Maths Adventure Year 5 / Year 6 - BBC

Maths Adventure Year 5 / Year 6

Maths Adventure Year 5 / Year 6 s Summer 2007

www.bbc.co.uk/schoolradio

Online Teacher’s Notes written by Sarah Hope-Gill Age: 9-11 These programmes are available to order (for UK schools only) on pre-recorded CDs from: BBC Schools’ Broadcast Recordings Tel: 08701 272 272 Monday to Friday 0800 to 1800 Or visit www.bbc.co.uk/schoolradio/howtoorder.shtml for more information Audio on demand. These programmes are also available as audio on demand from the School Radio website for 7 days following the original date of transmission. Refer to programme titles below to find out when programmes are available as audio on demand.

© This publication contains only BBC copyright material: its contents may be copied or reproduced for use in schools and colleges without further permission.

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Maths Adventure Year 5 / Year 6 Summer 2007 These programmes are available as audio on demand. Check below for the dates that each is available. Introduction

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Maths Adventure Year 5 1. Addition and subtraction AOD 27/04/2007 2. Multiplication and division AOD 04/05/2007 3. Fractions, decimals and percentages AOD 11/05/2007 4. Big numbers AOD 18/05/2007 5. Measurement AOD 25/05/2007 6. All sorts of problems AOD 08/06/2007

5 8 10 12 14 17

Maths Adventure Year 6 1. Addition and subtraction AOD 27/04/2007 2. Multiplication and division AOD 04/05/2007 3. Fractions, decimals and percentages AOD 11/05/2007 4. Big numbers AOD 18/05/2007 5. Measurement AOD 25/05/2007 6. All sorts of problems AOD 08/06/2007

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19 21 23 25 27 30


Introduction

Maths Adventure aims to provide ‘mental maths’ material that: • • •

compliments and consolidates your classroom work on numeracy builds on basic skills develops confidence

Maths Adventure and the National Curriculum: Maths Adventure Year 5 / 6 is similar to other School Radio mental maths programmes but extends pupils' work into the key area of 'problem solving', which has been emphasised by the National Numeracy Strategy. There are six separate programmes for Years 5 and 6. Each one begins with a warm-up task, introducing the maths focus and designed to sharpen pupils' mental skills. Following this are a number of 'word' problems which encourage pupils to apply their maths skills to everyday situations. Each programme ends with a final challenge for pupils to work on after the programme. These notes: These notes are intended to give a detailed guide to the programme content to help you plan and use the programmes. There are additional support materials available through the BBC Active School Shop at www.bbcactive.com/schoolshop School Radio CDs: Recording or purchasing the programmes on CD provides a flexible resource. You will have the option of listening to each programme before using it with your class. Please see the order form available from the School Radio website at: www.bbc.co.uk/schoolradio/howtoorder.shtml An MP3 version of the material is also available. To find this resource, please return to the home page www.bbc.co.uk/schoolradio and navigate from there for details. Using the programmes: The programmes can be played straight through in one session or split up into sections to be used at any time during the week. For example you may like to revisit a section for five minutes before playtime or end of the day as a ‘game.’ The material can be used with the whole class or group or by individuals. It is intended to be a flexible resource for you to use as needed. These notes provide you with a detailed guide to the content of the programmes which will help you choose which activities are suitable for your pupils and how you would like to integrate them into your programme of study.

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If you are using the programmes from CD you can press ‘pause’ (‘stop’ will take you back to the very beginning of the track on most equipment) at any time, to mediate the material. If you want to hear the question again then run back a few seconds and listen again. Before the programme: Getting ready to listen Settle the group so they are ready to listen, particularly if they are unfamiliar with audio resources. Make sure that the level of the sound is sufficiently loud for everyone to hear clearly. You may find that it helps to adjust the ‘tone’ controls. With most equipment turning the ‘bass’ down a little and the ‘treble’ up will help with clarity. If the sound is too loud it will be ‘fuzzy’ and the pupils will have difficulty in distinguishing the questions. If it is too quiet they will become restless and distracted. Preparing for the programme – You may like to focus the group on ‘listening’ with a listening game (such as everyone sitting as quietly as they can and seeing what sounds they can hear around the school and guessing what they are) or by repeating one of the games from a previous programme. During the programme: Encourage all the pupils to take part. Your attitude will help them participate fully. If some pupils are struggling, then try to find a time for them to revisit the material, perhaps having had some further discussion or teaching on the topic. ‘Achieving’ the correct answers will help build confidence and give them a firm foundation to build on for subsequent work. If they become restless it is worth considering returning to the material at some other time. After the programme: There are some extension activities suggested at the end of each programme page which you may like to consider incorporating into your regular sessions. Feedback: Your feedback is important to us. Comments from teachers or pupils are equally welcome! Please use the ‘Contact us’ button from the Home Page of the School Radio website at: www.bbc.co.uk/schoolradio/contact.shtml Or write to us at: Maths Adventure BBC School Radio London W12 7TS

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Year 5 programme 1: Addition and Subtraction Before the programme: • CD 1 Track 1

Discuss and record the related vocabulary to addition and subtraction. Questions

Teaching points

00:00

The characters for the adventure are introduced. The Maths Machine can move to any given place either in the past or in the future. Today’s programme is set in a theme park in the year 2100.

01:15

Pupils are introduced to the mental maths section of the programme. The children will have 5 seconds to write down their answers.

