© white rose maths 2019© whiterose maths 2019 · 2020-04-23 · • 3 km 3,000 m • 3,000 m 3 km...

© White Rose Maths 2019

In this document, you will find suggestions of how you

may structure a progression in learning for a mixed-age

class.

Firstly, we have created a yearly overview.

Each term has 12 weeks of learning. We are aware that

some terms are longer and shorter than others, so

teachers may adapt the overview to fit their term dates.

The overview shows how the content has been matched

up over the year to support teachers in teaching similar

concepts to both year groups. Where this is not possible,

it is clearly indicated on the overview with 2 separate

blocks.

For each block of learning, we have grouped the

small steps into themes that have similar content.

Within these themes, we list the corresponding

small steps from one or both year groups. Teachers

can then use the single-age schemes to access the

guidance on each small step listed within each

theme.

The themes are organised into common content

(above the line) and year specific content (below

the line). Moving from left to right, the arrows on the

line suggest the order to teach the themes.

2


Here is an example of one of the themes from the Year

1/2 mixed-age guidance.

In order to create a more coherent journey for mixed-age

classes, we have re-ordered some of the single-age

steps and combined some blocks of learning e.g. Money

is covered within Addition and Subtraction.

The bullet points are the names of the small steps from

the single-age SOL. We have referenced where the steps

are from at the top of each theme e.g. Aut B2 means

Autumn term, Block 2. Teachers will need to access both

of the single-age SOLs from our website together with

this mixed-age guidance in order to plan their learning.

Points to consider

• Use the mixed-age schemes to see where

similar skills from both year groups can be

taught together. Learning can then be

differentiated through the questions on the

single-age small steps so both year groups are

focusing on their year group content.

• When there is year group specific content,

consider teaching in split inputs to classes. This

will depend on support in class and may need to

be done through focus groups .

• On each of the block overview pages, we have

described the key learning in each block and

have given suggestions as to how the themes

could be approached for each year group.

• We are fully aware that every class is different

and the logistics of mixed-age classes can be

tricky. We hope that our mixed-age SOL can

help teachers to start to draw learning together.

3

Year 1 (Aut B2, Spr B1) • How many left? (1)• How many left? (2) • Counting back• Subtraction - not crossing 10 • Subtraction - crossing 10 (1)• Subtraction - crossing 10 (2)

Year 2 (Aut B2, B3)• Subtract 1-digit from 2-digits • Subtract with 2-digits (1)• Subtract with 2-digits (2)• Find change - money


In this section, content from single-age blocks are matched together to show teachers where there are clear links across the year groups.

Teachers may decide to teach the lower year’s content to the whole class before moving the higher year on to their age-related expectations.

The lower year group is not expected to cover the higher year group’s content as they should focus on their own age-related expectations.

In this section, content that is discrete to one year group is outlined.Teachers may need to consider a split input with lessons or working with children in

focus groups to ensure they have full coverage of their year’s curriculum. Guidance is given on each page to support the planning of each block.

Year 5 content

Year 6 content


Year 5/6 | Spring Term | Week 8 – Converting Units

6

Year 5 (Sum B4)• Kilograms and Kilometres• Milligrams and millilitres• Metric UnitsYear 6 (Spr B4)• Metric measures• Convert metric measures• Calculate with metric measures

Year 5 (Sum B4)• Imperial unitsYear 6 (Spr B4)• Imperial measures

Year 6 (Spr B4)• Miles and kilometres

Year 5 (Sum B4)• Converting units of time


Find the missing values on the double number line.

Write your conversions as sentences.

Complete the missing information.

1

10kilogram = grams

3

10km = metres

7 kg +1

4kg = g 12 km + km = 12,500 m

Compare the measurements using <, > or =

5 kg 4,500 g 12 kg 12,000 g

3.7 km 370 m 37,000 m 3.7 km

Children focus on the use of the prefix ‘kilo’ in units of length and mass, meaning a thousand. They convert from metres to kilometres (km), grams to kilograms (kg) and vice versa. It is useful for children to feel the weight of a kilogram and various other weights in order for them to have a better understanding of their value.

Bar Models or double number lines are useful for visualising the conversions.

What does ‘kilo’ mean when used at the start of a word?

Complete the stem sentence:

There are ______ grams in ___ kilograms.

How would you convert a fraction of a kilometre to metres?

What is the same and what is different about converting from kg to g and km to m?

8

Year 5 | Spring Term | Week 8 – Measurement: Converting Units


Amir buys 2,500 grams of potatoes and

2,000 grams of carrots.

He pays with a £5 note.

How much change does he get?

Amir receives

13 p change.

Eva is converting measurements.

She says,

Which conversions could Eva have

completed?

• 3 km 3,000 m

• 3,000 m 3 km

• 5,500 g 5.5 kg

• 2.8 kg 2,800 g

Eva could have

converted 3,000

m to 3 km or

5,500 g to 5.5 kg.

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I have divided by 1,000 to convert the

measurements.



Complete the conversions.

1,000 mm = 1 m 1,000 ml = 1 l

5,000 mm = m ml = 3 l

50,000 mm = m ml = 30 l

500 mm = m 300 ml = l

5,500 mm = m ml = 0.3 l

Complete the missing information

1

1,000m = mm

1

100m = mm

1

10m = mm

3 l + 1

4l = ml 2 l + ml = 2,500 ml

Compare the measurements using < , > or =

2 l 1,500 ml 60 l 6,000 ml

2.8 m 280 mm 3,700 m 3.7 mm

Children focus on the use of milli- in units of length and mass.

They understand that milli- means 1

1,000

They convert from metres to millimetres (mm), litres to millilitres (ml) and vice versa.

Using rulers, metre sticks, jugs and bottles helps children to get a better understanding of the conversions.

Can you complete the stem sentences to convert from millimetres to metres…

What does ‘milli’ mean when used at the start of a word?

Would it be appropriate to measure your height in millimetres?

Where have you seen litres before?

10



Cola is sold in bottles and cans.

Alex buys 5 cans and 3 bottles.

She sells the cola in 100 ml glasses.

She sells all the cola.

How many glasses does she sell?

Alex charges 50 p per glass.

How much profit does she make?

Alex sells 54

glasses.

Alex makes

£19.83 profit.

Ribbon is sold in 225 mm pieces.

Teddy needs 5 metres of ribbon.

How many pieces does he need to buy?

Teddy would like to make either a

bookmark or a rosette with his left over

ribbon. Which can he make?

Teddy buys 23

pieces of ribbon.

Teddy will have

175 mm left over.

A bookmark needs

240 mm, and a

rosette needs 140

mm so he can

make the rosette.

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To make 1 mini rosette you will need:4 pieces of ribbon cut to 35 mmA stapler

To make 5 bookmarks you will need:1.2 metres of ribbon1 pair of scissors



Measure the height of the piles of books in centimetres.

Find the difference between the tallest and shortest pile of books in millimetres.

Line A is 6 centimetres long.

Line B is 54 millimetres longer than line A.

Line C is 2

3of line B.

Draw lines A, B and C.

Here are the heights of 4 children.

Put the children in height order, starting with the shortest.

Write their heights in millimetres.

Children convert between different units of length and choose the appropriate unit for measurement. They recap converting between millimetres, metres and kilometre to now include centimetres (cm).

Children see that they need to divide by different multiples of 10 to convert between the different measurements.

What is the same and what is different about these conversions?

• Converting from cm to m

• Converting from m to cm

What does ‘centi’ mean when used at the start of a word?

Which unit of measure would be best to measure: the height of a door frame, the length of a room, the width of a book?

12

Jack124 cm

Rosie1.32 m

Mo141 cm

Whitney1.3 m



A plank of wood is 5.8 metres long.

Two lengths are cut from the wood.

How much of the wood is left?

Complete the conversion diagram.

Can you make a diagram to show

conversions from m and cm to mm?

There is 25 cm left.

÷ 10 ÷ 100

÷ 1,000

A 10 pence coin is 2 mm thick.

Eva makes a pile of 10 pence coins worth

£1.30

What is the height of the pile of coins in

centimetres?

Dora says,

Is Dora correct?

Explain your answer.

13

The pile of coins is

2.6 cm tall.

Dora is incorrect.

She has added the

number of times

bigger together

rather than

multiplying.

One metre is 1,000

times bigger than

one millimetre.

