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 a range of strategies to solve multiplication and division problems. Your keywords are on the screen now, and I'd like you to repeat them after me.

Multiplication.

Division.

Inverse.

Brilliant, let's move on.

The basic idea of multiplication is repeated addition.

Division is splitting into equal parts or groups, it is the result of fair sharing.

And inverse means the opposite in effect, the reverse of.

Our first lesson cycle is to do with reasoning about worded problems and in this lesson you'll meet and Andeep and Izzy.

Now when you solve problems, you need to decide what operations to use.

Sometimes there will be more than one step with different operations.

The language in a worded problem can help us decide on the operation.

Sometimes word problems can be really straightforward and we know what to do, but other times they can be a bit confusing.

So we are really going to decipher what to do, how to do it, and why we do it.

And I'll be giving you some key tips about how to do this, especially when it comes to any other worded questions that you may come across for the future.

So to divide or to multiply, Andeep says that seeing equal parts usually means he needs to divide, and that is true.

Sharing and dividing mean that we will have to multiply.

Dividing the dividend by the divisor.

Split and cut often means a division question.

Now onto multiplication.

Seeing 'groups of' usually means that you will have to multiply.

Double twice and triple often mean a multiplication question.

Times and lots of mean we will be multiplying our factors.

Now you can probably think of some more.

This isn't the final list, so there are probably some more terms out there that we haven't covered.

But generally these are the types of words that you may see in maths problems. And by knowing the words, we know what operation we will have to use to solve the problem.

Identifying the key words will help you to determine which operation to use.

So for example, Andeep has planted seeds of sunflowers in rows of 28.

How many seeds has he planted together? Have a look at that question.

Is there a word that tells us what operation we need to use? The part that I really focus on is seven rows of 28.

Seven rows of 28 means seven groups of 28.

And altogether tells us we are finding out the whole or total, which tells us that we are multiplying.

Now Andeep has planted 196 seeds of sunflowers in seven rows, how many seeds did he plant in each row? So let's compare.

The context is pretty much the same.

We're still planting some seeds.

However, this time we may be using a different operation.

Let's find out why.

So seeing 'each' usually means you need to divide.

Now, when I was younger, I always used to get this mixed up and I used to end up doing the wrong operation.

It also means that you are finding the missing part of your quotient.

So the division equation here is 196 divided by seven.

Our dividend is 196, our divisor is seven, we are figuring out what the quotient is.

Over to you.

What is the equation you are calculating? You can pause the video here.

So how did you do? Well, the multiplication equation that you should have got, was three multiplied by 21 or 21 multiplied by three.

And this is because we've got a phrase here times as many.

So three times as many, which means we need to multiply by three.

The factors are 21 and three, you are calculating the product.

Let's move on.

Andeep has collected 423 marbles.

He wants to share these between three of his friends.

How many marbles will each friend get? So the key word here is 'of' we have to multiply because it says 'of'.

Do you agree? In this example, we actually have to divide, and that's because of the context.

So let's have a look.

'Share' and 'each'.

Seeing 'each' and 'share' usually means that you have to divide.

That means in a sense it cancels out the word of.

And if we read it again, we can see that we have to share 423 marbles between three of his friends.

Our dividend is 423, our divisor is three and our quotient is what we are calculating.

So the inverse of division is multiplication.

When you solve problems for division, you can use the inverse to check your answer.

So if 423 divided by three is 141, that means means 141 multiplied by three should give us 423.

Now, the division equation is 423 divided by three, the quotient is 141.

You can multiply the factor by the quotient to get the whole, so we can see that the factor or the quotient is 141, and then you multiply that by our factor of three to get the whole, which is 423.

And that is how many marbles Andeep has altogether.

Back to you.

What is the division equation you are solving? You can pause the video here.

Off you go.

And when you're ready, click play to join us again.

So how did you do? The dividend is 125 because that's how many cupcakes there are, and because they're being split into five glasses our divisor is five.

Back to you again.

What is the inverse equation? You can pause the video here.

So how did you do? Our factor or quotient is 25.

We need to multiply this by a factor of five to get a whole, which is 125.

And we know that 125 is our whole because that's how many cupcakes we have.

So you can multiply the factor by the quotient to get the whole.

Now sometimes in worded problems, the language can be a little misleading.

For example, a local bakery is preparing for a grand opening.

606 cupcakes are being packed into boxes of six.

How many boxes are needed? Now the problem includes the word 'of'.

Can this worded problem be represented by 606 multiplied by six? Have a think.

Well, you do not know how many boxes the bakery needs, but you know the whole amount and how many boxes each are packed into.

You actually need to divide 606 by six.

Back to you.

What is the equation? What word might mislead us? You can pause the video here, have a think.

So how did you do? Well the words of three could make us think that this worded problem actually requires multiplication.

We could calculate 366 divided by three.

Onto your main task.

Look at the equations.

You are going to write down the inverse for each.

And then for question two, for each worded problem, decide on the operation and write the calculation you would carry out.

You do not need to solve the problem.

So 2A, a local bakery is preparing for a grand opening.

They pack 448 iced biscuits into boxes of eight.

How many boxes are needed? 2B, a local bakery is preparing for a grand opening.

They pack pastries into 30 boxes of five.

How many pastries have they packed? And 2C, a local bakery is preparing for a grand opening.

They pack boxes of 12 cream cakes.

They have 144 cream cakes.

How many boxes do they have? You can pause the video here.

Off you go, good luck.

So how did you do? So for question one, this is what you should have got.

You can pause the video here to mark your work.

Let's move on.

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

So let's have a look at 2A.

