What would be the next term in this sequence?                                                                                                  4.5,      4.75,      5,       5.25,      5.5,      5.75

What is the term to term rule in this sequence?                                                                                       9.2,      9.15,       9.1,       9.05

What would be the previous term in this sequence?   -3,    -1,    1,    3,    5

Look at the following sequence, which term below can not be part of that sequence?       56,  61,  66,  71,  76

Linear number sequences

﻿Hello. It's me, Ms. Jones, ready to start today's lesson. How are you feeling today? Hope you're feeling excited and ready to solve some problems. Shall we start with a brain teaser, a little riddle? Riddle me this, riddle me that. Today's riddle is what has many keys but can't open a single lock? What has many keys but can't open a single lock? Have a little think. The answer is a piano. A piano has many keys that you play but it doesn't open any locks. Did you like that one? Right. Are you ready to start today's lesson? Hopefully that warmed up your brain. Let's go. In today's lesson, we'll be expressing missing number problems algebraically or using algebra. Now, you might be wondering what algebra is, but don't worry. In today's lesson, we're going to start by talking about just that. What is algebra? Then we'll be looking at some algebra problems, including some algebra problems in context. And finally we'll be doing our task and our multiple choice quiz. All you'll need for this lesson is a pencil and a piece of paper or something else to write with and write on. If you haven't got what you need yet, go and get it now. Pause the video and then come back. Okay. Let's get started. So, let's begin by thinking about what algebra is. What on earth is algebra? Now, you might have heard of algebra before, you might have dabbled a little bit in it, you might never have heard of it and be thinking, "What on earth is it?" Actually, you might be interested to know that you have been doing algebra right since the beginning of primary school. Because algebra is simply a way of showing the relationship between two values when one or more than one of the values is unknown. So it's any problem where there is an unknown value. Now, have a think about whether you've dealt with a problem, with an unknown value before. How was the unknown represented? Now, it might've been represented like this. As a missing number problem where you've got one part added to another, which is unknown, to get your whole. It might've been presented in a pothole model or a bar model. We also look at unknown values when we're trying to figure out something like the area of the rectangle or the perimeter. We know that length times width gives us the area, but we don't know the value of the area yet. It's an unknown value. Have a look at some of these problems. These problems all contain unknown values. Here is that bar model that I mentioned. In each of these problems, how would you come about finding the unknown? Pause the video and have a quick think about that. Okay. Let's have a look at the first one. Now, to find the unknown here, I might think about my whole, which is 14. I know that my two triangles are the same value. So I might think about what two numbers added together make 14. These are the same value. I can simply divide 14 by two. Now, sometimes in algebra, we use symbols like this or like this, or a missing number box. But sometimes to be a little bit more simple, we replace the symbol with a letter. Let's have a look how we might do this on this first problem. Instead of saying triangle plus triangle equals 14, I might say a plus a is 14. Now all I have to do is try to work out what a is. And again, it's the same sequence as our triangle. All we have to do is find a, is divide 14 by two. Once we know the value of a, we can find the value of this unknown, which I've labelled b. What is the value of b? Well, if a equals seven, then b must equal two. We can write that like this. See, algebra isn't that difficult at all. It's exactly the same as finding a missing number. But the missing number here has been replaced by a letter. Okay, let's explore. I'm going to give you an equation with a letter. Now, the letter represents our missing number. We need to work out what the missing number is. Here we've got some explanations. 72 plus something is equal to 345. If I represent this in a bar model, I know that 345, I know the whole is 345 and that there are two parts. One part is unknown and the other part is 72. To find the value of the missing part, t, I need to subtract 72 from 345. Now here we've got two representations. We've got representation using a letter of t, but she's also represented it using a bar model. Let's see how they connect. So we've got our one part's here, 72, for a whole 345. Significantly bigger than 72, so you can see this part looks a lot bigger. And our missing part is t. To find t, we need to subtract 72 from our whole. This boy says, "I agree. "We can use the inverse operation of subtraction "to find out what was added to 72 to make the total. "So 345, take away 72, equals t." So he's written another calculation here that will find his answer. And this is also equal to t. There we go. Therefore t equals 273. I'm going to show you some more representations that use letters as their unknown parts or unknown value. I'd like you to have an explore and see if you can work out the value of the letter in each instance. And can you write the calculation that will help you to find the value. Pause the video now and have a quick go. Okay. Shall we have a look at these together? An important point before we go over these is that sometimes we call our unknown value a variable. This is because in some problems there can be more than one answer to our unknown. So a variable is sometimes the word we use. I'm going to be using both words throughout this lesson. So it's important that you know what I mean if I do say variable. So looking at each one of these, we've got our bar model first, we've got the bay window and the bookshelf. Now, our unknown is w. To find w, I need to find the difference between my window and my bookshelf. So if I subtract 296 from 328, I get 32. We can write w equals 32. In my next one, I've got a plus a plus a plus a. I've got four lots of the same value. So in order to find what one a is, I can divide by four. My calculation to help me is 96 divided by four. And I know that a is equal to 24. Here I've got 812, take away f, or take away our unknown part, is equal to 495. Now, in order to find 495, I need to find the difference between this part and my whole in order to find the other part. 812, take away or subtract 495, is equal to 317. f must equal 317. Now let's look at algebra in a context. We're going to look at it in the context of perimeter. We can use algebra to help us identify the perimeter of a shape. When we don't know the values of our length and our width, we could write the value of the perimeter as to lots of a added to two lots of b. We could also write the value of our permitter as two lots of a plus b. Here our brackets are used to make sure that this part of our calculation has priority. We could also say that a plus b plus a plus b equals our perimeter. Now, thinking about this one, we've got a square. So we could say our perimeter is two Lots of r added to two lots of r. Now in this equation, we know that multiplication takes priority. Or we could say four lots of r is equal to our perimeter. We're using letters to generalise here because we don't know the value of the length or the width, but we're making a generalisation. Algebra can help us to express rules for maths that we understand. And this is known as generalising. These expressions allow us to help us calculate the perimeter of any rectangle. So we can say for any rectangle, the perimeter is always two times the length, which is a, added to the width, which is b. But instead of writing out length and width every time, we've got a simple algebraic calculation that generalises that formula for us. An important point to note when using algebra is that we don't use the times symbol. Now, the reason why is because it sometimes gets confused with the letter x. Now we know that we use letters to express unknown values when we're using algebra. So if we use the times symbol, someone might think that that's an unknown instead of an operation. So instead of doing that, instead of writing two times a plus b, we simply write two, a plus b. Two lots of a plus b. Let's look at that with this one. Instead of writing four times r, because this might get confused as an x, we write four r. Simply means four lots of r. It's a bit like what we'd say in English. If we we're saying, "I want four apples," we wouldn't say, "I want four times apples." We would just say four apples. So all we need to do is say four r instead of four times r. Okay. Let's have a look at the shapes shown below. I want you to think about the rectangle's perimeter if a equals three and b equals one, the square's perimeter if r equals 0.25, and the length of b if the rectangle's perimeter is 30 millimetres and the length of a is 10 millimetres. And use our two expressions here to help you. Pause the video now and have a go at that. Okay. Let's have a look at this together. Okay. The rectangles perimeter if a equals three. Well, if a equals three and b equals one, I know that our perimeter will be two lots of three plus one or two lots of four. Two lots of four is equal to eight. And we're using metres here so it's eight metres. The square, if r equals 0.25. But I've got my expression here. I know that the perimeter of a square is four r or for lots of r. So four lots of 0.25 will get me one whole centimetre. 0.25 and 0.250 and 0.25 and 0.25. Four quarters is equal to one. And finally, what is the length of b if the perimeter is 30 millimetres? So this time, we've got 30 equaling our perimeter and the length of a is 10. So I'm just going to write that out. We don't know, our unknown is b. Can I work this one out? Well, I know my length is 10. Two lots of a plus b equals 30. Then that means one lot of a plus b must equal 15. Now, if we already know the length of the rectangle is 10, that means the width must equal five. Two lots of 10 plus five is equal to 30. Okay. It's time for your main task. For the first part of your task, you need to use the given value of each variable to answer each example. So looking at the first one, if you know that f is equal to 19, what is three f, takeaway four, and so on and so forth. Now for each question, try to represent the equation or expression pictorially. Okay. So you might want to use a bar model to help you make sense of each one or another pictorial representation of your choice. Once you've done the first part, go on to the second part of the task. Use your knowledge of arithmetic to find the value of the unknown variable. Okay. So use your knowledge to find out what two f is by rearranging this equation and using another calculation. Try and find out what two f is. Once you've found out what two f is, you can find out what f is. Then have a go at finding out c and then m. Okay, it's time to pause the video and go off and do your task. Once you finished your main task, come back to the video and we'll go over the answers together. Okay. Let's have a look at some of the answers. So for the first one, if f was 19, we know that three f is equal to 57. So our calculations to help us here is 19 times three, and then we need to take away four, and we get 53. Three f, takeaway four, is equal to 53. Let's have a look at the rest of the answers. So if z is equal to seven, two lots of z plus three was equal to 20. I've recorded my workings out here if you need to look at them. If a was equal to 2.5, six a, take away 15, was equal to zero. Zero, you say? Yes. So six lots of 2.5 was equal to 15. 15, take away 15, is equal to zero. Now here, two f plus 50 is equal to 100. You need to work out what the value of f is. First of all, if you take away 50, we can work out what two f is. Two f is equal to 50. If two f is equal to 50, f is equal to 25. Now we need to work out what c is. c, take away 11, is equal to 21. So to work out c, we can add together our two parts to find our whole. 21 added to 11 is equal to 32. c is equal to 32. And finally, three m, takeaway eight, is equal to 25. Well, to find out what three m is, we need to add together our parts, 25 and eight. Three m is equal to 33, therefore one m, or m, is equal to 11. How did you get on? If you'd like to share your work, ask your parents or carer if they could share it on our Instagram, Facebook or Twitter, tagging Oak National and #LearnwithOak. Now that we've finished, have a go at our multiple choice quiz. Thanks guys.

t + 7 = 20 What is the value of t?

If 5a = 35 What is the value of a?

How could we express the perimeter of the rectangle below?

How could we express the perimeter of the square below?

If 2f + 6= 20. What is the value of f?

Expressing missing numbers algebraically

In this lesson, we will be finding the unknown values in algebraic expressions.

Maths

Y6 Maths

Key Stage 2

Year 6

Miss

Calculation problems

Number

THEME

UNIT

Understanding which operations have equal priority

Order of operations

Consolidating order of operations

Expressing missing number problems algebraically

Finding solutions to problems with two variables

Consolidating linear sequences and representing problems with algebra

Reasoning and problem solving

Reasoning and problem solving (Part 2)

True or False? 130 - 26 + 14 = 130 + 14 - 26

3 x 5 + 2 =

Solve the equation: 4 x (3 + 3) = ?

Which expression would represent the following problem:  The cooking time for roast beef is 30 minutes for every kg plus an additional 15 minutes.

3c + 2d = 20. Which pair of numbers does does NOT work with this equation?

What would be the next term in this sequence?                                                                                                  5.5,      5.75,      6,       6.25,      6.5,      6.75

What would be the previous term in this sequence?   31,    36,    41,    46,    51

If a represents the amount of apples. How could we represent double the amount of apples?

Lesson overview:Expressing missing numbers algebraically

Core Content

Calculation problems: