It might be good to introduce (or re-introduce) the idea of the multiplication grid first:

before adding some negative numbers into the mix:

Here are some more to practice:

Some more ideas for this topic on Resourceaholic here.

It might be good to introduce (or re-introduce) the idea of the multiplication grid first:

before adding some negative numbers into the mix:

Here are some more to practice:

Some more ideas for this topic on Resourceaholic here.

These only cover adding and subtracting negative number, i.e. they can be used before going onto multiplying and dividing negative number.

They can be printed (here is the pdf), cut out and then stuck on A3 paper under the three headings with examples and counter-examples to explain why they have been put under that heading.

I should point out that two statements on here are deliberately vague, i.e. “two negatives make a positive” and “a positive and negative make a negative”. This is often how students remember them and this can lead to problems down the line (e.g. the misconception that -3-2=5). My idea with these is that the end up in the “Sometimes” column but ultimately we dismiss them and not being very useful.

Here is a simple task which would work well as a starter which practises negative numbers at the same time as (hopefully) leading into a nice discussion about sequences and term-to-term rules.

I created this on a spreadsheet here, so you can change the questions or the order. If you are feeling ambitious you could do this with decimals or fractions, or also include multiplication, which would generate quadratic sequences.

And here is another one which basically just seeks to reinforce the idea of what “n” means by substituting it into nth term expressions.

I made this a while ago for supporting Year 7 students on directed number (i.e. positive and negative numbers). I think there is something more intuitive about a vertical number line – if you are adding you go up, subtracting you go down. Having said this, I have always had a horizontal number line across the top of my board!

If the number line is stuck on the inside back cover of the exercise book, it is always there whatever page the child is working on. It can then be folded safely away whether using large or small format books.

Doing some work in primary this week, I realised that the same idea could be useful for supporting younger children learning the essential skills of counting back and counting on when doing addition and subtraction of positive numbers. So I have made another version just with positive numbers.

The end points of these lines are arbitrary of course. I have deliberately gone for something a bit random to start a discussion, *“Sir, why does it stop at 44?”. *But if that offends your preference for order in life, then feel free to adjust it on the spreadsheet that I used to create the pdfs in the first place.

Vertical number line to stick in books.xls

Vertical number line to stick in books zero to 44.pdf

Vertical number line to stick in books minus22 to plus22.pdf