Intro Quiz: Multiplying decimals using mental strategies

Video: Multiplying decimals using mental strategies

﻿Hello, my name is Miss Sew and I'm going to be your math teacher for today. Today's math lesson is all about multiplying decimals using mental strategies. So make sure you've got your brain ready, it's turned on, because we're going to use it today for lots of different maths. I hope that you're feeling really well. Get yourself comfortable. We're going to get started. Welcome to today's math lesson. We're multiplying decimals using mental strategies and today, we are going to be doing two strategies. Our first strategy is about doubling and our second strategy is called round and adjust. These are both really useful strategies that you might have come across before in previous math lessons, but it might be the first time you're using them with multiplication or with decimals. To start with, we're going to warm up by doubling whole numbers. Then we're going to be using our doubling strategies for multiplication with decimals. After that, we're going to be using our round and adjust method. And at the end of the lesson, there'll be an independent task and quiz so you can show what you have learned. For today's lesson, you will need a pencil and some paper. So if you don't have those, pause the video and go and get them now. Now that you've got your equipment, make sure you are in a calm, quiet space and that you've turned off any notifications or any apps that you have running. For the period of this lesson, I want you to make sure that you aren't distracted and that you can finish the work with your brain turned on without being distracted. To start with, we have got a warm up. I want you to double these numbers. I've got four numbers for you to double. And I want you to think, what strategies are you using when you double or when you halve numbers? Pause the video and off you go. Okay, time to show you my answers. And we'll think about some of the different strategies we could have used to double these numbers. So, here are the answers. Check your work and see what you got correct. Now, how did you double these numbers? What strategies did you use? Did you count in your twos? Did you use any of your other multiplication facts or times tables? Or maybe you partitioned and added the numbers up. So, to double 32 I partitioned 32 into 30 and two and I added the tens and the ones separately before adding them back together. For double eight, I know my two times tables and I know that double eight is equal to 16. So I knew that fact. For double 123, I partitioned into my hundreds, tens and ones and added up my hundreds. Hundred and a hundred, my tens, 20 and 20, and my ones, three and three separately. And for double 145, I know that 40 and 40 is equal to 80. Five and five is equal to 10. And so 45 and 45 is equal to 90. Double 100 is easy. I know that double 100 is 200. The answer is 290. Now, what strategy did you use to double these numbers? Did you do them mentally or did you do some jottings or write some written calculations? Today, I want to get in the habit of trying to do these questions mentally in our brains. You might want to write some quick notes like I've done here. But try and do the majority of our workout today in your brain. When we're doing our working on paper today, we'll be calling them jottings because we're not using a formal written method. We might be writing down certain numbers to help us remember so we don't forget, but we're not using the written strategy to help solve the entire equation. As you can see from these equations here, I didn't use any formal written methods, like short multiplication to multiply by two, because I could do the majority of these equations in my head. So, let's look at how we can use those doubling strategies that you used for whole numbers for our decimals. When I am doubling my decimals, I can use my known facts from doubling whole numbers to help me. I know my two times tables. So I know that double eight is equal to 16. Now, I need to double 0.8. If I know that 0.8 is 10 times more than eight, then the product of doubling or multiplying by two will be 10 times smaller. So if I double 0.8, my answer will be 1.6. It is 10 times smaller. I can use the same idea to double 0.08. 0.08 is 10 times more than 0.8 so the product will be 10 times smaller again. The answer is 0.16. This is also 10 times smaller. One more time, I'm going to double 0.008, which is 10 times smaller. Can you write down what the answer is going to be? So, my answer is going to be 0.016, which is 10 times smaller yet again. Now it's your turn. You are going to double some decimals that I show you and I want you to think about the known facts you know and think about how many times smaller it is. And that will help you double your decimals. When I show you the questions, if you can, I want you to try and do it at the same time as me. If you think you need a bit of extra time, pause the video and write your answer down. We're going to practise with a whole number first to get our brains warmed up. Double six. The answer is 12. Double 0.6. Write your answer down. Is equal to 1.2. Double 0.06. The answer is 10 times smaller again, 0.12 Double 0.006 is equal to 0.012. Did you spot a pattern? What pattern did you see? With each question I gave you, the number I asked you to double was 10 times smaller. This means that your answer was also 10 times smaller. Let's have a go with some trickier decimals. Now that runs down the pattern and our brains are already in decimal mode, let's try that again. Double 0.32 is equal to 0.64. Double 12.3, 24.6. Double 2.6, 5.2 Double 4.5 is equal to nine. Double 14.5 is equal to 29. I know this because 14 and 14 is equal to 28 and 0.5 and 0.5 is equal to one. Or, I know I'd previously doubled 4.5 which is equal to nine and then I could just double the 10 which is equal to 20. There is always more than one way to solve an equation. Fantastic mathematicians show their strategies and explain their thinking. If we double and then double again, what multiplication fact is this the same as? I'm going to show you an example using a bar model to represent my explanation. Here I have a whole and I'm going to double it. If I double it once, this is equal to multiplying by two. If I double it again, I've multiplied it by two again. So I had one group. Now I have two groups. And now I have four groups. If I have four groups, that's the same as multiplying it by four. Let's look at an example with numbers. If I start with 0.6 and I double it, I have two groups of 0.6. If I know that six at six