Just the ‘HARD’ Facts!

Let’s talk high-leverage MULTIPLICATION FACTS…

No more huge mountains to climb! It's not an infinite amount of unknown facts your learner doesn't know - it's only a small number! 

Here is a different way, that tries to build up from the multiplicative connections between the facts and deliberately avoids any  addition/subtraction/skip-counting approaches, so as to build on the multiplicative structure of the tables and work more in harmony with that.

Hear me out… What if (and stick with me here) the highly strategic order in which we teach the tables, however carefully we plan the sequence, was not ideal. Why not try exploiting the mathematical structure of the tables a bit more strategically!

I've taken some inspiration for this from Colin Fosters Mathematics Educational BLOG.

Here's a quick 'how to' guide:

 

So, this now leaves just 21 FACTS to learn  (because of the commutative law) which need some teaching. And these are the tougher ones!

Here’s the order that I would teach the rest of the ‘hard facts’. It’s rainbow coded ROYGBP (like the rest of our resources).  It’s certainly not prescriptive but I've found it a really impactful with my learners and own children. You'll notice that I recommend using small sets of interconnected facts: 

 

These are the FACTS that are contained in our  JUST THE ‘HARD’ FACTS: Mastering Multiplication Intervention and Recovery pack. 

• 42 DOUBLE SIDED, A7 FLASHCARDS includes FOUR different SUITS.  Each double sided card encourages relational thinking rather than answer getting. 
• Each pack is supplied in a calico drawstring bag. 
• Printed on 300g recycled, brown kraft card. Doing Mother Nature Proud - We’re big fans of this planet. We've gone PLASTIC FREE! This resource  is not laminated.

 

With multiplication facts, it’s much easier to use facts you’ve already learned as “stepping stones” to the harder facts rather than to memorise them by rote.

Once your child has learned how to use stepping-stone facts for a small set of facts, focus on just those specific facts for several days. Use a mix of practice techniques to give your child some variety and make learning multiplication fun!SA

Once your child has mastered the new facts, it’s time to mix up those multiplication facts with the facts they have already mastered. Mixing them together provides cumulative review so that the facts are cemented in the long-term memory.

Here’s where I suggest you start: 

Mental doubling and halving may need some work, but it is very important. None of these scalings are  hard to do quickly mentally, as none involves any 'carrying'.

 

 

 

Then there is 28 and 56 (in pink below), where 8×7 is just double 4×7 (which is just double 2×7). 

With practice, figuring out something like 7×8 by saying ‘double 7×4, which is 28, so that's 56’ can be extremely quick, and the more you do this the more you are incidentally practising doubling. (And this is one of the trickiest ones, because doubling 28 involves a mental 'carry'.) 

I really do think that where a learner has tried to learn the multiplication bonds and has repeatedly failed, then this kind of approach may be helpful. Here's a downloadable version of MASTERING THE HARD FACTS:

 

I think it’s worth mentioning that when learners practice their multiplication facts, they’re expected to move from concrete to abstract too quickly.  This takes time!!! Moving too quickly forces memorisation and avoids any possibility of multiplicative thinking.

 

1. What are your best strategies for teaching the multiplication tables? Do you work differently with older learners who have previously been unsuccessful learning their multiplication tables? 

2. What are the pros and cons of the different approaches you have tried?