Describe the rule for the number pattern. 64, 57, 50, 43, 36.
We are asked to describe the rule for this number pattern. And we would normally do so by looking at the numbers from left to right and seeing how they change. But before we start with the number 64, there’s actually a way to spot the rule by using a little bit of number sense. One of the numbers in our number pattern is easier to count up to and count from than the others. Which number is it? It’s the number 50. So we know why we can dive into our number pattern halfway along and use the number 50 to help us. What do we notice?
Well, the first thing we can see is that this is a decreasing number pattern. We seem to be counting backwards. The numbers are getting smaller as we move from left to right. Because 50 is a multiple of 10, it’s easy and quick to see how we get from 57 to 50. We subtract or count back seven. 57 take away seven equals 50. And again, subtracting from 50 is quick to do too. What do we subtract to get from 50 to 43? We subtract seven. Seven and three are a pair that make 10. And so by jumping into our number pattern halfway along, we’ve straight away found a rule that seems to work. Take away seven or count back seven.
Let’s use our number line just to check that we’re correct. What’s seven less than 64? Let’s count back seven. One, two, three, four, five, six, seven. 63, 62, 61, 60, 59, 58, 57. Our counting-back-seven rule works for the first two numbers too. And the difference between 43 and 36 is seven too. We found that this was a decreasing number pattern. The numbers were getting smaller. And we had to count backward. The difference between each of the numbers was the same every time. It was seven.
And so we can describe the rule for the number pattern as count backward by seven.