is equal to 12, then I know 0.6 and 0.6 is equal to 1.2 because 0.6 is 10 times smaller than six. If I double this again, I now have four groups of 0.6. If I have four groups of 0.6, this is the same as 0.6 multiplied by four or four groups of 0.6 and this is equal to 2.4. So if I double something and then double it again, that's the same as multiplying by four, which is a really handy trick if I have to multiply a decimal by four and I'm trying to do it mentally. I can just double it and double again. Now, what will happen if I double, then double again and then double again? Let's use the bar model to represent our thinking. If I have 0.6 and I double it, I've got 1.2 and I've multiplied it by two. I know if I double it again, I will have 2.4 and that is the same as multiplying by four. And if I double it again, I now have one, two, three, four, five, six, seven, eight groups of 0.6. If I have eight groups of 0.6, that is the same as 0.6 multiplied by eight which is equal to 4.8. So if I double something and double it again, and double it again, that's the same as multiplying by eight. So that's another great trick to use if I'm trying to multiply decimals and I'm doing it mentally. I can double, double, and double again to multiply it by eight. My doubling strategy can help me with a range of times tables. Doubling once is the same as multiplying by two. Doubling twice is the same as multiplying by four. And doubling three times in a row is the same as multiplying by eight. Time for quick quiz. Which of these calculations would you choose to complete with a doubling strategy? I want you to pause the video, choose which strategy you can solve with doubling strategy, and solve the equation. Okay, time for the answers. I can use my doubling strategy, 43.2 multiplied by two. This is because if I double once, it's the same as multiplying by two. The answer is 86.4 and I've shown my working out here. Which of these calculations would you choose to complete the doubling strategy? There might be more than one correct answer. Pause the video, choose your equations, and solve them. Let's have a look at the answers. B and C can both be solved with our doubling strategy. When I multiply by two, that's the same as doubling once. And when I multiply by four, that's the same as doubling and then doubling again. Which of these calculations would you choose to complete with the doubling strategy? Pick your equations, choose your strategy, and solve them. Let's look at the answers now. A and B could both be solved with the doubling strategies. If I double, then double and then double again, doubling three times in a row, that's the same as multiplying by eight. Here are my answers and here's my working out. How did we find solving these equations? How did you find our doubling strategy? Did you find it easier or did you find it harder than other strategies that we have previously learned? Can you think when you would use this strategy? now we're ready for our next strategy which is round and adjust. You might have seen this strategy before in previous lessons, but today we're using it for multiplication and decimals. The round and adjust strategy is really useful, especially when you go shopping. Lots things in shops end in 99, or 98, or 97 and those are really hard numbers to multiply by. However, using the round and adjust strategy, I could find these much easier to multiply. So here I have the equation 1.99 multiplied by eight. If I round 1.99 up to 2.0, I just add 0.01. I've now rounded 1.99 up to 2.0. 2.0 is much easier to multiply. If we multiply by eight, we are adding 0.08 extra. For each 1.99 I multiply, I'm adding 0.01. I am multiplying by eight. So I have eight groups of 0.01 extra that I'm adding to 1.99 to make it 2.0. Now, I know that two multiplied by eight is equal to 16. I've rounded this up and I'm imagining it's two instead. Now if I've rounded up and I've added 0.08 to round up, I then need to subtract it at the end. So, I know that two multiplied by eight is equal to 16, but I need to subtract to the 0.08 I added on earlier. If I know 100 subtract eight is equal to 92, then I know one subtract 0.08 is equal to 0.92. So 16 subtract 0.08 is equal to 15.92. The answer is 15.92. Using the round and adjust strategy, I was able to multiply by eight and solve this equation much more quickly than if I had tried to multiply 1.99 by eight without rounding. Time for another quiz. Which calculations would you choose to complete with the round and adjust strategy? Choose which equation you would use with a run and adjust strategy and tell me what number you would round to. Pause the video and have a go. The answer is B. I would round 3.99 up to 4.0 and then multiply it by two. 3.99 is really close to four. Which of these numbers would you round and what would you round them to? Let's have a look. I would round 1.99 to two and 5.01 I would round down to five. Have a look. Which of these calculations would you choose to complete with the round and adjust strategy? So, I would choose to round A and C. 9.1 can be rounded down to nine and 1.9 can be rounded up to two. Thank you so much for joining in with all my quizzes so far. It's now time for your independent task and you can show what you know. For your independent task, I want you to solve each of these equation using one of the mental methods that we have worked on today. Will you use round and adjust or doubles and halves? How did you find that? I'm going to show you the answers now for the independent work. Here are the answers for the independent work. If you'd like to, please ask your parent or carer to share your work on Twitter tagging @OakNational and #LearnwithOak. Thank you so much for joining in with my math lesson today and joining in with all the quizzes and making it to the end of the lesson. I have got one more quiz for you that I want you to go to now to show what you know. I hope you have a wonderful day finishing off your learning with any lessons you have and see you for our next math lesson. Bye!

Worksheet: Multiplying decimals using mental strategies

Exit Quiz: Multiplying decimals using mental strategies

Completed: Multiplying decimals using mental strategies

In this lesson we will use doubling and round and adjust strategies to multiply decimal numbers. We will use doubling to multiply by two, four and eight and round and adjust in the context of money (e.g. £2.99 x 3)

Maths

Multiplying decimals using mental strategies

Introductory Quiz

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Worksheet

Final Quiz

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