“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!