Thread by @ThatMathsMan

🧵 A short thread for primary teachers about x tables in maths...

This afternoon I've been brushing up on my subject knowledge in preparation for a course I'm running about teaching multiplication and division bonds and I found myself considering several questions...
1/n

Q1. Should we call them multiplication FACTS or BONDS?

I'm trying to train myself into saying BONDS, not facts. Why?

Just as each number bond for 10 is connected, the same is true for the factors and products in the multiplication grid. There's so many connections. Bonds!
2/n

Q2. In the 2x table, for instance, is 2 the multiplier or the multiplicand and does it matter?

Although the product is the same either way I think it does matter, because it's the distinction between thinking "2 multiplied BY of A, B, C etc." or "A, B, C... multiplied by 2."
3/n

If we are learning the 2x table as "2 is multiplied by A, B, C etc." then 2 is the multiplicand (the group size) and we are thinking about "What happens to 2 when I multiply it by any number?" and "If I share ... into groups of 2 then... " and so on.

On the other hand...
4/n

If we are learning the 2x table as "A, B, C... multiplied by 2" then 2 is the multiplier and we are doubling. 1x2, 2x2, 3x2..

So we're thinking about "What happens to any number when I multiply it by 2?" And "If what happens to ... when I share it into 2 groups?" and so on.
5/n

I think it's important to do both.

You could begin by thinking about the 2x table as multiples of 2 and record this 2x1, 2x2, 2x3...
make and investigate the patterns created by lots of 2. Then move onto multiplying by 2 and noticing what's the same and what's different.

6/n

(Btw I recognise that there's not a universal agreement whether its 'multiplicand x multiplier = product' or 'multiplier x multiplicand = product' but the former is the convention in the Y4 statutory assessment in England)

Q3. When learning a new times table, what language do your teachers and assistants mainly use to introduce the bonds?

Personally I don't like "2 timesed by..." and would suggest "2 multiplied by..." and encourage parents to do the same at home. What about you?

7/n

By the way, over time I would describe and represent the bonds in a variety of ways.

Q4. How do you represent the patterns in multiplication? Is there one or more agreed representation you use for each x table?

I'm a fan of dominoes and then arrays.

How about you?
8/n

Q5. Which order do you teach the bonds in?

This is a decision that some schools leave to the NC, or choose to copy the DfE's non-statutory RTP criteria.

Whatever you decide, this will make a difference to how you make connections between bonds and see related facts.

9/n

Finally, Q6. Once bonds have been introduced, how do you develop retrieval strength?

I find a combo of practices help, e.g., games, chanting, low stakes tests ... where retrieval practice is scheduled. (Yep like @TTRockStars)

Whatever you do, know why you do it.
End 🧵

If you'd like a little reading, check out the ATM and MA expert group position statement, the NCETMs articles about whole-school approaches, and search on YouTube for Robert Bjork retrieval strength. Interesting stuff.

(I can add links later)

If you are interested in attending a three-part online (Zoom) course about teaching multiplication and division bonds, get in touch with me to find out about availability etc.

@threadreaderapp please unroll this thread. Thanks!

Reading
ATM
atm.org.uk/Maths-Book-Rev…
Cambridge Espresso cambridgemaths.org/espresso/view/…
NCETM
ncetm.org.uk/features/six-r…
Bjork
golectures.com/index.php?go=s…