Theme: Problem Solving – patterns, sequences and rules
Year Target
Yr 1
Mathematical
challenges for able
pupils in Key
stages 1 and 2
Group Target
Must
Should
Finding rules and
describing
patterns problem
solving pack
Guidance booklet
Further
examples of
pitch and
expectations:
Foundation to
year 1
Key Resources /
Models and Images
I can use familiar objects
and common shapes to
create and recreate
patterns and build
models
Smart board resources
unit plans:
Autumn unit 3
Summer unit 8
Summer unit 9
I can continue simple
patterns and involving
numbers or shapes and
explain what I’m doing
and why.
I can describe patterns
and relationships
involving numbers or
shapes, make predictions
and test these with
examples
Nrich multiple pack
Numbertrack and counters
Increasing number grid
Ice cream
Bird eggs
Line of symmetry
Coloured shapes
Birthdays
Domino sequences
Shape sequences1
Shape sequences 2
Fireworks
Goldfish
Ones and twos
At the toyshop
Ben’s numbers
Arithmagon1
Information
Counter
Monty
- Divide and
rule2
- teaching
mental
calculation
strategies
Could
Write the number 14 in the
correct place. How did you
know? What will the largest
number on this grid be?
Recite number names in
order from 0 to 20 or more,
forwards and backwards, using objects, number tracks
and number lines
Count aloud in ones and continue the count after given a
sequence such as four, five, six…
Continue a simple
pattern of
dominoes or put
the domino
doubles in order.
Locate numbers on a number track and begin to
identify that the number before is one less and the
next number is one more.
Explore calculation patterns in pairs of numbers with a
total of 10, using their fingers in support
Count in a soft voice to ten, a loud voice to twenty,
a soft voice to thirty, and a loud voice to forty, and
so on
Continue the count after given a sequence such as
twenty-four, twenty-five, twenty-six, ...
Describe and extend number sequences such as
16, 14, 12, 10, ... or 15, 17, 19, 21, ... by responding
to questions such as: What numbers come next?
Describe the pattern. Make up another counting
pattern for others to solve.
They fill in missing numbers in sequences such as
12, 14, , 18, 20,
or 25, 20, 15, , .
Use number lines or the 100-square to see how the
words they are saying connect with the structure of
the number system
Begin to understand the idea of odd and even
numbers
Use 2-D shapes and 3-D solids to make patterns and
talk about them.
Look at these shapes.
Describe and extend number sequences by counting
on or back in repeated steps of the same size, including
2, 5 and 10.
e.g. 20, 30, 40, ... Count on to 70
Which two of the
shapes would fit
together to make the
shape below? Tick
the two shapes.
I know a secret sequence. It has these numbers in it: 60,
50, 40, 30 What numbers come next in the sequence?
Look at these numbers: 13 14 15
18
Which numbers are covered? How do you know?
Make a string of beads. First a red one, then a blue one.
Carry on threading one red, one blue. What colour is the
sixth bead on your string? What colour will the tenth bead
be? How do you know?
- teaching
written
strategies
- exemplification
of standards
I will clap where a number is missing. What is the
missing number? 12 22 32 42 [one clap] 62
ICT files
Year 1
- Divide and
rule1
Outcomes
Place the
objects on large
diagrams
prepared for the
task to show
what they have
found out.
Continue counting over the tens boundary when
started with a sequence such as 66, 67, 68, ...
find out how many birthday candles they have blown out
since they were born
What is special about the way I have ordered these
counters? Can you make a different pattern using
the same counters?
Tell me how to continue this pattern.
Can you make a pattern where the third counter is
blue? Is that the only way it could be done?
What is wrong with this pattern? Can you put it
right?
Year Target
Yr 2
Group Target
Must
Mathematical
challenges for able
pupils in Key
stages 1 and 2
Finding rules and
describing
patterns problem
solving pack
Should
Further
examples of
pitch and
expectations:
year 2
Information
- Divide and
rule1
- Divide and
rule2
- teaching
written
strategies
- exemplification
of standards
I can describe patterns
and relationships
involving numbers or
shapes, make predictions
and test these with
examples
I can solve problems by
Identifying patterns and
relationships involving
numbers or shapes.
