A Box of Buttons – Visualisation
For this topic, we used one of the In Focus tasks in the textbooks, which shows pupils a box of buttons and three additional buttons outside the box. Even those pupils who we had previously identified as struggling learners, were instantly able to notice that there were two groups of buttons in the picture and that we were going to need to find the whole.
Without pressure to count on or create a number sentence mentally which can, especially in a whole-class context, be a daunting prospect, they were able to focus on and even explain the mathematics in the problem. This gave them the chance to develop their understanding further and crucially, also allowed us as teachers to understand their thinking.
For example, there is a girl in one of the classes who finds one to one counting a struggle and is unable to confidently count to 10. When she is given a problem with an accompanying number sentence she panics, especially during a whole class input, and will often wait for one of her peers to answer for her. However, when we showed her the button problem and asked her to share what she could see and note how many there were, she was able to confidently tell the class that there were some buttons in the box and some buttons outside of the box and that she thought we might be able to work out how many buttons there were altogether. She was able to articulate her understanding of addition as adding two parts making a whole without the worry of counting or estimating.
Having determined as a class what we were going to be solving in the lesson and which (of several possible) methods we would be using, in this case a number line, we then moved on to solving the problem.
Prior to teaching this lesson, we felt confident that pupils would understand and be able to independently apply the skill of using a number line to ‘count on’. However, we found this was not the case! We noted that despite most pupils immediately solving addition problems by counting on in their head or on their fingers, they were unable to apply this on a number line. The first method pupils used was to circle both numbers within the number sentence and count the difference. Interestingly, they were not able to justify this method and had simply found (identified) the two numbers they could see in the picture. This could be corrected relatively easily as it was not a misconception, merely a lack of understanding.