A local bakery is preparing for a grand opening.

They pack 448 iced biscuits into boxes of eight.

Now initially you may have thought that this is meant to be a multiplication question because you've got of eight.

However, because we are finding out how many boxes are needed is actually a division question, and 448 is our dividend and our divisor is eight.

For question 2B, let's have a look at this one in detail as well.

A local bakery is preparing for a grand opening.

They pack pastries into 30 boxes of five.

How many pastries have they packed? Because we're calculating how many pastries they have packed.

This is actually a multiplication question.

So that of five represents multiplying by five.

So your multiplication equation should have been 30 multiplied by five.

And for 2C, a local bakery is preparing for a grand opening.

They pack boxes of 12 cream cakes.

They have 144 cream cakes, how many boxes do they have? So because we are calculating how many boxes they have, we must divide.

So 144 is our dividend and our divisor would be 12.

If you've got all of those correct, really good job, well done.

Let's move on.

For this lesson cycle, we're going to be solving problems using efficient strategies.

When dividing or multiplying a number, an efficient strategy should be chosen.

So on the left, you've got the formal method known as short division, and on the right you've got the formal method known as short multiplication.

Now Izzy is preparing for a party.

She has 633 party poppers.

She puts three party poppers in each gift bag.

How many gift bags will she need? Now Andeep says he's going to use short division because it's a three digit divided by a one digit number, and Izzy says, she thinks there's a more efficient way, and I think I have to agree with Izzy.

So let's have a look at Andeep's method.

He gets his pen and paper out and he starts to scribble down his short division method and he gets his answer.

Whereas, Izzy's method, she's used a partitioning strategy and a pothole model.

I use partitioning.

I found multiples of three and then divided each part by three.

So which method do you prefer and why? Now it is more efficient to use a partitioning strategy if the numbers are related by times tables.

Over to you.

Select the division equation which will be best suited for using short division, justify why to your partner.

You can pause the video here.

So how did you do? Should have got C.

Using short division if the numbers are not related by the times tables is the best approach, and that is because the numbers are not related by the times tables.

Now Izzy has collected 205 stamps, Andeep has collected three times as many.

How many stamps has Andeep collected altogether? Andeep says that he's going to use short multiplication because it's a three digit multiplied by a one digit number.

And Izzy says, she thinks we need to look at both factors more carefully.

I know we're multiplying by three, I will need to regroup.

Well, let's compare strategies.

So we've got 205 multiplied by three.

Now on the left we've got short multiplication and on the right we've got an informal written method.

Which method do you prefer and why? Do you know what? Sometimes there is no best approach.

It depends on two things.

If the approach is efficient, definitely use that approach, but if there is a method that you feel more confident in using, you can use that method as well.

Back to you.

Look at the multiplication equation.

Which method would you use for the question 403 multiplied by two? And I'd like you to explain your thinking to your partner.

You can pause the video here.

So how did you do? For A, you may choose A, because you can just double 403 and get 806, or some of you may have chosen partitioning.

So you can partition 403 into 403 and then multiply both by two.

I would recommend a mental strategy or a partitioning strategy over short multiplication because we should be solid in our multiplication facts to easily do this using the other two approaches.

Now bar models can be used to represent a worded problem.

Andeep collects 312 stamps every month.

How many stamps has he collected over five months? Now a bar model is very useful to help with our mathematical thinking, and it also helps us visualise what we are doing.

So here we can see that the total amount of stamps is what is unknown, that is our whole.

Now our parts are formed of five parts because they're are five months.

If Andeep collects 312 stamps, the value of each part is 312, and we must multiply 312 by five to get the total amount.

Over to you.

Tell your partner what is known and unknown in this worded problem.

Izzy scores 121 experience points in one round.

If there are four rounds, how many points does she score altogether? You can pause the video here, off you go.

So how did you do? Well, we know the part or a factor is 121, which is how many points are scored in one round.

We know another part, which is another factor is four, which is how many rounds she has played.

We don't know the value of the product, which are how many points she scored altogether.

Over to you.

This is our task for lesson cycle two.

So you are going to be using an efficient strategy to solve each problem.

You're going to use the inverse, to check your answer.

You may want to represent each using a bar model to help you choose the right calculation.

So for question one, Andeep has been collecting mini figurines.

If each box has 13 figurines, and Andeep has collected eight boxes, how many figurines does he have altogether? Question two.

Each glass of fresh orange juice made at the cafe requires the juice of four oranges.

If they have 483 oranges, how many four glasses of juice can they make? Question three.

Izzy and Andeep are planting seeds, they have 896 seeds to plant and decide to plant seven in each pot.

How many pots will they need altogether? Question four.

Andeep scores 208 points each round.

If he plays three rounds, what is the total amount of points scored? Question five, a bakery produces 873 white chocolate cookies per day.

If there are six cookies in each packet, how many full packets will they be able to make? You can pause the video here.

Off you go, good luck.

So how did you do? For question one, what we had to do first was multiply.

So 13 multiplied by eight is equal to 104.

And just to double check, 104 divided by eight would've given us 13.

So that means, Andeep has 104 figurines altogether.

For question two, you should have got 120 full cups of orange juice.

You can pause the video here to mark the rest of your work.

Well done, we've made it to the end of the lesson.

So to summarise our learning for today, you were solving problems involving multiplication and division.

The key skill here was to select whether we were multiplying or dividing and also use the inverse to check our work.

So hopefully, you can now look at the numbers in the problem to decide which strategy is most effective and explain why.

You should also be able to use partitioning strategies if the numbers are related by times tables, and you should be able to use short multiplication or division if the numbers are not related by timestables.

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