Lesson video

Hello, everyone.

Welcome to today's maths lesson with me Miss Jones.

Hope you're doing well today, really looking forward to getting started.

Before we start let's warm up our brains a little bit.

I've got a riddle for you.

Okay, you're ready.

You live in a one story house made entirely out of wood, what colour are the stairs? Say it again.

You live in a one-story house made entirely out of wood, what colour are the stairs? The answer is there are no stairs because it's a one-story house.

Not sure if I caught you out of that one.

Okay, I think our brains are warmed up now, so let's begin.

In today's lesson, we're going to be expressing missing number problems algebraically.

I'm going to start by thinking about how we represent a problem with algebra, then we go to let's explore task, our main task, and finally our multiple choice quiz.

You'll need a pencil and a piece of paper or something else the right with.

Make sure you've got what you need before you start, if you don't pause the video now and go and get what you need.

Okay, let's start with a problem, this is a problem all about roast dinner.

Do you like roast dinner? We have a roast dinner every Sunday.

Okay, I wanted to make a roast dinner for my family.

This is what I found in the recipe book.

The time needed to roast meat was 15 minutes per one kilogramme of meat plus an additional 20 minutes.

What do I need to know in order to roast the meat? And why doesn't the recipe book give me an exact quantity? Hmm, okay, so what do I need to know? It's 15 minutes per kilogramme plus an additional 20 minutes.

What I need to know is how many kilogrammes my meat is.

Now the recipe doesn't give us an exact quantity because it doesn't know how much meat we have, we might have bought a big joint of meat or a small one, so this recipe caters for any size.

So the amount or the mass of the meat we have the amounts of kilogrammes is our unknown, it's a variable and then the time needed is also a variable.

How could we represent this recipe? Hmm, I wonder if we could use a bar model for this.

Let's have a little look.

We know we need to add on 20, then we know it's 50 per kilogramme but we don't know how many kilogrammes.

This only shows one kilogramme, we might have more than one, we might have fewer than one, we might only have half a kilogramme for example.

So actually a bar model is really difficult to draw for this one because we don't know how long our bar should be or how many lots of 50 needs to be shown on our bar.

Hmm, so how else could we represent this? Okay, let's think about what we know.

The two variables in this problem are the length of time as mentioned and the quantity of meat.

So we've got two unknown values two variables in this problem.

Perhaps we could represent this using the letters.

What letters might you choose to represent these variables? Now it doesn't matter which letters you choose, you might choose a letter that relates to the problem completely or you might choose any obstruct letters, it doesn't actually matter.

How are we going to turn our letters into an algebraic expression that represents our problem? Hmm, pause the video and have a think about what you might think.

Okay, let's have a look together, shall we? Okay, so we know our roasting time is 50 minutes times by the mass of the meat in kilogrammes added to 20 minutes.

Now in my expression I'm going to call a, the roasting time, okay? So that will be a, and b, is the massive meeting kilogrammes.

So my expression is a, is equal to 50 times the mass meat which is b add 20.

I know that my calculation will get me the right answer so I know multiplication takes priority, and then we add on the 20 afterwards.

Have a look at that equation and see how it connects back to my equation up here in words.

Okay, let's explore.

I'm going to give you another problem.

Here we've got a problem, just an example.

Ice cream sundaes cost two pound 50 plus 75p for each additional topping scoop of ice cream.

And I'm going to give you some expressions to choose from, your job is to think about which expression matches my problem.

Have a look at these three.

Let's have a look at some explanations that might help us.

He says one variable in this problem is the total cost of the sundae, and the other variable is the number of additional toppings.

Okay, so he started well because he's thinking about what are our variables? Our variable is the cost of the sundae, and our second variable is the number of toppings.

She says it can't a equals 2.

5b plus nought.

75 because the equation is multiplying the number of toppings by 2.

5, nought 75.

Okay, I think she's right.

So looking back at this, they cost 2 pound 50, so that's what we need to add on that's our base rate plus 75p per scoop.

So we need to have 2 pound 50 added to 75 lots of how many scoops there are.

So let's look at which one matches, we've already decided it's not this one a equals two pound 50 takeaway nought.

75p.

Or do we want to take away the amount of scoops or do we want to add them on? Let's have a look at this one, a equals 75p 75 lots of the amount of scoop that make sense plus 250.

Now it's in 100s that just means they've put the calculation into Pence.

So 75 Pence added to 250 Pence.

So our answer will be in Pence so we might have to convert it into pounds if we wanted to.

So I'm going to go with this one.

Okay, let's have a look at a few more and you can have a go at these.

For each example, select the algebraic equation that best represents it.

Explain your reasons, and if you want to use a pictorial representation to support your idea.

Here's our two problems, and here are three algebraic expressions to choose from.

Pause the video now and see if you can think about which expression matches each problem.

Okay, let's have a look.

Okay, so did you identify the correct algebraic equation and did you explain why? This one matches with this one, let's have a loo why? So we've got the cost of the photo album book is one pound 25, so that's our flat rate, and then we've got 45p per photograph.

So our variables are the cost of our photo album and the amount of photographs.