Guidance booklet
- teaching
mental
calculation
strategies
I can continue simple
patterns and involving
numbers or shapes and
explain why.
Could
Key Resources
Outcomes
Smart board resources
unit plans:
Y2 autumn unit 4
Y2 spring unit 8
Y2 summer unit 8
Count on in tens from the number 27. Will the number
85 be in the count? How do you know?
Nrich multiple pack
We have worked out that 3 5 8 and 13 5 18.
Without calculating, tell me what 23 5 will be. What
about 63 5?
Write the missing digits to make this correct.
ICT files
Problem solving materials:
Ben’s numbers
Ice cream
Bird eggs
Line of symmetry
Card sharp
Fireworks
Goldfish
Ones and twos
At the toyshop
Triangles and pentagons
Farm problem
Simple sudoku
Shape puzzle
Colour coded digit mystery
Venn and Carroll diagram
templates
Caterpillar sequences
Counter
Monty
100 square jigsaw
Describe the patterns in the sequence 0 20 20, 1
19 20, predict the next calculation in the sequence
and continue the pattern to generate all the pairs of
numbers with a total of 20.
Recognise multiples of 2, 5 and 10; they know that
multiples of 2 are called even numbers and that
numbers which are not even are odd
Make and describe symmetrical patterns, for
example, using ink blots, pegboards or cubes,
What is the multiple of 10 before 70?
What three numbers come next: 35, 40, 45, ...?
What is the next even number after 24?
What do you notice about the numbers in the 5 timestable? If we carried on, what do you think the next
number would be? If we carried on, do you think the
pattern would continue? How do you know?
Think of a number bigger than 100 that would be in
the 5 times-table if we carried on. Why do you think
that number would be in the table?
They find missing numbers from sequences such as:
30, 40,
, 60,
55, 50, ?, 40, 35, ?, 25, 20
, 41, 43, 45, 47, 49, , 53 and
, 48 , 51 ,54 , , 60, ...
Consolidate counting on from zero in steps of 2, 5 and
10 and build up these times-tables, describing what
they notice about numbers in the tables. They use
this to predict some other numbers that would be in
the count.
Sort a set of numbers into those that can be halved
exactly and those that cannot. Relate findings to odd
and even numbers.
Find as many ways as possible to complete a missingdigit calculation such as 1
0, explaining the
patterns and relationships in the results.
e.g. place two red
squares, two green
squares and two blue squares in a line so that the
squares make a symmetrical pattern, and explore the
number of different ways of doing it.
On the graph, how do you
work out the numbers between
the labels? Which way of
getting to school was used by
7 children? These labels show
only 0, 2, 4, 6, 8 and 10. How
could you find 7?
If this scale carried on, what
other numbers do you think would be shown? Would
the number 34 be shown? How can you tell?
Chanting of tables is supported with a counting stick or
number line to establish the relationship between the
increasing steps and corresponding products.
A secret sequence has the numbers 13, 15, 17, 19 in
it. What numbers come next in my sequence? What
numbers come before? What clues did you use to
work this out? Give me a number greater than 40 that
is in my secret sequence. How do you know this
number is in my sequence? How could you check?
Choose different criteria for sorting the same set of
objects and explain their criteria to others.
Which are the even numbers in this list?
13, 4, 12, 8, 19, 16,
Draw rings around all the multiples of 5.
45, 20, 54, 17, 40
They identify missing numbers in a 100square.
Describe patterns in the sequences they generate
when they count on or back from any two- or threedigit number in steps of 1, 2, 3, 5 and 10
Year Target
Yr 3
Group Target
Must
Mathematical challenges
for able pupils in Key
stages 1 and 2
Finding rules and
describing patterns
problem solving pack
Should
Guidance booklet
Further examples of
pitch and expectations:
I can complete
sequences by
following simple
rules and
investigate
statements by
identifying and
using patterns,
relationships
and properties
of numbers or
shapes.
year 3
Teaching maths in year
3 booklet
Information
- Divide and rule1
- Divide and rule2
- teaching mental
calculation strategies
- teaching written
strategies
- exemplification of
standards
I can describe
patterns and
relationships
involving
numbers or
shapes, make
predictions and
test these with
examples
I can solve
problems by
Identifying
patterns and
relationships
involving
numbers or
shapes.
