If 3f + 8 = 20. What is the value of f?

Which expression would represent the following problem:  The cost of a photo album book is £1.50 for binding and printing with an additional cost of 25p per photograph.

a - 2b = 8. Which of the following pairs of numbers would work?

A function machine has the rule x = 2y + 1. Where y is the input and x is the output. If we put 4 into the function machine (y = 4) what would come out?

Reasoning and problem solving

﻿Hi, welcome to your math lesson with me, Miss Jones. Hope you're all feeling well today. Before we start I want us to warm up our brains. I've got a riddle for you. If you've got me, you want to share me. If you share me, you haven't kept me. What am I? I'll say it one more time. If you've got me, you want to share me. If you share me, you haven't kept me. What am I? Give yourself a little think. Okay, the answer is a secret. If you've got a secret, you want to share it. But if you share it, you haven't kept it. Hope you like that one. Okay, let's start our math lesson. In today's lesson we are going to be, hope you're excited, because we're going to be reasoning and solving problems. Can't wait. Okay, let's see what we're going to be looking at. We're going to be looking at our first problem, called Oak Tunes. Hm, sounds interesting. You'll have a go at a task and then we'll come back and do the solution together. Our second problem today is called how old is Gill? Sounds interesting. And again you'll have a go at a task and we'll come back and go over it together. Make sure you've got a pencil and a piece of paper or something else to write with today. If you haven't, pause the video now and go and get what you need. If you're ready let's begin. Task one is called Oak Tunes. Jack and Jill both buy music as digital download from Oak Tunes. Jack buys three albums and two singles, spending 27 pound 93 in total. Jill buys three albums and three singles, spending 29 pound 91. We need to find out the price of an album and a price of the single. Hm, let's look at this a bit more closely. So we need to find out an album and a single. We have two unknowns. We don't know the price of an album, we don't know the price of a single. But we know the total. But we also have an extra piece of information. So using both of our pieces of information, perhaps we can work it out. I think I need to represent this problem. So maybe I could represent it using an algebraic expression. 3a for album plus 2s for single is equal to 27 pound 93. Also I know that three albums plus three singles is equal to 29 pounds 91. Have a close look at both of our equations here. What's the same and what's different? You might have noticed that these equations are actually quite similar. The only difference in this part is the amount of singles. This one has one more single which has made our total slightly more. So if I want to find out the price of a single all I have to do is find the difference. Now you might have preferred to represent that as a bar model. Let's have a look at what it might look like as a bar model. Here we go. So we've got three albums plus two singles and three albums plus three singles so you can clearly see that if we could work out the difference between our two values we're going to find out the price of one single. So let's do that. 29 pounds 91, subtract 27 pounds 93 will be 1 pound 98. Therefore I know a single costs 1 pound 98. Hm, now we need to work out the price of an album. How can we do that? Well if we take just one of these equations and substitute our new information in, so instead of writing S now we can actually write two lots of nine, 1 pound 98, to see if we can work out what A is. So I'm going to do that, I'm going to just take the top piece of information only or if you're using your equation, take the top bit of your equation or the top bar of your bar model and put in our new information. Okay. So this time I'm going to subtract two lots of 1 pound 98 so the 2 S's and that should leave me with the information of what 3a is which is 23 pound 97. Now that I know what 3a is, I can divide by three to find out the price of an album which is 7 pound 99, okay. Now I know the price of an album and the single. Okay, I think you're ready to have a go at a similar problem. Let's have a look. Okay, this time we've got some different amounts. This time Lisa buys four albums and four singles, spending 40 pound 96. Fraya buys four albums and three singles, spending 39 pound 30. Hm, I'd like you to use the strategies that we discussed to solve this problem. Thinking about how you might want to represent it using algebraic expression or using a bar model or a combination of both, have a think about whether this problem is similar to any other problems that you've done and think about what you notice when you're trying to find your answer, okay. All right, go off and do your task one and then come back to the video and we'll go over it together and then start task two. Pause the video now. Okay hopefully you've had a go at task one. Let's have a look at the answers. Okay so this time we know that Lisa bought four and Fraya bought four so that's exactly the same in both our pieces of information. The difference is that the singles were slightly different. We had four here and three here. Now I know that Fraya had one fewer single. So if I work out the difference between both of these I can find out the price of a single. 40 pounds 96 take away 39 pounds 30 got me 1 pound 66. That was you first step. Once you know the price of a single you can have a look at one of these pieces of information, or one of your equations if you were using one, and use that in order to find out the price of an album. So I'm going to focus on this one. So we've got our key information now that a single costs 1 pound 66. So we need to work out and let's take away the singles from this piece of information so let's take away three singles which cost 4 pound 98. If we take that away from our total, we're going to end up with 34 pounds 32. Now that will just leave us with four albums so we need to divide by four. 34 pound 32 divided by 4 is equal to 8 pound 58. Okay it's time for task two. How old is Gill? Okay let's have a look at this to start with together. We know that Gill's age now is a multiple of four. Okay so I'm already thinking her age could be four, eight, twelve, sixteen. Wait a minute, there's a lot of possibilities here. I wonder if there's some more information. In one year's time her age will be a prime number. Okay that makes it interesting. We also know in two year's time her age will be a multiple of five. Okay but I'm struggling to visualise all of these possibilities in my head now. I need a representation to help me figure out, to help me figure out hold old Gill is now. The representation I've chosen here is a 100 square. I've chosen this one because it shows all numbers. I could easily tick off numbers as I go, as I'm working systematically. Now most people don't live beyond 100 so it's unlikely Gill will be older than 100 but it is something we can explore perhaps up to about 110 but then after that not many people live that long. Okay, so thinking about our first piece of information, Gill is a multiple of four. I'm going to mark the multiples of four on my 100 square. Now our second piece of information. In one year's time her age will be a prime number. Okay so I'm going to look and see after every multiple of four one year later which ones will be a prime number and I'm going to mark them in purple. Okay there are some prime numbers that I haven't marked in purple, for example 31, and that's because that can't be that age because it doesn't come straight after a multiple of four. So I've only marked the prime numbers that come straight after one of my pink numbers, the multiples of four. Now my final piece of information is that in two years time her age will be a multiple of five. So now I want you to go through each of my pink numbers, check if there's a prime number next to it, and check that the number after that two years later is a multiple of five to find out which of these could be a possibility. So looking at the number four I know that next to it is a prime number so that's good but in two years time we'll get to six which isn't a multiple of five so it can't be four. Looking at eight, there's no prime number next to it as nine is divisible by three so it can't be eight. Looking at 12, we do have a prime number next to it. Let's have a think about what it will be in two year's time, 14, is that a multiple of five? No, so it can't be 12. Have a think about 16. Two year's time would be 18, that's not a multiple of five. Have a think about 20, no prime number next to that one so it can't be that. Have a think about 24. No prime number next to that as 25 is divisible by five. Have a look at 28, there's a prime number next to that one. What would it be in two year's time? In two year's time it will be 30. Ah, that is a multiple of five. So actually one of the possibilities could be 28. What I'd like you to have a go at now is think about are there any other possibilities by working systematically just like I did. You can use 100 square if you like. That might help you. Can you find the other possibilities? Off you go and complete the task. Okay let's go through the solution together. So we've already discovered that Gill could be 28. Now if we kept going using my system of working systematically, checking the multiples of four, seeing if there's a prime number next to it and if there is, is the number, the following number after that a multiple of five. So far none of these are possibilities so I'm crossing them all out but as I get to higher numbers there is one more possibility that you might have found. Look at number 88. Now next to 88 there is a prime number, 89. Two year's time she'll be 90 so actually Gill could have been 88. So Gill could have been 28 or she could have been 88. Actually there is one more possibility. She could have been 108. I wonder if you found that one too. However I know that one is very unlikely so good job if you managed to find 88 and 28. Okay that brings us to the end of our lesson today. If you'd like to share your work, make sure you ask your parents or carer before you do so. Now that we've finished our lesson, you can have a go at our multiple choice quiz.

If 4f - 8 = 20. What is the value of f?

Which expression would represent the following problem: A singer makes money from selling music. They pay a one-off fee of £55 to Oak-Tunes for marketing and distribution costs and receive £1 for each copy of the album sold.

Instead of writing 7 x a in an algebraic expression, what could I write instead?

3c + 2d = 30. Which pair of numbers does does NOT work with this equation?

Kate's age now is a multiple of three. In two years' time, her age will be a prime number.  Which of the following could be her age?

Sam's age now is a multiple of four. In four years' time, her age will be a square number.  Which of the following could be her age?

In this lesson, we will continue to explore two types of problem in depth, thinking carefully about how to represent each problem in order to help us find a solution.

Maths

Y6 Maths

Key Stage 2

Year 6

Miss

Reasoning and problem solving (Part 2)

Calculation problems

Number

THEME

UNIT

Understanding which operations have equal priority

Order of operations

Consolidating order of operations

Linear number sequences

Expressing missing numbers algebraically

Expressing missing number problems algebraically

Finding solutions to problems with two variables

Consolidating linear sequences and representing problems with algebra

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

3 x 5 + 2 =

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

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

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:Reasoning and problem solving (Part 2)

Core Content

Calculation problems: