Level 4 to 5
Can I work out
the whole,
having been
given the
fraction?
1 CUN
Opportunities to use and apply
Possible contexts include:
Review questions
1/3 of the children in Class 6 are girls. There are 9 girls in the class.
How many children are in Class 6?
• Rob was given some money for his birthday. He spent a quarter of it
and put half of it into his money bank. He has £3 left. How much
money was he given?
• I think of a number. 7/10 of my number is 42. What is my number?
• Some children were asked to choose their favourite weekend pastime.
This pie chart shows the results. 9 children chose playing computer
games. Work out how many children were in the survey. Explain your
method.
•
•
Problems involving measures, e.g. There is 80 ml of liquid in this
measuring cylinder. Work out how much it will hold when full.
Money problems, e.g. a clothes shop is having a sale where all items
are reduced by 1/3. In the sale a jacket costs £24.00. How much
would it normally cost?
• Area problems, e.g. the purple area is 35 cm². What is the area of
the hexagon?
•
•
Can I
understand
and explain the
relationships
between two
or more parts
of a whole and
describe them
using the
language and
notation of
ratio?
•
In this tiling pattern, there are 3 yellow tiles for every 2 purple ones:
The ratio of girls to boys in a class is 2:3. Suggest how many boys and
how many girls might be in the class.
• The height of a model of a building is 2 m. The real building is 30 m
tall. How would you represent this ratio?
• Draw a plate of fruit where the ratio of grapes to strawberries to
cherries is 3:1:2
Geography, e.g. interpreting the scale on maps and plans.
Design technology or art, e.g. recording the scale that has been used
to create models or drawings.
• Interpreting signs in everyday life, e.g. drawing a diagram to explain
the meaning of a 1:10 incline.
•
•
•
Ben collected 1/6 of the pencils from the box. There were 15 pencils
left. How many pencils were in the box originally? Explain how you
worked out your answer.
• The pink area represents 24 m². Explain how you would work out the
area of the large square.
•
•
Which of these ratios are equivalent to 5:20? 4:1, 2:8, 6:21, 1:4, 10:25
Now give some more ratios that are equivalent to 5:20, justifying your
suggestions.
• A one-metre piece of ribbon is cut into two pieces. One piece is 65 cm
long. Write the ratio of the length of the shorter piece to the length
of the longer piece in its simplest form.
• Describe the relationship between the area of the purple shape and
the area of the blue shape using the language and notation of ratio.
•
Exploring important mathematical ratios, e.g. The Golden Ratio; Pi.
•
2 CUN
Can I solve
simple
problems
involving ratio
and
proportion?
3 CUN
These ingredients are needed to make a banana and berry smoothie
for 4 people: 2 bananas, 500 ml plain yoghurt, 400 g berries,
List the ingredients needed for 6 people.
• What proportion of the numbers from 1 to 100 inclusive: are multiples
of 10? contain the digit 3?
• A pack of nuts and raisins is made up of 1/3 nuts and the rest raisins.
The pack contains 100 g of raisins. How much does the pack weigh
altogether?
Explain how you worked this out.
• The ratio of a scale model to a real bridge is 1 to 50. The bridge is
425 m long. How long is the model?
•
•
•
•
•
•
•
Some children were asked to choose their favourite type of book.
This pie chart shows the results. 15 children chose adventure. Work
out how many children were in the survey. Explain your method.
Interpreting pie charts, e.g. working out the sample size when you
have only been given the number of items represented in one segment.
•
Describe this pattern and record it using ratio notation:
Confirming learning
Ask probing questions such as:
Geography, e.g. using scale to interpret/draw maps and plans.
Design technology/art, e.g. creating scale models or drawings.
Food technology, e.g. adapting recipes; proportions of ingredients.
Measures, e.g. conversion between units.
Data handling, e.g. proportions within pie charts; conversion graphs.
Important mathematical ratios, e.g. The Golden Ratio; Pi.
One-fifth of the children in Class 6 go home for lunch; the rest stay
in school. Which of these ratios represents the number of children
who go home compared to the number of children who stay in school?
Justify your choice. 1:5, 5:1, 1:4, 4:1
Fruit squash is to be mixed with water in the ratio 1:5. How much
squash and how much water should be put in to fill a 3 litre jug? How
did you work this out?
• Tina has 440 sweets of which 40 are red. Ryan has 540 sweets of
which 45 are red. Who has the greater proportion of red sweets?
Explain how you solved this problem.
• In this pie chart, the yellow segment represents 25 children. How
many children does the whole pie chart represent?
•
Level 4 to 5

Can I make
generalisations
about
sequences and
explain why
given numbers
do or do not
belong to the
given
sequence?

5 CUN
, 7, 10, 13, 16,
,
b) 9.8, 9.1, 8.4, 7.7,

c)
, 4, 8, 16, 32,
d)
,
•

,
,
, 21, 13, 5
e) −11, −7,
, 1,

,9
Confirming learning
Ask probing questions such as:

Investigating patterns and spatial representations of known
sequences of numbers, e.g. multiples, square numbers and
triangular numbers.
Sequences related to properties of shape, e.g. find the total
of the internal angles in a triangle, a quadrilateral, a
pentagon, etc.

Sequences produced from continuing patterns, e.g.
Sally says that the number 102 will be in this sequence:
3, 6, 9, 12...
Is she correct? How do you know?
Consider the sequence:
6, 11, 16, 21, 26 ...
What statements can you make that will be true for all
numbers in the sequence?
Will 77 be highlighted?
Explain your thinking.
Write a formula for the nth term of this sequence: 3, 6, 9, 12, 15 ...
Joe is planting several rows of beans. He needs two beansticks for
each metre that he plants plus one beanstick for the end of each row.
Write an expression to describe this relationship. How many
beansticks does he need for a row that is 10 metres long?
• I multiply a number by 7 then add 3. Which expression describes the
steps I have taken if n is the number I started with? 3n + 3, n + 7 + 3,
7n + 3
•

What numbers are missing from these sequences? Explain
how you know:
a)
4 CUN
Can I create
an algebraic
expression
that describes
a simple
relationship?
Opportunities to use and apply
Possible contexts include:
Review questions

Word problems, e.g. for every £20 you spend at a supermarket you
get a voucher for school equipment. How much do you need to spend
to get 1 voucher; 2 vouchers; 7 vouchers; 100 vouchers; m vouchers?
• Investigations, e.g. write an expression to describe the number of
squares in the 1st; 2nd; 3rd; 5th; 10th; nth shape?
•
Using function machines, e.g. creating algebraic expressions to
describe the relationship between input and output.
• Conversion and line graphs, e.g. interpreting a temperature conversion
chart to create an expression describing the relationship between
Celsius and Fahrenheit.
•
A sequence starts with 1 and has the rule 'add 6'. Work out
what the 5th term will be. Amy thinks that the sequence will
contain the number 100. Is she correct? Explain how you
know.
Josh continues this pattern. He counts the squares in each
shape and writes this down as a sequence. He says, 'No
matter how far you go, there will never be a multiple of 4 in
the sequence'. Is he right? How do you know?
Sequence A: 3, 6, 9, 12... Sequence B: 5, 10, 15, 20... Sequence
C consists of the terms that appear in both sequence A and
sequence B. Give a three-digit number that will be in
Sequence C and explain how you know. Can you give another?
Two numbers x and y have a product of 32 and a sum of 12. Write two
equations that are true for x and y. Find the values of x and y and
explain how you did this.
• Roast beef needs to be cooked for 30 minutes for each kg of weight
plus an extra 20 minutes. Write this relationship as an algebraic
expression. What cooking time is needed for a joint of beef that
weighs 1 kg, 2 kg, 4 kg, 7 kg, n kg?
• Describe how the pattern is growing and record this in a table. Use
this to help you write an expression for the nth pattern in this
sequence.
•
Level 4 to 5
Can I use
knowledge of
factors and
multiples?
6 KNF
Opportunities to use and apply
Possible contexts include:
Review questions
•
•
•
•
•
•
I am thinking of a number that is a factor of 24 and a factor of 40.
What is the largest possible number I could be thinking of?
How many factors does a prime number have? Work out whether 51 is
a prime number.
What is the lowest common multiple of 4 and 6?
Write down the first five numbers that are multiples of 6 and
multiples of 8. Describe what you notice about the sequence and
predict the next two common multiples.
Write a different prime number into each box to make the calculation
true:  ×  ×  = 231
I need to pay 51p postage using only 12p and 5p stamps. How many of
each should I put onto my parcel?
Confirming learning
Ask probing questions such as:
Word problems, e.g. In a shape sequence, every third shape is a
triangle and every fifth shape is red. Where in the sequence will the
fourth red triangle lie?
• Number properties, e.g. Find the prime numbers to 100 using the
Sieve of Eratosthenes.
• Fractions, e.g. write 24/32 in its simplest form. How did you use
highest common factors to do this?
• Data handling sorting diagrams, e.g. Where in this Carroll diagram
should the number 8 go? Write an appropriate number into the
bottom left cell.
•
•
Find a number between 230 and 240 that is a multiple of 9.
List all the factors of 36. How many does it have? Most numbers have
an even number of factors. Why is 36 a special case?
Which is larger, 7/8 or 5/6? Explain how you worked this out. Could
you have used a smaller denominator?
Jake and Darren did a sponsored run. Jake earned £5 for every
complete mile he ran. Darren earned £6 for every complete mile.
They each raised the same amount of money, which was over £40 but
under £80. How much money did each boy raise? How many miles did
each boy run?
It is possible to make the number 42 by multiplying together three
prime numbers. Find them.
Consider the numbers 20 and 12. What is their lowest common
multiple? What is their highest common factor?
A car park has 76 rows for parking. There are 52 car spaces in each
row. Which of these is the best way to estimate how many cars can
park altogether? 80 × 60 = 4800, 80 × 50 = 4000, 70 × 60 = 4200.
Explain your choice.
Which of these two numbers multiplied together give the product
closest to 24? 7.9, 9.2, 2.1, 2.8.
Without working out each calculation exactly, predict which will have
answers between 40 and 60: 6.8 × 7.5, 80.03 − 27.2, 997 ÷ 19.
Circle the closest estimate for the answer to 72.34 ÷ 8.91. Choose
from 6, 7, 8, 9, 10, 11. How did you decide?
Use approximation to predict the missing digits in this calculation:
1.2 × 1.9 = 778.68.
Find half of 4.7. Explain how you worked out the answer.
Ryan says that 0.18 ÷ 9 = 0.2. Where do you think he went wrong?
Explain his mistake and what he needs to do instead.
A chocolate bar weighs 0.125 kg. I eat 1/5 of it. How much chocolate
is this? How do you know?
