### Decimals Revisited

I recently bought a class set of overlapping decimal dart cards for the department - this pdf link is essentially the same resource.

I used them today with a class of 14 yr olds, all of whom have been working with decimals for at least two years, but none of whom were able to correctly order this list of decimals at the beginning of the lesson:

0.26
0.102
0.2
0.8
0.13
0.7
0.34

I did not tell them the correct order - just that none had got it right.

I handed out the decimal cards and started by asking them to hold up the one that would go exactly half way between 0 and 1 on the numberline I had on the board. 100% success.

I then asked them to show me whereabouts on the line 0.1, 0.01 and 0.001 would go.

We discussed this for a while, corrected some misconceptions, and moved on with the idea under our belts that 0.1 is small, 0.01 is tiny and 0.001 is incredibly tiny!

I then asked them to hold up the decimals that represented 4 tenths, 7 hundredths, 3 thousandths etc. All got there after a bit of discussion.

I then asked them to make 0.327 by holding together three of the cards (0.3, 0.02 and 0.007). Again they got this after a bit of discussion, and my clarification that it wasn't okay to use .3, .2 and .7, because these are all tenths. We did a few of these.

I then asked them to build pairs of numbers, think about the values of the cards that made them up and decide what order they should go in: 0.5 and 0.23, for example. Lots started by saying that 0.23 is bigger, but all realised once they built the decimals that 0.5 has 5 tenths whereas 0.23 only has 2 tenths, so 0.5 is bigger.

We had another go at to the ordering of the list at the beginning. All of them put them into the correct order this time.

One boy, who was clearly experiencing some turmoil with the final ordering task, eventually said "oh, I get it now!" and rapidly put them into the right order. Afterwards, he said "it's like alphabetical order isn't it? You put them in order by the tenths, then you look at the hundredths if the tenths are the same, and so on." This from a boy who had been indignantly adamant 10 minutes earlier that 0.102 was bigger than 0.8. His algorithm did suggest that he had maybe seen a rule to get the right answer rather than really understanding, but I was happy to take the win!

I can't wait to give them some decimals to order after the half-term break, to see if they have retained their new understanding.