Could
Key Resources
Outcomes
Springboard materials:
Unit 8; unit 9
Look at this calculation: 5 8
. Write a digit in
each box so that the calculation is correct. How else
can you do it? What patterns do you notice?
Repeat with 2 7
.
Unit plans
Spring unit 8
Summer unit 8
Nrich multiple pack
ICT files
Problem solving materials:
Spaceships
Suzie snake
Stamps
Maisie mouse
Kieron’s Cats
Fireworks
Sheepdog trials
Number puzzle
Farm problem
Three rings
Simple sudoku
Shape puzzle
Colour coded digit mystery
Venn and Carroll diagram
templates1
Venn diagram number sort
Carroll diagram number sort
Caterpillar sequences
Function machine
Excel files
Zids and zods
Pentabods and bipods
Duck sequencing game
Counter
Monty
What is the largest multiple of 10 you can add to 38 if
your answer must be smaller than 100?
Explain the relationship between adding 3 to 4 and
adding 30 to 40 and 300 to 400.
9 3 6. What is 90 30, and 900 600? How do you
know?
count on and back in steps of 1, 2, 3, 4, 5, 6 and 10
from zero and then from any given number
Enter the numbers 1 to 20 onto a Venn diagram and
answer questions such as:
Which numbers are
multiples of 5 but
not even?
Explain why the
number 17 is not in
either ring.
What measurement is shown on
these scales? Explain how you
worked this out.
What is each division on this scale
worth? How did you work this out?
How could you check that you are
right?
keep subtracting 6 from 49, what is the smallest
number you get?
recognise patterns of similar calculations , such as
25 20 45, 45 20 65, 65 20 85.
Continue the sequence and suggest other sequences
of calculations that follow similar patterns.
recognise the relationships between counting in: 2s
and 4s; 3s and 6s; 5s and 10s
What are the missing numbers in these patterns? How
did you find them?
locate and position multiples of 10 or 100 on a
number line
83, 78, , 68, 63, 58,
1, 7, 13, 19, , ;
, 26, 22, , , 10, 6, 2
Sort the numbers 1-20 into two groups:
Multiples of 5
Not multiples of 5
Sam says: 'When you count from zero in fours, every
number is even.' Is he right? How do you know?
What do you notice? Tell me a number greater than
100 that would go in each group.
Investigate general statements such as: When you
count in fives, the units digits form a pattern
Identify numbers to 1000 that are multiples of 2, 5 or
10
Sort a set of numbers using criteria such as: 'These
numbers are multiples of 5', or: 'These numbers are in
the 6 times-table''
Find the number of edges of assorted prisms to
investigate the general statement : The number of
edges of a prism is always a multiple of 3.
One of these shapes
is in the wrong place
on the diagram.
Which one?
Can 113 be a multiple of 5? How do you know?
Can a multiple of 4 ever end in a 7?
Start at 93 and count back in tens. What will be the
smallest number that you reach on a 100-square?
Classify objects, numbers or shapes according to
one criterion, progressing to two criteria, and display
this work on a Carroll diagram
Recognise simple patterns and relationships, for
example to find a pair of numbers with a sum of 17
and a product of 70
Children partition two- and three-digit numbers in
different ways. For example, they continue the
patterns:
72 70 2
853 800 53
72 60 12
853 700 153
72 =50 + 22
853 = 600 + 253
Year Target
Yr 4
Group Target
Must
Mathematical challenges
for able pupils in Key
stages 1 and 2
Finding rules and
describing patterns
problem solving pack
Should
Guidance booklet
Further examples of
pitch and expectations:
I can solve
problems by
Identifying
patterns and
relationships
involving
numbers or
shapes.