How does your knowledge of 56 ÷ 7 help you to calculate 0.56 ÷ 7?
Divide 0.9 by 6. Explain each step of your working.
•
0.05 × 8 =
•
•
•
•
•
•
Can I explain
how I use
approximations
to help
estimate the
answer to a
calculation?
7 KNF
•
•
•
•
•
Can I make use
of my
understanding
of place value
to explain how
to mentally
multiply or
divide a
decimal
number by an
integer?
8 C
Can I use an
appropriate
non-calculator
method for
dividing a
three-digit
integer by a
two-digit
integer?
9 C
Apples weigh about 190g each. How many apples would you expect to
get in a 2 kg bag?
Is 4, 5 or 6 the best estimate for the answer to 44.81 ÷ 8.92? Explain
how you decided.
I buy six books that cost £7.99 each and four CDs that cost £12.99
each. Use approximation to work out the total cost to the nearest
pound.
Estimate the answers to these calculations: 2593 + 6278,
2605 − 1997, 245 × 19, 786 ÷ 38. Explain your methods.
A lawn is 19.5 m long and 4.5 m wide. Is its area greater or less than
100 square metres? Explain how you know.
How many hundredths are equivalent to 0.35? Use this to work out
0.35 ÷ 5.
• Explain how you can use the fact 24 ÷ 6 = 4 to answer 2.4 ÷ 6.
• Find the answers to these calculations and explain your methods:
0.15 × 8, 1.2 ÷ 4, 0.2 ÷ 5, 0.005 × 6
•
•
Find the missing numbers and explain how you know:
× 6 = 3,
4.8 ÷
= 0.6
• Exercise books are 0.8cm thick. A pile of 9 exercise books is on the
table. How thick is the pile?
• A half metre piece of string is cut into 5 equal pieces. How long is
each piece in m? How many cm is this?
Work out 575 ÷ 25, explaining your method.
Peter says that, if you want to divide a number by 12, you can divide it
by 4 then by 3. Is he right? Explain how you know. Work out 768 ÷ 12
using Peter's method and using another method. Do you get the same
answer?
• How many 35p packets of stickers can I buy with £5? Explain how you
know.
• Coaches have 56 seats for passengers. How many coaches are needed
to take 275 people on a trip?
•
•
•
•
•
•
Word problems involving decimal measures, e.g. A carton of juice
contains 0.4 litres of juice. How many cartons are needed to have 2
litres of juice altogether?
• Measure problems, e.g. Gym mats are 1.6 metres long. If 5 mats are
placed end to end, what total length will they make?
• Currency conversion, e.g. £1 is equal to about $1.4. What is the
approximate value of £5 in US dollars?
• Division giving a decimal answer, e.g. Divide 9 by 5 giving your answer
as a decimal.
•
•
Missing number calculations, e.g.
4.2
•
Word problems, e.g. Pencils come in packs of 12. How many packs does
a school need to buy to get 310 pencils?
Problems involving money and measures, e.g. My mobile phone costs
18p per minute for national calls. If I put £5 on my card, how many
minutes can I talk for?
The area of a rectangular games hall is 384 square metres. If the
length is 24 metres, how wide is it?
Conversions, e.g. Convert 35,000 seconds into hours, minutes and
seconds.
Finding fractions of amounts, e.g. Find 5/12 of 600.
Missing number calculations, e.g. Write in the missing digits
•
•
•
Complete this calculation: 943 ÷ 41 = 2
Work out whether or not 29 is a factor of 811
Word problems, e.g. Roughly how many pot plants can I buy with £50
if each plant costs £2.99?
Checking calculations, e.g. Emma is trying to work out 29.5 x 7.8 and
her calculator displays 183.3. Do you think this is correct? Explain
your answer.
Missing number calculations, e.g. Use approximation to find the
missing digit: 1.2 x 18.9 = 778.68.
Games. e.g. Call my calculation bluff – children choose an answer to a
calculation from three given numbers.
Measures problems, e.g. If drawing pins weigh 4.2 g each, roughly how
many drawing pins would you expect to have in a 250g box?
•
•
•
•
•
23 ×
= 78
÷ 8 = 0.04; 0.6 ×
•
•
•
•
•
•
•
•
•
÷6
=
When 37
÷ 17, it has a remainder of 5. Work out what the missing
digit is.
• I bought some pencils that cost 15p each. I paid £5.85. How many
pencils did I buy?
• 12 inches are the same as 1 foot. How many feet and inches are the
same as 320 inches? Explain how you worked this out. How did you use
your knowledge of number facts and place value to help you?
•
Write in the missing digits: 323 ×
7 = 1518 .
Explain the steps you would take to work out 675 ÷ 45
• What is the remainder when 693 is divided by 20?
•
•
Level 4 to 5
Can I extend
my written
methods for
multiplying
whole numbers
to multiplying
decimals by
whole
numbers?
10 C
Can I solve
multi-step
problems
involving
percentages
and/or
fractions?
11 C
Mike works out that 14 × 12 = 168. What is 14 × 1.2? How do you
know?
• Use a written method to calculate 24 × 13. What do you need to
change to show a similar method to work out 2.4 × 13?
• Use a written method to find the area of a swimming pool which is
25m long and 7.5 m wide.
• Complete the missing sections to work out 35 × 2.1:
•
•
Which is closer to 100: 5.2 × 17 or 7.2 × 15? Use written methods to
prove your answer.
•
A shop has a sale where all items are reduced in price by 30%. A CD
player normally costs £45. How much will it cost now? Record your
method.
