Lesson Video: Number Patterns: Two-Digit Numbers Mathematics • 2nd Grade

In this video, we will learn how to find missing numbers in counting sequences and number patterns using addition and subtraction rules.


Video Transcript

Number Patterns: Two-Digit Numbers

In this video, we’re going to learn how to describe counting patterns. And we’re going to learn how to find missing numbers when skip counting.

Patterns are all around us. We see them in shapes, in all sorts of real-life objects, and also in numbers. And this is what we’re going to be thinking about in this video. Sometimes, we can see a number pattern straightaway just by the look of the numbers. All the numbers in this pattern end in a zero, don’t they? But at other times, we need to give it a little bit more thought.

Now the number patterns we’re going to look at in this video are either going to be increasing number patterns like this first one — the numbers are going to get bigger each time — or they’re going to be decreasing number patterns like this second one, where the numbers get smaller each time. But whether we have to count forwards or backwards, we need to look for the rule behind each number pattern before we decide how it continues or how to fill in the missing numbers.

Let’s imagine that you’re a postman. And you’ve been told that you need to deliver parcels to all these houses and that all the house numbers follow a pattern: 76, then you need to visit number 68, then number 60, but finally a house number that we don’t know. Looks like this is a two-digit number pattern. So it could be a two-digit number we’re missing. But how do we know which number is going to be on the parcels we need to deliver? To find out, we need to identify the rule behind the pattern. And the first thing that we can look for is whether the pattern is increasing or decreasing: 76, 68, 60. These numbers are going down, aren’t they? It’s a decreasing pattern. And this means if we need to skip count to find the answer, we need to count backward.

Now, we could start with the first number and see how many we have to count backward to get to 68. But can you see that the second two numbers are actually a little bit easier to work with? We can see just by looking at them what the difference between them is. To get from 68 to 60, we just need to take away eight or skip count backward eight. And we can check that this pattern works for the first two numbers too. And this looks right, doesn’t it? To get from 76 to 68, we count backwards eight too.

And now that we found the rule for our pattern, we can apply it to find our final missing number. Eight less than 60 is 52. And so the number we need to look for on our parcels is 52. This is a decreasing pattern of two-digit numbers. And we could describe it as a counting pattern because we need to skip count backwards eight each time: 76, 68, 60, 52.

Here’s another two-digit number pattern. We’ve got 18, 23, 28, then we’ve got a missing number, and then finally 38. Now, if you were a postman delivering to these house numbers, you might spot a pattern just by looking at them. Can you see the last digit in each number goes eight, three, eight, then we’ve got the missing number, and then eight again? It looks like the pattern might be that the numbers end eight, three, eight, three, eight, three, and so on, doesn’t it, in which case our missing number would end in a three.

This time, the numbers are getting larger each time; it’s an increasing pattern. And so we need to look for the number we need to add on each time. To get from 18 to 23, we add five. And the same is true when we count from 23 to 28. And so to find our missing number, we can skip count forwards by five again. And can you also see another way we could find the answer? Because our missing number is in the middle of the pattern, something else we could do is to look at the number that comes after our missing number and then count backwards. So we’ll use the same number. But instead of adding, we could subtract. In other words, we could find five less than 38. And we know that five less than 38, or five more than 28, is 33.

And just like we predicted, our number does end in a three, doesn’t it? This is because when we skip count in fives, whichever number we start on, there’s always a repeating pattern that goes on with the ones digit. In this case, it’s eight, three, eight, three, eight, three, because we started with an eight. So our completed pattern is 18, 23, 28, 33, 38. And the rule for our pattern was to count forwards in fives.

We’re going to try answering some questions now. We’re going to be given some patterns. We need to look for the rule and then try to complete them if there’re any missing numbers.

Complete the pattern: 42, 48, 54, what, what.

In this question, we’re given some numbers. And we know from the first phrase that they make a pattern. In other words, there’s a rule that we can use to help find the next number each time. Now, if we look at our numbers quickly, we can see that they’re all two-digit numbers and they’re all even. But there isn’t a clear pattern that we can see straightaway in the numbers, is there? But one thing we can see is that the numbers are getting larger each time. This is an increasing pattern.

Let’s have a look more closely at the difference between each number and think about what we’re adding each time to find the next number.

The first number in our pattern is 42. And then we jump to 48. What are we skip counting in if we go from 42 to 48? Well, we know that two add six makes eight. So 42 plus six makes 48. And we can see that this idea of adding six each time is the rule we’re looking for because 48 add six is 54, which is the next number in our pattern. Now that we’ve identified the pattern, we can use what we know to complete it. So we need to start with 54, and we need to carry on counting forwards in sixes: 54, 60, 66. We’ve completed the pattern by first working out what the rule was. We said it was to count forwards in sixes. And then we used a rule to carry on the pattern and find the two missing numbers. The whole pattern is 42, 48, 54, 60, 66. Our two missing numbers are 60 and 66.

Complete the pattern: 35, 31, 27, what, what.

The numbers in this question form a pattern. In other words, there’s a rule that links them together. Let’s look more closely at them. We start with 35. Then, our number goes down to 31 and then down again to 27. These numbers are getting smaller and smaller each time, aren’t they? It’s a decreasing pattern. And so the rule that we’re looking for is to count backwards or to take away the same number each time. Let’s try and work out what our rule is because this is going to help us to find our missing numbers.