I can complete
sequences by
following simple
rules and
investigate
statements by
identifying and
using patterns,
relationships
and properties
of numbers or
shapes.
year 4
When exploring
patterns,
properties and
relationships I
am able to
propose a
general
statement
involving
numbers or
shapes;
Information
- Divide and rule1
- Divide and rule2
- teaching mental
calculation strategies
- teaching written
strategies
- exemplification of
standards
Calculator activities
Reasoning about
numbers
Shape and space
activities
Could
Key Resources
Outcomes
Springboard materials:
Unit 6;
Count on in eights from zero. Now count back to zero.
This time, count on seven eights from zero.
Show me seven hops of eight from zero on the number
line.
How can you work out the 8 times-table from the 4 timestable? Or the 9 times-table from the 3 times-table?
Autumn: unit 4
Spring unit 8
Summer unit 8
Nrich multiple pack
ICT files
Problem solving materials:
Row of coins
Row of numbers
Shape coordinates
Stickers
Footsteps in snow
Esmareldas coins
Ski lift
Function machine
Money grids
Multiplication jigsaw
Venn diagram number sort
Carroll diagram number sort
Shape puzzle
Spaceships
Suzie snake
Stamps
Maisie mouse
Kieron’s Cats
Fireworks
Sheepdog trials
Number puzzle
Farm problem
Three rings
Colour coded digit mystery
Venn and Carroll diagram
templates
Caterpillar sequences
Function machine
Weakest link template
Blockbusters template
fraction mysteries
multiplication mystery
subtraction mystery
Duck sequencing game
Counter
Monty
Predict numbers that will occur in the sequence, and
answer questions such as: If I keep on subtracting 3 from
10 will -13 be in my sequence?
use the constant function on a calculator to check
their predictions
Tell me some numbers that will divide exactly by 2, by 5,
by 10. How do you know?
Tell me a number that will divide exactly by 4. How do
you know that a number will divide exactly by 4?
Continue this number sequence in both directions.
Use these four digit cards.
Write the two missing numbers in this sequence.
Sean counts his books in fours. He has one left
over. He then counts his books in fives. He has
three left over. How many books has Sean?
count in fractions along a number line from 0 to
1, for example, in tenths
Count in steps of 50p in a sequence such as 0.50,
1.00, 1.50, 2.00, or in steps of 25 cm in a
sequence like 1.25 m, 1.5 m, 1.75 m.
What would my sequence look like if I counted in
steps of 20p from 1.10?
Complete an equation such as
- 47
9, and
find the largest and smallest possible differences.
Lisa went on holiday. In 5 days she made 80
sandcastles. Each day she made 4 fewer castles
than the day before. How many sandcastles did she
make each day?'
Name a multiple of 6 that is also a multiple of 9.
Use each of the digits once to make a total that is a
multiple of 5.
Here is part of a number square.
The shaded numbers are part of a
sequence. Explain the rule for the
sequence.
Explain what you did to get your
answer to the problem.
count in steps of 6 from zero and investigate the
patterns of multiples in the 100-square.
classify polygons, using Carroll or Venn diagrams
If 7 9 63, what is 63
know?
7? What other facts do you
Are there any multiples of 7 that are also multiples of 8?
Draw an arrow on the number line to show 1
.
What colour is each shape? Write it on the shape.
Clues
Red is not next to grey.
Blue is between white and grey.
Green is not a square.
Blue is on the right of pink.
What are the missing numbers in this sequence?
Complete the number pattern.
Explore a number sequence arising from a given
rule, for example 'double the last number and
subtract 1' (2, 3, 5, 9, ...). What are the gaps
between the numbers? and What if the rule were
double and add 1?
Count on and back in halves, quarters, fifths and
tenths
Rosie spent 2 on 10p and 20p stamps. She
bought three times as many 10p stamps as 20p
stamps. How many of each stamp did she buy?
Year Target
Yr 5
Group Target
Must
Mathematical challenges for
able pupils in Key stages 1
and 2
Finding rules and describing
patterns problem solving
pack
Should
Guidance booklet
Further examples of pitch
and expectations:
year 5
Information
- Divide and rule1
- Divide and rule2
- teaching mental calculation
strategies
- teaching written strategies
- exemplification of
standards
Calculator activities
Reasoning about numbers
Shape and space activities
Could
I can complete
sequences by
following simple
rules and
investigate
statements by
identifying and
using patterns,
relationships
and properties
of numbers or
shapes.
