Formative assessment, developmental stages and starting the year well
The goal of formative assessment should always be to find out what each student NEEDS next, rather than focusing
Teachers often tell me how hard it is to get their students to understand subtraction.
I’ve been reflecting on this a lot lately while writing my new Back to Front Maths books and had the opportunity to develop and try out a new strategy for written algorithms that also works with blocks. The classes I worked with found it far easier than regrouping and it also transfers later to negative numbers, making it ideal for kids who are older and still stuck. This model uses the concept of “difference” or “comparing” rather than “take away”.
Let’s work through an example: 45 – 17
In this model, we start with a table. On the left is Have (+) and on the right is Need to subtract (-). We place the 45 in the “have” column” and the 17 in the “need to subtract” column so that we can compare them and find the difference.
Next, we find anything in common and remove it. We record what is left to do beneath.
If anything is left, we can regroup as needed and repeat.
Drawing helps solidify our thinking and builds mental models for abstract concepts. To represent our subtraction model, we would draw 45-17 and record our thinking like this:
If needed, you could also draw the second step using a different colour, by circling the 2 and the 2 in the 30:
This model does not formally introduce integers, but it is a good in-between step. It is also very efficient and easy to understand.
When using integers, it is very easy to use the same strategy. Let’s try it for 17 – 45
If needed, you could also draw the second step by circling the 2 and the 2 in the 30.
I hope that your class enjoys using this method as much as mine did!
Tierney
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