01:44

Question1: What number is 9 less than 16? Question 2: What is the sum of the first 3 odd numbers? Question 3: Add together the decimal numbers 0.8 and 1.3 Question 4: What is the difference between 1002 and 996? Question 5: Subtract 60 from 140

02:59

Answers: 1. 7 2. 9 3. 2.1 4. 6 5. 80 At the signal, pause the programme to discuss pupils’ scores.

03:38

This time could also be used to discuss the strategies the children used to solve the questions including any visual clues or jottings that they recorded.

03:55

The Maths Machine lands at the Maths Adventure Park.

There is a sound signal for each question.

04:48

Question 1: There are 56 ahead of us in the queue waiting to go on the runaway train. The next train has room for 24 of them. How many people will be left standing in the queue in front of you? Question repeated.

Subtraction

05:56

Solution: Subtract 24 people from the 56 in the queue which gives you 32. Answer: 32 people standing in the queue on the platform.

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06:18

Question 2: First slider came down in 8.1 seconds. The second slider was even faster just 6.8 seconds. What is the difference between the 2 sliders times? Question repeated.

07:17

Solution: Finding the difference is the same as counting on. Count on from 6.8 to 8.1 to find the answer. Answer: 1.3 seconds.

07:34

Question 3: The roller coaster has lots of carriages and can carry 62 passengers when it is full, but at the moment it is not very full at all. There are 17 empty seats. How many people are there on the ride? Question repeated.

08:36

Solution: Subtract the empty seats 17 from the 62 seats. Answer: 45 people on the ride.

08:53

Question 4: A burger costs £5.35, a squirt of tomato sauce costs 58p. How much will you have to pay in total? Question repeated.

09:48

Solution: A burger and tomato sauce costs £5.35 plus 58p. Answer: £5.93

10:12

Question 5: There are 185 people riding on the Super Speed Aqua jet boat. The boat arrives at Magical Island and 70 passengers get off and 34 get on. How many people are on the Aqua Jet Speed boat?

10:45

This is a two part question. Listen carefully. Question repeated.

11:33

Solution: Start with 185 people and then subtract the 70 people who got off, which leaves 115 staying on board. Add the 34 who got on to that 115 to find the answer. Answer: 149

12:00

Question 6: Theme Park T-shirts cost £14.80 and a hat to go with it costs £2.90. Buy them both. How much change will you have out of £20? Question repeated.

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Subtraction

Subtraction

Addition

Subtraction then addition

Addition and then count on to find change


13:19

Solution: Add the T-shirt price £14.80 to the hat (£2.90) That gives a total of £17.70. Work out the change by counting on from £17.70 to £20. Answer: £2.30.

14:02

Final Challenge: Consecutive Numbers. The challenge is to find a group of consecutive numbers that give the total of 123.

After the programme: • •

Discuss the strategies to approach the problem. Provide the children with other totals to find.

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Year 5 programme 2: Multiplication and Division Before the programme: • CD 1 Track 2

Discuss and record the related vocabulary to multiplication and division.

Questions

Teaching points

00:00

Introduction to programme

01:37

Pupils are introduced to the mental maths section of the programme.

01:45

Question1: What is 4 times 6? Question 2: If you divide 25 by 3 what is the remainder? Question 3: What is double 36? Question 4: What is 9 multiplied by 7? Question 5: What is 32 divided by 8?

02:43

Answers: 1. 24 2. 1 3. 72 4. 63 5. 4 At the signal, pause the programme to discuss pupils’ scores.

03:21

03:37

The Maths Machine lands at the Supermarket.

04:40

Question 1: CDs are on special offer today. For £18 you can get 4 CDs. All the CDs are the same price. So how much does each CD cost? The question is repeated.

05:35

Solution: If 4 CDs cost £18 divide 18 by 4. Or halve and halve again. Half of £18 is £9 and half of £9 is £4.50 Answer: CD is £4.50

05:57

Question 2: Golf balls are sold in packs of 3. A box of golf balls holds 35 packs. How many golf balls are there in each box? The question is repeated.

06:59

Solution: To work out the number of golf balls in each box you multiply 3 (the number of balls in a pack) by 35 (the number of packs in a box). Answer: 105.

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They will have 5 seconds to write down their answers.


Division

Multiplication


07:18

Question 3: In the butcher’s department they have a massive sausage, 220 centimetres long. It has been cut into 20 equal smaller sausages. How long is each of these smaller sausages?

08:25

Solution: To work out the length of each smaller sausage you divide the whole length - 220 centimetres - by 20. Answer: 11 centimetres.

08:43

Question 4: Toy ducks are sold in boxes of 6. If the store has a total of 100 ducks altogether, how many complete boxes can they fill? The question is repeated.

09:49

Solution: Divide the total number - 100 – by 6 to find the number of full boxes. That comes to 16 with a remainder of 4. Answer: 16 complete boxes.

10:12

Question 5: Balloons cost 30p each and I buy 12 of them. What change will I get from £5? The question is repeated.

11:22

Solution: First multiply the price of each balloon - 30p - by 12, which gives £3.60. Then take this amount away from £5. Answer: £1.40

11:48

Question 6: A 2 litre bottle of lemonade can fill 7 cups. How many bottles would you need to buy so that 80 people could have a cup of lemonade? The question is repeated.

12:44

Solution: Divide the 80 cups by 7. That makes 11, remainder 3. Those 3 cups will need an extra bottle. Answer: 12 bottles.

