Which of the set of numbers below have a mean of 6?

From the set of numbers below which does not have a mean of 8?

A footballer scores 3 goals in his first game, 5 goals in his second game and 1 goal in his third game. What is the average number of goals that he has scored across his games?

6 people have the following number of sweets: 3,8,5,8,6. If they were to share the sweets equally between them how many would they each get?

Tickets to the cinema cost £8 each. Five friends go and each friend has the following amount of money: £9,£11,£6,£7,£6 Do they have enough money between them to pay for 5 tickets?

Calculating and interpreting the mean as an average

﻿Hi there, my name is Miss Darwish, and for our maths lesson today, we are going to be developing some strategies to solve some word problems, or multi-step word problems especially. But before we start today's maths lesson, can I just ask you for a favour to take yourself to a nice quiet place, somewhere where you can work. Okay, so for the lesson, we're first of all going to be talking about some money, discussing some money and coins, and then we'll look at some one step problems, and then multi-step problems. And then at the end of the session, of course, there will be a quiz for to go and complete. So for this lesson, if I could just ask you to get yourself a pencil or pen ready, a sheet of paper and a ruler, and we can start. So, only by using three coins. So any three coins, how much money can you make? Go, I'm going to give you 10 seconds. So what possible amounts can you make only by using three coins? So for example, I know I can make 17 Pence. I can use a 10 Pence, a five Pence and a two Pence. I also know I can make one Pound 55, by using a one Pound 50 Pence and five Pence, or I can make two Pounds three Pence two Pounds, two P one Pence. What have you made? How much can you not make? Just by using three coins. Can we make three Pounds from using three coins? We've got a two Pound coin and a one Pound coin, but that's already three Pounds and we need another coin. What about if we took the one Pound coin, 50 P is there another 50 P there? Nope, so you can't make three Pounds. Can we make 74 Pence? Got 50 Pence a 20 Pence, only got one two Pence no. What did you come up with? Okay, so here is some souvenirs from an Olympic shop. Now, what would you buy? We've got a gold medal, very nice. a t-shirt, a Olympic flag, a key ring, or a key chain and a water bottle. What would you buy if you were at this shop? Lots of things to choose from. I would buy personally a t-shirt. I love a good t-shirt and a water bottle. 'Cause I'm always drinking water, and I've already probably got about four water bottles. So might as well collect more. So t-shirt and a water bottle is what I would buy. So the total cost for a t-shirt and a water bottle is four Pound 80, add four Pound 50 is equal to nine Pound 30. So it would cost me nine Pound 30 to buy two items from the souvenir shop. Four Pound 80 and four Pound 50 is equal to nine Pound 30. So if I went into the shop, I would spend nine Pounds 30. Now I'm going to pay with a 10 Pound note. So I'm going to use a 10 Pound note to pay for these items. And what change would I receive? So I'm paying with a 10 Pound note and the items cost nine Pound 30. So I should receive 70 Pence. What would you buy? Pick two items. So that sheets of paper and pen that you've got. I want you to choose two items and jot them down for me. What would your total cost be? So I shared my two items. You share your two items and work out how much it would cost you in total or altogether. How much is your total cost? Is it more or less than mine? Maybe it's the same. Let's have a look at Antoni now, Antoni bought three souvenirs and he paid with a 10 Pound note like me, I wonder what Antoni bought. He bought three souvenirs, two, three. He received 70 P change. Also like me, I received 70 P change when I paid for my souvenirs. So what do we know about Antoni, he bought three souvenirs. Do we know what the three souvenirs are? We don't know what the three souvenirs are. It could have been a t-shirt, a flag, a gold medal. We just know he bought three items okay. Any three items. And he paid with a 10 Pound note. So he received 70 Pence change. What was the total cost of the three items that Antoni bought, can you work that out? So the total costs of the souvenirs that Antoni bought. Have you written that down for me? Let's see what he could have bought. If he paid with a 10 Pound note and he received 70 Pence change, the three items and must have cost, we don't know what the three items are yet. We can work it out. But first I know that the three items or the three souvenirs he bought cost him nine Pounds 30. Because he paid with a 10 Pound note and he got 70 Pence back change. That means the cost must have been nine Pounds 30, because if something costs nine Pounds 30 and you pay with a 10 Pounds note, you should get 70 paid back. What three items could they have been? Again I'm going to give you a few seconds, jot down any three items and see if you can get three items be nine Pound 30. Can't be two souvenirs. It can't be one, It can't be five. It has to be three. What might the three things be? Have you got any ideas? Shall we have a look together? Let's have a look. I've worked out that if he bought two key rings and a water bottle, then the total cost would be nine Pounds 30. So one key ring cost two Pound 40. Another key ring would be another two Pound 40, and a water bottle costs how much? Four Pound 50. So if I total that up, if I add two Pounds 40 and two Pounds 40, and 4 Pounds 50, I get a total of nine Pounds 30. So I think maybe I might have worked out the three souvenirs that Antoni bought. Shall we have a look at another word problem? this time this is Yasmin. Now like Antoni she also bought three souvenirs, but, she paid with a 20 Pound note, let's have a look. She received 10 Pounds 70 change. So she received a lots of change, but she paid with a 20 Pound night. So like Antoni, Yasmin bought three souvenirs. And again, we don't know which souvenirs she bought. She could have bought two gold medals and a t-shirt. She could have bought three t-shirts, maybe a flag, a water bottle and a t-shirt, maybe three key rings. Let's see. So what would our first step be to do, before we work out what those three items are. Work out how much, work out the total cost of the three souvenirs, and we can work that out. We know she bought three souvenirs and paid with a 20 Pound note. So she handed over 20 Pound note and she received back 10 Pound 70. So how much were the three souvenirs? Work it out for me. The total cost of the three souvenirs. So the three items must've cost nine Pound 30, well done if you said nine Pound 30, how much was Antoni's total cost? Nine Pound 30 as well. Did you notice that? The only difference is that Yasmin paid with a 20 Pound note, and Antoni paid with a 10 Pound note. But her three souvenirs must've cost nine Pounds 30. So we saw two different calculations there, but the three souvenirs we're still the same. Okay, well done. Now it's time for you to pause the video and move on with the independent task, have a go, do your best that you can, check it and then come back and we can go through and mark the answers together, good luck. Okay welcome back. How was that? Shall we have a look together? Do you want to grab yourself a pen to mark with, we can check through the answers together. Okay so question one, I bought two souvenirs, which cost a total of seven Pounds 75. What did I buy? So we're still looking at the exact same souvenirs. We're still in that souvenir Olympic shop. We haven't left yet. So if I bought two souvenirs, they both cost seven Pounds 75, what could I bought? A gold medal and a t-shirt. Four Pound 80, add two Pound 95, is equal to seven Pound 75. So well done if you set the gold medal and the t-shirt. Question two now. My friend bought three souvenirs and she paid with a 20 Pound note. So she bought three souvenirs. She paid with a 20 Pound note and the change she received was six Pounds 50, what did she buy? So if she paid with a 20 Pound note and she received six Pounds 50, it must have cost her 13 Pounds 50. So it's about seeing which three items have a total cost of 13 Pounds 50. And actually if you divide 13 Pounds 50 by three, that will be four Pounds 50. And that's exactly the cost of one water bottle. So actually my friend bought one water bottle. So three water bottles would cost 13 Pounds 50. And if she paid with a 20 Pound note then she would receive six Pounds 50 in change. And then the last one, two souvenirs costs the same as three souvenirs. What could they be? So this is what I came up with. Two key rings and a water bottle. How much do they cost? Nine Pounds 30, and one t-shirt and one water bottle. How much do they cost? Nine Pounds 30. So that's three souvenirs that cost the same as two souvenirs. So for three things you could get, for nine Pounds 30 you could buy three things, or for nine Pounds 30 you could buy two things. If you would like to share your work with us here at Oak National, then please ask your parents or your carer to share your work for you on Twitter, tagging @OakNational and to use the #LearnwithOak. So before I leave you to get on with the quiz, I just want to say, well done all the brilliant learning that you have completed to date on the word problems and good luck with the quiz.

