I use these a lot at the early stages of understanding of place value. In my opinion, place value is the single most important mathematical concept that children need to master in upper KS2 to prepare them for secondary school maths. Many don’t, so it is incumbent on secondary maths teachers to ensure that any gaps are filled in Year 7.
As a pdf. Or if you want to change things, as a Google Sheets or MS Excel file.
If you print them out on card, you can put them inside transparent A4 plastic wallets and then use mini-whiteboard pens to write on them. There are different types of plastic wallet – you want the ones that have relatively thick plastic which is smooth, not textured. Otherwise you will have a hard time rubbing off the pen!
- Show me 3 tens. Now show me Thirty. Why do we need to put the zero in there?
- Show me 5 tenths. Show me 5 hundreths. Why do we need the zeros?
- Show me 34. What is 34 made up of?
- Show me 6.75. What is 6.75 made up of?
From here, of course, you might want to look at multiplying and dividing by powers of 10 and then eventually 4 operations involving decimals. But don’t rush into that until you are confident they have secured a depth of understanding. These questions are good for really testing that:
For me these are a crucial AfL tool to ensure the building blocks are in place before doing more complicated things with decimals.
We are spending the first term with Year 7 on fundamental number skills to ensure solid foundations. This week, we are looking at subtraction. There won’t be any specific methods or techniques that they haven’t already seen at primary school, but I know the degree to which they have mastered these techniques will vary markedly within the class.
Rather than feeling daunted at the prospect of teaching them something they already know, I’m seeing this an opportunity to show them some (hopefully) cool maths that requires them to use and practise their skills.
My new school has a wealth of manipulatives which I have had little opportunity to use before. I’m looking forward to using dienes blocks to show why the column subtraction method works and why we cross out digits before embarking on the subtraction.
It’s not really “borrowing” it’s “re-distributing” one of the tens into the ones column.
Next up, Diffy, which I learned about from Don Steward’s blog post here. The post contains some great ideas on how to do it. I love a good spreadsheet so created this which does all the calculations for you! The real reason though is so I can give my students a chart to help them structure their Diffy calculations.
I really want to focus on clarity of instruction with this class. They are a typical Year 7 class who need instructions broken right down and economy of language from me. My measure of success will be the number of questions I get asked before they start!
There is more about Diffy in this great blog post from Colleen Young
I also really like these rquestions from Maths Mastery:
I shall insist on 100% silence, pens down and do a Think, Pair, Share on this. The “Think” will be 30 seconds in complete silence with a timer with pupils just looking at the calculations. I’m hoping for an excited rush of discussion once the 30 seconds is up and they are itching to tell their neighbour what they’ve spotted. Then they will check their hypothesis by actually completing the calculations in their books.
And finally the old classic 1089. Powerpoint slide here.