Following this post, I’m blogging some lesson ideas which address some of the problems with how mathematical modelling has been taught in primary schools.
I asked my class “What questions pop into your head?”. After the expected “What is that man doing to that poor giraffe?”, we got some interesting ones.
What is the difference in weight between the man and the giraffe?
How many baby giraffes would weigh the same as an adult giraffe?
Now, I had an objective for this lesson, but I didn’t say anything about it straight away. I wanted my class to be able to read scales, but saying this at the beginning can kill lessons stone dead. Instead, I had a question of my own.
How much does the baby giraffe weigh?
Here we had to clarify why they can’t just put the baby giraffe on the scales. I asked them for an answer. Someone should say that they need to know more, but just in case, I asked them “What information do you need to know to answer the question?” I questioned further, asking what they might do with that information or why they think it’s important. We settled on the necessary requirements-weight of both man and giraffe, and weight of man alone.
I told them I didn’t know these weights, but I did have pictures of the scales when this was happening. But before I gave this to them (different scales for different children) I made sure that they knew how to read the scales. I modelled how to work out the size of the intervals; we recorded the success criteria, they practised on unrelated scales.
Then, they returned to the giraffe problem. I gave them the information they asked for earlier. The children worked through the problem, some quickly, some slower. At this point I had some related, but differently worded problems as ‘sequels’. Yes, these were more like the traditional word problems, but the children knew very well the context by now. Here are some of the prepared questions.
An adult giraffe weighs 3 times as much as the baby. Weight of adult and baby together?
In a year’s time the giraffe is weighed again. The man weighs the same but the giraffe’s weight has increased by 10%. Weight of man and giraffe? Weight of giraffe?
Also, the good quality original questions that children asked at the beginning could be answered.
Here, I could also formalise the lesson – talk lesson objectives and work on the accuracy of mathematical vocabulary. Name the lesson.
This way, there is little literacy demand at the beginning of the lesson. The purpose is made clear from the outset before any maths is introduced. The children were not simply given information; they had to work for it. I directly taught them how to read scales and they practised. They had a variety of question types.
With thanks to @ddmeyer for the concept of 3 Act Maths. This is far from polished and there are further opportunities to develop. I haven’t developed yet how to show children the answer to the original question. Seeing is believing and it validates the maths that they have been using.