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• Engage and excite pupils using challenging space-themed problem-solving activities

• Use open-ended questions to stretch pupils and develop their thinking and reasoning skills

• Detailed teaching guidance to support teachers and teaching assistants

Sample activities

Brand new activities that will challenge and stretch your more able

Mappedto the New Curriculum

MAM03 samples.indd 1 24/09/2013 11:26

How to use Maths for the More AbleThis exciting new series gives your students the opportunity to engage in contextualised mathematics that extends the programme of studies for the new National Curriculum. Its aim is for children to deepen their understanding of the mathematics involved through application and opportunities to reason at a higher level.

Each unit contains two pages of student activities, accompanied by one page of notes for the teacher, which provide an overview of the content. They also include prompts to help the teacher consider whether the children have the required skills and knowledge that will need to be applied to the problems (Key knowledge). Additionally, teachers are provided with prompts for assessing and evaluating the children’s strategies along with ideas to further extend a problem. There is also a comprehensive set of solutions for the questions in the unit.

The student activities are broken into four sections, ‘Starting Off ’, ‘Away We Go!’, ‘Free Running’ and ‘S.I.D.’s Challenge’, which are structured so that the problems become increasingly more demanding as the unit progresses. Units can be used flexibly so that, should an activity prove too challenging at one point, with a quick recap, it can be revisited later in the year when the children are ready to tackle the next stage in the challenge.

Mathematical reasoning is an integral part of this resource and children will be expected to explain their thinking as part of their solutions. On occasion, this will be accompanied by a language structure to guide explanations, e.g. ‘I think Dara is right because ...’

As part of the challenges, children will find hints as reminders, additional information or suggestions about how best to present their findings. However, generally they will be expected to show their findings in their own way.

With a strong focus on problem solving, there will be times when the use of a calculator should be encouraged so that the children have the freedom to explore more thoroughly and change their strategies more easily when an incorrect path has been followed.

We hope you and your students enjoy their Mission to Mars!

Off we go!

26

Starting Off

Away We Go

'Earth Control, We Have a Problem!' Solving more addition and subtraction problems.

� It seems some of the upgrades have caused other systems to go wrong. The alarm on the main warning system is flashing!

Jade and Zack race to the flight deck. Zack notices that the control measuring oxygen levels is no longer showing the correct information.

Help Zack correct this information.

1. 2502. 5253. 901

Jade is also having a problem with the oxygen controls.

All the information she is given is wrong, but this time the measurements are 101 too high.

1. Correct the information for Jade.

2. Which measurements were the easiest to correct? Why?

301

450

1000

2101

Oh no, it is 99 behind.All the measurements

will be wrong!

Emergency! Emergency! Earth Control has reported that we have a problem on

the flight deck. You must fix it now!

MAM03 samples.indd 2 24/09/2013 11:26

26

Starting Off

Away We Go

'Earth Control, We Have a Problem!' Solving more addition and subtraction problems.

� It seems some of the upgrades have caused other systems to go wrong. The alarm on the main warning system is flashing!

Jade and Zack race to the flight deck. Zack notices that the control measuring oxygen levels is no longer showing the correct information.

Help Zack correct this information.

1. 2502. 5253. 901

Jade is also having a problem with the oxygen controls.

All the information she is given is wrong, but this time the measurements are 101 too high.

1. Correct the information for Jade.

2. Which measurements were the easiest to correct? Why?

301

450

1000

2101

Oh no, it is 99 behind.All the measurements

will be wrong!

Emergency! Emergency! Earth Control has reported that we have a problem on

the flight deck. You must fix it now!

Maths for the More Able Year 2:

Addition and Subtraction

MAM03 samples.indd 3 24/09/2013 11:26

28

TEACHER’S NOTES

Curriculum Focus1. Use place value and number facts to solve problems.2. Solve problems with addition and subtraction. 3. Recognise and use the inverse relationship

between addition and subtraction, and use this to check calculations and missing number problems.

Running the ActivityBackgroundWhat experience have the children had of findingmissing numbers by applying the inverse?

Do they have strategies to support adding and subtracting near multiples of ten?

These tasks require children to recognise whenthe inverse operation has to be used and thencalculate accordingly.

Starting OffWithin Starting Off, children will add 99 to a set of given numbers. They should use what they know about adding 100.

Key knowledge: Addition will undo subtraction and vice versa.

Away We GoWithin Away We Go, children move on to a similar problem that requires them to subtract 101 from a range of three- and four-digit numbers. These include 301 and 2101. These can be partitioned to make the subtraction much easier.

