Lesson Video: Number Patterns: Three-Digit Numbers | Nagwa Lesson Video: Number Patterns: Three-Digit Numbers | Nagwa

# Lesson Video: Number Patterns: Three-Digit Numbers Mathematics

In this video, we will learn how to find missing numbers in counting sequences and number patterns using addition and subtraction rules and numbers up to 1000.

13:16

### Video Transcript

Number Patterns: Three-Digit Numbers

In this video, we’re going to learn how to describe counting patterns and find missing numbers when skip counting with numbers up to 1000.

This is a function machine. If we put a number into the machine, like 237, the function machine will apply its rule. In this case, it will add 100. And the number which comes out is 100 more than the number we put in. So 337 is 100 more than the number 237. So if we add the number 337 into the function machine, which number will come out? The number will be 100 more than 337. So the number that comes out will be 437.

What do you notice about the numbers in our number pattern? 237, 337, 437. Which digit is changing each time? It’s the hundreds digit. Two, three, four. The hundreds digit is increasing by one each time. This is because we’re adding 100 to each number. So if we put 437 into the function machine, the machine will add 100 and the number which comes out will be 537. The hundreds digit increased by one because we added 100 to a number. If we put 537 into the function machine, the number 637 will come out. Watch what happens if we change the rule of the machine. This time, the function machine will subtract 10 from any number we put in. So if we put the number 999 into the machine, the number which comes out will be 10 less. This time, we expect the tens digit to change. If we subtract 10, then the tens digit will decrease by one. So the number which comes out will be 989.

Which number do you think will be next in our pattern? In other words, what is 989 subtract 10? Which is 979. The next number will be 969. And if we put 969 into the function machine, the number which comes out is the number 959. We used our function machine to make an increasing number pattern and a decreasing number pattern. And we were given the rule for each number pattern. Let’s have a go at some questions now where we have to work out the rule and apply it to help complete either increasing or decreasing number patterns.

When skip counting backward by twos, subtract two each time. Find the missing numbers.

In this question, we’re given a number pattern to complete. And we’re told the rule is to subtract two each time. We have to find the missing numbers in the pattern and select the correct number line out of the four number lines we’ve been given. The first two numbers in the sequence have been given. 729 subtract two is 727. So to find the next number, we need to subtract two from 727, which is 725. Two less than 725 is 723, and two less than 723 is 721. And the final number in the sequence must be 719, which is two less than 721.

Which of the four number lines we’ve been given is correct? It’s not the first number line. It goes 729, 727, 722. We’ve gone wrong here. They subtracted five from 727. This is not the correct answer. Let’s look at the second number line. We’ve got 729 take away two gives us 727, but 727 take away two isn’t 726. They’ve only subtracted one. This number line is not correct either. How about this one? 729, 727, 729. Wait, that’s not right. They’ve added two to 727, and they kept on adding two. This number line is not correct either. How about the last number line? 729 and 727, 725, 723, 721, 719. This is the correct number line. The pattern follows the rule, to subtract two each time. So this is the number line which correctly followed the rule for the pattern, to subtract two each time.

Complete the pattern: 433, 383, 333, what, what, what.

In this question, we’re given a pattern. And we have to complete the three missing numbers. Before we can find the missing numbers, we need to work out the rule of the pattern. The first thing you might notice about these numbers is that they are decreasing. They’re going down in value. 433, 383, 333. We know the numbers are decreasing, but we have to work out by how much. How do we get from 433 to 383? To find the difference, we could subtract. We can take 383 from 433. That will tell us how much the number has decreased by.

We know that three ones take away three ones leaves us with zero. We’ve got three 10s. We need to subtract eight. So we need to exchange. We can take 100 and exchange it for 10 10s, which is 13 take away eight. 13 10s take away eight 10s leaves us with five 10s. And three 100s take away three 100s leaves us with no hundreds. So the difference between 433 and 383 is 50. We have to subtract 50. And to make sure that the rule is subtract 50, let’s find the difference between 383 and 333. Again, we’ve got three ones and we need to take away three ones, which leaves us with no ones. Eight 10s take away three 10s leaves us with five 10s. And three 100s subtract three 100s leaves us with no hundreds. The difference is 50.

So to find the next number in the sequence, we need to subtract 50 from 333. Three take away zero is three. Three 10s are less than five 10s, so we need to exchange. 13 10s take away five 10s leaves us with eight 10s. And two 100s take away nothing leaves us with two 100s. So the first of our missing numbers is 283. So what’s 283 subtract 50? Did you notice the pattern in the tens and ones digits? 33, 83, 33, 83. 283 subtract 50 is 233. To find the last number in the pattern, we need to take 50 away from 233. Can you predict what the number will be? 433, 383, 333, 283, 233, 183. The missing numbers in the pattern are 283, 233, 183. We realized that the rule of the pattern was to subtract 50 each time. And we used this to find the three missing numbers.

What comes before? What, what, 725, 624, 523.

In this question, we’re given a pattern, and the first two numbers are missing. We need to find the rule of the pattern to help us find the missing numbers. To help us find the rule, let’s look carefully at these three numbers. What’s changing each time? The tens digit has stayed the same, but the ones digit is decreasing by one each time. Five, four, three. The hundreds digit is also decreasing by one each time. Seven, six, five. So the numbers are decreasing by 101 each time.

So to find the number which comes before 725 in the pattern, we need to work backwards. We need to add 101 to 725. If we add one to the ones digit, we’ll have six ones. And if we add one 100 to our seven 100s, we’ll have eight 100s. 725 plus 101 is 826. And to find the number that comes before 826 in our pattern, we need to add 101. We know that 826 add one gives us 827. And 827 add 100 gives us the number 927. The two missing numbers in the pattern are 927 and 826. We looked closely at the numbers in the pattern and how the digits changed. We worked out the rule was to subtract 101 each time. The missing numbers in the pattern are 927 and 826.

What have we learned in this video? We have learned how to describe number patterns and find missing numbers when skip counting with numbers up to 1000.

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