constructed by a group of pupils and they are in control of the level of difficulty.

Activity 1: Setting up simple equations

Follow the basic activities with the following instructions:
(a) I think of a number and write an instruction
(b) & (c) Now I write an instruction
(d) The answer is write a number

Pupils fold the puzzle up tight and either pass it on one last time or hand them in (to be randomly distributed).

Pupils unfold their mystery puzzle and construct the equation, step by step. My pupils quickly realised the importance of simplifying, but many forgot the importance of using brackets. This was a useful misconception to identify.


Pupils then use inverse operations to calculate the unknown.


The algebraic operations and numerical operations can then be compared.


Activity 2: Problem solving

This follows the same structure as the equation activity, but pupils are describing a geometric problem. In the examples the blue sections are up to the pupils to choose.

Example 1

Example 2


In the second example pupils can visualise the problem as well as using algebraic terms.

Activity 3: Number Skills

This activity can also be used for setting up BIDMAS problems by omitting the algebra.