13:11

Final Challenge: Fizz Buzz Game. You can play the Fizz Buzz game in groups or even as a whole class. You start counting from 1 but whenever you come to a number that’s a multiple of 3 (a number that is in the 3 times table) you say Fizz instead of the number. Also try multiples of 5, and say ‘Buzz.’

Division

Division with a remainder

Multiplication and then subtraction


Multiples of three


Play Fizz Buzz again. See how far you go without anyone crashing. With a more able group try going a bit faster to really sharpen up your mental maths skills!

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Year 5 programme 3: Fractions, decimals and percentages Before the programme: • • CD 1 Track 3

Discuss and record the related vocabulary. Remind of the equivalent values – e.g. 25 % = 0.25 = one quarter. Questions

Teaching points

00:00

Introduction to the programme, set in Ancient Rome.

01:14


01:22

Question1: What is one third of 24? Thinking time.

01:34

Question 2: Which is larger - two fifths or one half? Thinking time.

01:46

Question 3: What is 50% of £3? Thinking time.

01:59

Question 4: What fraction of 1 metre is 75 centimetres? Thinking time.

02:11

Question 5: What is 4.6 rounded to the nearest whole number? Thinking time.

02:24

Answers: 1. 8 2. One half 3. £1.50 4. Three quarters 5. 5 At the signal, pause the programme to discuss pupils’ scores.

03:03

03:20

The Maths Machine lands in Ancient Rome.

03:56

Question 1: The street is 3.6 kilometres long. We are exactly half way along it. How many kilometres do we have to walk to reach the end of the street? The question is repeated.

05:01

Solution: Divide 3.6 kilometres by 2 to find the answer. Answer: 1.8 kilometres.

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The children will have 5 seconds to write down their answers.


Decimals and fractions


05:18

Question 2: There’s a stall on the market selling jars of olives. Three quarters of the 24 jars are already sold. How many jars are still for sale? The question is repeated.

06:22

Solution: If three quarters are sold that means one quarter is still for sale. To find a quarter divide the total number by 4. Answer: 6 jars.

06:46

Question 3: One double pace for a Roman soldier measures about 1.5 metres. The soldiers count out 1000 paces, then mark the spot with a stone. How far do they travel? The question is repeated.

08:00

Solution: Multiply 1000 by 1.5 metres. Answer: 1500 metres.

08:21

Question 4: The race started with 16 chariots but now only 25% are still running. How many chariots are still in the race? The question is repeated.

Percentages and fractions

09:30

Solution: Divide the total number of chariots - 16 - by 4 to find the answer. Answer: 4 chariots are still racing.

25% is the same as one quarter

09:47

Question 5: Two fifths of the soldiers carry spears. How many soldiers don’t carry spears? The question is repeated.

A century of Roman soldiers is a unit of 100 men

10:57

Solution: One fifth of 100 is 20. Two fifths of 100 is two times 20 – therefore 40 soldiers carrying spears. Then subtract 40 from 100 to find the answer. Answer: 60 soldiers not carrying spears.

Fractions and subtraction

11:26

Question 6: There are 30 men in the warm pool to start with and 10% get out. How many will be left in the warm pool? The question is repeated.

Percentages

12: 30

Solution: Work out 10% of 30 by dividing 30 by 10 – making 3. So the number left in the warm pool is 30 minus 3. Answer: 27 men are left in the warm pool.

Percentages; Division and subtraction

13:03

Final Challenge: Imagine that the answer to a question is one fifth, then devise as many different questions as you can – e.g. what fraction is the same as 20%?

Fractions

Division and multiplication

After the programme: •

Repeat challenge for other answers – e.g. one quarter; or 10%; or 0.5

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Year 5 programme 4: Big numbers Before the programme: • • CD 1 Track 4

How many different questions did pupils manage to devise to the answer ‘one fifth’? Allow pupils time to record in numerals and words a selection of large numbers. Questions

Teaching points

00:00

Introduction to the programme - set in outer space.

00:58


01:18

Question 1: Is 2065 an odd or an even number? Question 2: Which whole number comes before 7000? Question 3: What is 3655 rounded to the nearest 100? Question 4: What number is 1000 less then 3038? Question 5: What number is 100 times greater than 58?

02:28

Answers: 1. An odd number 2. 6999 3. 3700 4. 2038 5. 5800 At the signal, pause the programme to discuss pupils’ scores.

03:19

03:33

The Maths Machine lands in outer space.

04:28

Question 1: Write down the number you hear in numerals – i.e. using digits not words. The asteroid we are heading for is one hundred and eighty two thousand and forty five kilometres away. The question is repeated.

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This time could also be used to discuss the strategies the children used to solve the questions, including any visual clues or jottings that they recorded. You may like to repeat this section with any pupils who have found this difficult or give them some supplementary material.

Writing down big numbers


05:26

Solution: The digits you should have written down are 182,045.

05:43

Question 2: Planet X is 8,650 light years away from Earth and the Space Station is half way between the Planet and Earth. How many light years away from Earth is it? The question is repeated.

07:04

Solution: To work out the answer divide the distance away of Planet X – 8,650 - by 2. Answer: 4,325 light years.

07:31

Question 3: In the first minute the rocket travels 1,289 kilometres. In the second minute it travels 1,304 kilometres. In the third minute it travels 1,085 kilometres. In which minute did the rocket travel the furthest? The question is repeated.

09:08

Answer: the second minute – 1,304 was the longest distance recorded.

