Number bonds are one of those things that seem to produce unusual passion and concern in young mathematicians and their parents.
The name's Bond, Number Bond (Image:Wikipedia)
Parents and students often ask us if we do number bonds, at Maths-Whizz, as though they are mathematical methods exclusive to the initiated few. Nothing could be further from the truth.
Money makes the maths go down...
Money can make the maths go down, to coin a phrase.
Since Britain’s currency was decimalised many of us have had their first introductions to base ten maths and decimal concepts in money.
Most children are likely to have got a basic grasp of the notion of pennies and pounds, and how they relate, from an early age. And children are likely to have understood this long before they are required by national curricula to have understood tenths, hundredths, performing operations on decimal numbers, and the like.
If nothing else, this proves that if there is a need and a daily context in which to learn, we can acquire complex skills without really realising. But it also gives us a useful tool when tackling calculating with decimal places.
Take the question “3.6 divided by 12″.
It sounds pretty tough to the unconfident. After all, 12 is larger than 3.6, which means the answer will be smaller than one, a decimal value.
Now take the question “£3.60 split amongst twelve people”.
Does the question seem easier? Suddenly it’s about a dozen students going Dutch on an order of poppadoms (substitute scenario as appropriate!).
As soon as we add a pound sign in front of a decimal value in a calculation, it can seem easier to visualise, to handle.
0.01 is one hundredth, an abstract concept. Whereas £0.01 is a penny – it’s solid, and there’s a hundred of them in a pound – easy!
If you struggle with decimal calculations, it might just help to shove a pound sign in front of the numbers, turn 0.4 into £0.40 or 40p, etc. One of the commonest pitfalls of multiplying or dividing with decimals is the failure to show the answer in the right order of magnitude.
For instance, taking 3.6/12, we could make the question easier by writing it 36/12 – the answer is 3. But now what do we do to find the answer to 3.6/12? This can stump people, but using the context of money means that we know £3.6 is 36 10p coins, or 360 pennies.
If the answer to 36/12 is 3, that means three 10p coins, or 30p! And how do we write 30p in pounds? £0.30. Easy! We’ve just converted the whole-number answer to our simplified calculation back into the final decimal answer.
This Maths-Whizz tip comes courtesy of Hilary Koll and Steve Mills, the esteemed and award-winning maths boffins who designed all our Maths-Whizz lesson concepts, people to whom even the God of Whizz tugs his forelock.
The long summer holidays will soon be upon us. But those endless warm afternoons of childhood may conceal a hidden menace – ’summer learning loss’.
Policy wonks have found that summer learning loss, an established side-effect of long school holidays, is particularly pronounced in some groups:
…children from the poorest backgrounds suffered most with ’summer learning loss’ because they were the least likely to practise reading and writing during the six-week break.
The Education Guardian has reported on plans from think-tank The Institute for Public Policy Research (IPPR) to shorten the long summer holidays. This should interest parents from any wealth bracket – without the right attention even the most expensively educated can suffer.
According to the Maths-Whizz Teachers’ Resource dictionary, a number line is: “a line that shows numbers ordered by magnitude from left to right, or bottom to top.” Pretty simple? Yes, and then again, no.
The number line can be a powerful beast, employed in addition and subtraction, and frequently in concepts of place value. The number line describes the world in the way instantly familiar to most of us, with smaller items on the left (if horizontal) or towards the bottom (vertical).
We could investigate the many ways culture and psychology define our experience of numbers, and why so many (but not all) of us perceive numbers increasing in those two directions, but that would be beyond the scope of this blog – even if the God of Whizz might enjoy the intellectual excursion…
Number lines in addition and subtraction
