What equation is represented here?

What is the whole?

What is the missing symbol?

What could the calculation be?

Solve the equation using a method of your choice.

Consolidating multiplication strategies

﻿Hi, and welcome to the lesson. I'm so glad you've tuned in. We've got some really exciting division work coming up in today's lesson. So I hope you're ready to get started. My name's Miss Thomas. I'll be going through the lesson with you. Off we go. In today's lesson agenda, we'll be using known multiplication facts to divide mentally. Then we'll go to our talk task. After that, we'll be delving in deeper into efficient multiplication methods where you can choose which method is the most efficient to solve maths problems. Finally, we'll finish with an end of lesson quiz where you can test yourself. You're going to need a pencil, paper and a ruler. Pause the video now, if you need to gather your equipment. Our new star word is, my turn, Inverse. Your turn. Inverse means the opposite operation. Multiplication and division are the inverse operations. They are the opposite. Here we have a word problem. I'll read it out loud. Follow along with me. "Miss Roberts takes Year 4 on an overnight camping trip near the Rocky Mountains. Each tent sleeps three people. There are 96 pupils in Year 4. How many tents are needed?" My questions are, number 1, "What is known? What is unknown?" Well, I know that each tent sleeps three people. And I know that there are 96 pupils in Year 4. What I don't know and what I want to find out is how many tents are needed. So how would I solve this? Well, if each tent sleeps three people and there are 96 pupils, I need to share 96 pupils by three. I need to do 96 divided by three to find how many tents are needed. So let's have a go with our counters. So I've got 96 counters here, shared into three equal groups. And in each group there are three tens and two ones, so 32. 96 divided by three is equal to 32. This is quite a long way to do it with my counters to share them all out. I wonder what multiplication facts could be used to solve this? Perhaps it would be more efficient. Well, I know that 96 could be partitioned into 90 and six because I can't calculate 96 divided by three mentally in my head before I do that partitioning the numbers. So if I've got, let's begin with the 90. I know that three times three is equal to nine. So because multiplication is the inverse of division, I know that nine divided by three is equal to nine, but I wasn't asked to find nine divided by three. I wanted to find 90 divided by three, but I can derive this fact because 90 is 10 times greater than nine. So the answer will be 10 times greater. 90 divided by three is equal to 30. There are 30 groups of three in 90. Let's look at the six now. I know that three times two is equal to six. So because multiplication is the inverse of division, I know that six divided by three is equal to two. There are two groups of three in six. The last thing I need to do is add the groups of three. So 30 plus two is equal to 32. There are 32 groups of three in 96, and we can see that on our counters when we're checking. I've got another problem here and I'm going to need your help with it. The problem says, "A group of 125 tourists are taken on a guided tour of Niagara Falls. There are five tour guides and each gets an equal group. How many tourists are in each group?" You need to decide what is known and what is unknown and what calculation is needed. Pause the video and explain out loud to your screen the answer to the two questions. Welcome back. You might've found that we know that there are 125 tourists and the five tour guides gets an equal sized group. What we don't know is how many tourists are in each group. So what calculation do we need to do? Shout out your answer. Great. We need to share 125 tourists by five tour guides. We need to do 125 divided by five and here I've got my representations for that equation. So how might we use multiplication facts to solve this? Pause the video, but before we pause, let's have a look at our array. So I've got an array here of 125 counters shared equally into five groups. So one of those groups, so 125 divided into five would be, we've got two tens and five ones. So 125 divided by five is equal to 25. Have a go now. Pause the video and see what multiplication facts you can use to solve 125 divided by five. Welcome back. You might have decided to partition 125 into 100 and 25. If you did it differently, don't worry. We're going to go through this way together. So we know that if we start with our 25, 25 divided by five is equal to five. We know this because five times five is equal to 25 and division is the inverse to multiplication. So there are five groups of five in 25. Next, let's look at the 100. 100 divided by five is equal to 20. There are 20 groups of five in 100. We know we can derive this fact because we know that two times five is equal to 10. So 20 times five is equal to 100 because 20 is 10 times greater than two. So the last thing we need to do is add the groups of five. So 20 plus five is equal to 25. 125 divided by five is equal to 25. There are 25 groups of five in 125. And we can check that now, looking at our array, we can see that there are 25 groups of five in 125. Now we've reached the talk task. Use your known multiplication facts to solve these division equations. Pause the video to complete your task. Let's take a look at the answers. Hopefully you managed to partition the numbers and use your known multiplication facts. I'm going to go through the answers now. You may have done it some differently and partitioned the numbers differently, and that's absolutely fine. Okay. So we can do 88 divided by two, which is equal to 44. And then we're going to do 44 divided by two, which is equal to 22. Two plus two is equal to four, so I can halve it and halve it again. So 88 divided by four is equal to 22. Next, let's look at 96 divided by six. I partitioned 96 into 90 and six. Let's start with the six. Six divided by six is equal to one. We know this because one times six is equal to six and multiplication is the inverse. There is one group of six in six. Next let's look at the 90. 90 I partitioned further into 30 and 60 because I thought they were they were more useful for my know multiplication facts. So 30 divided by six is equal to five because five times six is equal to 30 and multiplication is the inverse of division. There are five groups of six in 30. Next, let's look at the 60. 60 divided by six is equal to 10. I knew this because 10 times six is equal to 60. There are 10 groups of six in 60. The final step is to add the number of groups of six, so 10 plus five plus one is equal to 16. 96 divided by six is equal to 16. Well done with your calculations. If you did it slightly different to me, that's absolutely fine. We have a new word problem here. The problem says, "A new group of 160 tourists are taken on a guided tour of Niagara Falls. There are five tour guides and each gets an equal group. How many tourists are in each group?" So the first question says, what is known and what is unknown? Pause the video and explain out loud. Welcome back. I love it when you explain out loud to your screen. So we know that there are 160 tourists and that there are five tour guides and they each get an equal-sized group. What we want to find out is how many tourists are in each group, that's what we don't know. So what will the equation be? Call out your answer. Great. So we're going to do 160 divided by five. We're sharing 160 tourists by five tour guides. So how might dividing by 10 help us with this problem? If we've got the equation 160 divided by five, how would dividing by ten first, help us with this problem? Explain your thinking out loud. Pause the video. Welcome back. If you're not sure, that's absolutely fine. Let's go through it together. So 160 divided by five. We could do 160 divided by 10 because we don't know, well, I don't know, 160 divided by five mentally first. So I'm going to do 160 divided by 10, which is equal to 16. Next, I'm going to take 16 and times it by two, because I've divided it by 10 when really, I should have divided it by five. So it's been divided too many times. It's been divided double the amount of times. So now I need to halve it. I need to divide it by two. 16 divided by two is equal to 32. 160 divided by five is equal to 32. We've got another problem here. It says, "A new group of 396 tourists are taken on a guided tour of Niagara Falls." Gosh, Niagara Falls is having a busy day. There are four tour guides and each group gets an equal-sized group. How many tourists are in each group? So I know that there are 396 tourists and there are four tour guides and each tour guide gets an equal-sized group. So my calculation is going to be 396 divided by four. Pause the video and decide how you might solve this equation. Welcome back. Maybe you found that there was more than one way of solving this equation. Let's take a look together. You might have said I can calculate half of 396 then find half again. So first I would divide 396 by two because I'm halving it, which would equal 198. Then I would take 198 and divide it by two, which would equal 99. I've divided by two and I've divided by two again because I was actually asked to divide by four. So divided by two and divided by two again is equal to dividing by four. So I know that 396 divided by four is equal to 99. Next, let's take a look at another strategy. 396 is one group of four less than 400. So 100 times four is equal to 400. So I have 100 groups of four. This is easier to calculate than 396 groups of four, but now I have one too many groups of four. So the inverse would be 400 divided by four, which is equal to 100. So I've got 100 groups of four, but that's one too many groups of four. So if I have 100 groups of four, I need to take away one group of this four. So I need to do 400, take away four, which is equal to 396. That's good. That's what we needed to do. So now, if I had 100 groups of four, I need to do 100, take away one of those, which is equal to 99. So 396 divided by four is equal to 99. There are 99 groups of four in 396. You're now ready for your independent task. Choose an efficient strategy to solve the equation. Use key vocabulary to explain your calculations out loud once you've solved each equation. Hopefully you'll find different strategies more efficient for difficult problems. And you'll use a variety of strategies during the independent task. Pause the video to complete your independent task. Welcome back. Here are the answers. Hopefully you thought of using a range of strategies. In division, some problems suit a strategy more than others. It's great to think about your known multiplication facts and the inverse, where you can. Check your answers compared to mine and go back and correct any mistakes if you found any. Now the time has come to complete your quiz. Well done for all your hard work in today's lesson. Hopefully you've had a go at using a range of different strategies and you've found some that you're particularly comfortable with for certain problems, and others that you would use for other problems. And that's really the aim, that you're able to pick and choose which one you use depending on the problem. So great work. Well done.

