Fill in the blanks: We can factorise a number or expression by writing it as a ____ of two or more _____.

Fill in the blanks: a + 2 + a + 2 = _____ + _____ = 2(_____ + _____ )

Factorise 12x + 3.

Factorise 2y − 10.

Factorise −6p + 15m

Factorising Expressions Quiz

﻿Hi, everyone. And welcome to today's lesson. I'm Ms. Jones. And today we are going to be looking at forming and exploring equations. Before we can begin however, you need to make sure that you have a pen and some paper to write down some important notes and to have a go at some of the questions, because even I can't do all of these in my head. And you need to make sure you've got rid of all of your distractions and try and find somewhere quiet to work if you can. Pause the video here to make sure you've got all of that ready to learn. Okay, let's start. The first thing I would like you to do is to find the value of each of the remaining rods in each of the following cases. A, when the white rod has a value of five, B, when the red rod has a value of 12, and C, when the white rod has a value of w. That is really hard to say. White rod, white rod, white rod. Try and say that loads of times, it's very difficult. The rods are, as you can see in this diagram, you got a purple rod, a green rod, a red rod, and a white rod. I would like you, as I said to find, first of all, the value of all of the other colours when the white rod has a value of 5. So I'll do that one as an example for you. If the white rod has a value of 5, we can see that for example, let's look at the green rod. It's 3 of the whites. So it's 3 lots of 5. So it's 15. And I would like you to do that for all of the colours and for each of these scenarios. So pause the video here to have a go at that. So hopefully, you managed to get these answers. And really well done if you did. And you'll notice, hopefully that there's a pattern with these. The white is, well the green is 3 times the white, the purple is 4 times the white, and the red is 2 times the white. And we can see that quite clearly with our algebraic expressions at the bottom. If you wrote 2 multiplied by w, then well done for getting that, but extra well done if you simplified that as an expression to 2w. That's how we should be writing those algebraic expressions and terms. An equation is a way to express an equality. Think about the start of that word. That makes sense. As an equation, equality, equal. What equations can you form using this image? So the rods again. Binh over here has done two equations for you. She has said G - R = w. So if you'd imagine that little space there, that's a w that's left. She's also done the equation R = 2w. So she's done addition and subtraction and she's done multiplication or division. So you can do lots of different ones. Try and come up with around five. Pause the video to have a go. So hopefully you manage to get lots of them, some of them. And there's lots more that you could have gotten as well. So you might have got some different ones that aren't on there. So really well done for that. Binh notice the following equation, 3w = G, you might have found that one yourself. She added P to the expression 3w. So she's now got 3w + P. What is G going to be? What have we got to add to G to also keep that equality, to preserve the equality? So we've got 3w = G, if I now have 3w + P, what have I got to have, G add what to continue that being equal? Pause the video to have a go at that. We need to add on an expression equivalent to P. So it might be that you just add on P, it might be that you thought P is the same as 4w so I'm going to add on 4w. It doesn't matter, but it needs to have the same value as P. And that leads us nicely to basically whatever you do to one side of the equation, you have to do the same to the other to make sure that equation stays equal. We need to preserve that equality. So well done if you managed to get that. Pause the video now to do your independent task. So for the first question, you were completing the following equations. So we're just making sure we really understand that on either side of that, it needs to be the same. So if I've got 3 lots of 4 here, which is 12, I need to make sure the other side also equals 12. So 4 add what equals 12? Hopefully you managed to get 8. And similar for the other ones. For question two, you are told that R = 2w, and you may have wanted to draw this out. And G = w + R. These are facts that you have been told, then you needed to use those facts to complete the following equations. So, for example, if I had R + w, how many w's is that altogether? If I know that R is the same as 2w, it's kind of like substitution again, we've got 2w + w, which is 3w. So here are the rest of the answers. Really well done if you managed to get all of those, or even some of those correct. Well done. Now we would like you to do the following. Decide whether each of the following equations are true or false. If you find that they are false, I would like you to correct them to make them true. So, for example, we have R + w = 3w, it might help to draw this out, or just looking at it might work for you. So if I've got R, and I'm going to add another w, is that going to give me the same as 3w? Is that equation true? So pause the video to have a go at that. And these are your answers. So the first one was true, R + w is the same as 3w and you can see that we've drawn it out here. P - R does not leave me with G. In fact, P - R would actually leave me with R. So that's been corrected there. And so on. Again, massive well done if you managed to get those ones correct. Some of those were a little bit tricky, but hopefully you really understand what equations are and how they're all about having equal things on both sides of our equation. And that whatever we do to one side, we've got to do the same thing to keep them equal. Well done for today's lesson, make sure you fill out the quiz and test your understanding, and I'll see you next time.

Fill in the gaps: An equation is a way to express an ______.

Use the equation r = 2w to find the value of r when w = 3.

Use the equation p = 4w to find the value of w when p = 16.

Given that r = 2w, fill in the gaps: r + r = ___ + 2w.

Given that r = 2w and p = 4w, fill in the blanks: r + p = __w.

Forming and Exploring Equations Quiz

In this lesson, we will learn the concept of an equation and use models to form equations.

Maths

Y7 Maths

Key Stage 3

Year 7

Miss

Forming and exploring equations

Expressions, equations and inequalities

Algebra

THEME

UNIT

Algebraic expressions

Collecting like terms

Distributivity and expanding

Factorising expressions

Exploring equality

Inequalities

Further inequalities

Perimeter expressions

Perimeter inequalities

Counting strategies

Growing tree patterns

Use the distributive property to fill in the gaps: 4(10 + 5) = ____ × 10 + ____ × 5

Expand 8(n-3)

Expand -7(n+5).

Which value of y means that -3y - 1 > 2y

Fill in the gaps: 5a + 9a = ___ × a = ____

Simplify the expression -20x + 3 - 8y + x -y

If 19 > 14, which symbol would go in the gap: 7 × 19 __ 7 × 14?

Which inequality best compares the expressions for the perimeters of the 2 shapes below?

Which inequality is true when a = 3?

Lesson overview:Forming and exploring equations

Core Content

Expressions, equations and inequalities: