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.

Today, you'll be able to solve multiplication and division problems in a range of contexts.

Your keywords are on the screen now and I'd like you to repeat them after me.

Operation.

Inverse.

Fantastic, let's move on.

So operation is a mathematical process.

The most common are add, subtract, multiply, and divide.

Inverse means the opposite, in effect, the reverse of.

So in this first lesson cycle, you are going to be solving two step problems. And in this lesson you will meet Andeep and Izzy.

When solving division problems, sometimes you may come across a two step problem.

This means we need to identify what operations we must use to solve the problem.

So in two step problems, there will be more than one step, often, with different operations.

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

Altogether, often means an addition question.

Seeing how much more usually means I need to subtract.

If it says shared equally or split and cut, it means we have to divide.

Groups of, rows of, and array usually mean we need to multiply.

Now this isn't the final list of all the words for the different operations, there are more, but these are probably the most common.

So can you think of any more for the different operations? Now the words lead us to the operation and the numbers lead us to the calculation.

Andeep has collected 673 figurines.

He shares them between himself and three other friends.

Izzy gives him 99 more, how many figurines does Andeep have now? So the key words are highlighted, shares, himself and three other friends, 99 more.

Step one, Andeep is sharing, which usually means division is the operation.

So you'll have to divide 673 by four for step one.

Now step two, Izzy then gives Andeep more, which means the next operation is addition, to add 99 to your quotient from step one.

Back to you, identify the operations and calculations needed to solve the problem.

How do you know? You can pause the video here.

So how did you do? Well this is a two step problem.

So for step one, you have 157 packs of three pencils.

Now of usually means to multiply, so multiplication is the operation that you should have used for this step.

So you'll multiply 157 by three first.

Now step two.

So the bit where it says reorganising into bundles usually means we have to divide.

So division is the operation there.

You divide the total amount of pencils by five.

Now to help you decide which operations you need to use, you can think about what is known and what is unknown.

Bar models can be used to represent a worded problem.

What do I know? What don't I know? And can I draw it? You can think about what is known and what is unknown.

A toy factory makes 584 toys, but 32 are faulty.

The toys are sold in packs of eight.

How many packs will be filled? So you know that the whole is 584.

You know that one part is 32, which is the amount of faulty toys.

You do not know the other part, which is the number of packs of non-faulty toys.

It's important to know that the non-faulty toys are sold.

The faulty toys will be discarded to the side, they won't be sold.

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

So this is step one of our bar model.

So 584 is our whole.

Now, 32 are faulty, we need to figure out how many non-faulty toys there are.

So as the factory cannot sell the faulty toys, you need to subtract.

So subtraction is the operation, you subtract 32 from 584.

So this is step two, the non-faulty toys are the whole, and we need to figure out how many there will be in each pack.

Now you can draw a bar model for each step or combine them.

Andeep can now see to use subtraction to find the non-faulty amount and then he must use division to find how many packs will be filled.

Over to you, tell your partner what is known and unknown in this worded problem.

You can pause the video here.

So how did you do? So we know that 865 is how many cakes are produced per hour.

We know that they are produced in batches of eight.

We don't know how many batches are made in seven hours.

Back to you again.

Draw a bar model to represent the first steps needed to solve this problem.

You can pause the video here.

So how did you do? If you got something like this, you are correct, well done.

Now step one, now we need to figure out how many batches of eight are produced per hour first.

So you can see that you must use division first to find the amount of batches baked per hour.

808 is the dividend and our divisor here is eight.

Once we've calculated the quotient, we can then multiply by five to calculate how many batches are made in five hours.

Onto our main task for lesson cycle one.

You're going to use an efficient strategy to solve each problem.

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

So question one, a sports coach is organising tennis balls into boxes of three.

So far, 369 tennis balls have been organised.

Then, a further 219 balls have been donated.

So how many boxes are needed altogether? Question two, a baker has 48 cupcakes out for display and 327 ready to sell.

She puts all the cupcakes into boxes of five at the end of the day, how many boxes does the baker need? Question three, Izzy has 224 playing cards and Andeep has 483.

They combine the amount and share them between six friends.

How many cards does each friend get? Are there any leftover? Question four, a librarian is putting away books.

She has 647 books to place onto five shelves equally.

51 books are taken out by a class.

How many books will be placed on each shelf? And question five, Andeep scores 35 points each time he plays one round, he plays five rounds, how many points has Andeep scored? If Izzy scores three times as many, how many points did she score? You can pause the video here.

Off you go, good luck.

So how did you do? For question one, we would've first had to use addition.

