Solving multiplication calculations using the distributive law

Which equation does not have the answer of 20?

Select the correct calculation for distributive law for the array.

Select the calculations that do not represent the array.

Which calculation does the array not represent?

To calculate multiplication facts using the distributive law

﻿Hello and welcome to today's maths lesson my name is Miss Thomas and I'll be going though the lesson with you today, but, before we start, I thought I'd show you some of my artwork that I've been doing, it's something I like to do in my spare time. I wonder if there's something that you like doing in your spare time. Let's get started on today's maths learning. In today's lesson agenda, first we will be using area models to solve multiplication problems. After that, we'll go to the let's explore task, where you can have a practise. Next, we'll use a distributive law to compensate multiplication equations. Finally, we'll finish off with the end of lesson quiz. For the lesson, you are going to need: a pencil, paper and a ruler. Pause the video now if you need to get this equipment. Let's look at the star phrase, my turn, distributive law, your turn? Distributive law means that in multiplication we can reach the same answer when parts are solved separately. Here, we have a word problem, let's read it together. There are 34 felt tips in a packet. If there are 6 packets, how many felt tips are there altogether? I've got some questions for you about the problem. What is known? What is unknown? And, what would this look like as an area model? Pause the video now, and answer the questions. You may like to call your answers out. Great! We know that there are 34 felt tips in a packet and that there are 6 packets, what we don't know is how many felt tips there are altogether. As an area model, this is how to represent the problem. However, what do you think the problem might be when we draw an area model like this one? Call out your answer. You might have said that the problem is drawing all of those boxes, that's going to take an awfully long time, and we might not get it right, by the time we've counted them all up. Luckily, we can draw a not to scale area model, like this one, which is much quicker. We have a new star word. My turn, partitioning, your turn? Partitioning means to separate parts of a whole. Here is a not to scale area model, that represents the word problem, however I don't know my 34 times table. Pause the video now, and use the word partitioning to explain what I have done in my not to scale area model this time. Great Job! I've partitioned 34 into 30 and 4. I need to times both these values by 6. I don't know my 30 times tables, but I do know my 3 times tables, and 30 is 10 times greater than 3. I then need to times the product, product means answer, by 10, because 30 is 10 times greater than 3. Now, I have completed timesing 30 by 6, I can move on to the 4. 4 times 6, I know is equal to 24. Finally, I must add both the products to reach the whole. 180 plus 24 is equal to 204, that means 34 times 6 is equal to 204. I know that there are 204 felt tips in all 6 of the packets. Now its your turn, first read the word problem. Then, represent it in a not to scale bar model. Finally, solve the problem using the distributive law. Pause the video now to complete your task. Great! Once you've represented the word problem, you should have found that you need to multiply 63 by 9. I'm going to ask you a question, and I want you to call out the answer, out loud. Why might we partition this number to help us solve it? Why would we partition this number, 63? Call out your answer. Great! We don't know our 63 times table, so we can partition the number and use the distributive law. 63 can be partitioned into 60 and 3. Let's go through the calculations together. First, I shall do 6 times, 6 times 9, why would I do that? Call out your answer. Great! Because we don't know our 60 times table, but 6 is 10 lesser so we can do 6 times 9, and then after that, we'll have to times it by 10, because 60 is 10 times greater than 6. So, we take our product 54 and we multiply it by 10 to get 540. Next, we have to find out what 3 times 9 is, which is equal to 27. The last step is to add our two products, 540 plus 27 is equal to 569, 7 sorry, 567. So, we know that there are 567 chocolates in total. You're now ready for the let's explore task, you're going to need to draw an area model to solve the multiplication equation, 83 times 6. Once you've done this, say the sentence stem out loud to check your calculations, you'll need to add the missing words and numbers. Pause the video now to complete your let's explore task. Fantastic work! Let's go through one of them together. So, here we've got 83 times 6. Here is the partitioned area model. Let's read the sentence stem out loud together, filling in the gaps as we go. To multiply 83 and 6. I'm going to partition the number 83 into 80 and 3. 80 multiplied by 6 is equal to 480. 3 multiplied by 6 is 18. 480 plus 18 is equal to 498. You may have partitioned the area model further. If you're not sure of your 6 times table, you could have partitioned it into two groups of 3. Or, if you weren't sure of your 80 times table, you could have partitioned it into two groups of 40. There are many different ways to solve mass problems, that's why it makes it so exciting! So, if you did it differently to me, no problem. Here, the world problem says, read along with me, a chocolate square weighs 56 grammes. The packet weighs 9 times as much as one square. How much does 1 packet weigh? What is the maths that needs to be done to solve the problem? Pause the video now and decide, explain out loud. Fantastic explaining! I really like it when you explain out loud. We need to do 56 times by 9. As one square of chocolate is 56 grammes, and a packet is 9 times as heavy. To find out the weight of the packet, we must times 56 by 9. I'm going to ask you a question, and I want you to call your answer out loud. How could we partition this to solve it? Call your answer out loud. Great! You may have partitioned it into 56 you may have partitioned 56 into 50 and 6. Or you might have found another way, which is great so long as you get the same product as 56 times 9. We're going to look now at another way to solve this problem. 56 times 9 could also be calculated through the compensation method. 9 is 1 less than 10, and multiplying by 10 is easy to do mentally. I know 56 times 10 is 560, but, that's 10 lots of 56, I wanted 9 lots of 56. I've got 1 group of 56 too many, so I need to subtract one group of 56 to find 9 groups of 56, which is what the problem's asking me to do. So, I need to do 560 take away 56, take away one of those groups, which is equal to 504. So, I know that 9 times 56 is also equal to 504. Pause the video now and explain why the compensation method would be useful for this calculation in particular, 56 times 9. Why is it useful for this particular calculation? Explain out loud. Great explaining! The compensation method is useful because 9 is close to 10 and we can do that quickly in our head and then just subtract one group of 56 after, because we were meant to multiply by 9 and not by 10. Read the word problem and draw the area model to represent it. This time, use the compensation method to calculate the answer. Pause the video now. Great work! Let's check how to use the compensation method. You may have found that the word problem was asking you to times 99 by 7. 99 is very close to 100, we know that 10 times 7 is 70, so 100 times 7 will be 10 times greater, which is 700. Multiplication is continuous addition, so now me must take away one group of 7, that we added, because, we've added one too many groups of 7. 700 take away 7 is 693, so we know that there are 693 straws used each month. Great Job! You're now ready for your independent task. Use the distribution law or compensation method to calculate the equations. Pause the video and complete your independent task. Excellent work today on using the distributive law to partition and compensate calculations to solve multiplication problems. It's time to check our answers now. If you spot a mistake, go back and find and correct your work. I haven't shown you examples of representations as there are so many different ways you could have decided to partition or compensate when solving the multiplication equations. Here are the answers, you can go and check that the method you used, gave you the correct answer. Fantastic work! The time's come to complete your quiz to show off just how well you've learnt in today's lesson. And we've come to the end of the lesson. Well done! See you next time.

27 + ___ = 9 x 5

Which area model shows the compensation method?

Which area model matches the bar model?

Which calculations correctly find the value of the array?

End of lesson quiz

In this lesson, we will explore the distributive law in multiplication. We will solve 2-digit multiplication problems using the partitioning method and the compensating method.

Maths

Y4 Maths

Key Stage 2

Year 4

Miss

Solving 2-digit multiplication calculations using the distributive law

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

Solving three 1 digit multiplication equations

Multiplying 3-digit numbers by 1-digit numbers

Exploring multiplication strategies

Consolidating multiplication strategies

Dividing mentally

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

What is the missing symbol?

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:Solving 2-digit multiplication calculations using the distributive law

Core Content

Multiplication and division: