Theme: Problem Solving – patterns, sequences and rules
Year Target / Group Target / Key Resources / Models and Images /Outcomes
Yr 1 / Must / I can use familiar objects and common shapes to create and recreate patterns and build models / Smart board resourcesunit plans:
Autumn unit3
Summer unit8
Summer unit9
Nrich multiple pack
ICT files
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
Counter
Monty / 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
Use 2-D shapes and 3-D solids to make patterns and talk about them.
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
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?
Place the objects on large diagrams prepared for the task to show what they have found out. / I will clap where a number is missing. What is the missing number? 12 22 32 42 [one clap] 62
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
Look at these shapes.
Which two of the shapes would fit together to make the shape below? Tick the two shapes.
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?
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:
Foundation to year 1
Year 1
Information
- Divide and rule1
- Divide and rule2
- teaching mental calculation strategies
- teaching written strategies
- exemplification of standards / Should / I can continue simple patterns and involving numbers or shapes and explain what I’m doing and why.
Could / I can describe patterns and relationships involving numbers or shapes, make predictions and test these with examples
Year Target / Group Target / Key Resources /
Outcomes
Yr 2 / Must / I can continue simple patterns and involving numbers or shapes and explain why. / Smart board resourcesunit plans:
Y2 autumn unit 4
Y2 spring unit 8
Y2summer unit 8
Nrich multiple pack
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 / Count on in tens from the number 27. Will the number 85 be in the count? How do you know?
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.
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 times-table? 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 missing-digit calculation such as 1 0, explaining the patterns and relationships in the results.
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 100-square. / 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,
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.
Describe patterns in the sequences they generate when they count on or back from any two- or three-digit number in steps of 1, 2, 3, 5 and 10
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 2
Information
- Divide and rule1
- Divide and rule2
- teaching mental calculation strategies
- teaching written strategies
- exemplification of standards / Should / I can describe patterns and relationships involving numbers or shapes, make predictions and test these with examples
Could / I can solve problems by Identifying patterns and relationships involving numbers or shapes.
Year Target / Group Target / Key Resources /
Outcomes
Yr 3 / Must / I can describe patterns and relationships involving numbers or shapes, make predictions and test these with examples / Springboard materials:Unit 8; unit 9
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 / Look at this calculation: 58 . 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 27 .
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.
936. What is 9030, and 900600? 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
keep subtracting 6 from 49, what is the smallest number you get?
recognise the relationships between counting in: 2s and 4s; 3s and 6s; 5s and 10s
locate and position multiples of 10 or 100 on a number line
Sort the numbers 1-20 into two groups:
Multiples of 5 / Not multiples of 5
What do you notice? Tell me a number greater than 100 that would go in each group.
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? / 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?
recognise patterns of similar calculations , such as 2520 45, 4520 65, 6520 85.
Continue the sequence and suggest other sequences of calculations that follow similar patterns.
What are the missing numbers in these patterns? How did you find them?
83, 78,, 68, 63, 58,
1, 7, 13, 19, , ;
, 26, 22, , , 10, 6, 2
Sam says: 'When you count from zero in fours, every number is even.' Is he right? How do you know?
Investigate general statements such as: When you count in fives, the units digits form a pattern
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
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 3
Teaching maths in year 3 booklet
Information
- Divide and rule1
- Divide and rule2
- teaching mental calculation strategies
- teaching written strategies
- exemplification of standards / Should / I can solve problems by Identifying patterns and relationships involving numbers or shapes.
Could / I can complete sequences by following simple rules and investigate statements by identifying and using patterns, relationships and properties of numbers or shapes.
Year Target / Group Target / Key Resources /
Outcomes
Yr 4 / Must / I can solve problems by Identifying patterns and relationships involving numbers or shapes. / Springboard materials:Unit 6;
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 / 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 times-table? Or the 9 times-table from the 3 times-table?
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.
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 7? What other facts do you know?
Are there any multiples of 7 that are also multiples of 8?
Draw an arrow on the number line to show 1 .
/ Write the two missing numbers in this sequence.
Sean counts his books in fours. He has oneleft 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.
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?
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 4
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 / Should / I can complete sequences by following simple rules and investigate statements by identifying and using patterns, relationships and properties of numbers or shapes.
Could / When exploring patterns, properties and relationships I am able to propose a general statement involving numbers or shapes;
Year Target
/ Group Target /Key Resources
/Outcomes
Yr 5 / Must / I can complete sequences by following simple rules and investigate statements by identifying and using patterns, relationships and properties of numbers or shapes. / Autumn: unit8; unit12Spring: unit 2unit 11
Summer: unit6bunit12
ICT files
Problem solving materials:
Arithmagons2
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 / Create a sequence that includes the number -5. Describe your sequence to the class.
Here is part of a sequence: , -9, -5, -1, .