Exit quiz: Again for this quiz we are revising everything you have learned in the lesson. Which equation will solve each problem?

Sofia is 134.7cm tall. Her sister is 107.4cm tall. How much taller is Sofia than her sister?

How much taller is Sofia than her sister?

It is Grandad’s birthday soon and he wants to hire a sports car for his present. A sports car costs £49.50 initial payment then £29.50 per hour. Grandad is bought 4 hour's hire. How much did Grandad’s present cost?

How much did Grandad's present cost?

To visit his grandmother, Zaid takes a train 6.37 km and a car 5.45 km. How many kilometres is his journey in total?

The temperature in the classroom was 21.8 °C. Claire left the door open and the temperature dropped by 3.7 °C. What was the temperature now?

To solve and represent decimal problems

﻿Hello, it's Miss Sew and today we're going to be completing our math lesson together. How are you doing? I hope you're really well. Today's math lesson is all about deriving decimal facts. Make sure you're in a calm, quiet space and we can start our learning today. Welcome to today's math lesson, all about deriving decimal multiplication facts. Why do I derive a fact? I'm using my known facts such as my times tables to help me solve other calculation problems. This is a skill you will have learned and used in previous math lessons. So hopefully once we get started, some of the language I am going to be using will feel really familiar for you today. To start with, you need a pencil and some paper, something to write on and something to write with to start this lesson. If you don't have those, pause the video and go and get them now. Once you have all the equipment you need for your learning, make sure you're in a calm, quiet space, and you've turned off any notifications on apps that might distract you. Let's get started. We'll begin the lesson with the star words. Then we'll be using arrays to multiply, and next we'll be using this sentence structure: If I know... then I know..., and finally, we'll still have an independent task and quiz to see if you could check what you have learned in our lesson today. To start the lesson, we're going to be doing some star words. I'm going to do an action and I want you to copy me. My turn, first. Derive. Your turn, together. Derive. Why do I derive something? I need to understand or work out an answer. We derive problems all the time in math lessons. For example, this is an example of a derivation I've made. If I know two add three is equal to five, then I go 0.2 add 0.3 is equal to 0.5. I've used my known facts. I know about my ones. And so I can also know about my tenths. Our next star word is array. Your turn, array. And array is an arrangement of counters or numbers in columns and rows used to represent an equation. If we look at this equation, I've got one, two, three, four dots in a horizontal line, and another line below it are four dots, and another line below it are four dots. I might say this could be four add four add four, because I have four dots, four dots, and four dots. This array can represent different equations. Our next star word is multiply. Together, multiply. So why do I multiply something? We might see this symbol, just like the one with our hand actions. We might also say groups of, we might say lots of, we might say times by, all of these words mean the same as multiply. Now we've had all star words, we're ready to go over the rest of our learning. I'm going to be using these words a lot during this lesson, so make sure you understand them. So, what multiplication and division facts could this array represent? I can see that these yellow place value counters all have a value of one. I've got one group of two. I've got two groups of two, two ones. And I've got three groups of two. So, when I say groups of, I can also say times or multiply by. Our multiply and time symbol is the same as saying groups of. So instead of saying three groups of two, which I have here, I could say three groups of two is equal to six, which is the same as three multiplied by two is equal to six, which is the same as two groups of three, which is equal to six, or three lots of two, or three equal parts with a value of two. So I have looked at how this array can represent all of these different equations and sentences. Let's have a look at how it could also represent division which is the same as sharing. Six shared into three equal groups of two. I have six in my total, one, two, three, four, five, six, and I've shared them into three groups, one group, two groups, three groups. Each group has a value of two. This is the same as six divided by three is equal to two. Now, let's have a look at how I could represent this array in different groups. So previously I had vertical groups and now let's look at having horizontal groups. I have one group of three, and now I have two groups of three. Let's look at how we can represent this in equations or sentences. Can you help me? If you remember what I showed you in the last picture. Pause the video and tell me how many groups there are and how I share this. Can you say with a multiplication side or the division side? Pause the video and write it down. Okay, let's see if your sentences and equations are the same as mine. Two groups of three. Two times three is equal to six, or two multiplied by three is equal to six. Three multiplied by two is equal to six. Two lots of three. Two equal parts, each with a value of three. Let's have a look at our division facts. I have two equal groups of three. And this is six divided by two, which is equal to three. So, this one array that I've made into two groups using horizontal, horizontal groups can create all these sentences and equations. So just remember how we can learn lots of different facts from these arrays. That's what we're going to be doing today. So I've just shown you my example with these two groups of ones. I have six ones in my home. Both of the arrays are exactly the same. The only thing that's different is the groups that I have drawn around them. Thinking about what we just learned and what I've just shown you. Pause the video and have a go saying your own sentences which I've highlighted in pink below, and writing your own equations which I've highlighted in green below. Pause the video and tell me your sentences and your equations. Okay. So, for my vertical groups that is starting up this way, I have got three groups of two. This is the same as three times by two, three groups of two. For our horizontal groups here, I've grouped horizontally. I've got six shared into two equal groups. This is the same as six divided by two is equal to three. So, now we started to explore what all arrays represent. Let's move on to our decimal facts. Now I have got tenths. These green place value counter is 0.1 or one tenth each. I've got one, two, three, four, five, six. There are six tenths in this array. I want you to pause the video and tell me your sentence or your equation. If you want a clue, I'll be showing you in the next five seconds. So your first clue is this. Can you tell me the equation? Something multiplied by something is equal to something else. Next clue is coming up. Hmm groups of hmm, can you fill in the blanks and tell me your sentence? Okay. Time for the answers and I'm going to show you what my sentences and equations about this array were. What information and what multiplication facts could this represent? So first, let's have a look horizontally. I have got two groups of three. Two groups of 0.3 is equal to 0.6. Or 0.3 times by two is equal to 0.6. I have got two groups of three tenths. 