So we would've summed together 369 and 290.

This would've given us 588 tennis balls altogether.

Then we would've used division, so 588 divided by three would've given us 196 boxes.

For question two, we would've had to use the operation of addition first.

So we would've added together 327 and 48 to get 375 cupcakes altogether.

And then we would've had to use division, so 375 divided by five would've given us a total of 75 boxes.

You can pause the video here to mark the rest of the questions.

And this is your answer for question five.

If you got Andeep's score as 175 points in a month, and Izzy's score as 525, you are correct, good job.

Let's move on.

Now we're going to move on to lesson cycle two, which is to solve inverse problems. Now in maths, we can use the inverse to check our answers.

We can also use the inverse to solve problems. The inverse of addition is subtraction.

The inverse of multiplication is division.

Use the inverse to find Andeeps missing number.

I'm thinking of a number, I divide it by eight and end up with seven, what number did I start with? So this is what we can visualise as to what is happening when Andeep is explaining the number that he's thinking of.

The inverse of division is multiplication, so that means you must multiply seven, which is the number that he ended up with, by eight, to find the number that Andeep had actually started with.

So seven multiplied by eight is 56.

So that means Andeep's number must be 56.

So you can now check if this works by redoing the calculation.

Over to you, which inverse operation would you pick to solve this problem? Justify your thinking to your partner.

You can pause the video here.

So how did you do? Well if you got B, you are correct and this is because the inverse of addition is subtraction.

So you would subtract 257 from 512 to find the missing number.

Now sometimes these types of challenges may be presented as a two step or three step problem.

Use the inverse to find Izzy's missing number.

So Izzy says that she's thinking of a number.

I subtract 99 and divide it by seven.

The number I end up with is eight.

What number did I start with? So we've got two operations, subtract and divide.

We can lay out our thinking like this.

Now the inverse operations you must use are multiplication and addition.

You must multiply eight by seven and then add 99 to find the number Izzy started with.

And this is what it would look like.

So eight multiplied by seven is 56.

56 add 99 is equal to 155.

That must mean the number that Izzy was thinking of is 155.

So what did you notice? This is very key, you must work backwards through the questions to get the right answer.

Over to you, the inverse operations you must use are.

Have a read of what Izzy said, you can pause the video here.

Off you go.

So how did you do? So you should have got subtraction and division.

You must divide 784 by seven and subtract 101 from the answer to find the number Izzy started with.

I'm thinking of a number, I add 10, multiply it by four, and then subtract two, I end up with 254.

What number did I start with? So here's Andeep's thinking.

254 takeaway 10 is equal to 244, 244 divided by four is 61, 61 add two is 63.

So you must have started with 63.

That is not the number I was thinking of.

What mistake do you think Andeep has made? Andeep did not complete the problem in the correct order.

He needs to work backwards in order.

So if we look at what Izzy said, the last thing she did was subtract by two.

So that means we need to add two first and that gives us 256.

Then she multiplied by four, so that means we need to divide by four.

I want you to think about what division strategy would be most efficient when dividing by four.

Well you can halve and halve again.

So 256 halved twice gives us 64.

Then instead of adding 10, we have to take away 10 and that leaves us with 54.

So that means Izzy started with 54.

Yes, that is correct.

So do remember you need to work backwards in order to find the missing number.

Over to you, look at Izzy's question, select the operations in the order you would calculate.

You can pause the video here.

So how did you do? Well, you should have got C.

And that is because instead of subtracting, we must add first, then we must divide because that is the inverse of multiplying.

And then we must multiply because that is the inverse of dividing.

Onto the main task for lesson cycle two, you are going to be using efficient multiplication and division strategies to find the missing number.

Do remember to work backwards.

You can pause the video here, off you go, good luck.

So how did you do? For the first question, you should have divided by eight first and then subtracted 20, that means I started with nine.

For question two, you should have taken away 54 to leave you with 72 first, because the last thing you did was add 54, and then you multiplied by six, which means the last operation you would've used is division, so you would've divided by six, ultimately, meaning that I started with the number 12.

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

If you managed to get all of that correct, well done.

It means you have a really good understanding so far of using inverse operations and also applying it to different contexts.

Let's summarise our learning.

So today you are able to solve problems involving multiplication and division in a range of contexts.

You can look at the numbers in the problem to decide which strategy is most effective and explain why.

You can use partitioning strategies if the numbers are related by times tables.

And lastly, you can use short multiplication or division if the numbers are not related by times tables.

I've had a great time teaching you this lesson and I really hope you enjoyed it.