Exploding Dots/ Touch Decimals

I am a maths teacher based in Devon, England.

One of my classes is a Year 7 and 8 nuture group, a collection of around 7 students with various SEN needs from the Year 7 and Year 8 cohort. They are working to P-standards, or possibly (the old) level 3.

The first thing to say about them is that they are lovely. I have seen a lot of posts and read articles that insinuate that there is a link between behaviour and SEN. These students debunk this link totally.

Most of my lessons with this group are focused on life skills; basic numeracy, using money, measurements. Recently I read on twitter about a teaching idea that I had not come across before exploding dots/ touch decimals: https://twitter.com/macajo/status/1002070280909488128

It might be that my implementation of this is not correct, so apologies in advanced to https://twitter.com/macajo et al, if this is not the correct method.

I wanted to start by getting the students to add some numbers, and using Craig Barton's Minimal Variation (found at https://www.amazon.co.uk/How-Wish-Taught-Maths-conversations/dp/1911382497).






The important point for the students was for them to line up their units, tens and hundreds properly, which most of them did well. As there is little variation in the questions the students were able to concentrate on the lining up and not worrying to much about the actual adding.



We then looked at using boxes and dots to help with the maths. This stage took a long time, and I had to resort to dressing the question up in terms of money. What is the first column when using money; yes pence; what should we call pence when doing calculations; yes units. Then we were able to label the other two boxes relatively quickly, tens and hundreds.



We then discussed how many dots you can put into a box. This was a difficult question to answer, but I feel that might have been because of the way I was asking the question. With the nuture group I need to ensure every question is clear, this is something I would like to look in to for a later blog - how to ask the right type of question for a (lovely) low ability group.

As soon as the students got the hang of nine dots, then the next dot means wipe out the dots in that box and put one dot in the next box up. In retrospect I should not have started with the units column as I needed to get over the point that this process applies for every box, not just the starting box.

On the image below you can see that I have counted up to 9 with the students (top row), then, after our discussion, I have wiped out all the dots in the units column and put one dot in the second row.






Unfortunately I did not take a photo of the next stage, which was to discuss what happens when we move to the right of the unit box. This was a real part for the students to learn, i.e. the names of the boxes before the decimal point. But once they had seen the names they were happy, and they understood that the boxes still behave the same way, 10 dots in the box to the right? then erase these dots and put one dot in the next box up. Below is an example of work from a students book.

With this group I decided that it was better to leave a box blank if there were no dots in it, but when translating it into numbers the students understood to replace a blank box with a '0'.

We then moved onto adding involving decimal numbers. For each sum we used three rows, one for each number we were adding and one for the answer. The students spotted how to do the addition quite quickly, they put a dot into the box in the third row for each dot in the first two rows. They were then able to quickly replace 10 dots in one box with one dot in the box to the left. This meant that the final part of the sum for them was to translate the number of dots into numbers. The progress made was tangible, they would not have been able to add 3.62 to 13.62 as efficiently and error free without these dots (last image).



This is my first blog; hopefully it will not be my last. I am always looking for feedback/ constructive feedback, especially if there is someway of me teaching my students in a better way. For example, does anyone have ideas on asking the right type of question for low-ability students?



My twitter account:

https://twitter.com/Maths_Devon