Key knowledge: Use partitioning in different ways to make calculations easier, e.g. 301 partitioned into 200 and 101 makes it easy to subtract 101.

The next part of the task will also require partitioning and knowledge of place value.

Free RunningWithin Free Running, children begin to investigatesequences of numbers. They should recognise andbe able to explain why some calculations are easier than others, e.g. 303, 202, 101, 0.

In S.I.D's Challenge, this idea is then developed so that children identify other sequences that work in the same way.

Sharing Results and EvaluatingLook for children who round and adjust to add 99or subtract 101.

Share the sequences that are created by subtracting 101 from, say 505, so that children can confidently describe the patterns they see.

AnswersStarting Off1. 3492. 6243. 1000

Away We Go1. 200, 349, 899, 2000

2. 301 and 2101 are easier to correct because 101 can be seen within the number, i.e. 301 can be partitioned into 200 + 101 2101 is 101 more than 2000

3. For 4000, Zack needs to add 5000 For 600, Zack needs to add 300 For 30, Zack needs to add 60 For 0, Zack needs to add 9

Free Running1. 303 202 101 0

451 350 249 148

500 399 298 197

S.I.D.’s ChallengeOther measurements such as 404, 505, 606, 707 …, are easy to correct and will always finish on zero if 101 continues to be subtracted.

'Earth Control, We Have A Problem!'

Year 2

27

Irina at Earth Control tells Zack that he must fix the problem with the oxygen indicator.

3. Help Zack to fix the problem. Find a way to show what Zack must do.

Free Running

Jade is not having any luck fixing the oxygen indicator.In fact, it is getting worse!

To get the correct measurement she has to subtract 101, then subtract another 101 from this answer and then subtract 101 again!

1. Copy and complete Jade’s work to help her find the correct measurements.

S.I.D.’s Challenge

HINT: Start by writing down the value of each digit.

HINT: Remember that landing on zero helped her before.

Jade found that 303 was the easiest measurement to correct. Landing on zero helped a lot!The problem continues and Jade has to subtract 101 from lots of different measurements.

Which ones do you think she will find easy to correct?

All that landing on 0 did the trick! Well done,

everyone – the oxygen indicator is fixed!

4 6 3 0

303

451

500

To fix the problem you must reset all dials to 9, but you can only do this by adding the correct number each time. Don’t forget to use place value, it won’t

work otherwise!

28

TEACHER’S NOTES
















Away We Go1. 200, 349, 899, 2000



Free Running1. 303 202 101 0

451 350 249 148

500 399 298 197



Year 2

MAM03 samples.indd 4 24/09/2013 11:26

28

TEACHER’S NOTES
















Away We Go1. 200, 349, 899, 2000



Free Running1. 303 202 101 0

451 350 249 148

500 399 298 197



Year 2

27

Irina at Earth Control tells Zack that he must fix the problem with the oxygen indicator.

3. Help Zack to fix the problem. Find a way to show what Zack must do.

Free Running

Jade is not having any luck fixing the oxygen indicator.In fact, it is getting worse!

To get the correct measurement she has to subtract 101, then subtract another 101 from this answer and then subtract 101 again!

1. Copy and complete Jade’s work to help her find the correct measurements.


HINT: Start by writing down the value of each digit.

HINT: Remember that landing on zero helped her before.

Jade found that 303 was the easiest measurement to correct. Landing on zero helped a lot!The problem continues and Jade has to subtract 101 from lots of different measurements.

Which ones do you think she will find easy to correct?

All that landing on 0 did the trick! Well done,

everyone – the oxygen indicator is fixed!

4 6 3 0

303

451

500

To fix the problem you must reset all dials to 9, but you can only do this by adding the correct number each time. Don’t forget to use place value, it won’t

work otherwise!

28

TEACHER’S NOTES
















Away We Go1. 200, 349, 899, 2000



Free Running1. 303 202 101 0

451 350 249 148

500 399 298 197



Year 2

MAM03 samples.indd 5 24/09/2013 11:26

6

Jade writes down these five measurements.

3. Help Jade write all of these measurements in order, fromsmallest to largest. Find a way to prove your decisioneach time.

4. Write down another two measurements that would go between the ones shown here. One of thenumbers should have only tenths and the other should have tenths and hundredths.

smallest largest

Free Running

HINT: You could use partitioning to help you prove your decisions.

The Mariners are in the Rover and on their way to Olympus Mons.

Dara is driving, so Jade, Ceri and Zack have been busy taking many digital images along the way.

Each Mariner is using a different lens on their camera.

1. Use the clues below to find out which Mariner has taken which images and what lens they are using.

• The Mariner was standing 2850 m away when they took the image of Olympus Mons.• Jade used the lens that made the strange rock look 3.05 m away when it was really 305 m away!• The image of Mount Sharp makes it look only 125.4 m away.• Ceri took the image of the mountain that appeared to be about 3 m away.


Use what you have found out to complete this table.

2 .34 m 2.43 m 3.24 m 2.04 m 2.3 m

10× zoom 100× zoom 1000× zoom

Lens used Actual distance Distance in image, e.g. 3.41 m

Rounded to one decimal place, e.g. 3.41 m rounds to

3.4 mOlympus Mons × ?

Strange rock × ?Mount Sharp × ?

5

Starting Off

The special lenses make objects appear much closer. The 10× zoom lens makes objects appear 10 times closer. This means than an object 20 metres away would look like it was only 2 metres away!

1. Copy and complete the table to show how the different lenses work.

Away We Go

Destination – Olympus Mons Solving problems about decimals.

� An expedition to Olympus – the highest mountain and largest volcano in the Solar System. It is almost three times the height of Mount Everest.

Jade writes down the new measurements like this using partitioning to help her: 3.45 m = 3 m + 4

10m + 5

100m

1. Find the new measurements with the 100× zoom and show the value of each digit in the same way that Jade has done here.

2. Round each of the new measurements to the nearest whole metre (e.g. 3.45 m would round down to 3 m).

Attention, Mariners! Today you must start your expedition to Olympic Mons. We are keen to explore this mountain and volcano as scientists on Earth want more photographic

evidence of its magnitude.

20 metres 42 metres ? metres 258 metres ? metres10× zoom 2 metres

100× zoom 1.75 metres


100× zoom

345 m 3.45 m73 m ?105 m ?99.9 m ?

Let’s write some of these measurements down so we can put this information with the images. We will need to show the value of each digit in

the number too.

We’ll need to take the camera equipment and the special lenses

to get some good shots!

Maths for the

More Able Year 4:

Decimals

MAM03 samples.indd 6 24/09/2013 11:26

6




smallest largest

Free Running






• The Mariner was standing 2850 m away when they took the image of Olympus Mons.• Jade used the lens that made the strange rock look 3.05 m away when it was really 305 m away!• The image of Mount Sharp makes it look only 125.4 m away.• Ceri took the image of the mountain that appeared to be about 3 m away.



2 .34 m 2.43 m 3.24 m 2.04 m 2.3 m

10× zoom 100× zoom 1000× zoom

Lens used Actual distance Distance in image, e.g. 3.41 m

Rounded to one decimal place, e.g. 3.41 m rounds to

3.4 mOlympus Mons × ?

Strange rock × ?Mount Sharp × ?

5

Starting Off

The special lenses make objects appear much closer. The 10× zoom lens makes objects appear 10 times closer. This means than an object 20 metres away would look like it was only 2 metres away!

1. Copy and complete the table to show how the different lenses work.

Away We Go

Destination – Olympus Mons Solving problems about decimals.

� An expedition to Olympus – the highest mountain and largest volcano in the Solar System. It is almost three times the height of Mount Everest.

Jade writes down the new measurements like this using partitioning to help her: 3.45 m = 3 m + 4

10m + 5

100m

1. Find the new measurements with the 100× zoom and show the value of each digit in the same way that Jade has done here.

2. Round each of the new measurements to the nearest whole metre (e.g. 3.45 m would round down to 3 m).

Attention, Mariners! Today you must start your expedition to Olympic Mons. We are keen to explore this mountain and volcano as scientists on Earth want more photographic

evidence of its magnitude.

20 metres 42 metres ? metres 258 metres ? metres10× zoom 2 metres



100× zoom

345 m 3.45 m73 m ?105 m ?99.9 m ?

Let’s write some of these measurements down so we can put this information with the images. We will need to show the value of each digit in

the number too.

We’ll need to take the camera equipment and the special lenses

to get some good shots!

6




smallest largest

Free Running






•The Mariner was standing 2850 m away when they took the image of Olympus Mons.•Jade used the lens that made the strange rock look 3.05 m away when it was really 305 m away!•The image of Mount Sharp makes it look only 125.4 m away.•Ceri took the image of the mountain that appeared to be about 3 m away.



2 .34 m2.43 m3.24 m2.04 m2.3 m

10× zoom100× zoom1000× zoom

Lens usedActual distanceDistance in image, e.g. 3.41 m

Rounded to one decimal place, e.g.

