Making and Breaking the Whole
Linking the Four Operations
I've written before about the importance of children establishing a good understanding of the connections between the four operations : adding, subtracting, multiplying and dividing.
The adults working with our children also need to feel confident about this! Most primary teachers are not maths specialists, and it has become clear to me through my work with trained teachers that many are in the unenviable position of teaching maths with only precarious foundations themselves.
This poster has proved a useful talking point in teacher training sessions. It pushes at the edges of knowledge in different ways for different people.
For some, this poster helped establish the basic idea that multiplication and division is all about combining or partitioning into EQUAL parts.
For others, the challenge was unpicking whether they were comfortable with describing this bar model with two different division equations. If so, how would they verbalise each of the two division equations?
With that group we went on to consider whether teachers (and ultimately students) are equally comfortable with verbalising the two equations as
12 split into 2 groups
and
12 split into groups of 6.
The next question was then: are you confident to say which is the so-called grouping model and which the so-called sharing model? We then talked about the terms partitive and quotitive division.
For another group, the poster sparked a discussion about the idea that division is about breaking a whole. Is that actually an adequate description? When does it become unhelpful? We ended up talking about scaling and the limits of the repeated addition/repeated subtraction model.
This poster is a resource which bears revisiting with teachers and students because it provokes and challenges and the discussions which follow stimulate thinking and deepen understanding.
A useful exercise would be to get students, or for that matter teachers, to recreate the poster, or even better, to create their own mind map for what the four operations are, and how they are linked.