Which is greater: 80% of 35 or 3/5 of 60?
A bar of chocolate contains 12 squares. Ann eats 1/6 of the bar. Ben
eats 3/4 of the bar. What fraction of the bar is left?
Charlie has saved £15 towards buying a computer game. This is 3/5 of
the cost of the game. How much does the game cost?
In a packet of 40 biscuits, 20% are chocolate, 3/8 are plain and the
rest are custard creams. How many are custard creams?
Sam gets £3.50 pocket money. He spends 2/5 of it. What is left?
•
•
•
•
•
Can I solve
multi-step
problems that
involve using
inverse
operations and
explain my
methods?
•
Can I make and
justify
decisions
about when
and how to use
a calculator
effectively to
solve
problems?
For each of these problems, decide whether to use a mental, written or
calculator method. Give reasons for your choice and solve each problem:
12 C
13 C
Opportunities to use and apply
Possible contexts include:
Review questions
Sam thinks of a number. She divides it by 5 and gets the answer 20.
What number did Sam think of?
Find the missing numbers:
+ 15 = 25 × 5,
× 4 − 19 = 5
If you double Joe's age and add 8, you get his mum's age. Joe's mum
is 32. How old is Joe?
• I buy some packets of chewing gum. Each packet costs 25p. I pay with
a £2 coin and receive 25p change. How many packets of chewing gum
did I buy?
• When a number is divided by 9, it gives an answer of 13 with a
remainder of 7. What is the number?
•
•
Find the missing digits 3
+ 85 = 1 3
Coach fares from Oxford to London are £13.50 for adults and £6.85
for children. How much will the total fare be for 3 adults and 6
children?
• Amir buys a 5 kg sack of peanuts for £9.99. He measures out 150 g
bags of peanuts and sells these for 65p each. How much profit will he
make?
• Apples weigh about 150 g each. How many apples would you expect to
get in a 3 kg bag?
•
•
•
29.6 ×
= 1110
Word problems, e.g. A can of drink contains 0.33 litres. How many
litres are in 15 cans?
• Area problems, e.g. Find the area of this shape:
•
•
Gap calculations, e.g. Use a written multiplication to work out the
•
missing number:
÷ 3.8 = 17
Puzzles and problems, e.g. Organise the digits 9, 7, 5 and 3 into this
calculation to give the greatest possible product
.
×
Word problems, e.g. 200 people attended a concert. 1/5 of the people
had complimentary tickets. The rest paid £7.50 each. How much
money was collected from selling tickets?
• Money and measures, e.g. Which is longer: 3/4 of an hour or 2500
seconds?
• Every day scenarios, e.g. Peter's family have a meal out to celebrate
his birthday. The meal costs £52 and the restaurant adds a 15%
service charge. How much is the bill altogether?
•
•
Missing number calculations, e.g. (
÷ 5) + 19 = 25;
25 ×
= 3 × 50
• Word problems, e.g. Robert saves his pocket money for 7 weeks. He
uses his savings to buy his mum a present that costs £9.99. He has
51p left over. How much pocket money does he get each week?
• 'I think of a number' problems, e.g. I think of a number, add 99 and
then double. I get the number 288. What number did I think of?
Word problems, e.g. A pencil weighs about 3g. A school buys 135
packs of 12. Approximately how much will these weigh in kg?
• Money problems, e.g. How many notebooks costing £1.65 is it possible
to buy with £50?
• Data handling, e.g. Finding the mean of a set of data.
• Problem-solving questions involving trial and improvement, e.g. Find
the number that, when multiplied by itself, gives 2116
•
•
Empty box calculations:
÷ 35.2 = 16.5
Confirming learning
Ask probing questions such as:
•
Look at this example of a grid method. Complete the calculation and
work out the answer.
Abbie says that 23.4 × 5 will be bigger than 53.4 × 2. Is she correct?
Use a written method to prove your answer.
• I buy 1.6 kg of apples. They cost 65p per kg. Work out how much I will
pay for the apples using a written method.
•
•
Work out the missing number:
÷ 3.8 = 17
Emma gets 16 out of 20 in a test on Monday and 38 out of 50 in a test
on Tuesday. On which day did she score a higher percentage? Explain
how you know.
• A bag contains 1 kg of sugar. I use 1/4 of it in baking and pour 2/3 of
what is left into a jar. How many g of sugar are left in the bag?
• A camera normally costs £85 in shop A but is reduced by 20%. In
shop B the same camera normally costs £100 but is reduced by 35%.
Where should I buy the camera?
• At a concert there are about 20,000 people. 2/5 of the people are
women and 15% are children. How many men are at the concert?
•
I think of a number, divide it by 3 and add 11. I get the answer 21.
What number did I think of?
• Becky buys 3 milkshakes. She pays with a £5 note and gets 35p
change. How much does each milkshake cost? Draw a function machine
to represent the process you went through to find your answer.
• What number when multiplied by 4 gives itself plus 60?
• Ricky is at school from 8:40 am to 3:15 pm. He has 20 minutes
registration, 25 minutes break and 50 minutes for lunch. The rest of
the school day is organised into 6 equal lessons. How long is each
lesson?
•
Decide which of these problems you would solve using a calculator.
Explain why and solve those problems:
• A runner runs the 100 m four times. His times are: 11.25 sec,
11.69 sec, 10.8 sec and 12.13 sec. Find his average time.