3.41 m rounds to 3.4 m

Olympus Mons× ?Strange rock× ?Mount Sharp× ?

MAM03 samples.indd 7 24/09/2013 11:26

Starting Off

� e Mariners all fetch their nuggets to see how much they have in total. All pieces have been melted and shaped into small cubes or cuboids.

Jade180 mm3

Zack

216 mm3

Ceri126 mm3

Dara

91.125 mm3

1. Find possible dimensions for each of the Mariners’ nuggets. No measurements are 1 mm.

2. Two of the Mariners have cube shaped nuggets.Which Mariners are these? What do we call these numbers?

3. One of the dimensions for each of the other cuboid shapes is not a whole number.Find a possible solution for each cuboid.

Away We Go1 gram = 0.052 cm3 1 gram (Gagarin-gold) = £83

Find the value of these nuggets of ‘Gagarin-gold’.

1. 0.416 cm³ 2. 1.066 cm³ 3. 10.4 cm³

4. What is the volume of a nugget with a value of £4150?

a hard bargainSolving problems about volume and money.

� Earth has sent the supply ship for it be returned loaded with a cargo of gold/minerals mined on Mars. Plans have been made to mine and export ‘Gagarin-gold’.

32

Attention, Mariners! � e supply ship will arrive on Mars shortly. We have all waited a very long time for this and I

know that one of you is keen to return to Earth, but the return trip can only be

made if it is � nancially worthwhile.

HINT: If you have already found a possible solution

for Q3 in Q1, try to � nd an alternative solution for Q3.

I wonder how much di� erent nuggets of

Gagarin-gold are worth?Gagarin-gold are worth?

I have a small nugget of ‘Gagarin-gold’ as a souvenir.

I wonder if that will help?

Y6_MoreAbleMaths_pages.indd 32 05/09/2013 12:16

7

Remember that it is always important to check the scale when measuring. That should help you decide

who has the most soap.

TEACHER’S NOTES

Curriculum Focus1. Find the effect of dividing a one- or two-digit

number by 10, 100 (and 1000), identifying thevalue of the digits in the answer as units, tenthsand hundredths.

2. Round decimals with one decimal place to thenearest whole number (and with two decimalplaces to the nearest number with one decimalplace).

3. Compare numbers with the same number ofdecimal places up to two decimal places.

Running the ActivityBackgroundHow secure are the children using a place value gridto multiply and divide numbers by 10, 100 (and 1000)?How confidently can they explain the effect on the digits and the use of zero as a place holder?

What experience do they have of working with measure and applying knowledge of place value to make sense of the value of each digit, particularly for decimals? Can they explain the rules for rounding?

Can they confidently partition numbers with one or two decimal places using this notation? U + ?

10+ ?

100These tasks require children to multiply and divide numbers by 10, 100 and 1000 in a problem-solving context and be able to round to the nearest whole number and to one decimal place.

Starting OffWithin Starting Off, children use the given criteria to divide values by 10, 100 and 1000. They are also required to use the inverse.

Key knowledge: When dividing by 10, 100 and 1000, thedigits move to the right by one, two or three places, respectively. Zeros are needed as place holders so that we know that the number is now 10, 100 or 1000 times smaller.

Away We GoWithin Away We Go, children move on to partitioning decimal numbers to include tenths, hundredths and thousandths. The problem extends to ordering decimals including comparing one and two decimal places.

Key knowledge: To compare one and two decimal placenumbers, it is useful to consider tenths expressed in hundredths, i.e. 2.3 as 2.30 to help compare it with 2.34.

Free RunningWithin Free Running, children are presented with a logic problem involving the skills used so far.

In S.I.D.’s Challenge they must also apply skills of rounding to one decimal place.

Sharing Results and EvaluatingLook for children who make use of the place value grid to help them make sense of dividing by 10, 100 and 1000. Look for children who confidently explain the use of the zero as a place holder.Share examples of rounding and ask children to suggest other decimal numbers that can be rounded to the same amount.

AnswersStarting Off1.

Away We Go1. 73 0.73 0.73 = 0 +

710

+ 3100

105 1.05 1.05 = 1 + 5100

99.9 0.999 0.999 = 0 + 910

+ 9100

+ 91000

2. 0.73 m,1.05 m and 0.999 m all round to 1 m.3. 2.04 m, 2.3 m, 2.34 m, 2.43 m, 3.43 m4. 2.4 (one decimal place) is the only value that can go between 2.34 m and 2.43

m. There are more solutions for a value with two decimal places, e.g. 2.35 m, 2.36 m, 2.37 m (2.40 m!), 2.41 m and 2.42 m.

Free RunningJade 100× zoom strange rockCeri 1000× zoom Olympus MonsZack 10× zoom Mount Sharp


Destination – Olympus Mons

Year 4

20 metres 42 metres 175 metres 258 metres 500 metres10× zoom 2 metres 4.2 m 17.5 m 25.8 m 50 m

100× zoom 0.2 m 0.42 m 1.75 m 2.58 m 5 m1000× zoom 0.02 m 0.042 m 0.175 m 0.258 m 0.5 m

Lens usedActual

distanceDistance in image,

e.g. 3.41 m

Rounded to one decimal place, e.g. 3.41 m

rounds 3.4 mOlympus

Mons×1000 2850 m 2.85 m 2.9 m

Strange rock ×100 305 m 3.05 m 3.1 mMount Sharp ×10 1254 m 125.4 m 125.4 m

28

TEACHER’S NOTES
















Away We Go1. 200, 349, 899, 2000



Free Running1. 303 202 101 0

451 350 249 148

500 399 298 197



Year 2

MAM03 samples.indd 8 24/09/2013 11:26

Starting Off

� e Mariners all fetch their nuggets to see how much they have in total. All pieces have been melted and shaped into small cubes or cuboids.

Jade180 mm3

Zack

216 mm3

Ceri126 mm3

Dara

91.125 mm3

1. Find possible dimensions for each of the Mariners’ nuggets. No measurements are 1 mm.

2. Two of the Mariners have cube shaped nuggets.Which Mariners are these? What do we call these numbers?

3. One of the dimensions for each of the other cuboid shapes is not a whole number.Find a possible solution for each cuboid.

Away We Go1 gram = 0.052 cm3 1 gram (Gagarin-gold) = £83

Find the value of these nuggets of ‘Gagarin-gold’.

1. 0.416 cm³ 2. 1.066 cm³ 3. 10.4 cm³

4. What is the volume of a nugget with a value of £4150?

a hard bargainSolving problems about volume and money.

� Earth has sent the supply ship for it be returned loaded with a cargo of gold/minerals mined on Mars. Plans have been made to mine and export ‘Gagarin-gold’.

32

Attention, Mariners! � e supply ship will arrive on Mars shortly. We have all waited a very long time for this and I

know that one of you is keen to return to Earth, but the return trip can only be

made if it is � nancially worthwhile.

HINT: If you have already found a possible solution

for Q3 in Q1, try to � nd an alternative solution for Q3.

I wonder how much di� erent nuggets of

Gagarin-gold are worth?Gagarin-gold are worth?

I have a small nugget of ‘Gagarin-gold’ as a souvenir.

I wonder if that will help?


7

Remember that it is always important to check the scale when measuring. That should help you decide

who has the most soap.

TEACHER’S NOTES

Curriculum Focus1.

Find the effect of dividing a one- or two-digitnumber by 10, 100 (and 1000), identifying thevalue of the digits in the answer as units, tenthsand hundredths.

2. Round decimals with one decimal place to thenearest whole number (and with two decimalplaces to the nearest number with one decimalplace).

3. Compare numbers with the same number ofdecimal places up to two decimal places.

Running the ActivityBackgroundHow secure are the children using a place value gridto multiply and divide numbers by 10, 100 (and 1000)?How confidently can they explain the effect on the digits and the use of zero as a place holder?

What experience do they have of working with measure and applying knowledge of place value to make sense of the value of each digit, particularly for decimals? Can they explain the rules for rounding?

Can they confidently partition numbers with one or two decimal places using this notation? U + ?

10+ ?

100These tasks require children to multiply and divide numbers by 10, 100 and 1000 in a problem-solving context and be able to round to the nearest whole number and to one decimal place.

Starting OffWithin Starting Off, children use the given criteria to divide values by 10, 100 and 1000. They are also required to use the inverse.

Key knowledge: When dividing by 10, 100 and 1000, thedigits move to the right by one, two or three places, respectively. Zeros are needed as place holders so that we know that the number is now 10, 100 or 1000 times smaller.

Away We GoWithin Away We Go, children move on to partitioning decimal numbers to include tenths, hundredths and thousandths. The problem extends to ordering decimals including comparing one and two decimal places.

Key knowledge: To compare one and two decimal placenumbers, it is useful to consider tenths expressed in hundredths, i.e. 2.3 as 2.30 to help compare it with 2.34.

