This is the first in a series of blog posts about how to systematically teach problem-solving skills using I See Problem-Solving, outworking the EEF research (recommendation 3) about using rich problems to learn mathematics.

Here’s the task that the class were given part-way through the lesson:

Before we get to this point, I want to break down the sub-steps involved in answering this question. First, a little pre-teach group are given this open task to bring back some prior learning:

Then we show the first part of the question that we are building up towards answering and these three example sequences. The children calculate (or spot) the first and then the second negative number in each sequence:

Now the children have a go at this short task. They identify that -4 is the second negative number in the first two sequences. I explain that, when writing the first two sequences, I actually started from -4 and added in equal steps, rather than starting from the positive number and subtracting (which would be more akin to trial and error):

Now the children are equipped to deal with the task. We work to find all the possible answers, noting that the sequence must decrease by more than 3 but less than 7. There ‘support’ prompt for children who need help, and some children also attempt the ‘explain’ or ‘extend’ tasks:

The free I See Problem-Solving Worked Example is used to show the three possible solutions. The following day, we pick up on a few misconceptions and look for ways to become more efficient, including looking at the example above and considering how we could add a multiple of 4 and 5 rather than the repeated adding.

I’m trying to make problem-solving accessible for all children, whilst ensuring that every child is challenged. I hope you find I See Problem-Solving super-helpful. The LKS2 and KS1 versions are in production!

Also in this series:
Equals Means Same As
Sum of the Digits Place Value Challenge

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2 thoughts on “Learning to Problem-Solve: number sequences and negative numbers

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