Charlie Harber is the Deputy Lead Adviser for Primary Mathematics at Herts for Learning. A passionate advocate of bar modelling, her last blog on the subject RUCSAC pack your bags, dealt with a KS2 SATs question. Here Charlie turns her attention to KS1 bar modelling.
In my last blog on bar modelling I used an example from the 2016 KS2 test. Subsequently, I had had a number of requests asking for a similarly worked example of a KS1 test question.
As I discussed in my previous blog, it is challenging for children to solve problems which start with ‘some’ as it gives them nothing to act on, leaving them floundering in the dark. Bar modelling encourages them to take a ‘leap of faith’. It provides a consistent way to deal with the information and even though we don’t initial know what the ‘some’ represents, we can give it form and act on it. To add to the complexity, the word half is prominent in the question, however we don’t half find the answer – we need to double. A word that doesn’t appear anywhere.
Let’s take it sentence by sentence, following my fundamental rule of bar model
When we get to some punctuation – let’s stop and think, is there any new information?
How can I add this to my model?
Is there another way I could add this?
Did anyone do it differently?
Abdul has some toy cars. By the way – who has toy cars that look like the picture? Not helpful!
OK so let’s just draw a bar to represent his cars. Make sure that the children do understand what we are doing.
He gives half of them to Ben. This really does dig deeply into their understanding of halving as we don’t have any numbers – it is checking that they have a generalised understanding of what half looks like. However, with the bar model they do have something on which to record the implications of the action.
He has four toy car left. Finally some numbers! So ‘Do we have some new information?’ Yes. ‘What?’ That he has four cars left. ‘Where does this go on the model?’
How many toy cars did Abdul have to begin with? Where is the unknown? Can they rephrase the question to make an answer sentence – with a space for the (in this case) numerical solution? This helps the children really identify what they have been asked to find out, also it helps them check the reasonableness of their answer.
The bar doesn’t tell the children that the answer is eight – but strongly supports them in identifying that they need to double the four. As I mentioned at the beginning, double is not used in the question, but half is.
They can then put their answer back into the answer stem.
By using the bar model the children can follow the actions of the story problem, acting them out as presented in a calm and systematic way. They don’t have to spot that it’s an inverse calculation right at the start – the bar model emerges along the way, exposing any misunderstandings of language and then supports the children in identifying the calculation required to solve the question.
Bar modelling isn’t a magic bullet, it won’t overnight give your children a super power, but it does provide a consistent, logical and secure approach to EXPLORING contextualised mathematics. I have seen the confidence levels of children raise again and again, from refusing to start to getting stuck in and talking about the different models in the room. And don’t even get me started on the language/reasoning outcomes…
At HfL we believe so strongly in the power of the bar that we have developed a year by year whole school progression from pre-operational learning to Year 6, addressing many of the learning statements and showing how you can use the bar not only to crack word problems but to challenge, support and to develop deep conceptual operational understanding (using the CPA approach) in maths.
Purchase HfL Bar Modelling Progression document here
Sample page from HfL Progression in Bar Modelling document