Free RunningWithin Free Running, children are presented with a logic problem involving the skills used so far.

In S.I.D.’s Challenge they must also apply skills of rounding to one decimal place.

Sharing Results and EvaluatingLook for children who make use of the place value grid to help them make sense of dividing by 10, 100 and 1000. Look for children who confidently explain the use of the zero as a place holder.Share examples of rounding and ask children to suggest other decimal numbers that can be rounded to the same amount.

AnswersStarting Off1.

Away We Go1. 73 0.73 0.73 = 0 +

710

+ 3100

105 1.05 1.05 = 1 + 5100

99.9 0.999 0.999 = 0 + 910

+ 9100

+ 91000

2. 0.73 m,1.05 m and 0.999 m all round to 1 m.3. 2.04 m, 2.3 m, 2.34 m, 2.43 m, 3.43 m4. 2.4 (one decimal place) is the only value that can go between 2.34 m and 2.43

m. There are more solutions for a value with two decimal places, e.g. 2.35 m, 2.36 m, 2.37 m (2.40 m!), 2.41 m and 2.42 m.

Free RunningJade 100× zoom strange rockCeri 1000× zoom Olympus MonsZack 10× zoom Mount Sharp


Destination – Olympus Mons

Year 4

20 metres 42 metres 175 metres 258 metres 500 metres10× zoom 2 metres 4.2 m 17.5 m 25.8 m 50 m

100× zoom 0.2 m 0.42 m 1.75 m 2.58 m 5 m1000× zoom 0.02 m 0.042 m 0.175 m 0.258 m 0.5 m

Lens usedActual

distanceDistance in image,

e.g. 3.41 m

Rounded to one decimal place, e.g. 3.41 m

rounds 3.4 mOlympus

Mons×1000 2850 m 2.85 m 2.9 m

Strange rock ×100 305 m 3.05 m 3.1 mMount Sharp ×10 1254 m 125.4 m 125.4 m

Maths for the More Able Year 6:Volume

28

TEACHER’S NOTES
















Away We Go1. 200, 349, 899, 2000



Free Running1. 303 202 101 0

451 350 249 148

500 399 298 197



Year 2

MAM03 samples.indd 9 24/09/2013 11:26

34

TEACHER’S NOTES

Curriculum Focus1. Recognise when it is possible to use formulae for

volume of shapes.2. Calculate, estimate and compare volume of cubes

and cuboids using standard units, includingcentimetre cubed (cm3) and cubic metres (m3),and extending to other units such as mm3 and km3.

3. Solve problems involving addition, subtraction,multiplication and division (in the context of money).

Running the ActivityBackgroundDo the children recognise that volume is expressed in cube units whereas capacity is expressed in units such as litres?

What experience do the children have of calculating volume using di� erent units of measurement?

How well do they link the formula for fi nding the volume of a cuboid with that of the area of a rectangle? Do they recognise the importance of place value when calculating with diff erent units of measurement?

Are they con� dent to explain which operations they will need to use when solving number problems and the order in which to use them?

� ese tasks also require the children to calculate values based on volume expressed in cm³.

Starting OffWithin Starting O� , children identify possible dimensions for given volumes. � ey should also identify cube numbers.

Key knowledge: Volume can be defi ned as a measureof the amount of 3D space which is occupied by an object.

Away We GoWithin Away We Go, children move on to calculating the value of gold using the equivalents given. � ey must select the appropriate operations to use and recognise when the inverse is required.

� e problem extends to converting mm³ to cm³.

Key knowledge: To convert measurements in mm³ to cm³,we must divide the volume by 1000, and vice versa.

Free RunningWithin Free Running, children calculate volumes in m³. � ey must also use a given ratio to � nd the likely volume (and then value) of gold in two di� erent mines.

In S.I.D.’s Challenge, they must apply the inverse to � nd out what volume of gold is required for a value of £1 million and what volume of soil and rocks must, therefore, be mined.

Sharing Results and EvaluatingLook for children who con� dently apply the formula for � nding the volume of a cuboid and can use this to ‘undo’ any calculations.

Look for those that can con� dently explain how they must convert between units when dealing with volume and how this di� ers from area (i.e. mm² to cm² need to divide area by 100).

Share solutions for S.I.D.’s Challenge and consider other large values of ‘Gagarin-gold’ in the same way.

AnswersStarting Off1. Jade (9 × 5 × 4 mm or 18 × 5 × 2 mm or 4.5 × 10 × 4 mm etc.)