482 ÷  2

250 ÷ 5

297 ÷  3

125 ÷ 5

Dividing mentally

In this lesson, we will explore a range of mental division methods, including partitioning through the distributive law and using our known multiplication facts.

Maths

Y4 Maths

Key Stage 2

Year 4

Miss

Multiplication and division

Number

THEME

UNIT

Multiplication and Division

Representing word problems using bar models

Representing 2-Step Word Problems

Deriving Multiplication Facts

Deriving Division and Multiplication Facts

To calculate multiplication facts using the distributive law

Solving 2-digit multiplication calculations using the distributive law

Solving three 1 digit multiplication equations

Multiplying 3-digit numbers by 1-digit numbers

Exploring multiplication strategies

Dividing using knowledge of multiples

Short division (Part 1)

Short division (Part 2)

Short division (Part 3)

Problem solving: Choosing operations

Problem solving: Using all four operations

Consolidating division strategies

6800 ÷  100

The Maid of the Mist boat carries six passengers in one trip. The boat does 713 trips in a day. How many passengers does it carry in one day?

An ice hockey player is paid £315. If they win,they are paid seven times as much. How much is the player paid when they win?

Solve the equation 7 x 2 x 5

What is the product of this array?

Solve the equation. 134 X 6

225 ÷ 5

Select the bar model that does not represent a division or multiplication problem.

The helicopter carries six passengers in one trip. The helicopter carries 4704 passengers in a week. How many trips were taken?

Lesson overview:Dividing mentally

Core Content

Multiplication and division: