© white rose maths 2019© whiterose maths 2019 · animals dexter saw and explain why the others...

© 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 2 content

Year 3 content


Year 2/3 | Spring Term | Week 3 to 4 – Statistics

6

Year 2 (Spr B1)• Draw pictograms (1-1)• Interpret pictograms (1-1)• Draw pictograms (2, 5 and 10)• Interpret pictograms (2, 5 and 10)Year 3 (Spr B3)• Pictograms

Year 2 (Spr B2)• Make tally charts

Year 3 (Spr B3)• Tables

Year 2 (Spr B1)• Block diagramsYear 3 (Spr B3)• Bar charts


Children are introduced to tally charts as a systematic method of recording data.

They should already be able to count in 5s and understand the vocabulary of total, altogether, more, less and difference.

What do you notice about the groups? How would we count these?

How would you show 6, 11, 18 as a tally?

Why do we draw tallys like this?

When do we use tallys?

Year 2 | Spring Term | Week 3 to 4 – Statistics

Complete the tally chart.

What does the data tell you? Tell me the story.

Complete the tally chart for Year 2 and Year 3

Make a tally chart about one of the following topics:• Equipment in class (scissors, glue etc.)• Favourite sport• Favourite fruit• Ways of getting to school (walk, car, cycle etc.)• A choice of your own

8


Dexter makes a tally chart of the animals he saw at the zoo

Tick one box below that shows all of the animals Dexter saw and explain why the others are incorrect.

Class 1 and Class 2 were each asked their favourite ice-cream flavours. Their results are shown in the tally charts.

What is the same? What is different?

The same:Both classes have 20 votes for chocolate. Both tally charts show that chocolate is the favourite flavour and mint is the least favourite flavour. The order of preference for all four flavours is the same.Different: In Class 1, three more children like Vanilla. There are more children in Class 1 than Class 2. 2 more children chose mint in class 2


Box 1 is incorrect

because there are

not enough

elephants to

match the tally

chart.

Box 2 is incorrect

because there are

not enough

pandas to match

the tally chart.

Box 3 is incorrect

because there are

too many turtles.

9


Children use tally charts to produce pictograms. They build pictograms using concrete apparatus such as counters or cubes then move to drawing their own pictures.They need to be able to complete missing column or rows. They should use the same picture to represent all the data in the pictogram and line this up carefully.

It is important that children see pictograms both horizontally and vertically.

How do you know how many images to draw?

What is the same and what is different about these two pictograms? (same data but shown horizontally and vertically)Which pictogram is easier to read? Why?

What simple symbol could we draw to represent the data? Why did you choose this?


Complete the pictogram.

Use the tally chart to help you complete the pictogram.

Complete the pictogram using the data given.

= 1 person

Key

= 1 goal

Key

= ____

Key

11


Here is a pictogram showing the number of counters each child has.

How could you improve the pictogram?

Use the clues below to help you complete the pictogram. • More Caramel was sold than

Bubblegum flavour, but less than Strawberry flavour.

• Mint was the most popular flavour.• Vanilla was the least popular.

Can you find more than one way to complete the pictogram?

Various answers,

e.g.

Strawberry – 8

Vanilla – 1

Chocolate – 4

Mint – 9

Caramel – 6

Bubblegum – 4


Possible answer

Children show

understanding that

the pictogram is

hard to read as the

symbols are

overlapping each

other. The pictures

must be lined up

and evenly spaced.

There are also

different sized

circles

representing the

data. The pictures

need to be the

same size. There

isn’t a key.

12


Children use their knowledge of one-to-one correspondence to help them interpret and answer questions about the data presented in pictograms.

It is important that children are able to compare data within the pictograms.

What is the pictogram showing us?

What can you find out from this pictogram?

Can you think of your own questions to ask a partner?


Here is a pictogram to show Class 5s favourite t-shirts.

What is the most popular colour t-shirt?What colour is the least popular t-shirt?How many more children chose blue t-shirts than red?How many children are in Class 5?

Here is a pictogram to show minibeasts collected by Class 5.

There are ____ ladybirds.There are ____ centipedes and worms altogether.There are ____ more worms than centipedes.What else does the pictogram tell us?

= 1 T-shirt

Key

= 1 minibeast

Key

13


Teddy writes these statements about his pictogram:

• There were more cows than sheep.• There were the same number of

sheep and horses.• There were more chickens than any

other animal.• There were less cows than goats.• There were 8 goats.

Can you draw a pictogram so that Teddy’s statements are correct?What title would you give it?

Here is a pictogram.

Do you agree with Eva?

Explain why and correct any mistakes.

Eva is wrong

because the green

sweets are not

lined up correctly.

There are 11 green

and 12 blue.

It should look like

this:


Possible answer

Children may have

different numbers

from this and still

be correct.