Zack (6³ or 3 × 12 × 6 mm or 2 × 18 × 6 mm etc.)Ceri (3 × 7 × 6 mm or 6 × 3.5 × 16 mm or 1.5 × 14 × 6 mm etc.)Dara (4.5³ or 9 × 2.25 × 4.5 mm etc.)

2. Zack and Dara – cube numbers3. See question 1

Away We Go1. £664 (8 g)2. £1701.50 (20.5 g)3. £16,600 (200 g)4. 2.6 cm³5.

Possible dimensions of nugget (mm)

Possible dimensions of

nugget (cm)

Volume in cm3

Weight in grams (g)

Value in £

Jade 4.5 × 10 × 4 0.45 × 1 × 0.4 0.18 3.462 £287.35

Zack 6 × 6 × 6 0.6 × 0.6 × 0.6 0.216 4.154 £344.78

Ceri 6 × 3.5 × 6 0.6 × 0.35 × 0.6 0.126 2.423 £201.11

Dara 4.5 × 4.5 × 4.5 0.45 × 0.45 × 0.45 0.091125 1.752 £145.42

6. The ‘numbers’ are 1000 times smaller in cm³. This happens because the number of each dimension in cm is 10 times smaller than in mm so the total volume is 10 × 10 × 10 times smaller i.e. 1000.

Free Running1. a) 2998.125 m³ b) 23,985 m³ (19.5 x 20.5 x 60 m)2. Mine a) 14.734 cm³ b) 117.869 cm³3. £188,137.06

S.I.D.’s Challenge1. £1 million is the value of 12,048.19277 g of gold. This is 626.5060241 cm³ of gold. 2. This is 72.84953769 lots of 8.6 cm³ so the volume of soil and rocks to be mined is

127486.691 m³ (72.849 etc. × 1750).

a hard bargainYear 6


� e Mariners quickly realise that their volumes are in mm³ and they need to be in cm³.

5. Complete the table to � nd the value of each Mariner’s nugget.


Possible dimensions of nugget (cm)

Volume in cm3 Weight in grams (g)

rounded to the nearest thousandth

Value in £

rounded to the nearest pence

Jade

Zack

Ceri

Dara

6. What have you noticed about the place value of the volumes in mm³ andthe volumes in cm³?How can you explain why this happens?

Free Running

� e Mariners start to calculate the volume of soil and rocksthey would need to remove to dig a mine that is 30 metres deep.

1. What volume of soil and rocksmust they remove for:a) this mine?b) a mine where each dimension is

double the dimensions here?

2. What volume of ‘Gagarin-gold’ are theylikely to � n d in each of the mines from question 1?Round your answers to the nearest thousandth of a cm³.

3. What is the value of the gold in the larger mine?


1. What volume of gold is this?

2. What volume of rock and soil must they dig?Show your calculations.

33

Ok, so how about our nuggets?

Mariners, they are going to want more gold than that

to make the return trip worthwhile. You will need to think about mining for gold!

Mariners, by my calculations, you will � nd 8.6 cm³ of Gagarin-gold in every 1750 m³ of soil and

rocks.

What volume of rock and soil must they dig?

I think that Earth Control will be happy with

£1 million’s worth of ‘Gagarin-gold’!

10.25 m

30 m

9.75 m

Y6_MoreAbleMaths_pages.indd 33 05/09/2013 12:16MAM03 samples.indd 10 24/09/2013 11:26

34

TEACHER’S NOTES

Curriculum Focus1. Recognise when it is possible to use formulae for

volume of shapes.2. Calculate, estimate and compare volume of cubes

and cuboids using standard units, includingcentimetre cubed (cm3) and cubic metres (m3),and extending to other units such as mm3 and km3.

3. Solve problems involving addition, subtraction,multiplication and division (in the context of money).

Running the ActivityBackgroundDo the children recognise that volume is expressed in cube units whereas capacity is expressed in units such as litres?

What experience do the children have of calculating volume using di� erent units of measurement?

How well do they link the formula for fi nding the volume of a cuboid with that of the area of a rectangle? Do they recognise the importance of place value when calculating with diff erent units of measurement?

Are they con� dent to explain which operations they will need to use when solving number problems and the order in which to use them?

� ese tasks also require the children to calculate values based on volume expressed in cm³.

Starting OffWithin Starting O� , children identify possible dimensions for given volumes. � ey should also identify cube numbers.

Key knowledge: Volume can be defi ned as a measureof the amount of 3D space which is occupied by an object.