09:23

Question 4: The three recycling robots have collected a total of 1,900 kilograms of rubbish from the space station. Robot A collected 400 kilograms and Robot B collected 700 kilograms. How much did Robot C collect? The question is repeated.

10:54

Solution: Subtract 1100 kilograms from 1900 kilograms to find the answer. Answer: 800 kilograms.

11:29

Question 5: There is one jet pack for each of the 362 people living on the space station. Jet packs come in boxes of 100. How many boxes are needed for 362 people? The question is repeated.

12:45

Solution: 362 rounded up gives 400. 400 divided by 100 gives 4. Answer: 4 boxes of jet packs are needed.

13:03

Final Challenge: Number Cards. You will need number cards: 8, 1, 4, 6, 9. Now try using the number cards to make as many different 5 digit numbers as you can. Who can make the biggest number and who can make the smallest number? Then pick any 5 digit number like 50000 and use your cards to make the nearest number you can.

Division

The biggest number

Addition and subtraction of big numbers

Round up and divide


Repeat the game using different cards and different totals to find.

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Year 5 programme 5: Measurement Before the programme: • • CD 2 Track 1

Play the game from the end of the previous programme once more. Discuss and record the vocabulary related to weight, length and capacity.

Questions

Teaching points

00:00

Introduction to the programme, which is set in an athletics stadium.

01:20


01:30

Question1: Which is heavier - 3.5 kilograms or 400 grams? Question 2: How many millimetres are there in 1 metre? Question 3: On a 24 hour clock the time is 17:45. What is the time using a 12 hour clock? Question 4: A square has an area of 16 square centimetres. What is the length of each of the square’s sides? Question 5: One 100th of a litre is the same as how many millilitres?

02:45

Answers: 1. 3.5 kilograms 2. 1,000 millilitres 3. 5.45 or a quarter to 6. 4. Each side is 4 centimetres long 5. 10 millilitres At the signal, pause the programme to discuss pupils’ scores.

03:30

03:45

The Maths Machine lands at an athletics stadium.

04:28

Question 1: A runner covers 400 metres doing 1 complete lap of the stadium’s track. How many laps will she complete in a race 2,000 metres long? The question is repeated.

05:15

Solution: Divide 2,000 metres by 400 metres to find the answer. Answer: 5 laps of the track.

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This time could also be used to discuss the strategies the children used to solve the questions, including any visual clues or jottings that they recorded.

Division


05:28

Question 2: The last runner in the marathon has just finished. He took 3 hours and 17 minutes to complete the course. The winner finished in 2 hours 29 minutes. How many minutes were there between the winner and the last runner to complete the marathon? The question is repeated.

06:36

Solution: The winner finished 48 minutes before the last runner. Answer: 48 minutes.

06:58

Question 3: The Australian javelin thrower has thrown a distance of 74.8 metres. That’s only 15 centimetres shorter than the winning throw. How far is the winning javelin throw? The question is repeated.

07:56

Solution: To find the answer add 74.8 metres and 15 centimetres. Answer: 74.95 metres.

08:13

Question 4: Men throw a 7.3 kilogram shot. The women throw a 3.6 kilogram shot. What is the difference between the weights of the shots? The question is repeated.

09:28

Solution: Take 3.6 kilograms away from 7.3 kilograms to find the answer. Answer: 3.7kilograms.

09:45

Question 5: A German high jumper has just cleared the bar at 1 metre 92 centimetres. His personal best though is 2 metres and 6 centimetres. How many more centimetres does he need to jump to reach his personal best? The question is repeated.

10:58

Solution: Count on from 1 metre 92 centimetres to 2 metres 6 centimetres. Answer: 14 centimetres.

11:17

Question 6: In this race 4 different runners have to run a section of the race each passing a baton to each other as they change over. Runner 1: 48 seconds; Runner 2: 50 seconds; Runner 3: 52 seconds; Runner 4: 50 seconds. So what was the team’s total time in minutes and seconds? The question is repeated.

12:56

Solution: the times are equivalent to 200 seconds. Answer: 200 seconds - which is 3 minutes and 20 seconds.

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Subtraction of time

Subtraction and addition of decimals

Subtraction of decimals

Subtraction / counting on

Addition of minutes and seconds


13:40

Final Challenge: Perimeters The rectangle you need to investigate is one with an area of 24 square centimetres. The challenge is to work out the different perimeters that the rectangle could have – e.g. if it had sides of 6 centimetres and 4 centimetres the perimeter would be 6 plus 6 plus 4 plus 4 - which is 20 centimetres. What other perimeters can you find?

Remember it is the perimeter you are finding


Present pupils with rectangles with different areas and ask them to calculate the perimeters.

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Year 5 programme 6: All sorts of questions Before the programme: • •

Repeat the challenge from the end of the previous session. Can the pupils still remember how to calculate the perimeter? Discuss with the children any key vocabulary they think that they might need with a focus on addition, subtraction, multiplication and division.

CD 2 Track 2

Questions

Teaching points

00:00

Introduction to the programme - set under the sea.

01:30

Question1: What is double 62? Question 2: Which is heavier – 3,500 grams or 3 kilograms? Question 3: What is 8 multiplied by 9? Question 4: What is the difference between 3.9 and 4.6? Question 5: What fraction is equivalent to 0.25?

02:35

Answers: 1. 124 2. 3,500 grams 3. 72 4. 0.7 5. One quarter At the signal, pause the programme to discuss pupils’ scores.

03:18


03:34

The Maths Machine lands under the sea.

04:24

Question 1: Dive down to 12 metres below the surface. Go up by 8 metres. Then go down again 5 metres. What depth have we finished at? The question is repeated.

Addition and subtraction

05:37

Solution: Picture a vertical number line with a zero at the surface go down to 12 metres then up 8 metres arriving at 4 metres. Then go down 5 metres, arriving at 9 metres. Answer: 9 metres.

Imagine a vertical number line with a zero at the top

06:02

Question 2: A school of 30 fish swim by. Three fifths of them are blue and the rest are yellow. How many fish are yellow? The question is repeated.

Fractions

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07:07

Solution: Two fifths of the fish are yellow. One fifth of 30 is 6, so two fifths of 30 is 12. Answer: the number of yellow fish is 12.

07:25

Question 3: We swim around a rectangular piece of a wreck. Its perimeter is 18 metres. If 2 sides of the rectangle measure 4 metres what is the length of each of the other 2 sides? The question is repeated.

08:44

Solution: 2 sides of the rectangle are 4 metres each, which adds up to 8 metres. Take that way from the perimeter of 18 metres. That gives the length of the other sides - 10 metres – which is divided by 2. Answer: 5 metres.

09:10

Question 4: A treasure chest weighs 22 kilograms. When we pour out all the water its weight is 8 kilograms less. If the chest itself weighs 10 kilograms what is the weight of the treasure? The question is repeated.

10: 31

Solution: Subtract the weight of the chest - 10 kilograms - from the total weight - 22 kilograms. That gives 12 kilograms. Take away the weight of the water and sand - 8 kilograms to find the answer. Answer: the treasure weighs 4 kilograms.

11:01

Question 5: There are a total of 160 jewels inside the treasure chest. They are put into bags which each hold a maximum of 9 jewels. How many bags are needed to hold all the jewels? The question is repeated.

12:21

Solution: Divide 160 by 9 which is 17, remainder 7. There are 17 full bags of jewels and the remaining 7 jewels will also need a bag. Answer: 18 bags are needed.

12:21

Final Challenge: Doubles Starting with £1, how many doubles would you need to get past 1 million pounds?

Addition, subtraction and division

Subtraction

Division with remainder


Go through the answers to all the questions and take time to discuss pupils’ answers. Repeat the challenge from the end of the programme. What answer did they find?

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Year 6 programme 1: Addition and Subtraction Before the programme: • •

Discuss the vocabulary for addition and subtraction. Encourage pupils to compile their own list and add to it after the programme.

CD 2 Track 3

Questions

Teaching points

00:00

The characters for the adventure are introduced. The Maths Machine can move to any given place, either in the past or in the future. Today’s programme is set during the reign of Queen Victoria.

01:12


01:36

Question1: What is the difference between 0.5 and 0.75? Question 2: What is the total of 6, 7 and 8? Question 3: Add together 29 and 9. Question 4: What must you add to 65 to make 100? Question 5: Subtract 800 from 1300.

02:50

Answers: 1. 0.25 2. 21 3. 38 4. 35 5. 500

03:36

At the signal, pause the programme to discuss pupils’ scores.


03:56

The Maths Machine lands in Victorian England.

There is a sound signal before an important number is said in the word problems.

04:41

Question 1: Queen Victoria was only 18 when she became Queen in 1837. So the question is in which year was she born? Question repeated.

Subtraction

05:47

Solution: You have to subtract 18 from 1837 to get the answer. Answer: 1819.

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06:06

Question 2: This small theatre has 230 people in the stalls and 185 people up in the balcony seats. How many people are there altogether? Question repeated.

07:02

Solution: Add the number of people in the stalls – 230 - to the number of people in the balcony – 185 to find the answer. Answer: 415 in the theatre altogether.

07:29

Question 3: This Victorian steam train travels at an average speed of 80 kilometres per hour. To travel from London to Bristol takes 2 and a half hours. So approximately how many kilometres is it from London to Bristol? Question repeated.

08:38

Solution: 2 hours at 80 kilometres an hour means you travel 160 kilometres. In a further half an hour the train travels 40 kilometres. Add 160 kilometres to 40 kilometres to find the answer. Answer: 200 kilometres.

09:09

Question 4: In 1851 the Great Exhibition was held full of wonderful exhibits and inventions. On the first day there were 6,800 visitors. On the second 4,900 visitors. How many visitors came in total over the two days? Question repeated.

10:24

Solution: Add the numbers of visitors together. That’s 6,800 plus 4,900. Answer: 11,700 people.

10:49

Question 5: A barge starts with 3.4 tonnes of coal. At its first stop 0.8 tonnes are taken off. Then at its next stop a further 1.5 tonnes are unloaded. So how much coal is left on board? Question repeated.

12:31

Solution: First add together the coal that is unloaded - 0.8 plus 1.5 tonnes, giving 2.3 tonnes. Then take that away from the full load of 3.4 tonnes to find the answer. Answer: 1.1 tonnes were left on board.

13:13

Final Challenge: Palindromes. These are numbers that read the same backwards and forwards. Take any 3 digit number (e.g. 123) reverse the digits (321) now add the 2 numbers together. 123 plus 321 equals 444 - a palindromic number. Your challenge is to add together any 3 digit number and its reverse to find out if you always reach a palindromic number?

Addition

Multiplication

Addition then subtraction


Challenge the children to find the largest / smallest 3 digit palindromic number.

