 This is a mathematical snack from the Association of Teachers of Mathematics for you to enjoy. This is an activity entitled consecutive sums. It's about consecutive numbers and adding them together. You may already know what a consecutive number is, but if not, here are some examples. Four, five, six are consecutive. Thirty-seven, thirty-eight, thirty-nine are consecutive. They follow on from each other. Ninety-eight, ninety-nine and a hundred and one are not consecutive because there's a gap where the hundred should be. What we're going to look at is using consecutive numbers to add together, which is where the sum comes in, to make other numbers. For example, I'm starting with the number fifteen. Fifteen, I can make by adding seven and eight together. Seven and eight are consecutive numbers. However, it's not the only way I can make fifteen. Fifteen, I can also make by adding four, five and six together. Four out of five is nine. Nine out of six is fifteen. But that's not the only way I can make fifteen. I can also make fifteen by adding these five consecutive numbers together. One and two and three and four and five. One plus two is three. Three plus three is six. Six plus four is ten. Ten plus five is fifteen. Some numbers you can't make. For example, two is only made by one plus one. They're not consecutive numbers, so that's not possible. Three you can make from one plus two. My challenge to you, starting with three and going up to thirty, work out if possible as many consecutive sums as you can for each number. See what you find. See what you notice. Have fun.