Away We GoWithin Away We Go, children move on to calculating the value of gold using the equivalents given. � ey must select the appropriate operations to use and recognise when the inverse is required.

� e problem extends to converting mm³ to cm³.

Key knowledge: To convert measurements in mm³ to cm³,we must divide the volume by 1000, and vice versa.

Free RunningWithin Free Running, children calculate volumes in m³. � ey must also use a given ratio to � nd the likely volume (and then value) of gold in two di� erent mines.

In S.I.D.’s Challenge, they must apply the inverse to � nd out what volume of gold is required for a value of £1 million and what volume of soil and rocks must, therefore, be mined.

Sharing Results and EvaluatingLook for children who con� dently apply the formula for � nding the volume of a cuboid and can use this to ‘undo’ any calculations.

Look for those that can con� dently explain how they must convert between units when dealing with volume and how this di� ers from area (i.e. mm² to cm² need to divide area by 100).

Share solutions for S.I.D.’s Challenge and consider other large values of ‘Gagarin-gold’ in the same way.

AnswersStarting Off1. Jade (9 × 5 × 4 mm or 18 × 5 × 2 mm or 4.5 × 10 × 4 mm etc.)

Zack (6³ or 3 × 12 × 6 mm or 2 × 18 × 6 mm etc.)Ceri (3 × 7 × 6 mm or 6 × 3.5 × 16 mm or 1.5 × 14 × 6 mm etc.)Dara (4.5³ or 9 × 2.25 × 4.5 mm etc.)

2. Zack and Dara – cube numbers3. See question 1

Away We Go1. £664 (8 g)2. £1701.50 (20.5 g)3. £16,600 (200 g)4. 2.6 cm³5.


Possible dimensions of

nugget (cm)

Volume in cm3

Weight in grams (g)

Value in £

Jade 4.5 × 10 × 4 0.45 × 1 × 0.4 0.18 3.462 £287.35

Zack 6 × 6 × 6 0.6 × 0.6 × 0.6 0.216 4.154 £344.78

Ceri 6 × 3.5 × 6 0.6 × 0.35 × 0.6 0.126 2.423 £201.11

Dara 4.5 × 4.5 × 4.5 0.45 × 0.45 × 0.45 0.091125 1.752 £145.42

6. The ‘numbers’ are 1000 times smaller in cm³. This happens because the number of each dimension in cm is 10 times smaller than in mm so the total volume is 10 × 10 × 10 times smaller i.e. 1000.

Free Running1. a) 2998.125 m³ b) 23,985 m³ (19.5 x 20.5 x 60 m)2. Mine a) 14.734 cm³ b) 117.869 cm³3. £188,137.06

S.I.D.’s Challenge1. £1 million is the value of 12,048.19277 g of gold. This is 626.5060241 cm³ of gold. 2. This is 72.84953769 lots of 8.6 cm³ so the volume of soil and rocks to be mined is

127486.691 m³ (72.849 etc. × 1750).

a hard bargainYear 6


� e Mariners quickly realise that their volumes are in mm³ and they need to be in cm³.

5. Complete the table to � nd the value of each Mariner’s nugget.


Possible dimensions of nugget (cm)

Volume in cm3 Weight in grams (g)

rounded to the nearest thousandth

Value in £

rounded to the nearest pence

Jade

Zack

Ceri

Dara

6. What have you noticed about the place value of the volumes in mm³ andthe volumes in cm³?How can you explain why this happens?

Free Running

� e Mariners start to calculate the volume of soil and rocksthey would need to remove to dig a mine that is 30 metres deep.

1. What volume of soil and rocksmust they remove for:a) this mine?b) a mine where each dimension is

double the dimensions here?

2. What volume of ‘Gagarin-gold’ are theylikely to � n d in each of the mines from question 1?Round your answers to the nearest thousandth of a cm³.

3. What is the value of the gold in the larger mine?


1. What volume of gold is this?

2. What volume of rock and soil must they dig?Show your calculations.

33

Ok, so how about our nuggets?

Mariners, they are going to want more gold than that

to make the return trip worthwhile. You will need to think about mining for gold!

Mariners, by my calculations, you will � nd 8.6 cm³ of Gagarin-gold in every 1750 m³ of soil and

rocks.

What volume of rock and soil must they dig?

I think that Earth Control will be happy with

£1 million’s worth of ‘Gagarin-gold’!

10.25 m

30 m

9.75 m

Y6_MoreAbleMaths_pages.indd 33 05/09/2013 12:16 MAM03 samples.indd 11 24/09/2013 11:26

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