19 June 2019
###### Talking Maths in Public
12 September 2019

# Multiplication facts matter

Fluency with multiplication facts makes learning later skills easier. When simplifying fractions, it is helpful to know multiples of numbers. When learning division algorithms, fluency in the basic facts means that the brain is free to learn the new procedure. In algebra, it is extremely helpful to be able to recognise common factors of two numbers, such as 36 and 24. Being fluent with multiplication facts is invaluable for estimating in many areas of life. A recent survey of high school teachers reported that they value knowledge of tables highly.

## Parents helping

The advantage a parent has over the class teacher is the opportunity to work one-to-one with a child. However here are multiple traps in parents helping their children. Maths anxiety is catching. If you have a bad relationship with maths, it can be difficult for you to mask this so that it does not pass on to your child. This is particularly important for mothers with daughters, as this has been found to be the relationship that best transmits and maintains intergenerational maths anxiety. As a parent you need a growth mindset around mathematics. “I used to find mathematics difficult, but I know if I work at it, I will get better and so will you”, is a much better message than “I was no good at maths and you get that from me.”

Conversely a parent who has a particular inclination towards mathematics can also be intimidating to the child. It can be difficult to be patient when you have no idea why they are finding something so difficult. This impatience is counter-productive.

Another problem is that the child may be taught in school in a way that makes no sense to the parent and teaching the “old-fashioned” way may confuse the child or annoy the teacher who is trying to embed a different method. When it comes to long addition, multiplication or division, parents are best to find out what method the teacher is using and try not to teach tricks. (see Nix the Tricks)

## Fluency is not speed

Many of us have emotionally charged memories of being tested for multiplication facts and worrying that we would be too slow. It is very helpful for learners to gain automaticity with multiplication, but speed tests do not develop speed, nor do they test for fluency.

Flash cards are ok – it’s what you do with them that matters!

The nice thing about flash cards is that you can choose just a few to focus on and you get instant correct answers. Speed is NEVER important. Using a timer creates anxiety and blocks the kind of thinking that is needed. I am fluent and confident with my mathematical facts but put a timer on and that is all I can think about. How much worse is it for learners who are already struggling?

## Learn in the best order

A commonly encouraged order to learn your multiplication tables are: 2, 10, 5, 0, 1, squares, 3, 4, 6, 8, 9, 7.

The foundational facts are the 0, 1, 2, 5, 10 and squares. Do not move on to the other tables until these are mastered.

From these foundational facts, the other facts can be built up. Three times is two times plus one time. Four times is double then double. When learners build on a foundation, their understanding grows at the same time as mastery. Learning unconnected facts by rote does not help long term conceptual understanding, and the facts are more easily forgotten.

## Stories are important

Stories help us to understand what is happening with multiplication, and having a sensible context makes very wrong answers more obvious. Here are some examples of multiplication contexts that can occur around the home.

• “There are three children in this family. I need to make enough cookies for one each day for each of them for a week. How many cookies am I going to need?” “What if I need two each for each day?”
• We have two pets and each pet has four legs.
• How many legs altogether on the table and chairs?
• Every day for the next five days I am going to walk for twenty minutes. Is that going to be two hours altogether?
• We are having KFC and want two pieces each. How many pieces?

Multiple card showing arrays of sixteen.

## Meanings of multiplication

The first way children are introduced to multiplication is the idea of equal groups. Two equal groups of ten blocks gives a total of twenty blocks.

Another meaning is repeated addition. Adding four fives together is the same as multiplying four times five.

Arrays occur when equal groups of items are arranged in rows. We would think of 2 times 5 as being two rows of five objects. We use this representation in our Multy Facty resources, poster and game.

## Equipment helps understanding

Our free resource helps develop number sense

We all have access to objects for rearranging. I like milk bottle tops, but Lego bricks, counters, stones and beads are all good for counting and arranging.

Take a number of objects – for example 21 and count it in different ways. Can you count it in twos? There is one left over. Count in threes, count in fours. Rearrange in arrays and in groups. This helps build number sense and the idea of “tidy” numbers and primes.

## Practice using games and puzzles

Mastery requires substantial and enjoyable practice.  Well chosen games help apply multiplication facts and procedures. We recommend our own game Multy Facty, which embeds mathematical principles into the game and develops fluency. Well-designed games encourage flexible use of number facts and remove the pressure from “doing tables”.

## Personal note and confession

I was not a good maths parent for my older son, W. His father and I both had mathematically-oriented careers so it was a mystery to us that he did not seem to grasp mathematics as intuitively as we did. Sadly I did not keep that to myself. I can not remember doing much except helping with algebra when needed. He was grateful then to have a maths teacher for his mother. W edited many of my statistics videos and managed to stay wilfully ignorant of most of it.

Our other son, J, is blind and autistic. He could subitise (tell how many something is at a glance) with his fingers at a very early age, and is a calendar counter who can tell you the day of the week of any date. He was also remarkable at converting between ways of expressing time – we would say 6:45 and he would say quarter to seven. My greatest mathematical teaching achievement with J was teaching him to solve linear equations.

How have you helped your children with maths?

Let me know in the comments below.