20


Year 6 programme 2: Multiplication and Division Before the programme: • • •

Play some more with palindromic numbers. What did pupils discover at the end of the last session? Discuss and record the related vocabulary to multiplication and division.

CD 2 Track 4

Questions

Teaching points

00:00

Introduction to programme.

00:58

The children are introduced to the mental maths section of the programme.

01:14

Question1: What is 8 times 8? Question 2: What remainder do you get if you divide 38 by 4? Question 3: What is 56 divided by 7? Question 4: What is double 2.7? Question 5: What is 99 shared equally between 9?

02:18

Answers: 1. 56 2. 2 3. 8 4. 5.4 5. 11

02:56


03:11

The Maths Machine lands at the fun fair.

04:01

Question 1: There are 8 people in each of the carriages. If there are 9 carriages altogether how many people are on the ride in total? The question is repeated.

04:54

Solution: To work out the answer to the problem you multiply 8 by 9. Answer: 72 people.

05:13

Question 2: On the super bingo 3 people shared the top prize of £2,430. How much did each person win? Question repeated.

06:10

Solution: To work out how much each person wins you divide £2,430 by 3. Answer: £810.

21



Multiplication

Division


06:29

Question 3: The big wheel has space for 2 people on each seat and there are 36 seats altogether but 7 of the seats are empty. How many people are riding on the big wheel? The question is repeated.

07:50

Solution: Start by working out the number of full seats - 36 take away the 7 empty seats gives 29. There are 2 people in each seat, so 29 multiplied by 2 is 58. Answer: 58 people.

08:12

Question 4: In the target shooting game there are 500 prizes. If 1 shelf holds 40 prizes. How many shelves are needed to hold all 500 prizes? Question repeated.

09:24

Solution: To work out the answer you divide the 500 by 40 – which gives 12, with remainder 20. These 20 prizes need an extra shelf. Your answer is 12 plus 1. Answer: 13 shelves.

09:46

Question 5: Candy floss costs 80p for each stick. If I buy 9 sticks how much change will there be from £10? Question repeated.

10:59

Solution: 9 sticks of candy floss at 80p each makes £7.20. Take this amount from £10 to find the answer. Answer: £2.80

11:19

Question 6: 300 people want to go on the rocket ride. Only 4 rockets are launched and each rocket takes 40 people. So the question is in two parts: how many rockets will be launched and how many people will be left behind? The question is repeated.

12:43

Solution: 300 divided by 40 equals 7, remainder 20. Answer: there will be 7 rockets launched with 20 people left behind.

13:26

Final Challenge: Write down this 5 digit number: 15,873. Now trying multiplying it, using a calculator or in your head, by any multiple of 7, or 14 or 21. You should find some interesting number patterns.

Top tip: This is a 2 stage problem. 1. Work out how many seats are full first. 2. Multiply this answer by 2.

Division. Top tip: You need to have enough shelves for all the prizes.

Multiplication and then subtraction Top Tip – a 2 stage problem



Discuss the patterns that pupils have found and draw conclusions.

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Year 6 programme 3: Fractions, decimals and percentages Before the programme: • •

Look at the patterns pupils discovered at the end of the last session. What conclusions did they come to? Discuss and record the related vocabulary.

CD 3 Track 1

Questions

Teaching points

00:00

Introduction to the programme - set in space.

00:57


01:10

Question1: What is three quarters of 16?

01:20

Question 2: What is 12.6 rounded to the nearest whole number?

01:34

Question 3: Which is heavier - 3.15 kilograms or 3.6 kilograms?

01:50

Question 4: What is 10% of £5?

02:02

Question 5: Which is smaller - two fifths or three tenths?

02:20

Answers: 1. 12 2. 13 3. 3.6 kilograms 4. 50p 5. Three tenths

02:56


03:15

The Maths Machine orbits in outer space.

03:59

Question 1: A hippo is 4.83 metres in length. What is its length rounded to the nearest metre? The question is repeated.

05:03

Solution: 4.83 metres is rounded up to the next whole metre. Answer: 5 metres.

05:30

Question 2: A masked shrew weighs 2.9 kilograms but the pigmy shrew weighs only half that amount. What is the weight of the pigmy shrew? Question repeated.

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The children will have 5 seconds to write down their answers.

This time could also be used to discuss the strategies the children used to solve the questions.

Decimals

Fractions


06:37

Solution: To work out half divide by 2 - so half of 2.9 kilograms is 1.45 kilograms. Answer: 1.45 kilograms.

06:53

Question 3: The elephants get through 12 tonnes of food a week. 90% of this is hay; the rest is vegetables. How much do the vegetables weigh? Question repeated.

08:20

Solution: If 90% of the food is hay that means that 10% is vegetables. 10% of 12 tonnes is 1.2 tonnes. Answer: 1.2 tonnes.

08:41

Question 4: There are 25 penguins in total. Two fifths of them are dozing on the rocks; the rest are swimming in the water. How many are swimming? Question repeated.

Fractions Top tip : work out one fifth of 25 first.

10:00

Solution: If two fifths of the penguins are dozing then three fifths of the penguins are swimming. One fifth of 25 is 5; multiply this by three to find the answer. Answer: 15 penguins are swimming.

20% is the same as one fifth

10:20

Question 5: A cheetah runs at 100 kilometres an hour. A gazelle runs at three quarters of this speed. What is the speed of three gazelle? The question is repeated.

Fractions TOP TIP :work out one quarter of 100 is first.

11:38

Solution: One quarter of 100 is 25; to find three quarters multiply 25 by 3. Answer: 75 kilometres per hour.

11:57

Question 6: On planet Zoo there are two different types of camel. 20% of the 30 camels have two humps. How many twohumped camels are there? Question repeated.

13:23

Solution: 10% of 30 is 3. Multiply that by 2 to get 20%. 20% of 30 is 6. Answer: There are 6 two humped camels.

13:58

Final Challenge: Imagine that the answer to a question 75%. Then devise as many different questions as you can with that answer – e.g. what percentages is the same as three quarters? Answer is 75%.

Percentages

Percentages Top tip : work out 10% of 30 first.


Allow the children to devise questions to different answers - such as 60%; 0.33; 12; a half %; etc.

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Year 6 programme 4: Big numbers Before the programme: • • CD 3 Track 2

How many different answers did pupils get for the answer 75%? Share them together. Ask pupils to say the number before and the number after numbers with more than 5 digits - such as 14,567. Questions

Teaching points

00:00

Introduction to the programme - set in the depths of an ocean.

01:08


01:18

Question1: Which whole number is between 1,748 and 1,750? Question 2: What is the value of the digit 7 in the number seventeen thousand two hundred and eighty? Question 3: Which whole number comes before 200,000? Question 4: What number is 100 times greater than 90? Question 5: What is 4,150 millimetres rounded to the nearest thousand?

02:33

Answers: 1. 1,749 2. 7 thousand 3. 199,999 4. 9,000 5. 4,000 millimetres

03:29


03:58

The Maths Machine lands on the sea bed.

04:27

Question 1: The submarine is given a code to locate a giant squid. The code is the largest number that can be formed from these six digits. Write them down carefully – 4, 5, 7, 2, 9 and 1. The question is: what is the biggest number you can make with these digits? The question is repeated.

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This time could also be used to discuss the strategies the children used to solve the questions including any visual clues or jottings that they recorded. You may like to repeat this section with any pupils’ who have found this difficult or give them some supplementary material Writing down big numbers


05:39

Answer: 975,421 (nine hundred and seventy five thousand and four hundred and twenty one).

05:54

Question 2: The submarine dives 3,500 metres, then goes down a further 4,200 metres. How many metres below the surface is it now? Question repeated.

07:05

Solution: The submarine has dived 3,500 metres plus a further 4,200 metres. Add the two numbers together to find the answer. Answer: 7,700 metres.

07:30

Question 3: A shoal of fish is chased by a shark. The size of the shoal is given in words and it needs to be recorded in numerals. The shoal contains eleven thousand and twenty four fish. Question repeated.

08:16

Answer: 11,024 (or 11 024)

08:30

Question 4: Over three hours the submarine travels a total distance of 38,000 metres. It travels 17,000 metres in the first hour and 8,000 metres in the second. How far does it travel in the third hour? Question repeated.

09:55

Solution: In the first two hours the submarine travels 25,000 metres. Subtract that number from the total distance of 38,000 metres to find the answer. Answer: 13,000 metres.

Addition and subtraction of big numbers

10:14

Question 5: The submarine is positioned exactly halfway between 47,400 metres and 48,000 metres. Where exactly is the submarine positioned? The question is repeated.

Top tip - do this in two stages Work out the difference between the two numbers first

11:36

Solution: The difference between 47,400 metres and 48,000 metres is 600 metres. Half of this is 300 metres. Add this to 47,400 to find the answer. Answer: 47,700 metres.

11:56

Question 6: Microscopic creatures are collected in test tubes. There are 28 creatures in each tube. The tubes are put into bags of 10 and 10 bags are put in a box. How many creatures in each box? Question repeated.

13:15

Solution: 10 tubes in each bag and 10 bags in a box means that there are 100 tubes in a box. Multiply that by the 28 creatures in each tube. Answer: 2,800 creatures in each box.

13:53

Final Challenge: Write down these words - kilo, mega, giga. The challenge is to explore their meaning and to find out how many zeros each represents?

Addition

The biggest number

Top tip – picture the problem


Create a display using these words and examples from everyday life.

26


Year 6 programme 5: Measurement Before the programme: • •

Did pupils discover what kilo, mega and giga mean? Share your answers together. Discuss and record the vocabulary related to weight, length and capacity.

CD 3 Track 3

Questions

Teaching points

00:00

Introduction to the programme - set in a castle in the past.

01:10


01:20

Question1: What is 2.5 litres in millilitres? Question 2: Each side of a square is 4.5 centimetres in length. What is the square’s perimeter? Question 3: On a 24 hour clock the time is 20:05. What is the time using a 12 hour clock? Question 4: What is 2,385 grams rounded to the nearest kilogram? Question 5: Is a gallon a unit of length, mass or capacity?

02:35

Answers: 1. 2,500 millilitres 2. 18 centimetres 3. 8.05pm or 5 past 8 4. 2 kilograms 5. Capacity

03:16


03:33

The Maths Machine lands at a castle.

04:16

Question 1: The castle walls are 3.2 metres thick. An entrance is being dug through the wall but so far the builders have only managed to dig through by 150 centimetres. How far have they got to dig to get right through the whole wall? The question is repeated.

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05:17

Solution: 150 centimetres is the same as 1.5 metres. The amount left to dig is 3.2 metres minus 1.5 metres. Answer: 1.7 metres or 170 centimetres.