When exploring
patterns,
properties and
relationships I
am able to
propose a
general
statement
involving
numbers or
shapes;
I can
represent and
interpret
sequences,
patterns and
relationships in
different ways,
including using
simple
expressions and
formulae in
words then
symbols
Key Resources
Outcomes
Autumn: unit 8; unit 12
Spring: unit 2 unit 11
Summer: unit 6b unit 12
Create a sequence that includes the number -5.
Describe your sequence to the class.
ICT files
Problem solving materials:
Arithmagons 2
Age old problems
Zids and Zods
Jacks book
A bit fishy
Eggs (excel eggs)
Spendthrift
Handshakes
addition and subtraction
puzzles
Sleigh ride
Oranges and lemons
Library area
Roses for sale
Bunches of grapes
Ages to ages
Ages and ages
Fruit bowl
Arithmagons 3
Double scoop ice cream
Nicknames
Which number where?
Weakest link template
Blockbusters template
Pyramids
More pyramids
Leapfrogs
Function machine
Caterpillar sequences
fraction mysteries
multiplication mystery
subtraction mystery
Duck sequencing game
Counter
Monty
Here is part of a sequence: , -9, -5, -1, .
Explain how to find the missing numbers. Explain how
you would find the missing numbers in this sequence:
10,
, 4, 1,
, -5,
What is the 'rule' for the sequence?
Put a ring around the numbers that are factors of 30: 4
5 6 20 60 90
Create sequences by counting on and back from any
start number in equal steps such as 19 or 25
Identify the rule for a given sequence. And use this to
continue the sequence or identify missing numbers, e.g.
complete- 89, , 71, 62, ,
Explore sequences involving negative numbers using
a number line. For example, they continue the
sequence -35, -31, -27, ... by recognising that the rule is
'add 4'.
Use calculators or the ITP 'Moving digits' to explore the
effect of repeatedly multiplying/dividing numbers by 10.
-
Place the digits 0 to 9 to make this
calculation correct:
Two numbers have a total of 1000
and a difference of 246. What are
Simon's birthday is on
August 20th. Tina's birthday
is on September 9th. On
what day of the week was
her birthday in 1998?
What is the next number in
this sequence: 0, 0.2, 0.4,
0.6, 0.8?
What is the rule for this
sequence: 3, 2.7, 2.4,...?
Suggest some other numbers that will be in the
sequence.
Write
in the
missin
g
number on this number line.
Find two numbers between 3 and 4 that total 7.36. Use
a written method to check your answer.
Write what the four missing digits could be:
10 3
What is the total mass of the
apples on the scales?
A piece of cheese has a mass
of 350 grams. Mark an arrow
on the scale to show the
reading for 350g.
the two numbers?
The area of a rectangle is 32 cm2. What are the lengths
of the sides? Are there other possible answers? How
did you work it out?
Explain why 81 is a square
number.
One number is in the wrong
place on the sorting diagram.
Which one is it?
What do you notice about numbers that are multiples of
both 2 and 5?
Find as many pairs of numbers as you can with a
product of 160.
Choose from these digit cards each time: 7, 5, 2, 1.
Make these two-digit numbers:

an even number

a multiple of 9

a square number

a factor of 96

a common multiple of 3 and 4
Tell me
a
number
that is both a multiple of 4 and a multiple of 6. Are there
any other possibilities?
The sum of two even numbers is a multiple of 4. Is
this sometimes true, always true or never true? Justify
your answer with examples
Find different ways to complete:
Two square tiles are placed
side by side. How many tiles
are needed to surround them
completely? What if there
were five tiles? How many
tiles would be needed if 100 tiles were laid side by
side? Explain your answer.
Identify all the factors of a given number; eg, the
factors of 20 are 1, 2, 4, 5, 10 and 20
My age is a multiple of 8. Next year my age will be a
multiple of 7. How old am I?