• A film starts at 4:25 pm and ends at 6:05 pm. How long is it?
•
0.09 ×
= 0.72
Find a number n such that n × (n+1) = 1332
• Elena has a £50 budget to spend on a garden. She buys 18 packets of
seeds costing £1.49 each, a spade costing £7.99 and a hose costing
£12.49. How much money does she have left?
• I buy a sheet of stamps. On the sheet there are 18 rows each
containing twelve 35p stamps. How much will this cost?
•
•
Level 4 to 5
Can I explain
and record my
method when I
use a
calculator to
solve a
problem?
14 C
Confirming learning
Ask probing questions such as:
Word problems, e.g. Erasers weigh 23 g each. They come in a pack of
50. The box weighs 10.5 g. How much will the pack weigh altogether?
• Money problems, e.g. I buy 15 sheets of card that cost 24p each. Use
a calculator to work out how much change I will get from £5.
• Shape problems involving area and perimeter, e.g. The perimeter of a
rectangular pool is 86 m. The pool is 27.5 m long. How wide is it?
• Problem solving questions involving trial and improvement, e.g. The
same digit is missing from each box. What is it?
Use a calculator to solve these problems. Explain your method and
record each step:
• Martyn wants to buy some 35p stamps. Work out how many stamps he
can buy with £10.
• The letters A, B and C stand for three numbers. A is double B. C is
double A. Work out the value of A if A × B × C = 27,000 using trial and
improvement.
• At a snack bar, Jay buys three sandwiches that cost £1.75 each. He
buys a carton of juice for 85p and a milkshake for £1.20. How much
change will he get from a £20 note?
• 320 people attend a school concert. 1/4 of the people are children.
The tickets for the concert cost £3.50 for adults and £2 for
children. How much ticket money does the school collect?
•
Jim wants 9 cartons of juice for a party. His wife says it will be
cheaper to buy 10 cartons on special offer and to have one spare. Is
she right? Solve this problem, explaining and recording your method.
• What calculation will you key into your calculator to find the missing
•
number? Explain how you know. 21.97 ÷
= 16.9
Billy saves £2.25 a week to buy a game that costs £12. How many
weeks will it take to save enough? Explain how you got your answer.
• How many 20p pieces make £35.80? Explain your method.
•
Can I identify
matching nets
for 3D shapes,
visualizing
corresponding
features?
Opportunities to use and apply
Possible contexts include:
Review questions
Arrange six rectangles to form the net for a cuboid. How many
different nets can you make to form the same cuboid?
• Draw 2 ticks, 2 crosses, 2 stars and 2 dots onto this net so that
symbols on parallel faces of the hexagonal prism will match:
•
15 US
2
•
5×
8 = 89
0
Missing number calculations:
+ 35.2 = 101.19
Design and technology, e.g. Design and build packaging for a product;
design and build a set of nesting cartons.
• Art, e.g. Create a picture/pattern on a net so that it flows around the
faces of the 3-D shape.
• Visualising, e.g. Look at some unusually shaped boxes, visualise
flattening them out and describing the nets, use a construction kit to
build net or draw it, fold up to check.
•
•
Complete this net for a triangular prism: Can you create a net for a
different triangular prism using the same face as a starting point?
The number of spots on opposite faces of a normal die add up to
seven. Draw a net for a die and include the spots.
• This net folds to make a tetrahedron. Shade the blank face so that
the shading matches along each edge:
•
•
A cube has shaded triangles on three of its faces.
Here is the net of the cube. Draw in the two missing triangles.
•
Can I use the
language
perpendicular
and parallel to
classify,
describe and
draw shapes
and lines?
16 US
•
Here is a shape on a square grid.
For each sentence, put a tick () if it is true. Put a cross (x) if it is
not true. Angle C is an obtuse angle. Angle D is an acute angle.
Line AD is parallel to line BC. Line AB is perpendicular to line AD.
Write your own true sentence about the shape using perpendicular.
• Using dotty paper, draw quadrilaterals with: only one pair of parallel
sides, only one pair of perpendicular sides, two pairs of parallel sides
• Visualise a hexagonal prism where the hexagonal faces are regular.
How many pairs of parallel faces does it have?
Art, e.g. Look at pictures by Mondrian and identify parallel and
perpendicular lines. Create Mondrian-style pictures given particular
criteria.
• Design technology, e.g. Consider strategies to ensure that adjacent
struts in a wooden box frame remain perpendicular.
• Everyday objects, e.g. Identify parallel and perpendicular lines in
everyday objects, e.g. gates, flags.
•
Sorting activities, e.g. classify shapes onto Venn, Carroll and tree
diagrams using properties such as has at least one pair of parallel
sides/faces.
• Coordinates, e.g. Draw the straight line between points (1,1) and (6,6).
Draw a line perpendicular to this that goes through the point (1,6).
•
Use isometric paper to make a net for a hexagonal prism. Colour it in
three colours so that no two touching faces are the same colour.
Give a time when a clock's minute and hour hands are perpendicular.
Investigate which of these quadrilaterals have diagonals which are
perpendicular to each other: square, oblong, kite, parallelogram.
• Name a 3-D shape that has: only one pair of parallel faces; three pairs
of parallel faces; no pairs of parallel faces.
• Draw a quadrilateral where all touching sides are perpendicular. What
is the relationship between opposite sides?
• Points a, b and c are three of the vertices of a quadrilateral. Give the
coordinates of the fourth vertex, if the quadrilateral has: only one
pair of parallel sides; two pairs of parallel and perpendicular sides;
only one pair of perpendicular sides.
•
•
Level 4 to 5
Can I use my
understanding
of angles and
shapes to work
out missing
angles?
A triangle has one angle of 55° and one of 78°. How big is the third
angle?
• Look at this diagram.
•
17 US
Work out the size of angle a and angle b without using a protractor.
What is the angle between the hour hand and the minute hand of a
clock at 7 o'clock? Explain how you worked this out.
• Work out the missing angles in this kite:
•
Can I describe
and predict
transformation
s of shapes?
•
Predict the co-ordinates of vertex c after this shape is rotated about
point a through: 90° anti-clockwise, 180°
18 US
Explain how you made your prediction.
• On dotty paper, draw a parallelogram. Choose one side of the
parallelogram to be the mirror line. Draw the reflection of the
parallelogram in this mirror line. Which lines in your diagram are
parallel?
• A shape is translated 5 squares right and 2 squares down. It is then
rotated 720° clockwise about its centre and translated 2 squares left
and 7 squares up. Describe a reflection, translation or rotation that
will return it to its starting position.
Can I solve
problems
involving the
conversion of
units?
19 M
Opportunities to use and apply
Possible contexts include:
Review questions
Each episode of my favourite cartoon lasts 25 minutes. How many
episodes can I record onto a 3-hour video tape?
• A plum weighs 70g. Is this equal to: 0.7kg, 0.07kg or 0.007kg? Explain
how you know.
• How many 5ml spoonfuls would fill a 20cl cup?
• A path is made up of eight square concrete tiles placed in a row. The
side of each tile measures 70cm. What is the perimeter of the path
in metres?
•
Confirming learning
Ask probing questions such as:
Investigating shape properties, e.g. Find the sum of the internal
angles of 2-D shapes such as triangles, quadrilaterals, pentagons.
What patterns do you notice? Does it matter whether the shapes are
regular?
• Investigating general statements, e.g. When a shape is enlarged its
angles do not change; triangles can have 0, 1, 2 or 3 obtuse angles –
true or false?
• Drawing shapes accurately, e.g. Draw a rhombus with side length of 5
cm and two angles of 125°.
• Using ICT, e.g. use your knowledge of angles to draw an equilateral
triangle using software.
•
Art, e.g. Produce wrapping paper designs using reflection, rotation and
translation of shapes; Create Rothko-like pictures by translating
rectangles; Translate patterns through block printing.
• ICT, e.g. Use draw packages to design a pattern involving rotation,
reflection or translation of shapes; use the repeat command in
drawing software to produce a pattern and then produce translated
versions.
• Everyday objects, e.g. Identify objects that would map onto
themselves exactly when reflected or rotated.
• Coordinates, e.g. Find the coordinates of vertices of shapes after
reflections, rotations and translations.
•
Decide whether you would use a reflection, rotation or translation or
combination of these to turn the pink shape into the: yellow shape,
green shape, white shape
Describe each transformation. Are there different possibilities?
•
Point a is reflected in the line shown. Is it reflected onto point b, c or
d? Explain how you know. Draw the original points for the other two
reflected coordinates.
•
•
Sketch an isosceles triangle with an angle of 40° and work out the
size of the other angles. Try to find more than one way to do this.
• Work out the sizes of angles a, b and c.
How many degrees does the minute hand of a clock turn between 9 am
and 11:55 am on the same day? Explain how you worked this out.
• Find angle a by marking known angles onto the diagram.
•
Using dotty paper, draw an equilateral triangle. Rotate it through 60°
clockwise about one of its vertices. What shape is formed by the two
triangles together?
• What calculations would you do to find how many seconds there are in
a day?
• How much more liquid needs to be poured into this jug to make 3/4
litre?
•
Practical measuring activities, e.g. Find the approximate amount of
water you use in a day.
• Word problems, e.g. A rabbit eats 60 g of rabbit food a day. How long
will a 1kg bag of food last?
• Ratio and proportion, e.g. Cheese costs £7.50 for 1 kg. How much
does 200 g of cheese cost?
• Data handling, e.g. This bar graph shows rainfall. What is the total
rainfall in metres from May to August?
•
A calculator display shows 3.2851. This represents metres. What
would the answer be rounded to the nearest cm? To the nearest mm?
• 1kg is approximately the same as 2.2 pounds. There are 16 ounces in a
pound. Work out roughly how many ounces are equivalent to 1kg.
• Sam says there are 1000 square cm in a square m. Is he right?
•
I swim 1.5km each morning – if the length of the pool is 50m, how
many lengths do I swim?
• Using a ruler that shows cm and inches, convert 3½ inches into mm.
•
Level 4 to 5
Can I read a
variety of
partially
labelled scales
and explain
how I know
what each
unlabelled
division
represents?
20 M
Can I list all
the outcomes
that may
result from
repeating an
experiment?
21 HD
Opportunities to use and apply
Possible contexts include:
Review questions
•
What measurement is marked by the arrow if: A = 1kg and B = 2kg,
A = 3.5m and B = 4m, A = 300ml and B = 400ml, A = 3:30 pm and
B = 4:30 pm?
If a scale represents 1kg to 2kg and there are 4 unlabelled, equally
spaced divisions, what does each unlabelled division represent? Draw a
sketch to illustrate your answer.
• 1/4 of a litre of liquid is poured out of this jug. How much liquid would
be left in the jug? Write this in ml. Write this in litres. Mark the new
level onto the jug.
Practical measuring activities, e.g. Find the average weight of an
apple.
• Word problems, e.g. The flour on the scales came from a 1kg bag of
flour. How many grams are left in the bag?
•
•
A coin can land in two ways: Heads up or tails up.
If you toss two coins, what are all the possible combinations of heads
and tails?
Rajat said, 'If I toss one coin twice, there are four possible
outcomes. I think that if I toss the coin again, there will be 6 possible
outcomes'. Is he right? Use a diagram to explain how you decided.
• Karen and Huw each have three cards, numbered 2, 3 and 4. They
each pick one of their own cards. They then add together the
numbers on the two chosen cards. Draw a table to show all the
possible outcomes.
• Karen and Huw play the game again, but this time they have four
cards numbered 2, 3, 4 and 5. How many possible outcomes are there?
How do you know?
•
PE, e.g. Measure how far you can throw a ball over a series of PE
lessons. Plot this on a graph and use this to describe your progress.
• Data handling, e.g. The graph shows how a liquid's temperature
changes over time. Read from the graph how many minutes it takes
for the temperature to reach 40°C. Read from the graph how many
minutes the temperature is above 60°C.
•
Devising games, e.g. Make up rules for a simplified lottery game – only
numbers 1 to 3 are available and you can pick two numbers. How many
possible outcomes are there? Can you devise a game where there are
12 possible outcomes?
• Dice experiments, e.g. Throw two (or three) dice and find the total,
identifying all the possible outcomes for the experiment.
• Spinner and card experiments, e.g. Design an experiment using two
different spinners and identifying the possible outcomes.
•
Confirming learning
Ask probing questions such as:
•
On the scale, mark in some divisions that will help you to mark more
accurately the positions of 35cm and 13cm. Explain your methods.
Find a range of measuring cylinders and jugs. On each one, identify
the level for 360 ml of liquid. Use the measuring equipment to work
out the rough equivalent of 360 ml in other units such as litres, fluid
ounces or pints.
• Use a scale representing grams and ounces. About how many ounces is
400 grams? About how many grams is 6 ounces?
•
•
A door has a security lock. To open the door you must press the
correct buttons. The code for the door is a letter followed by a single
digit number, for example B6.
How many different codes are there altogether?
Explain how you are sure you have found all possibilities.
Can you design a code that is harder to crack? How many different
combinations does your code have?
•
These two spinners are spun at the same time.
The two scores are added together. Record all the possible outcomes.
Design two spinners that would give fewer possible outcomes for the
experiment.
Level 4 to 5
Can I use the
0-1 probability
scale to
measure the
probabilities
of outcomes?
22 HD
Can I interpret
and explain
data presented
in line graphs?
Opportunities to use and apply
Possible contexts include:
Review questions
Imagine rolling a normal 1–6 dice. Mark on the scale below the
probability of: rolling a 5, rolling a number greater than 2, rolling a
zero, rolling an odd number
• Which example gives the probability closest to 1? Explain why.
•
•
Make a statement in which the probability is: 1; 1/3; 5/6
I have a 6-sided dice numbered 1–6 and an 8-sided dice numbered 1–8.
Use the probability scale to illustrate and compare the chance of
getting a 6 on the 6-sided dice with the chance of getting a 6 on the
8-sided dice. What about getting an even number, or a multiple of 4?
•
Decide whether the chance of landing on green is greater than, less
than or equal to 1/2 for each spinner. Explain your answers.
•
Explain what this graph tells us about the temperature over the
course of 12 hours starting at 8 am.
23 HD
Confirming learning
Ask probing questions such as:
Games, e.g. Probability based game shows such as 'Play your cards
right'; card and dice games, for example: Use two 1–6 dice. Player A
wins a point if the numbers on the two dice total 2, 3, 4, 5, 10 or 12.
Player B wins a point if the numbers total 6, 7, 8 or 9. Is this fair?
Explain your answer. If the game is not fair, devise new fair rules.
• 3-D shape, e.g. Use nets of regular polyhedra, to make dice. Ask the
children to compare the likelihood of getting a particular number with
different shapes and explain their conclusions.
• Problems, e.g. Colour a spinner so that it is twice as likely to land on
green as it is to land on blue. Justify why you think your shading
represents the given probability. Use the language of probability and
the probability scale to justify your answer.
•
Measures, e.g. Use conversion graphs to convert between units (e.g.
£s/Euros, Miles/Km,).
• Literacy, e.g. Represent the plot of a story/play in a graph
(mood/level of danger).
• Speaking and listening, e.g. Remove the line showing the final stages
of a line graph. Ask children to explain and justify a suitable ending.
• Science, e.g. cooling experiments.
•
Jack gave a report on the swimming race shown in the graph but he
has made a few mistakes. Explain why each statement is correct or
incorrect. They are about to swim 100 metres. Sam stops after 40
metres. Sam goes quickly into the lead. After 28 seconds, Janet
overtakes Sam. Sam wins by 10 seconds. What else could you add to
Jack's report?
Science, e.g. Record the resting heart rates of the class using the
Data Handling ITP and compare to this graph:
•
The pie charts show the results of a school's netball and football
matches. The netball team played 30 games. The football team played
24 games.
•
•
Decide whether each statement is true or false. Explain how you
know. Use the probability scale to illustrate your explanation.
Spinners A, B & C are equally likely to spin a 2.
The chance of spinning a 3 on spinner B and on spinner C is equal.
