“Surely 3.12 is a lot bigger than 3.2 because 12 is bigger than 2…!” said one of my students the other day. I do see where students are coming from with this misconception and you can dive into place value and talk about hundredths being smaller than tenths, but another model that I’ve found successful is the “zooming in on the numberline” approach:

This approach gets them to realise that when we need a number between 3.1 and 3.2 that we break the numberline down into ten more increments by putting another digit on the end.

I found this approach useful when it comes to rounding to decimal places and you’re trying to get them to spot which two numbers the number could round to, for example 3.453 could round to 3.4 or 3.5 to 1 d.p. They then know that 3.45 is half way between the two so it rounds up to 3.5 …

Generally I have found this approach to be more successful than talking in terms of tenths and hundredths with pupils who don’t find maths easy. Do you know any others? If so share them in the comments!

Have you seen this iOS app?

https://itunes.apple.com/us/app/motion-math-zoom/id451793073?mt=8

It is an intuitive and fun way to zoom in on the number line. My kids love it.

This model is a great idea. I can imagine it would really help students to understand the idea of precision on the numberline and what it means to keep on extending digits after the decimal place.

In terms of getting students to understand the size difference of 3.2 and 3.12, I took my students through a stage process of concrete, visual, abstract. For Concrete, they created the decimals with blocks and counters on a place value mat, comparing the number of blocks in each place value column. The next stage involved just writing 3.2 and 3.12 in a place value column and comparing the numbers in each column.

Then after mastering these stages, they solved the problem in a more abstract sense, just looking at the 2 numbers themselves and determining size.

Great idea. Check this out for an interactive version of the same thing.

http://www.mathsisfun.com/numbers/number-line-zoom.html

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Couldn’t agree more – so effective. You may have seen the primary national strategies interactive teaching program’s (ITPs) they have a fantastic one that does exactly this. I love them! (Number dials is my favourite!)