WEBVTT
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Complete the table below by following the pattern.
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So what can we see in front of us?
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We have a three-by-three table containing some numbers.
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We’ve got a complete top row.
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Well, if you want to think about columns, we’ve got a complete first column too.
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There are also three missing numbers.
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And we’re asked to complete the table.
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We’re asked to do so by following the pattern.
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Now, where’s the pattern in this table?
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Is there a pattern working across each row from left to right?
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Or is there a pattern going down each column from top to bottom?
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Let’s look at the numbers that we do know in the table.
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We’ll see if we can find any patterns.
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First of all, is there a pattern working across each row?
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The only full row that we’ve got to look at is the top one.
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And the first thing that we notice about these three numbers is that they all have the same number of ones.
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They all end in a three.
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So when we look at how each number changes, we only need to look at the hundreds and the tens digits.
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Our first number has digits that show 380, which is the same as 38 tens.
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And then, we have 42 tens and then, finally, 46 tens.
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How are these numbers increasing each time?
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Well, they’re getting larger by four tens.
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In other words, we’re adding 40.
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383 add 40 is 423, and then 423 add 40 is 463.
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Now, we could use this pattern of adding 40 across each row to help us find our missing numbers.
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But there’s also another way we could use to find the answer.
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And it’s worth just mentioning this before we carry on.
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The only full column that we can look at is the first one.
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But if we look at the numbers going down that column, we can see a pattern there as well.
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The first thing that we notice about these numbers is that they all have the same number of tens and ones.
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They all end in 83.
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And so, when we’re looking for a pattern, we can ignore the tens and the ones.
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And we just need to look at the hundreds and thousands digits.
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How do the hundreds and thousands digits change in these numbers?
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Well, firstly, we can see that the hundreds digit increases by one each time.
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We can see 300 in the first number then 400 then 500.
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And the thousands digit increases by four.
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There’s no digit in the thousands column in the first number.
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And then, we have 4000 and finally 8000.
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So the pattern of numbers going down the column is that we add 4100 each time.
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So we found a pattern going across the table and a pattern going down the table.
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And we can choose whichever pattern we like to complete the table with our missing numbers.
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Let’s use our plus-40 pattern to find the first missing number.
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We’ll start with 4483.
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And then, we’re going to add four tens, 4483, 4493, 4503, 4513, and then finally 4523.
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If you want to check that this is a correct answer, we can always look down from 423 and see whether we’ve added 4100.
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That’s our other pattern, isn’t it?
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Now, it’s a little bit easier to add 40 to this number because we don’t have to cross into the next 100.
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4523 plus 40 is going to be 4563.
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Notice how the last two digits of our numbers are the same.
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Our first number ended in 23, just like the number above.
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And our second number ended in 63, just like the number above.
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So we can predict that our third missing number is going to end in 23.
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Let’s count on four tens from 8583, 8593, 8603, 8613, 8623.
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There are lots of patterns that we can find in this table.
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And we can use them to find the three missing numbers.
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Our three missing numbers, as we look through the grid from left to right and from top to bottom, are 4523, 4563, and 8623.