The most popular

colour sweet is green.

14


Children draw pictograms where the symbols represent 2, 5 or 10 items.

The children will need to interpret part of a symbol, for example, half of a symbol representing 10 will represent 5

Children count in twos, fives, and tens to complete and draw their own pictograms.

If a symbol represents 2, how can you show 1 on a pictogram? How can you show 5? How can you show any odd number?

When would you use a picture to represent 10 objects?

Discuss with children that when using larger numbers, 1-1 correspondence becomes inefficient.


Use the tally chart to complete the pictogram.

Use the information to complete the pictogram about the number of books read in each class.

Year 2 sell cakes at a bake sale. The tally chart shows the data. Draw a pictogram to represent the data.

Pet Tally

Dog

Cat

Rabbit

Fish

15

= 5 books

Key


Create a pictogram to show who was born in what season in your class.

Use what you know about pictograms to help you.

Here is an example.

Teddy and Eva both draw a pictogram to show how many cars they counted driving past their school.

What is the same? What is different?Whose pictogram do you prefer? Why?

Possible answer.

Same – both

pictograms show

the same

information. Both

easy to read.

Both used circle.

Both are in the

same order.

Different – Eva

counts in 10s,

Teddy counts in

5s

Teddy’s is vertical

and Eva’s is

horizontal.


16

= 2 children

Key


To help children to fully understand pictograms, it is important they have collected their own data previously in tally charts and constructed larger scale pictograms practically. Children also need to be able to halve 2 and 10

It is important the children are exposed to both horizontal and vertical pictograms.

How can we represent 0 on a pictogram?

What does the pictogram show? What doesn’t it show?

What is each symbol worth?


How many more sparrows are therethan robins?What is the total number of birds? How did you calculate this?Can you think of your own questions to ask a friend?

Which is the most popular sport?How many children voted for football and swimmingaltogether? What could the title of this pictogram be?

Use the pictogram to decide if the statements are true or false.

17


Jack and Whitney have carried out a traffic survey.

Jack says;

Is he right? Convince me.Whitney says;

Is she correct? Explain your answer.

Convince meThere are more ice-creams sold at the weekend than during the rest of the week.

True or False (Why?)Three ice creams were sold on Tuesday.

JustifyIf the staff needed to pick one day to have off during the week, which would be the best day and why?

There were 36 ice

creams sold at the

weekend and only

28 sold during the

rest of the week.

There were not 3

ice creams sold on

Tuesday, there

were 6 sold. One

symbol represents

2 ice creams.

The best day off

would be Monday

because that is the

day they sold the

least amount.


To find the total number

of vehicles I need to count

the symbols. There are 16

and a half vehicles.

If I add the number of

lorries and bikes together

then it will be equal to

the number of cars

Jack is correct

because there are

20 lorries and 30

bikes. That means

there are 50

lorries and bikes

altogether. This is

the same as the

number of cars.

Whitney is

incorrect because

she has ignored

the key.

That means there

will be 165 cars,

not 16 and a half.

Ice creams sold in a week

18


4 classes are recording how manybooks they read in a week.Here are the results of how manybooks they read last week.

• Which class read the most books?• Which class read the least books?• How many more books did Class 4 read than Class 2?

Complete the pictogram using the information. • Group 2 collected 40 apples.• Group 4 collected half as many

apples as Group 1• Group 5 collected 20 more apples

than Group 3How many apples did each group collect?

Class 3 are counting the colour of cars that pass the school.

Draw a pictogram to represent their findings.

Children build on their understanding of pictograms from Year

2. They continue to read and interpret information in order to

answer questions about the data. It is important that children

understand the value of each symbol used and what it means

when half a symbol is used.

Children construct pictograms and choose an appropriate key.

Encourage children to carry out their own data collection.

What is each symbol worth?

What does half of the symbol represent? Is it always possible to use half of a symbol? Why?

What other questions could you ask about the pictogram?

What would each symbol represent in your pictogram? Have you used the same key as a friend? Could it be represented in different ways?


19


Ron, Amir and Alex record the scores of six football matches. Unfortunately, Ron spilt paint on them.

Record the results based on what thechildren remember.

Possible answer: Whitney and Teddy are making pictograms to show how many chocolate eggs each class won at the school fair.

What’s the same and what’s different about their pictograms?Whose pictogram do you prefer and why?


Match 1 had 3 more

goals than match 3

Match 6 had 1 less

goal than match 2

Match 4 had twice as

many goals as match 3

Possible answer:

Same

image/symbol for

key, same total of

eggs, different

values for the

key…

20


Moving from concrete to pictorial, children build block diagrams using cubes and then move to drawing and interpreting block diagrams.

Children use their knowledge of number lines to read the scale on the chart and work out what each block represents.

Children ask and answer questions using their addition, subtraction, multiplication and division skills.

Can you draw a block diagram to represent the data? What will each block be worth?

Can you make a block diagram to show favourite colours in your class?

Can you create your own questions to ask about the block diagram?


Class 4 are collecting data about favourite colours.

Make a block diagram using cubes to represent the data. Now draw the block diagram. What will the title be?Remember to label the blocks and draw a clear scale.

5 classes collected their house points. Here are their results.Which class collected the most house points?Which class collected the fewest house points?How many more points did Class 2 get than Class 4?How many fewer points did Class 3 get than Class 5?How many points did Class 2 and Class 3 get altogether? Class

Num

ber of H

ouse Poin

ts

Block graph to show House Points Collected

22


Here are three tables of data. Which set of data could you display using the block graph? Which could use the pictogram? Which could use the tally chart?Explain your reasoning.

Split into groups. Everyone needs to write their name on a sticky note. Use your sticky notes to create a block diagram to answer each question.

• How many boys and how many girls are there in your group?

• Which month has the most birthdays for your group?

• What is your favourite sport?

What other information about your group could you show?

Possible examples:

Boys Girls


Data Set 3 would best suit the block diagram because the numbers are all under 20

Data Set 2 would best suit the pictogram because the numbers are larger but all multiples of 5 or 10

Data Set 3 would best suit the tally chart because some numbers are larger than 20 but not all multiples of 5 or 10

Footb

all

Sw

imm

ing

Gym

nastics

23


Use the information from the pictogram to complete the bar chart.

The bar chart shows how many children attend after school clubs.Which day is the most popular? Which day is the least popular?What is the difference between the number of children attending on Tuesday and on Thursday?What information is missing from the bar chart?

Here is a tally chart showing the number of children in each sportsclub. Draw a bar chart to represent thedata.

Children interpret information in pictograms and tally charts in

order to construct bar charts. They interpret information from

bar charts and answer questions relating to the data.

Children read and interpret bar charts with scales of 1, 2, 5 and

10. They decide which scale will be the most appropriate when

drawing their own bar charts.

What’s the same and what’s different about the pictogram and the bar chart?

How does the bar chart help you understand the information?

Which scale should we use? How can we decide whether to have a scale going up in intervals of 1, 2, 5 or 10?

What other questions could you ask about the bar chart?


Key= 5 cupcakes

Group

Num

ber

of

cup

cake

s A bar chart to show the number of cupcakes eaten

24


Which would be more suitable to represent this information, a bar chart or a pictogram?Explain why.

Possible answer:

I think a bar chart

would be more

suitable because

in a pictogram you

would need to

draw symbols

representing 1 or 2

which would make

it less efficient.

Children may

draw both to

experiment which

representation is

clearer.

Rosie and Jack have drawn bar charts to show how many people have pets

Rosie says,

Jack says,

Who is correct? Explain why.

Possible answer:

They are both

incorrect as they

asked the same

amount of people

but they have just

used different

scales on their bar

charts.

Children could

discuss which

scale is more

efficient.


I asked more people

because my bars are taller.

I asked more people

because my scale goes up

in larger jumps.

25

ChildNumber of Skips in

30 Seconds

Teddy 12

Annie 15

Whitney 17

Ron 8


The table shows which sports children play.

How many children play tennis?Which sports does Mo play?Which children play football and tennis?Which child plays the most sport?

The table shows the increase in bus ticket prices.• The cost of Ron’s new ticket is 60p. How much

was his ticket last year? How much has the priceincreased by?

• Which ticket price has increased the most from 2016 to 2017? Which ticket price has increasedthe least?

Children interpret information from tables to answer one and

two-step problems.

They use their addition and subtraction skills to answer questions accurately and ask their own questions about the data in tables.

What information can we gather from the table?

Can you explain to a friend how to read the table?

Where do we need to use tables in real life?

What other questions could I ask and answer using the information in the table?


27


How many questions can you create for your partner about this table?

Possible answers:

How many hours

does the shop

open for in total?

Which day does it

open the longest?

How many more

hours does the

shop open for on

Saturday than

Thursday?

Which day was the

shop open the

shortest amount

of time?

Eva has created a table to show how many boys and girls took part in after school clubs last week.

Eva says,

Is Eva correct?

Explain why.

Possible answer:

Eva is incorrect.

She has counted

all the children

rather than just the

boys. 59 boys took

part in after school

clubs last week.


106 boys took part in

after school clubs last

week.

28

DayNumber of hours shop

is open

Monday 8

Tuesday 8

Wednesday 4

Thursday 10

Friday 7

Saturday 12

© white rose maths 2019© whiterose maths 2019 · animals dexter saw and explain why the others...

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