0.1 and one tenth are equal. So each of these groups has got three tenths. There are two groups of 0.3. There are two lots of 0.3. And 0.3 multiplied by two is equal to 0.6. And I have three tenths times by two. Let's have a look. If I grouped these vertically, you might have done this instead. I've got one group, two groups, three groups. This is three groups of 0.2 is equal to 0.6. Three times 0.2 is equal to 0.6. Or 0.2 multiplied by three is equal to 0.6. Three groups of two tenths. Three groups of 0.2. Three lots of 0.2. And 0.2 multiplied by three. Two tenths times three. The value of each part is 10 times smaller than our array of yellow ones that I showed you at the beginning of this lesson. So, the whole is also 10 times smaller. Now, let's have a look at this example. I've got blue place value counters with the value of 0.01. This is one hundredth. This is a hundred times smaller than the yellow place value counters I showed you at the beginning of this lesson. What do you notice? And what facts could you write? Pause the video and have a go. So, here are the answers of what you could have written about 0.01. Pause it and take a look at what you've written. Here are the answers for what you could have written about a hundredth if we grouped them vertically. It's now time to move on to the next part of our lesson using the sentence structure: If I know... then I know... We're going to be comparing two different sets of arrays and work out what we can derive from our existing knowledge. If I know... then I know... Let's have our yellow place value counters with all value of one. I can see I've got one, two, three, four, five in each row. I have got one group of five. I have got two groups of five. I have got three groups of five. Three groups of five is equal to 15. Three multiplied by five is equal to 15. Let's have a look at our green place value counters, our tenth, 0.1. One, two, three, four, five. The first thing I notice is that 0.1 is 10 times smaller than one, but I have the same layout of this array. I also have one group of five. One group of five tenths, so this is one group of 0.5. Two groups of 0.5. Three groups of 0.5. Three groups of 0.5 is equal to 1.5. My answer is 10 times smaller than my answer for my ones. If the value of each of my place value counters is 10 times smaller, then the value of my answer will also be 10 times smaller. Five and 0.5 are related, but 0.5 is 10 times smaller than five. If I know that three multiplied by five is equal to 15, then I know three multiplied by 0.5 is equal to 1.5. My counters and my answer is 10 times smaller. We have grouped all arrays horizontally. Now I want you to group our arrays vertically and tell me what you know about each of these arrays. Let me start off for you. Here I've got one group, two groups, three groups, four groups, five groups. And the same for our tenths. Pause the video and tell me what you know. What sentence can I write with: If I know... then I know...? If I know five multiplied by three is equal to 15, then I know five multiplied by 0.3, five groups of 0.3 is equal 1.5. Look at the blue, the 0.01, the one hundredth place value counters. What do you know from this array? Use the example above to help you. We have just looked at this example and I want you to fill out what you know about this example at the bottom. What equation can you write? And what sentence can you write? Pause the video and write it down. Here are the answers. We know that one hundredth is a hundred times smaller than one and 10 times smaller than 0.1. Three groups of 0.05 is equal to 0.15, five groups of 0.03 is equal to 0.15. This answer is related but it is different to our answer above. Well done for joining in with all my learnings so far. If you found a bit tricky at the end, rewind and watch the start of the video again to help you. Now, it's time for independent task. Let me show you what you have to do. Here's your first part of your independent task. You need to write two multiplication statements for each of the sets of place value counters. This is very similar to what we did earlier, but the arrays have a different value. When you have six equations, write two sentences using the sentence stem below. For the second part of your independent task, this time you only have your arrays in ones. Complete the equations, using If I know... then I know... to support you. This time, you also need to use thousandths. I have given you array of ones, but all of these facts are related. Challenge: What do you notice when you multiply by a decimal less than one? Pause the video to complete your independent task. Well done for finishing independent task. It's time for the answers. Here are the answers for task one. Here are the answers for task two. For our challenge, if we multiply number by decimal less than one, our product is smaller than the largest factor. Thank you so much for joining in with our lesson at Oak National today. If you'd like to, please ask your parent or carer to share your work on Instagram, Facebook or Twitter, tagging @OakNational and #LearnwithOak. Now it's time for you to go and complete your quiz. Thank you so much for joining in with today's lesson. Good luck and enjoy the rest of your learning today. Bye.

Exit Quiz: Can you spot the pattern and complete this quiz mentally?  That's the challenge!

9 x 7

7 x 9

7 x 0.9

9 x 0.7

7 x 0.09

9 x 0.07

7 x 0.009

9 x 0.007

Deriving decimal multiplication facts

In this lesson, we will derive multiplication facts involving decimal numbers, exploring a range of language structures and models. By the end of this lesson we will be able to use a known fact (e.g. 2 x 6 = 12) to derive a decimal calculation (e.g. 0.2 x 6 =1.2).

Lesson overview:Deriving Decimal Multiplication Facts

Core Content

Calculating with whole numbers and decimals: