There are three non-negotiable skills that a child needs to succeed at high school maths:
- counting
- addition
- multiplication
Now, that list may seem overly simplistic but it really is at the heart of what every child needs succeed in higher level maths. In fact, even the dreaded algebra is really just basic arithmetic (adding, subtracting, multiplying and dividing) mixed with a little bit of logic and a dose of abstract thinking.
The reason most kids fail at maths beyond year five (when fractions and percentages start becoming the focus) is that their basic arithmetic skills have not been truly mastered. As a tutor, I’ve seen it more times than I can count.
The cognitive load problem
Now, what exactly does a child need to be able to do?
To succeed at maths, children must be able to count accurately and reliably without consciously thinking about it. They should have a fairly decent grasp of the addition facts to 20 and total instant recall of the addition facts to 10. Similarly, they should near instant recall of all the single-digit multiplication facts to 100 and be able to multiply any number by 10. (So a 10 × 10 multiplication table.)
Why the emphasis on instant recall?
It’s a simple fact that has been established by recent research on cognitive load: your brain can only deal with one thing at a time. So, if your brain is engaged in a long algebraic proof, it doesn’t have space to deal with adding or multiplying two single digit numbers. If you don’t know those facts instantly, you have to “park” the logical problem solving train of thought and switch over to a basic calculator mode then back again. Even if you did stop to do that calculation on a physical calculator, you would have lost your train of thought to do so.
The humble number bond
So, how do we get our kids to learn how to add, subtract, divide and multiply like math ninjas? One powerful resource is the humble number bond. Number bonds may seem like a new idea (and on the Australian Curriculum, they are the relatively new kid on the block) but they were actually invented over 100 years ago and you’ll find the basic idea in many old arithmetics.
So, what is a number bond?
A number bond is a way of thinking about related number facts that not only makes the addition and multiplication tables easier to memorise, but also makes the relationships between the facts much easier to see. This does more than just remove the road block to learning algebra down the track: actually lays the foundation for algebraic thinking. Total win-win!
There are many ways to draw number bonds but in Milestone Maths they look like this:
The equations shown below the number bonds above are what is often called a “fact family.”
The secret weapon
Now, number bonds are a great way to teach the concepts but number bond flashcards are the secret weapon that will supercharge your facts practice.
The Milestone Maths number bond flashcards have the number bond diagram on the front and the “fact family” equations on the back. That makes them ideal for self-directed practice. Your child can choose a card at random then write the fact family associated with it on a piece of paper, whiteboard, or whatever surface takes your fancy (maybe even the car window on a cold morning!)
You can also use them as traditional flashcards with a clever twist: you can mix up the teaching of addition and subtraction almost without your child realising it. The trick is to show the front of the card to your child with one of the numbers covered with your finger. Your child can then tell you the number that is missing.
Number bonds have so many teaching and learning advantages that we use them extensively in Milestone Maths, even when the numbers get big.
Want your own flashcards?
Would you like to try these ideas with your very own set of number bond flashcards? Check out the resources section of our shop where there are several options, including a free download!