You would be more likely to spin a 1 on spinner D than on any other.
There is a 25% chance of getting a 3 on spinner C.
You are more likely to spin an odd number on spinner C than any other.
The chance of spinning a number greater than 4 on spinner C is 2/6.
• A fair dice has the numbers 1, 3, 3, 3, 4 and 4 on it. Draw your own
probability scale and mark the probability of rolling: 2; 3; 4; a number
smaller than 10.
'The temperature rose between 11 am and 1 pm faster than it fell
between 6 and 8 pm'. Is this correct, and if so, how do we know?
• Make up two further correct statements about the temperature
during the time represented. Use the graph to justify these.
• What might the graph look like for 12 hours on a winter's day?
Sketch the graph and explain your thinking.
•
Can I interpret
sets of data
with different
sample sizes
represented in
pie charts?
•
Some children were asked to choose their favourite drink from A, B,
C or D. Pie charts 1 and 2 represent 32 children. Pie chart 3
represents 24.
•
Estimate the percentage of games
that the netball team lost.
24 HD
John says drink B was chosen by the same number of children in each
group. Explain why this cannot be true.
• Choose two of the pie charts: Create two statements to compare and
explain the data.
• Can you write a statement based on these pie charts that isn't true
for someone else to correct?
• Imagine pie chart 1 still represents 32 children but pie chart 2
represents 128 children. Make statements to compare the two pie
charts.
•
PSHE, e.g. A healthy diet consists of 15% fat, 17% protein and 68%
carbohydrate. Ask children to keep a food diary for a day and create
their own pie chart showing the ideal proportions.
• Comparing data with similar data from other classes, for example,
deciding in which class an author from a given list is more popular.
• Real-life data, e.g. Compare proportions of people in different age
ranges in a village and a city in geography; compare proportion of
earnings spent in different ways in two different eras in history.
•
David says, 'The two teams won the same number of games'. What
error might he have made? Make a valid statement based on the
charts.
• These pie charts show the creatures that Tony and Gemma have
collected from their gardens. Who found more snails? Explain how you
know.
•
Level 4 to 5
Can I explain
what different
diagrams and
graphs
represent,
read
information
from them and
draw
conclusions
from this
information?
25 HD
Can I explain
range, mode,
median and
mean and use
them to
describe data
in order to
make
decisions?
26 HD
Opportunities to use and apply
Possible contexts include:
Review questions
•
This graph shows the temperature of a liquid as it cools.
How many minutes does it take to reach 40°C? For how many minutes
is the temperature above 60°C?
• This bar graph shows responses from Year 6 pupils about whether
they would buy a magazine.
•
Rajshree has six cards with a mean of 10 and a range of 6. What are
the numbers on the other two cards? How do you know? Are there
any other possibilities? Explain your thinking.
The following numbers of tokens for school computers were collected
over five weeks by four children:
Gurpreet
15
7
10
6
12
Claire
28
0
30
2
18
Ben
19
2
7
0
2
Mark
7
7
7
10
4
• Use the mean, mode, median and range to make some statements
about each child's collection. Who is the best collector of tokens?
Who is the most consistent? Explain your decision.
•
Exploring issues in school, e.g. graphs created to explore issues that
may support School Council decisions, such as homework.
• Real-life graphs and charts, e.g. from newspapers, magazines and
websites.
• Cross-curricular contexts, e.g. line graphs produced in science
experiments; real-life data linked to geography and history projects.
• Measures, e.g. conversion graphs - create and interpret line graphs to
show the relationship between linked measures, such as comparing
pounds with euros, converting Celsius to Fahrenheit.
•
Using practical resources, e.g. Empty out 2 tubes/boxes of sweets
one at a time and compare the mode, median and mean of colours in
each packet. Predict what you expect in a third packet and compare
with expectations.
• Comparing real-life media, e.g. Categorise adverts in 10 pages taken
from a tabloid papers and 10 pages from a broadsheet. Compare the
mean, mode, and median of adverts in the different types of
newspaper. Are there any differences and if so how would you explain
these? Justify your own decision about which paper is best.
• Speaking and listening, e.g. Remove the line showing the final stages
of a line graph. Ask children to explain and justify a suitable ending.
• PE, e.g. A group of children each throws a ball 10 times and measures
their throws. How could you decide whom you would want on your
team? Which would you use out of range, median, mean or mode?
Justify your choice.
•
Confirming learning
Ask probing questions such as:
•
A car and a motorbike drive along the same road. This line graph
shows details of their journey.
What can you say about the car and the motorbike at the point that
their lines cross on the graph?
Compare the journeys of the two vehicles using the information from
the graph.
•
Here are the long jump results for a school. They are measured to the
nearest centimetre. Steve jumped 315 cm. He says 'Only 2 people
jumped further than me.' Could he be correct? Explain your answer.
•
Joe can take the Transit Bus or the Direct Bus. Over 5 journeys he
has had to wait this number of minutes for a bus.
Which bus do you think he should catch? Explain your choice using
range and averages.
There are three people in John's family. The range of their shoe
sizes is 4. Two people in the family wear shoe size 6. John's shoe size
is not 10. What is John's shoe size? Explain your thinking.
• Ten witnesses to a robbery were asked how many robbers took part in
the crime. Their answers were: 5 4 5 3 4 4 5 5 5 3
• Together with the range, which average (mode, median or mean) is the
most useful for the police to use when investigating the crime?
Explain your answer.
•