Now although we read our pattern from left to right, when we just write their numbers out, if we were to mark it on a number line, we’d look at it from right to left because these numbers are getting smaller. Now to get from 35 down to 31, can you see what we’ve skip counted in? The difference between five and one is four. So the difference between 35 and 31 is also four. And we can see that this is definitely the rule because if we count back four from 31, we reach 27. So to complete the pattern, we just need to keep applying the same rule each time. We need to keep skip counting backwards in fours: 27, 23, 19.

In order for us to complete this pattern, we needed to find out what the rule was. And so we looked at all the numbers we have to begin with. We worked out that it was a decreasing pattern. And we noticed that the rule was to skip count backwards in fours. The whole pattern is 35, 31, 27, 23, 19. And our two missing numbers are 23 and 19.

Describe the rule for the number pattern 64, 57, 50, 43, 36.

In this question, we can see five two-digit numbers. And then after the last number, which is 36, we can see some dots. When we see dots written in a row like this, it usually means that something carries on. In this case, the pattern could go on and on and on. But we don’t need to know every number in the pattern because the five numbers we’re given are enough. When we’re working with number patterns like this, we need to think about the rule behind them. What is it that helps us find the next number in the pattern each time? Now, the first thing we can say about our pattern is that these numbers are getting smaller each time: 64, 57, 50, and so on. It’s a decreasing pattern of numbers. And so if the rule is something to do with skip counting, we’re going to guess that we’d have to be skip counting backwards.

Now one way of finding the rule might be to start with 64, our first number, and look at how it changes to get to 57. But there are actually two numbers that it might be a bit quicker if we looked at first. Can you spot them? Because 50 is a multiple of 10, it’s really quick for us to spot what happens to get from 57 to 50. We take away seven, don’t we? 57 take away seven leaves us with 50.

Now we could look at this answer and say, “Well, I think it’s counting backwards in sevens each time.” But we’ve only looked at two numbers, haven’t we? What if the difference between the first number was eight, then seven, then six, then five? That would be a pattern. But the rule would change every time. Or maybe the pattern is subtract three, then seven, then three, then seven. We can’t be sure that it’s take away seven each time unless we look at all the other numbers. So let’s quickly do that. The difference between 64 and 57 is seven. And as we’ve just seen to get from 57 to 50, we count back seven too, the same to get from 50 to 43, and then from 43 to 36. So we can see that the rule is the same each time. We need to count back seven. The rule for the number pattern 64, 57, 50, 43, 36 is to count backward by seven.

Numbers have been covered on each of these number lines. Which number is the arrow pointing at? And then we’re asked the same question again. Which number is the arrow pointing at?

Number lines are a way of showing a sequence of numbers. The numbers usually get larger as we move along them from left to right, don’t they? And whilst often number lines go up in ones, sometimes they don’t. And in this question, we’re given some number lines that don’t increase in ones. Not only that, but we’ve got some missing numbers on them. Can you see the ink blobs that are covering up the numbers? Let’s have a look at our first number line.

Which number is the arrow pointing at? To find the answer, we need to think about the rule behind this sequence of numbers. We can see 19, 22, then we’ve got a missing number, then 28, and then another missing number. So we’ve only got two numbers that are right next door to each other. But we can use this to help us to get from 19 to 22. What do we need to add?

It’s a jump of three, isn’t it? And if the rules are the same all along this pattern, then we’d expect another jump of three will take us to our missing number and a second jump of three will take us to 28. So that’s two jumps of three or a jump of six to get from 22 to 28. And we know that the difference between 22 and 28 is six, isn’t it? So we know that this particular number line is labeled in intervals of three. And if we say each number, we need to skip count forwards in threes. Now, we can see that our missing number is the one that comes after 22. And we know that three more than 22 or 22 plus three is 25. The arrow is pointing where the number 25 belongs.

If we look at our second number line, we can see the number 74, then a missing number, then 84, 89, and another missing number. It’s interesting that this particular pattern contains the numbers 74 and 84. And there’s a number in between. We know that to get from 74 to 84, it’s a jump of 10, isn’t it? But once again, we can start by looking at the two numbers that are sitting right next door to each other, 84 and 89.

Now we know that to get from four to nine, we need to add five. So to get from 84 to 89, we also need to add five. It looks like the intervals on this number line might be worth five. And this would make sense, wouldn’t it, because those two first jumps of five are the same as the jump of 10 that takes us from 74 to 84. Now, we can see that the number the arrow is pointing at is the second number. It’s the number that comes after 74. Now, as we’ve said already four plus five is nine. So we know 74 plus five is 79. Look at how when we skip count in fives, there’s a pattern to the ones digit: four, nine, four, nine; 74, 79, 84, 89.

To find each of the numbers that was labeled with an arrow, we had to discover what the rule was behind each number line or what the intervals on the number line were worth. To move from one number to the next on the first number line, we had to skip count forwards in threes. And on the second number line, we had to skip count forwards in fives. Our first missing number was 25, and our second missing number was 79.

What have we learned in this video? We’ve learned how to describe counting patterns and find missing numbers when skip counting.

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