All things being equal…
3 November 2017
Author: Mari Palmer
On Friday 3rd November the EEF released its latest guidance report: Improving Maths in Key Stage 2 and 3. This meta-analysis has produced a clearly written and highly focussed set of guidelines that point the reader towards the elements of teaching that could have the greatest impact on children’s development.
In this blog we will examine the equals sign – taken from section 6 of the report:
‘Pupils often regard the equals sign as an instruction to calculate rather than an indication of a relationship (Jones and Pratt 2012)’
For me, possibly one of the easiest ways to understand mastery and how we can provide greater depth for children without instantly moving to larger numbers or ‘higher level’ tasks is through tasks involving the equals sign. If a child can calculate
5 + 5 = ? can they calculate 5 + ? = 10 or 10 = ? + 5 or 5 + 5 = 10 + 0?
We have tried to work very hard with our children throughout school to ensure that they have a good grasp of the meaning of the equals sign and so we were very pleased to see this mentioned in the new EEF report. In reception our children begin with activities where the equals sign is seen as a balance – it signifies that the value of one side of the equals sign should be the same as the other side. Our aim with this work is to try and help the children in the future with, amongst other things, missing number problems and algebra but also to show they have a true understanding of the value of the numbers on each side of the =.
We begin to explore this idea with the 4 year olds in school through Numicon on scales, number balances and Cuisenaire amongst other things. We have found if we begin this from a very young age they do not develop the concept of an equals sign signalling ‘an answer’.
Here is one of our younger children experimenting with a range of equipment and then the equations they were able to write independently after this work:
Which led to…
As they move through school our aim is that they are then confident with manipulating expressions, either using concrete, pictorial or abstract methods. Sometimes this is more successful than at other times, however as we began this work around three years ago we are gradually seeing growing confidence in the pupil’s abilities to manipulate number sentences.At this point in time this child is ‘clinging’ to the number bonds she has worked on with her class teacher – number bonds for the number ten (even though this work was child led and completed after the work in class). Though hopefully soon, with guided support, she will be able to generalise to other numbers – initially below 10.
Here is a Year 2 child making a ‘times table’ shop, continuing practices they first learnt in Reception:
Here is a Year 6 child who feels happy with the relationship that the equals sign has with the number sentence (4a + 15 = 5a + 10) and he is happy discussing how to manipulate this.
“I figured out ‘a’ by realising 5 x the unknown +10 has to be in the five times tables because it ends with a zero. Then I went through my 4 times tables which were common multiples of five. The first one is twenty so I did 20 + 15 = 35 and then 5 x 5 + 10 = 35. 35 and 35 are equal so that is your answer.”
We would like to ensure that pupils are happy to complete missing number problems, perform algebraic operations and have a sense of the approaches to manipulating number sentences. If this is how they view the = sign from the beginning of school we hope that they can then move more easily towards missing number problems. We are not at this point yet with all our pupils but we are trying!
Posted on 3 November 2017
Posted in: Blog