175 cm 3 4

5m

One metre is 100 times

bigger than one centimetre.

One centimetre is 10 times

bigger than one millimetre.

So, one metre is 110 times

bigger than one millimetre



Choose the unit of measure that would be the most appropriate to measure the items.

cm kg km g tonnes ml mm litres

• The weight of an elephant• The volume of water in a bath• The length of an ant• The length of a football pitch• The weight of an apple

Estimate how much juice the glass holds:

250 ml 2 litres 0.5 litres 1

2kg

Estimate the height of the door frame:

20 mm 20 cm 20 m 2 km 2 m 0.2 km

Children read, write and recognise all metric measures for length, mass and capacity. They may need to be reminded the difference between capacity (the amount an object can contain) and volume (the amount actually in an object).

They develop their estimation skills in context and decide when it is appropriate to use different metric units of measure.

Which units measure length? Mass? Capacity?

When would you use km instead of m? When would you use mm instead of cm?

Which is the most appropriate unit to use to measure the object? Explain your answer.

Why do you think _____ is not an appropriate estimate?


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Teddy thinks his chew bar is 13.2 cmlong.

Do you agree? Explain why.

Ron’s dog is about 1

4of the height of the

door.Ron is three times the height of his dog.Estimate the height of Ron and his dog.

Teddy is wrong because he has not lined up the end of his chew bar with zero. It is actually 8.8 cm long.

Door = 2 m (200 cm)Dog = 50 cmRon = 150 cm

Here is a train timetable showing the times of trains travelling from Halifax to Leeds.

An announcement states all trains will

arrive 3

4of an hour late.

Which train will arrive in Leeds closest to 09:07?

The first train from

Halifax, which will

now arrive in

Leeds at 08:54.


Halifax Leeds

07:33 08:09

07:49 08:37

07:52 08:51

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There are ___ grams in one kilogram.

There are ___ kilograms in one tonne.

Use these facts to complete the tables.

There are ___ mm in one centimetre.

There are ___ cm in one metre.

There are ___ m in one kilometre.

Use these facts to complete the table.

Children will use their skills of multiplying and dividing by 10, 100 and 1,000 when converting between units of length, mass and capacity. Children will convert in both directions e.g. m to cm and cm to m. Using metre sticks and other scales will support this step.They will need to understand the role of zero as a place holder when performing some calculations, as questions will involve varied numbers of decimal places.

How could you work out what each mark is worth on the scales?What do you think would be the most efficient method for converting the units of time?What’s the same and what’s different between 1.5 km and 1.500 km? Are the zeroes needed? Why or why not?What do you notice about the amounts in the table? Can you spot a pattern?What’s the same and what’s different about km and kg?


g kg

1,500

2.05

1,005

kg tonnes

1,202

4.004

125

mm cm m km

44,000

2,780

15.5

1.75

16


Mo thinks that 12,000 g is greater than 20 kg because 12,000 > 20

Explain why Mo is wrong.

Put these capacities in order, starting with the smallest.

12,000 g = 12 kg, which is less than 20 kg.

0.035 litres330 ml0.4 litres450 ml3 litres3,500 ml

A shop sells one-litre bottles of water for 99p each.

300 ml bottles of water are on offer at 8 bottles for £2

Whitney wants to buy 12 litres of water. Find the cheapest way she can do this.

£11.88 to buy 12 one-litre bottles.

12 litres = 40 bottles of size 300 ml.40 ÷ 8 = 5 so this will cost 5 × 2 = £10Whitney should buy 40 bottles of 300 ml.


3 litres 3,500 ml

0.4 litres 0.035 litres

450 ml 330 ml

17


A tube of toothpaste holds 75 ml.

How many tubes can be filled using 3 litres of toothpaste?

A parcel weighs 439 grams. How much would 27 parcels weigh? Give your answer in kilograms.

To bake buns for a party, Ron used these ingredients:

600 g caster sugar0.6 kg butter

18 eggs (792 g)3

4kg self-raising flour

10 g baking powder

What is the total mass of the ingredients?Give your answer in kilograms.

Children use and apply their conversion skills to solve measurement problems in context.

Teachers should model the use of pictorial representations, such as bar models, to represent the problem and help them decide which operation to use.

What operation are you going to use and why?

How could you use a bar model to help you understand the question?

How many ___ are there in a ___?

How can we convert between ___ and ___?


18


Jack, Alex and Amir jumped a total of 12.69 m in a long jump competition.

Alex jumped exactly 200 cm further than Jack.

Amir jumped exactly 2,000 mm further than Alex.

What distance did they all jump?

Give your answers in metres.

Dora made a stack of her magazines.Each magazine on the pile is 2.5 mm thick. The total height of the stack is 11.5 cm high. How many magazines does she have in her pile?

Jack jumped 2.23 m.Alex jumped 4.23 m.Amir jumped6.23 m.

There are 46 magazines in Dora’s pile.

Each nail weighs 3.85 grams.

There are 24 nails in a packet.

What would be the total mass of 60 packets of nails? Give your answer in kilograms.

How many packets would you need if you

wanted 1

2kg of nails?

How many grams of nails would be left over?

5.544 kg

6 packets

(554.4 g)

55.4 g left over


19


5 miles ≈ 8 kilometres

Use this fact to complete:

• 15 miles ≈ ________ km

• 30 miles ≈ ________ km

• ________ miles ≈ 160 km

If 10 miles is approximately 16 km, 1 mile is approximately how many kilometres?

• 2 miles ≈ ________ km

• 4 miles ≈ ________ km

• 0.5 miles ≈ ________ km

In the United Kingdom, the maximum speed on a motorway is 70 miles per hour (mph). In France, the maximum speed on a motorwayis 130 kilometres per hour (km/h). Which country has the higher speed limit, and by how much? Give your answer in both units.

Children need to know that 5 miles is approximately equal to 8 km. They should use this fact to find approximate conversions from miles to km and from km to miles.

They should be taught the meaning of the symbol ‘≈’ as “is approximately equal to”.

Give an example of a length you would measure in miles or km.

If we know 5 miles ≈ 8 km, how can we work out 15 miles converted to km?

Can you think of a situation where you may need to convert between miles and kilometres?


21


Ron and Annie are running a 5 mile race.

Who has the furthest left to run?

The distance between Cardiff and London is 240 km.

A car is travelling at 60 mph.

How long will it take them to get to London from Cardiff?

Annie has 1 mile left to run, whereas Ron has 1.2 miles left to run. Ron has the furthest left to run.

240 km ≈ 150 miles

150 ÷ 60 = 2 1

2

hoursOr60 miles ≈ 96 km

240 ÷ 96 = 2 1

2

hours

Mo cycles 45 miles over the course of 3 days.

On day 1, he cycles 16 km.

On day 2, he cycles 10 miles further than he did on day 1

How far does he cycle on day 3?

Give your answer in miles and in kilometres.

On day 1 he cycles

16 km / 10 miles.

On day 2 he

cycles 32 km / 20

miles.

On day 3 he

cycles 24 km / 15

miles.


I have run 6.4 km so far

I have run 3.8 miles so far

22


One inch is approximately 2.5 centimetres

1 inch ≈ 2.5 cm

Use the bar models to help with the conversions.

16in ≈ cm 10cm ≈ in

15in ≈ cm 1cm ≈ in

33in ≈ m 5.5m ≈ in

1 kilogram is approximately 2 pounds

1 kg ≈ 2 lbs

Use this information to complete the conversions.

2 kg ≈ lbs 5 kg ≈ lbs

kg ≈ 22 lbs 55 kg ≈ lbs

There are 568 millilitres in a pint.

How many litres are there in:

2 pints 5 pints 0.5 pints 2.5 pints

Children are introduced to imperial units of measure for the first time. They understand and use approximate equivalences between metric units and common imperial units such as inches, pounds (lbs) and pints.

Using the measurements in the classroom, such as with rulers, pint bottles, weights and so forth, helps children to get an understanding of the conversions.

1 kg is sometimes seen as approximating to 2.2 lbs.

What do we still measure in inches? Pounds? Pints?

Why do you think we still use these imperial measures?

What does approximate mean?

Why do we not use the equals (=) sign with approximations?

How precise should approximation be?24



Jack’s house has 3 pints of milk delivered

4 times a week.

How many litres of milk does Jack have

delivered each week?

He uses about 200 ml of milk every day

in his cereal. Approximately, how many

pints of milk does Jack use for his cereal

in a week?

12 pints is

approximately

6,816 millilitres, or

6.8 litres.

200 × 7 =

1,400 ml

1400 ÷ 568 =

2.46 pints

So Jack uses

approximately 2

and a half pints.

• Dora weighed 7.8 lbs when she was

born.

• Amir weighed 3.5 kg when he was

born.

Who was heavier, Dora or Amir?

Explain your answer.

25


Children convert

both measures to

the same unit.

Dora weighed

approximately 3.9

kg and Amir

weighed 3.5 kg so

Dora was heavier.


Use these facts to complete:

2 feet = ____ inches 6 inches ≈ ____ cm

____ feet = 36 inches 4 feet ≈ ____ cm

Use this fact to complete:

2 lbs = ____ ounces 5 stone = ____ lbs

____ lbs = 320 ounces ____ stones = 154 lbs

• How many gallons are equivalent to 64 pints?• How many pints are equivalent to 15 gallons?• How many gallons are equivalent to 2 pints?

Children need to know and use the following facts:• 1 foot is equal to 12 inches• 1 pound is equal to 16 ounces• 1 stone is equal to 14 pounds• 1 gallon is equal to 8 pints• 1 inch is approximately 2.5 cmThey should use these to perform related conversions, both within imperial measures and between imperial and metric.

Put these in order of size: 1 cm, 1 mm, 1 inch, 1 foot, 1 metre.How do you know?

When do we use imperial measures instead of metric measures?

Why are metric measures easier to convert than imperial measures?


26

2.5 cm ≈ 1 inch 1 foot = 12 inches

1 stone = 14 pounds (lbs)1 pound (lb) = 16 ounces

1 gallon = 8 pints


Jack is 6 foot 2 inches tall.

Rosie is 162 cm tall.

Who is taller and by how much?

60 gallons of water are drunk at a sports day.

Each child drank 3 pints.

How many children were at the sports day?

Jack is 185 cm tall, he is 23 cm taller than Rosie.

60 gallons = 480 pints480 ÷ 3 = 160 children

Eva wants to make a cake.

Here are some of the ingredients she needs:• 8 ounces of caster sugar• 6 ounces of self-raising flour• 6 ounces of butter

This is what Eva has in her cupboards:• 0.5 lbs of caster sugar• 0.25 lbs of self-raising flour

•3

8lbs of butter

Does Eva have enough ingredients to bake the cake? If not, how much more does she need to buy?

Eva has the exact amount of butter and caster sugar, but does not have enough self-raising flour – she needs another 2 ounces.


27


Complete the conversions.

1 year = months years = 24 months

years = 60 months 2.5 years = months

3 years 2 months = months

years months = 75 months

Complete the table.

Use this information to complete the conversions.1

3hour = minutes

3 and 24 = 204

1.5 minutes = seconds

1.05 minutes = seconds

Children convert between different units of time including years, months, weeks, days, hours, minutes and seconds.

Bar modelling will support these conversions.

Use of time lines, calendars, clocks is recommended to enhance pupils’ understanding.

It is worth reminding pupils that time is not decimal so some methods may not be effective for conversions.

How many months / weeks / days are there in a year?

How many hours / minutes / seconds are there in a day?

Can 21 days be written in weeks? Can 25 days be written in weeks? Explain your answers.

Is 0.75 hours the same as 75 minutes? Why or why not?

29



Teddy’s birthday is in March.

Amir’s birthday is in April.

Amir is 96 hours older than Teddy.

What dates could Teddy and Amir’s

birthdays be?

28th March and

1st April

29th March and

2nd April

30th March and

3rd April

31st March and

4th April

Three children are running a race.

• Whitney finishes the race

in 3 minutes 5 seconds.

• Eva finishes the race in

192 seconds.

• Alex finishes the race in

2 minutes and 82 seconds.

Who finishes the race first?

Whitney: 3 min 5 s

Eva: 3 min 12 s

Alex: 3 min 22 s

Whitney finishes

the race first.

30


© white rose maths 2019© whiterose maths 2019 · 2020-04-23 · • 3 km 3,000 m • 3,000 m 3 km...

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