I buy three souvenirs for £2.90, £3.60 and £4.10. How much did I spend in total?

A lemonade costs £2.25. I buy 2 for me and my friend and I pay with a £10 note. How much change do I receive?

I buy a meal deal and a tub of cream from the shops. I pay with a £10 note and receive £4.75 in change. How much did I spend on the meal deal and the tub of cream

A child's cinema ticket costs £4.60 and an adult cinema ticket costs £8.55. If I spent a total of £26.30, which tickets did I purchase?

A child's cinema ticket costs £4.60 and an adult cinema ticket costs £8.55. If I received £27.65 from a £50 note, which tickets did I purchase?

Developing strategies to plan and solve problems

In this lesson, we will investigate and model multiple-step worded problems involving money.

Maths

Y5 Maths

Key Stage 2

Year 5

Miss

Problem solving with whole numbers and decimals

Number

THEME

UNIT

Calculating intervals across zero

Solving problems involving division with remainders (Part 1)

Solving problems involving division with remainders (Part 2)

Adding 2 or more numbers mentally

Calculating across zero

Investigating properties of number

Exploring properties of palindromic numbers

Exploring properties of number

Which of the below gives the answer for 8 ÷ 5 ?

Which of the calculations below does not have any remainders or decimals?

Which of the calculations below has the smallest answer?

What is the answer to 87 - 88 + 89

Which of the following numbers is not a multiple of 11?

Which of the following numbers is not a multiple of 9?

I am in an elevator (lift) and I'm currently on level 6 but I need to get to -2. How many floors away is -2 from me?

The Olympic golf course in Rio has a par of 71 (expected number of strokes needed), if David scores 65, 70 and 66 on his 3 rounds, what is his total score?

Lesson overview:Developing strategies to plan and solve problems

Core Content

Problem solving with whole numbers and decimals: