Lesson video

Hello, I'm Miss Miah and I'm so excited to be a part of your learning journey today.

I hope you enjoy this lesson as much as I do.

In this lesson, you'll be able to use knowledge of the relationships, between the three and six times tables to solve problems. Your key words are on the screen now and I'd like you to repeat them after me.

Multiple.

Double, doubling.

Halving.

Fantastic, let's move on.

Now a multiple is the result of multiplying a number by another whole number.

To double means to become twice as many or to multiply by two.

Halving means to divide into two equal parts.

Now, this lesson is all about our threes and six times tables.

Now, we've got two lesson cycles here.

The first lesson cycle is all about finding the missing number and the second lesson cycle is to solve worded problems. So, let's get started with our first lesson cycle and to help us with our mathematical thinking and learning, we've got Andeep and Izzy to join us on our journey.

Let's get cracking.

Now, Andeep and Izzy are exploring the relationship, between the threes and sixes.

Now we've got an array here we can see six groups of six.

There you are.

So, that's six groups of six.

That's six times six, which is 36 and six sixes are 36.

And six, six times is 36.

So, there are many ways to represent this fact.

Whoa, okay.

So, half the side's been covered now.

Half.

This represents six groups of three.

Now, this can also be represented in many ways.

So, six groups of three, three times six, which is 18, six times three, which is 18, because there's six groups of three, six threes are 18, three, six times is also 18.

Andeep says he's noticed a pattern.

I wonder what he's noticed.

If a factor halves, so does the product.

I'd like you to keep this in mind.

Let's look at another example.

Andeep and Izzy are continuing to explore the relationship between the threes and sixes.

Now this time we've got four groups of six.

So, we can represent this as four groups of six, four times six, which is equal to 24.

Four sixes are 24.

Four, six times is 24.

Oh, we've covered half of it.

I wonder what facts we can get now.

Well, two groups of six, I can see two groups of six.

This can be written as two times six, which is equal to 12.

Six times two is equal to 12.

Six twos are 12 and two six times is 12.

Izzy's noticed a pattern.

If a factor doubles, so does the product.

Over to you, I'd like you to fill in the blanks, what happens to the array? Now, you've got some key points to help you along with this.

So, Andeep says if a factor halves, so does the product.

And Izzy says if a factor doubles, so does the product.

Using this information fill in the gaps.

You can pause the video here and click play when you're ready to rejoin us.

So, how did you do? Well, there were three groups of six, which is 18.

But then when we halved one of the factors to three, our product also halved.

So, three times three is nine.

If you managed to get that, fantastic.

Now did you know pairs of facts can help you to quickly solve multiplication equations? Here's an example.

If you know that three times 10 is 30, you should also know that six times 10 is 60.

But let's look at that in a little bit more detail.

Well, when one factor doubles, so does the product.

And in this example, the three in three times 10 has doubled to six in six times 10.

So, because that's happened, the product has also doubled.

That's been outlined here.

So the three has doubled to six.

So, the product has doubled to 60.

Now, when one factor halves, so does the product.

So, if you were to do this in reverse and halved six to make it become three, the product would've also halved.

So for example, if I know that six times 10 is 60, I can halve six and get three.

So, I also know then three times 10 must be 30, because half of 60 is 30.

You can now use this to spot patterns.

Let's have a look at this.

So, you've got two occasions there, you've got two times three, which is equal to six and two times six is equal to 12.

Again, when one factor doubles, so does the product.

So in this case, the factor is on the right hand side as opposed to the left hand side.

So, it doesn't matter which order the factor is in.

If one factor has doubled, so does the product.

Now when one factor halves, so does the product.

So, if you know that the six is half to three, the product would've also halved.

So, knowing that two times six is 12, then also know that two times three is six.

Over to you, I'd like you to fill in the gap, using what you know about doubling.

If you know that eight times three is 12, then you also know that eight times six must be? You can pause the video here and click Play when you're ready to rejoin us.

So, how did you do? Well, you should have got 48 and that's because the three in eight times three has doubled to six, which means the product must also double.

So, 24 doubled is 48.

Eight times six is 48.

Now back to you.

I'd like you to fill in the gap.

You've got six times six which is equal to 36.

If you know that fact, then you also know that six times three is equal to? Think about what's changed in your factors and use this to help you.

You can pause the video here and click play when you're ready to rejoin us.

So, how did you do? Well, we've halved and that's because one of our factors, six has halve to three.

So, that means our product has also halved.

So, if you know that six times six is 36, then you also know that six times three is 18.

Onto the main task for your lesson cycle.

So question one, you are going to be using the relationship of the threes and sixes and the array to find the missing multiplication facts.

You've got four questions there; A, B, C, and D, all with different arrays and half that has been covered up.

And for question two, you're going to find the missing numbers for 2A and 2B.

Can you spot a pattern? So, if you have a look at 2A, you've got two times three is equal to gap multiplied by six.

Then you've got four times three is equal to gap multiplied by six.

Then you've got six times three is equal to gap multiplied by six.

Oh, I think I can spot a pattern, between the questions as well.

I wonder if that will also help me figure out, some of the answers.

You can pause the video here.

Off we go.

Good luck and click Play when you're ready to rejoin us.

So, how did you do? For question 1A this is what you should have got.

So, if you know that three times three is nine, you also know that six times three must be 18, because one of our factors have doubled.

So, that means our product has doubled.

So, nine needs to double to 18 for the second part.

1B, well I can see six groups of three.

This can also be written as three times six, which is 18.

Using that you then also know that six times six is 36, because if one factor's doubled, the product will also double.

So, 18 doubled is 36.

For 1C, you should have got three times seven, which is equal to 21.

Now, if three times seven is equal to 21, you also know that six times seven must be equal to 42, because you've doubled one of the factors, which means you must double the product.

And lastly, 1D, three times nine is equal to 27, which means that six times nine must be equal to 54, because we can see that the factor three has doubled to six, which means that our product must also double.

So, 27 doubled is 54.

Now, this is what you should have got for question two.

So, two times three is equal to one times six.

That's because for every two groups of three, there's one group of six, four times three is equal to two times six.

And that's because for every four groups of three we've got two groups of six.

Or if the product has to say the same, when one product doubles, the other must in order to get the same product.

Six times three is equal to three times six.

That's because six groups of three is equal to three groups of six.

Next, we've got eight groups of three, which is equal to four groups of six.

And 10 groups of three is equal to five groups of six.

So, we can see that there is a relationship here of doubling and halving to get our product.

For question B, this is what you should have got.

Please tick your answers.

Now, let's look at 10 times six, which is equal to 20 times three, and 11 times six, which is equal to 22 times three in a little bit more detail.

Now, if you know that 10 times six is 60, we should also know that 20 times three is 60 as well.

Now can you see a pattern? When one factor doubles, so does the product.

Let's move on to lesson cycle two, solving worded problems. So, we're going to use everything we've learned in the first lesson cycle and apply it to calculating the answers to these worded problems. Let's go.

Now, when you solve problems, you need to decide what operation and calculation is needed.

The language in a worded problem can help you to decide the calculation.

So for example, sometimes you may come across worded questions which involve multiplication or division.

So, the real question is to divide or to multiply.

Now, Andeep and Izzy are going to give us some tips on whether we are going to be using the division operation or the multiplication operation.

Let's go.

Andeep says equal parts usually means he needs to divide.

Izzy says, groups of usually means you need to multiply.

Halving means dividing by two.

Doubling and twice, often mean we need to multiply by two.

Splits and cut often means that it is a division question.

And lastly, times and lots of, means that you'll be multiplying your factors.

Now keep these in mind because this will help you identify which operation to use for your calculation.

Identifying the keywords, will help you to find which operation to use.

You've got a question here and I'm going to read it to you now.

Alex runs three kilometres each for two days.

He runs six kilometres in total.

Izzy runs six kilometres each of the two days.

How far does Izzy run altogether? Let's begin by highlighting the key parts.

We need to calculate how much Izzy has ran, so we can see that they're both running for two days, but in this case Izzy runs six kilometres.

So, we actually don't need to focus on what Alex has done.

So, if you know that three times two is six, you also know that six times two is 12, because six is double three.

You know that you need to multiply, because altogether tells us that you're finding the whole all total.

So in this case, you are multiplying.

This means that Izzy ran 12 kilometres altogether.

So, when one factor doubles, so does the product.

Andeep bakes three cakes a day for a party.

Izzy bakes six cakes.

Now if Izzy bakes 30 cakes, how many did Andeep bake in that time? Now, Izzy says you must halve, because Andeep baked three cakes a day.

Do you agree? Hang on, let's read this carefully.