Year Target
Group Target
Yr 6
Must
Mathematical challenges for
able pupils in Key stages 1
and 2
Finding rules and describing
patterns problem solving
pack
Guidance booklet
Further examples of pitch
and expectations:
year 6
Should
Information
- Divide and rule1
- Divide and rule2
- teaching mental
calculation strategies
- teaching written
strategies
- exemplification of
standards
Calculator activities
Reasoning about
numbers
Shape and space
activities
Could
When
exploring
patterns,
properties
and
relationships
I am able to
propose a
general
statement
involving
numbers or
shapes;
I can
represent
and interpret
sequences,
patterns and
relationships
in different
ways,
including
using simple
expressions
and formulae
in words
then
symbols
I can use
letters and
symbols to
represent
unknown
numbers or
variables
and find the
nth term in a
sequence
Key Resources /
Outcomes
Springboard:
Unit 21; unit 22; unit 26; unit
29;
Unit plans
Autumn: unit 12
Spring: unit 4 unit 11
Summer: unit 5; unit 9; unit
10
Here is a repeating pattern of shapes. Each shape is
numbered.
ICT files
Problem solving materials:
Moneybags
Five numbers
Jacks book
Arithmagons 2
Age old problems
addition and subtraction
puzzles
Zids and Zods
A bit fishy
Eggs (excel eggs)
Spendthrift
Handshakes
Sleigh ride
Oranges and lemons
Library area
Roses for sale
Bunches of grapes
Ages to ages
Ages and ages
Fruit bowl
Arithmagons 3
Which number where?
Tower of Hanoi
chessboard problem
Pyramids
More pyramids
Leapfrogs
Caterpillar sequences
Function machine
Investigating consecutive
numbers
Twelve days of Christmas
Hexagon pattern
Weakest link template
Blockbusters template
fraction mysteries
multiplication mystery
subtraction mystery
Square ages
Sticky triangles
Duck sequencing game
Counter
Monty
The pattern continues in the same way. What will the 35th
shape be? Explain how you can tell.
Start from a two-digit number with at least six factors, e.g.
56. How many different multiplication and division facts can
you make using what you know about 56?
John says that every multiple of 4 ends in 2, 4, 6 or 8.
Persuade me that John is wrong.
Convince your partner that 2140 will not be in this
sequence.
40 80 120 160 200 ...
Investigate the differences between terms of the sequence
of square numbers 1, 4, 9, 16, ...
Describe the pattern and use it to continue the sequence.
Investigate the statement: 'Every square number is the
sum of two triangular numbers'.
Parveen has the same number of 20p and 50p coins. She
has 7.00. How many of each coin does she have?
What multiplication table does this
image represent? How do you
know? What other numbers will
you see in the boxes outside?
Find two numbers with a product
of 899.
Count forwards in jumps of 19 from 7 and backwards in 7s
starting at 19 and continuing below zero
In a village where all the roads
are straight, every time two
streets intersect a street lamp is required. Investigate the
number of street lamps required for 2 streets, 3 streets, 4
streets, ...
Count in thirds from 0 using mixed numbers and in steps of
0.3 from 0, and backwards in 100s from 21 and 213
What is the minimum and maximum number of lamps
needed for 5 streets? n streets
Identify the rule for a given sequence. For example, 1, 3,
7, 15, 31
How many different flights there would be connecting 2, 3
and 4 airports if each airport is connected by return flights.
Predict how many flights will be needed for 5, testing their
predictions. They find a general rule and express it in
words, then using symbols.
A number multiplied by itself gives 2809. Find the number
Describe the relationship
between terms in this
sequence:
2, 3, 8, 63, ...
Make the ITP '20 cards'
generate this sequence of
numbers:
1, 3, 7, 13, ...
Explain why a square number always has an odd number
of factors.
The first two numbers in this sequence are 2.1 and 2.2.
The sequence then follows the rule: 'to get the next
number, add the two previous numbers'. What are the
missing numbers?
2.1, 2.2, 4.3, 6.5, ,
Find two square numbers that total 45.
Explore the pattern of primes on a 100-square, explaining
why there will never be a prime number in the tenth column
and the fourth column.
Convince me that in a number grid starting at 1 with nine
columns, there will never be a prime number in the sixth
column.
