Classroom Assessment
All bar modelling starts with the part–whole model. It’s an essential maths mastery strategy that helps learners visualise the relationships between numbers.
Are you using bar modelling in your maths lessons? This visualisation tool is an essential maths mastery strategy. It supports the Concrete, Pictorial, Abstract (CPA) approach to learning.
All bar modelling starts with the part–whole model. These simple diagrams help learners make the jump from relying on concrete resources to thinking pictorially. Part–whole models are a great way for learners to make sense of a problem and decide which operation they need to use and why.
The part–whole model (sometimes called the part–part–whole model), is a simple pictorial representation of a problem that helps learners see the relationships between numbers.
A horizontal bar shows the ‘whole’ amount. Underneath it, an identical bar is divided into pieces to show the ‘parts’ of the whole. Here’s how to use a part–whole bar model to represent a simple addition question.
Part–whole bar models show that you know some information, but still need to find some information out. The bar can be split into as many parts as you need, depending on the amount of information you’ve been given. If the total is unknown, you might see the ‘whole’ bar replaced with brackets and a question mark.
Maths lessons should always start with handling and exploring concrete items. Get your class to line objects up as they add and subtract with them. Make sure they can count with accuracy.
When your learners are ready to move on to visual representations, start by keeping one-to-one correspondence with connecting cubes. Learners should see that each cube is a representation of the physical object. Making each part a different colour helps children see that they’re different pieces of the whole.
Next, show the equivalence of the parts to the whole bar. You could, for example, make a ten-cube bar just using red cubes. Or make another bar using eight blue cubes and two yellow ones. Now it’s easier to see that the two bars are equivalent to each other. You can rearrange the bars to make number sentences.
In time, you can draw a bar and display it alongside the cubes to help your learners to see a fully visual representation. Move away from one-to-one correspondence by working with larger amounts.
Learners will soon see that it’s far too cumbersome to use cubes or draw individual squares for a calculation like 25 + ? = 60. Ask them why you might use a smaller bar to represent a much larger amount.
Problem solving is always going to be difficult for primary learners. Applying mathematical knowledge can be hard when learners don’t understand which operation they need to use. A part–whole model shows learners the problem in an accessible way.
Part–whole bar models are ideal for:
They’re particularly useful for time and measurement problems as children often find these problems challenging.
Part–whole bar models are a simple way to show word problems with a missing number element. Addition and subtraction questions are useful for demonstrating that you can break bars into unequal sizes.
Example subtraction questions:
Learners need to know that a bar must be cut into equal parts when multiplying and dividing. Use a different colour to show any remainders.
Example division questions:
Part–whole bar models are perfect for visualising problems using fractions and percentages. Learners often find these hard to solve because they struggle to work out what the question is asking them to do.
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Using bar modelling is a simple step towards algebra. Equations like 3a + 7 = 25 are easy for learners to visualise because they’re familiar with finding an unknown amount.
Bar models are useful, but they’re not the end goal — nor the only way to visualise word problems. Eventually, your class will move on from drawing out the bars but can always return to them if they need to. Use them as a bridge to move from concrete to abstract understanding.
Bar modelling is fast becoming the favourite approach for teaching problem solving. They’re easy to draw, simple to understand, and require no equipment. Plus, you can use them to tackle a huge range of maths questions.
Why not give it a try with your class? You could be surprised at the level of understanding your learners can demonstrate, just by using this simple visualisation tool.
Classroom Assessment