So, Andeep says that because he bakes half the amount, that means he will bake half of what Izzy baked altogether.

So if she's baked 30 cakes, we know that we have to halve what Andeep has baked.

So, 30 is the whole our divisors is two and our quotient, which means he baked 15 cakes altogether.

Over to you.

What is the equation that you are calculating? Andeep bakes three cakes a day for a party.

Izzy bakes six cakes.

If Izzy bakes 36 cakes in six days, how many cakes did Andeep bake in six days? You can pause the video here and click play when you're ready to rejoin us.

So, how did you do? Now if I were you, I would start off by identifying the key words to this question.

Now, you know that Izzy bakes six cakes in six days, which is equal to 36 cakes.

You also know that Andeep baked half the amount.

This means he will bake half the amount that Izzy baked.

So, if you know that Izzy baked 36 cakes, 36 divided by two is 18 or you could use a multiplication factor to help you.

So, if he's baking three cakes every day and he does that for six days, our factors are three and six.

So, three times six is equal to 18.

18 is our product.

He would've baked 18 cakes.

Over to your main task for this lesson cycle.

For question one, I'd like you to complete the word problems. One A, Andeep is making a cake.

He has three boxes of six eggs.

How many eggs are there altogether? 1B, one pack of Guinea cards cost six pounds.

Andeep buys one pack.

Izzy buys three times as many as Andeep.

How much does Izzy spend? Izzy is wrapping presents.

She has a 24-centimeter length of ribbon.

She can make for six centimetre lengths from this.

How many three centimetre lengths could she make instead? And 1D, an orangutan jumps six metres with every jump.

A monkey jumps three metres with every jump.

If that orangutan jumps 36 metres, how far will the monkey have jumped with the same number of jumps? 1E, chickens can be kept in coops of threes or sixes.

If they are kept in threes, they need 30 coops.

How many coops will they need if they are kept in coops of six? 1F, if there are 60 chickens, how many coops will be needed if each coop can hold six chickens or three chickens? Now remember, do highlight the keywords, so you can identify the operation you are using and then think about the numbers within the question.

Can they help you with your calculation? You can pause the video here and click play when you're ready to rejoin us.

So, how did you do? So for question one, our factors were three and six, and that's because there's three boxes of six eggs.

So, three times six is 18, there were 18 eggs altogether.

Question 1B.

So, one pack of Guinea cards cost six pounds.

Izzy bought three times as many.

So, those are our factors six and three.

So, six pounds multiplied by three, gives us 18 pounds altogether, which means Izzy spent 18 pounds.

For question C, Izzy can make eight three centimetre lengths from the ribbon because if four times six is 24 centimetres, then eight times three centimetres is equal to 24 centimetres.

And lastly, let's have a look at this question in more detail.

Now, if an orangutan jumps six metres and a monkey jumps three metres with every jump, we know that the monkey jumps half the amount.

So, if the orangutan has jumped 36 metres, we know that the monkey, would've had to have jumped half the amount.

So, 36 divided by two is 18.

Alternatively, you could have used your multiplication factor help you.

So if six times six is 36, we also know that three times six is 18, so he would've jumped 18 metres.

Well done if you got all of those questions correct and you managed to highlight the key words that identified the operation.

Let's move on.

Question 1E, if three times 10 is 30, then six times five is 30, which means five coops are needed for 30 chickens if the coops hold six chickens each.

And for question F, we needed to calculate how many coops were needed for different amounts of chickens.

So, there were 60 chickens.

Now, if one coop can hold six chickens, we know that six times 10 is 60.

So, that would mean we needed 10 coops for 60 chickens.

And if the coop could only hold three chickens, well we know that three times 20 is 60, so that means we need 20 coops for the chickens if they were only to hold three chickens.

Now, if you managed to get all of those questions correct, really good job, well done.

I'm proud of you.

We've made it to the end of this lesson.

Let's summarise our learning.

So, today you use knowledge of the relationships, between the threes and six times tables to help you solve problems. You should now understand that all multiples of six are multiples of three, but not all multiples of three are multiples of six.

So, let's look a bit deeper into that.

You know that an even number by three, will give you a multiple of six.

Lastly, you should now understand that multiples of six are double the multiples of three, and that multiples of three are half the multiples of six.

Well done.

I really hope you enjoyed this lesson and I look forward to seeing you in the next one.

Bye.