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