Delicious Decimals!

Today I took four of my top students (for maths) and did a half hour session on decimals. 

Although they don't necessarily NEED to know about decimals at this level, these students have the mental capability to understand this concept and actually have been asking to learn about it for a while..

Sue modelled to myself and another teacher Kaveeta last term how to use Decimats. I had never heard of these before, so was quite intrigued by that session. So for today's decimal session, I printed my own decimats and used them with the kids.

Firstly, we established what was one whole. These kids have a very solid understanding of fractions, so all I asked them to do was cover their 'whole' with the light orange squares. One of the boys instantly said 'these are tenths because ten pieces altogether make up one whole'. Amazing! The decimats afforded a visual way for the kids to see that the ten orange pieces did indeed cover/make up the 'whole' (the white piece of paper). We kept the 'whole' piece under our work all the time to remind us that with fractions and decimals, we are talking about something that is smaller than one whole.

Once we had established that the light orange squares covered one tenth of the whole each, I wrote down the number 0.1. We talked for a little bit here, to ensure that we understood the 1 in this number showed one tenth, not one whole. If it was one whole, it would be 1. Having the numbers written down, and having the decimats at the same time really helped clarify this. 

Next, I gave the students some challenges...
(These I wrote down, not said allowed, to check if they understood the place value while written down)

Show me 0.8

Next, I tested them by asking them to work with their buddy..

After some initial 'huh?' about how they could show one whole number AND part of a number, they remembered that one whole is the same as ten tenths, so both pairs covered one 'whole' with tenths then used another 'whole' to show the 5 tenths/0.5... I was quite impressed!

Show me 1.3

Show me 1.9

Show me 2.5

Next, I introduced hundredths. I put ten small dark orange pieces on top of one light orange tenth. We talked about how that piece is EVEN smaller than one tenth, so the number must be bigger (i.e. one tenth is smaller than one fifth in reality, but the number/word is bigger - ten/five). 

After some discussion, and various illustrations, they clicked that ten pieces inside ten pieces must mean that there are 100 pieces - hence one hundredths. 

We did some 'show me...' using hundredths as well. Then we talked about thousandths. In all honesty, they got a bit lost here, but thats perfectly okay. Their minds had already been stretched so much in the past 20 minutes I wasn't going to go on and on about thousandths (and they don't need to know about them for Stage 5 maths anyway!). 

Then we did some 'show me...' using all the different types of paper/decimal place value. 

I would write down the number e.g. 2.43 and not explain it or give any hints. They worked out and discussed between themselves what the numbers meant - 2 whole, 4 tenths and 3 hundredths. Then they would use the paper to illustrate it.
Then I would ask them to explain it to me...

I was so proud of these four for pushing themselves to understand how decimals are connected to fractions. We hadn't talked about fractions in class for a few weeks (ala the school holidays) so it was hard and fast revision for them to get tenths so quickly. They definitely need more practice to truly understand the concept, and I would have liked to do some addition/subtraction of decimals using the decimats as well, but the curse of the lunchtime bell... Oh well, next week!

The decimats, just like when Sue used them, were a fantastic way for the kids to visualise how the pieces got smaller and smaller, even when their 'name' (e.g. hundredths) got larger. I will definitely be using this resource again, it was great!