By the time they reach Year 6, Gateway children can add and subtract with ease, confidently manipulating even very large numbers, and understanding that the methods they have learned lower down the school can be applied to millions, billions or to tiny decimal fractions.
This week, the focus was on the sheer variety of methods of adding and subtracting, and ensuring that the most efficient methods were chosen for every calculation. This is part of the joy of maths, realising that it can be creative, that there are a number of routes to the right answer, and that some of them can be quicker, and can involve less potential obstacles than others. Children can become very wedded to particular methods. It is important for them to understand that using column subtraction to find 100 less than 3 million might not be the most efficient approach, and that counting up (like a shopkeeper giving change) is a more effective method.
Part of the skill is in spotting connections between numbers. When looking at 15,082 plus 14,997, for example, we would like our Year 6s to notice that both numbers are close to 15,000. They can double 15,000 and then adjust by adding 82 and subtracting 3 to find their answer. 6,249,730 - 7,999 can also be calculated simply mentally (rather than by using column subtraction) by rounding the smaller number to 8,000 and then adjusting our answer by adding 1.
Year 6 used their ‘number sense’ this week to help them identify patterns and solve a range of different reasoning tasks this week. Here’s one they did for you to try:
Five numbers are added together in pairs to produce the following answers:
What are the five numbers?
Year 6 quickly spotted that at least one of the numbers must be a negative one. Can you work out the rest?
Flexible thinking and pattern spotting will be useful for all our children as they progress through school, and through life. We all know that calculators begin to take the strain of number-crunching work as we get older, but creativity in problem-solving remains our domain.