Many of us know that 12 x 12 = 144 as a snap fact, but children learn to break it down as follows:
(12 x 10) + (12 x 2) = (120) + (24) = 144.
If we were to then ask the child what 24 x 12 is, their response would be
24 x 12 is twice 12 x 12 and so the answer is 144 + 144 = 288.
Children’s ability to stretch their mind and do higher order computation is because they are able to draw from a variety of strategies (multiplication/ distributive property/addition etc.) to respond to a question rather than rely on rote/memorization. I can say with certainty that most adults will have to whip out their pens and do long multiplication to solve 24 x 12! Also if you were to learn 1,2 …10 times table by rote, that will be over 100 facts to memorize. Hardly an efficient strategy!
So, here are some of the strategies we have been using in class to help with multiplication proficiency:
1. Facts that have 2 as a factor are equivalent to adding doubles (children already know this from their addition facts).
2 × 6 is double 6 and so is 6 × 2. We cemented the understanding by using word problems – for example, Every bicycle has 2 wheels. If there are 8 bicycles, how many wheels in all?
2. Skip counting for learning 2s, 5s, and 10s tables.
3. Using Identity property when multiplying by 1 and zero property when multiplying by 0
4. When you multiply any number by 9 you can use a pretty nifty trick: Hold up both hands (palm facing outside). Starting with the pinky on your left hand, count over for which fact you are doing. For example, for 4 × 9, you move to the fourth finger (your pointer). Bend it down. Look at your fingers: You have three to the left of the folded finger representing 3 tens and six to the right—36! (Barney, 1970).
5. Solve problems using commutative property: if you know your three times table well then you will know 3 x 9 = 27 is the same as 9 x 3 = 27. So as you progress along the 4,5 6 tables, you have already completed many of the facts for the 7, 8 and 9 times tables (e.g. 6 x 9 = 54 means you know that 9 x 6 = 54)!
Using the above strategies, 75 of the 100 multiplication facts can be covered and is a much better way to learn and retain than trying to memorize 100 separate multiplication facts.
Still, watching your 8 year old take a whole minute to solve 8 x 6 may irk you! And if you do want to improve their speed, here are a few things you can do (introducing drills at this stage will help with their speed/agility without compromising on their understanding):
1. While you walk your child to school, ask them 7 random facts (I found 5 to be too few and 10 was way too much. But you can pick a different number if you don’t like 7!). If they get any fact wrong, make sure you include that as part of the next day’s drill.
2. Quiz them on the “squares” – 8 x 8, 7 x 7, as these are special numbers that will help them learn exponents later on.
3. Here are some youtube videos that you could play for your child when you are snowed in or while you are in you car driving them to that next weekend getaway : https://www.youtube.com/watch?v=qxICbEQCS1s
Do you have any other strategies/videos you would like to share with the group? Please share in the comments section below.
PS: Love the book “ Elementary and Middle School Mathematics- Teaching Developmentally” by John A. Van De Walle – one of my favorite teaching resource!