05:39

Question 2: There are lots of beehives in the castle grounds. 900 grams of honey is collected in 1 day. So the question is how much honey was collected in 1 week? The question is repeated.

06:40

Solution: To work out the answer multiply the amount of honey collected in 1 day 900 grams - by the number of days in the week – 7. That is 900 x 7. Answer: 6,300 grams or 6.3 kilograms

07:01

Question 3: The castle keep is a square tower. The perimeter of the tower is 72 metres. What is the length of each of the tower’s walls? The question is repeated.

08:01

Solution: To find the answer divide the perimeter - 72 metres - by the number of walls – 4. Answer: 18 metres.

Division

08:13

Question 4: The well used for drinking water has a large bucket that can collect 25 litres every time. Each day the people in the castle need at least 170 litres of water. How many bucketfuls must be collected to provide enough water? The question is repeated.

Top tip – make sure there is enough mater for each person.

09:34

Solution: 7 bucketfuls of 25 litres is 175 litres – which gives 5 litres more than needed. Answer: 7 bucketfuls.

Division

10:06

Question 5: An archer fires an arrow through a slit in the castle wall at a target 1 kilometre a way. His arrow travels one fifth of this distance. How far does the archer’s arrow travel? Question repeated.

Top tip – there are 1000 metres in a kilometre.

11:21

Solution: One fifth of 1 kilometre is the same as 1000 metres divided by 5. Answer: 200 metres.

Division

11:36

Question 6: Vegetables are grown in a rectangular area of the castle grounds. The rectangle is 30 metres long and 20 metres wide. Turnips are grown on 50% of this land. What is the area of the land used for growing turnips? The question is repeated.

Do this in two parts: 1. Work out the area. 2. Divide it in two.

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Subtraction

Multiplication


13:06

First work out the area of the rectangle by multiplying 30 metres by 20m metres giving 600 square metres. To find 50% of this area divide the number by 2. Answer: 300 square metres.

13:55

Final Challenge: How old is someone who has lived for a million minutes (assume there are 365 days in a year)?

Multiplication and division


Can pupils work out their own ages in minutes? Their siblings? Their parents? Grandparents?

29


Year 6 programme 6: All sorts of questions Before the programme: • •

Can pupils remember how many minutes there are in a year? How old are they in minutes? Discuss and record the vocabulary with a focus on addition, subtraction, multiplication and division.

CD 3 Track 4

Questions

Teaching points

00:00

Introduction to the programme - set at the North Pole.

01:00

Mental maths section.

01:16

Question1: What is one fifth of 20 kilograms? Question 2: What is double 3.8? Question 3: What is 9 multiplied by 9? Question 4: What is the difference between 706 and 697? Question 5: What is 25% of £2?

02:20

Answers: 1. 4 kilograms 2. 7.6 3. 81 4. 9 5. 50p

02:55


03:03

The Maths Machine lands at the North Pole.

03:54

Question 1: The summer temperature is 5 degrees Celsius but the winter temperature is just minus 23 degrees Celsius. What is the difference between those temperatures? Question repeated.

Difference

04:54

Solution: To find the answer count on from minus 5 to 23. Answer: 28 degrees Celsius.

Imagine a number line from minus 23 to 5.

05:10

Question 2: The ice is 800 metres thick. It takes a drill 30 seconds to go down 100 metres. How many minutes will it take to drill all the way through the ice? The question is repeated.

Multiplication

30



06:21

Solution: It takes 30 seconds to drill through 100 metres. So it will take 8 times 30 seconds to drill through 800 metres. 8 times 30 seconds is 4 minutes. Answer: 4 minutes.

06: 42

Question 3: An adult polar bear weighs about half a tonne. A polar bear cub is one tenth of the weight of an adult. What is the approximate weight of the cub in kilograms? The question is repeated.

07:54

Solution: One tenth of half a tonne is the same as one tenth of 500 kilograms - which is 50 kilograms. Answer: 50 kilograms.

08:11

Question 4: You don’t see most of an iceberg because nine tenths of it is below the surface of the water. If you can see 6 metres above the surface of the water what is its total height?

09:12

Solution: If nine tenths of the iceberg are below the water then that means one tenth is above it. One tenth is 6 metres, then 10 tenths or the full height of the iceberg is 60 metres. Answer: 60 metres.

09:31

Question 5: A team of well driven husky dogs can pull a sled 40 kilometres in 5 hours. At this speed how far would they travel in 3 hours? Question repeated.

10:33

Solution: A sled travelling 40 kilometres in 5 hours does 8 kilometres per hour. So in 3 hours the sled will travel 24 kilometres. Answer: 24 kilometres.

10:50

Question 6: There are approximately 24,000 Inuit people in Canada with 20,000 more than this in Greenland. How many Inuit people are there altogether?

12:12

Solution: The number in Greenland is 20,000 more than Canada so the total is 44,000. Add this to the 24,000 in Canada to find the answer. Answer: 68,000 people.

12:53

Final Challenge: Which packet of fish fingers is better value? The first packet weighs 2.5 kilograms and cost £5. The second packet weighs 1 kilogram and costs £2.50. Which packets is better value?

Division. Top tip: 1 tonne is the same as 1000 kilograms.

Multiplication

Division and multiplication

Addition Top tip Do this in 2 stages.

After the programme: • Encourage pupils to compare prices and quantities of items to decide which is better value.

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