So we need to have one pound 25 or 125 Pence added to 45 lots of how many photographs they are.

So in this, y tells us how many photographs and x is the total cost.

This one matches this one.

A singer makes money from selling music, they pay a one-off fee of 12 pound 50, she's here to Oak-Tunes for marketing distribution costs and they receive 45p for each copy of an album sold.

So we've got 45p take away 12 pound 50.

May I ask why it's subtract here? They had to pay a fee, so they lost some money but they are gaining money for every copy of the album sold.

So 45 lots of every album, which is why but when taking away the initial fee that they had to pay.

Let's return to the problem we looked at earlier, all about roast dinner.

Hmm, it's making me feel a bit hungry this one.

Okay, if we remember correctly the time needed to roast meat was 50 minutes per kilogramme of meat plus an additional 20 minutes.

If we have a piece of meat that weighs 1.

6 kilogrammes how long should I roast it for? Hang on a minute we've got an extra piece of information here.

Now we know how many kilogrammes or how heavy or how much mass the meat is.

We have all the information we need in order to solve this problem and find out the other variable, the time.

Now that we have this extra piece of information I wonder if we could now draw a bar model.

I think it would be a lot easier to draw a bar model now but looking at this second question do we need to draw a bar model? Hmm, well, that's entirely up to whoever's solving the problem, a bar model might help you to make sense of the problem, visualise it, and if you wanted to explain it to somebody else that might be a really useful tool.

But we can also use our letters or algebraic expression to represent the problem.

Remember earlier, we came up with this expression, a which was the time is equal to 50, b, which was the amount of meat plus 20.

Now that we know that the meat weighs 1.

6 kilogrammes we can substitute that in for b to find out other variable, a, okay? I'm going to have a go at this, have a look at my work.

This is how I've worked it out, do you think I'm right? Have I made an error anywhere? And if I have, where did I go wrong? Pause the video now to have a look at that.

Okay, did you spot any errors? If I look really closely at my calculations I've made a mistake.

I haven't thought about order of operations, here we've got 50 times by 1.

6 added to 20.

Now this looks correct to me, so what I've done is take my 1.

6, my new piece of information, and I've put it instead of b.

We know that 50b is the same as 50 lots of b, 50 lots of 1.

6 added to 20, that looks right.

But underneath on my next line I've written that this is the same as 50 times by 21.

6.

So I've accidentally added this before I timed by 50 and we know that multiplication takes priority and I should have multiplied first and then added 20, and that suits our problem.

Remember we had to multiply 50 times by the amount of meat before we added on the 20.

So actually I haven't.

Although I've substituted in the right amount in the right place I haven't done my calculations correctly.

Let's have a look at how we should have done it.

So 50 times by 1.

6 added to 20 it's the same as 50 times 1.

6 is 80, same as 80 added to 20, which is 100 minutes.

Now we know 100 minutes is over an hour 'cause it's over 60, So we could write that as one hour and 40 minutes.

This is our correct answer.

Okay, it's time for your main task.

For your main task I'm going to give you a series of situations, and I want you to think about how you would write it as an equation, and I've told you what letter to use for what variable to help you.

Once you've done that think about how you can use your equation to solve the problems in the last column.

For example, here we've got Mike is doing a sponsored cycle ride.

For every mile he cycles Mike 30 pound in sponsorship.

His company also adds 1,000 pounds to the total.

Now you can represent his amount of cycles with f.

So what you need to do now is write an equation that represents this problem.

Once you've done that, try and work out the answers to these two.

I'm going to give you a chance to pause the video go off and do your task and then when you come back we'll go through the answers together.

Pause the video now.

Okay, let's go through some of these problems. Okay, so for our first one where we've got Mike who was doing his sponsored cycle ride, we can express this as 30f where 30f represents the number of cycles.

So he did 30 lots of those.

and then he gets an extra 1,000 pounds to 30f + 1,000.

Now, if he does 340 miles we can times 340 by the 30, add 1,000, we get 11,200 and for the second one and we get 112 x 30, and again, add the 1,000 we get 4,360.

Let's have a look at number two.

And number is put into a function machine, the machine divides number by four subtracts three so we're using b our equation would be b divided by four subtract three.

We know that works because it's a vision takes priority and we do the division first.

So if our letter b was replaced of 600, 600 is entered into the machine, it would simply be 600/4 and then that would be 150 we'd subtract the three to get 147, the 168 we substituted for b, we would end up with 39.

And finally problem three Sally by six notebooks and she paid with 20 pound note and get some change.

Want you to represent c with change, now in this problem there is actually two variables.

We've got here, the price of the notebook.

She buys six notebooks n is the price of the notebook.

So I added in an extra variable here to see if you could write an equation for it.

But here we have both bits of information, each notebook cost one pound 45 so that would be a value for n, so we need to work out the value for c.

C equals 20 take away six timed by one pound 45.

Hope you enjoy today's lesson, ask your parents or care.

if you can share your work from today's lesson.

Now that we've finished, please go and have a go with our multiple choice quiz for this lesson.

Thank you.