The rule for this sequence of numbers is 'add 3 each time'.:
1, 4, 7, 10, 13, 16 ... The sequence continues in the same
way. I think that no matter how far you go there will never
be a multiple of 3 in the sequence. Am I correct? Explain
how you know.
What is the value of 4x
know.
7 when x 5? Explain how you
Draw the next two terms in this sequence:
Describe this
sequence to a friend
using words. Describe
it using numbers. How
many small squares
would there be in the
10th picture?
I want to know the 100th term in the sequence. Will I have
to work out the first 99 terms to be able to do it? Is there a
quicker way? How?
This sequence of numbers goes up by 40 each time.
40 80 120 160 200 ...
This sequence continues. Will the number 2140 be in the
sequence? Explain how you know.
Year Target
Group Target
I can use
letters and
symbols to
represent
unknown
numbers or
variables
and find the
nth term in a
sequence
Yr 6
Mathematical challenges for
able pupils in Key stages 1
and 2
Finding rules and describing
patterns problem solving
pack
Guidance booklet
Further examples of pitch
and expectations:
year 6 into year 7
Information
- Divide and rule1
- Divide and rule2
- teaching mental
calculation strategies
- teaching written
strategies
- exemplification of
standards
Calculator activities
Reasoning about
numbers
Shape and space
activities
Could
Key Resources /
Outcomes
Springboard:
Unit 21; unit 22; unit 26; unit
29;
Unit plans
Autumn: unit 12
Spring: unit 4 unit 11
Summer: unit 5; unit 9; unit
10
ICT files
Problem solving materials:
Patterns and sequences
Moneybags
Five numbers
addition and subtraction
puzzles
Jacks book
Arithmagons 2
Age old problems
Square ages
Zids and Zods
A bit fishy
Eggs (excel eggs)
Spendthrift
Handshakes
Sleigh ride
Oranges and lemons
Library area
Roses for sale
Bunches of grapes
Ages to ages
Ages and ages
Fruit bowl
Arithmagons 3
Chalk problem;
fraction mysteries
multiplication mystery
subtraction mystery
Tower of Hanoi
chessboard problem
Which number where?
Pyramid numbers
Pyramids
More pyramids
Leapfrogs
Function machine
Caterpillar sequences
Hexagon pattern
Squares and circles
Weakest link template
Blockbusters template
Sticky triangles
n stands for a number. Complete
this table of values.
k, m and n each stand for a whole number. They add
together to make 1500.
k + m + n = 1500
m is three times as big as n.
k is twice as big as n.
Calculate the numbers k, m and n.
Ann makes a pattern of L
shapes with sticks.
Ann says : ‘I find the
number of sticks for a
shape by first multiplying the shape-number by 4,
then adding 3.’
Work out the number of sticks for the shape that
has shape-number 10.
Ann uses 59 sticks to make another L shape in this
pattern. What is its shape-number?
Debbie has a pack of cards numbered from 1 to 20 She
picks four different number cards.
The graph shows
a straight line.
The equation of
the line is y = 3x..
Does the point
(25, 75) lie on the
straight line y =
3x? Tick () Yes
or No. Explain
how you know.
Exactly three of the four numbers are multiples of 5.
Exactly three of the four numbers are even
numbers. All four of the numbers add up to less than 40.
Write what the numbers could be. Write two further
questions that you could ask about the cards.
30 children are going on a trip. It costs £5 including
lunch. Some children take their own packed lunch. They
pay only £3. The 30 children pay a total of £110. How
many children are taking their own packed lunch?
A sequence starts at 500 and 80 is subtracted each time.
500
420
340 ...
The same number is missing from each box. Write the
same missing number in each box.
 ×  ×  = 1331
Here is a sequence.
The sequence continues in the same way. Write the first
two numbers in the sequence which are less than zero.
The rule is to add the same amount each time.
Write in the missing numbers.
Here are five number cards.
The formula for
the number of
circles (c)
in shape
number (n) is:
c = 3n – 1
A and B stand for two different whole numbers. The sum
of all the numbers on all five cards is 30. What could be
the values of A and B?
This four digit number is a square number. Write in the
missing digits.
Use the formula
to work out the
shape number
99
that has 104 circles.
Write the three missing digits:
  ×  = 371