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In the run-up to Y6 SATs, teachers are faced with not only recapping previous years’ learning but also teaching the new Y6 content of the curriculum.
In order to ensure SATs don’t turn into a memory test, we need to make clear links between new learning and prior knowledge so children can build on their understanding, rather than starting afresh with every new concept.
One of the most important concepts that children need to understand is the use of equal groups throughout the curriculum.
In KS1, children are introduced to equal groups within multiplication and division; this starts with a basic understanding that 2 × 3 is two equal groups of three (or three equal groups of two) before deepening their understanding by comparing equal groups.
Take this example from the 2016 KS1 SATs:
Complete the number sentence below.
3 x 8 = 2 x __
Using a bar model, children can visualise the equal parts in order to help them solve the problem.
Drawing the bar model supports us to decide which calculation to use.
Here, we need to find out the total of the each bar. If we multiply 3 by 8, we find the total of the bar is 24.
Once we have found the total, we can see that as the bars are equal, the second bar will also be worth 24 but this time it is divided into two equal parts.
Therefore, to find the missing information, we need to divide 24 by 2 to find our missing box is 12.
The use of the bar model for this question helps to support children to see how 24 is split into three equal parts on the top bar and into two equal parts on the bottom bar.
Imagine taking this learning a step forward. Moving into KS2 you can start to explore factors, fractions or percentages of 24.
All would involve dividing 24 into equal parts and using a consistent pictorial method will help children see the links between the concepts.
Here’s a question from the 2017 KS2 reasoning paper.
3 pineapples cost the same as 2 mangoes. One mango costs £1.35. How much does one pineapple cost?
Again, let’s use a bar model to visualise the problem.
Here we can see that we need to find two equal groups of £1.35 to make £2.70 and then we need to divide £2.70 between three equal groups to find that one pineapple would cost 90p.
Interestingly, if we look at the bar models we have used for the KS1 and the KS2 question, they are pretty much identical. The only difference is the numbers used and the calculations required. The structure of the problem is the same.
In order to support children to tackle problems like this, we need to encourage them to represent their thinking through pictorial representations.
As teachers, we need to model and explain the clear links between questions. Another concept that builds upon children’s prior understanding of equal groups is ratio. Take this question for example:
Lucy and Jemima share £30 in the ratio 2:3. How much money does Lucy receive?
Here is a worked example on a bar model.
The bar model supports the procedural understanding of calculating ratio by dividing the amount by the total number of equal parts.
We can also stretch children’s thinking to answer questions such as ‘How much more money does Jemima have?’ or ‘Lucy and Jemima share some money in the ratio 2:3.
If Lucy has £24, how much money do they have altogether?’ Once again, within ratio, the understanding of equal parts is essential to children’s understanding.
If we can help children to understand equal groups and parts clearly and help them to use bar models to represent their thinking, we can give all children the tools to tackle more complex problems.
Instead of seeing the SATs as a memory test of procedures that the children do not fully understand, we need to give them the tools to apply their knowledge across the curriculum in order to visualise the maths within the problem.
Beth Smith is senior primary maths specialist for White Rose Maths. Download free White Rose Maths assessments on TES, along with schemes of learning to support the teaching of maths. Follow her on Twitter at @beth_89.
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