Working systematically



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 |Smart board resources |Write the number 14 in the correct place. How did you know? |I will clap where a number is missing. What is the |

| | |common shapes to create and |unit plans: |What will the largest number on this grid be? |missing number? 12 22 32 42 [one clap] 62 |

| | |recreate patterns and build |Autumn unit 3 | | |

| | |models |Summer unit 8 |Recite number names in order from 0 to 20 or more, forwards and|Count in a soft voice to ten, a loud voice to twenty, a |

| | | |Summer unit 9 |backwards, using objects, number tracks and number lines |soft voice to thirty, and a loud voice to forty, and so |

| | | | | |on |

| | | |Nrich multiple pack |Count aloud in ones and continue the count after given a | |

| | | | |sequence such as four, five, six… |Continue the count after given a sequence such as |

| | | |ICT files | |twenty-four, twenty-five, twenty-six, ... |

| | | |Numbertrack and counters |Continue a simple pattern of dominoes or put the domino doubles| |

| | | |Increasing number grid |in order. |Describe and extend number sequences such as 16, 14, 12, |

| | | |Ice cream | |10, ... or 15, 17, 19, 21, ... by responding to questions|

| | | |Bird eggs |Locate numbers on a number track and begin to identify that the|such as: What numbers come next? Describe the pattern. |

| | | |Line of symmetry |number before is one less and the next number is one more. |Make up another counting pattern for others to solve. |

| | | |Coloured shapes | | |

| | | |Birthdays |Explore calculation patterns in pairs of numbers with a total |They fill in missing numbers in sequences such as 12, 14,|

| | | |Domino sequences |of 10, using their fingers in support |[pic], 18, 20, [pic] |

| | | |Shape sequences1 | |or 25, 20, 15, [pic], [pic]. |

| | | |Shape sequences 2 |Use 2-D shapes and 3-D solids to make patterns and talk about | |

| | | |Fireworks |them. |Use number lines or the 100-square to see how the words |

| | | |Goldfish | |they are saying connect with the structure of the number |

| | | |Ones and twos |Describe and extend number sequences by counting on or back in |system |

| | | |At the toyshop |repeated steps of the same size, including 2, 5 and 10. | |

| | | |Ben’s numbers |e.g. 20, 30, 40, ... Count on to 70 |Begin to understand the idea of odd and even numbers |

| | | |Arithmagon1 | | |

| | | |Counter |I know a secret sequence. It has these numbers in it: 60, 50, |Look at these shapes. |

| | | |Monty |40, 30 What numbers come next in the sequence? | |

| | | | | |Which two of the shapes would fit together to make the |

| | | | |Look at these numbers: 13 14 15 [pic][pic]18 |shape below? Tick the two shapes. |

| | | | |Which numbers are covered? How do you know? | |

| | | | | |Continue counting over the tens boundary when started |

| | | | |Make a string of beads. First a red one, then a blue one. Carry|with a sequence such as 66, 67, 68, ... |

| | | | |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 |find out how many birthday candles they have blown out |

| | | | |know? |since they were born |

| | | | | | |

| | | | |Place the objects on large diagrams prepared for the task to |What is special about the way I have ordered these |

| | | | |show what they have found out. |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 |Should |I can continue simple patterns | | | |

|challenges for able | |and involving numbers or shapes | | | |

|pupils in Key stages 1| |and explain what I’m doing and | | | |

|and 2 | |why. | | | |

| | | | | | |

|Finding rules and | | | | | |

|describing patterns | | | | | |

|problem solving pack | | | | | |

| | | | | | |

|Guidance booklet | | | | | |

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|Further examples of | | | | | |

|pitch and | | | | | |

|expectations: | | | | | |

|Foundation to year 1 | | | | | |

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|Year 1 | | | | | |

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|Information | | | | | |

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|- Divide and rule1 | | | | | |

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|- Divide and rule2 | | | | | |

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|- teaching mental | | | | | |

|calculation strategies| | | | | |

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|- teaching written | | | | | |

|strategies | | | | | |

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|- exemplification of | | | | | |

|standards | | | | | |

| |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 |Smart board resources |Count on in tens from the number 27. Will the number 85 be |Describe the patterns in the sequence 0 [pic]20 [pic]20, 1 |

| | | |and involving numbers or shapes |unit plans: |in the count? How do you know? |[pic]19 [pic]20, predict the next calculation in the |

| | | |and explain why. |Y2 autumn unit 4 | |sequence and continue the pattern to generate all the pairs |

| | | | |Y2 spring unit 8 |We have worked out that 3 [pic]5 [pic]8 and 13 [pic]5 |of numbers with a total of 20. |

| | | | |Y2 summer unit 8 |[pic]18. Without calculating, tell me what 23 [pic]5 will | |

| | | | | |be. What about 63 [pic]5? |Recognise multiples of 2, 5 and 10; they know that multiples|

| | | | |Nrich multiple pack |Write the missing digits to make this correct. |of 2 are called even numbers and that numbers which are not |

| | | | | |[pic] |even are odd |

| | | | |ICT files |What is the multiple of 10 before 70? | |

| | | | | |What three numbers come next: 35, 40, 45, ...? |Make and describe symmetrical patterns, for example, using |

| | | | |Problem solving materials: |What is the next even number after 24? |ink blots, pegboards or cubes, |

| | | | |Ben’s numbers |What do you notice about the numbers in the 5 times-table? | |

| | | | |Ice cream |If we carried on, what do you think the next number would |e.g. place two red squares, two green squares and two blue |

| | | | |Bird eggs |be? If we carried on, do you think the pattern would |squares in a line so that the squares make a symmetrical |

| | | | |Line of symmetry |continue? How do you know? |pattern, and explore the number of different ways of doing |

| | | | |Card sharp | |it. |

| | | | |Fireworks |Think of a number bigger than 100 that would be in | |

| | | | |Goldfish |the 5 times-table if we carried on. Why do you think that |On the graph, how do you work out the numbers between the |

| | | | |Ones and twos |number would be in the table? |labels? Which way of getting to school was used by 7 |

| | | | |At the toyshop | |children? These labels show only 0, 2, 4, 6, 8 and 10. How |

| | | | |Triangles and pentagons |They find missing numbers from sequences such as: |could you find 7? |

| | | | |Farm problem |30, 40, [pic], 60, [pic] |If this scale carried on, what other numbers do you think |

| | | | |Simple sudoku |55, 50, ?, 40, 35, ?, 25, 20 |would be shown? Would the number 34 be shown? How can you |

| | | | |Shape puzzle |[pic], 41, 43, 45, 47, 49, [pic], 53 and |tell? |

| | | | |Colour coded digit mystery |[pic], 48 , 51 ,54 , [pic], 60, ... | |

| | | | |Venn and Carroll diagram | |Chanting of tables is supported with a counting stick or |

| | | | |templates |Consolidate counting on from zero in steps of 2, 5 and 10 |number line to establish the relationship between the |

| | | | |Caterpillar sequences |and build up these times-tables, describing what they notice|increasing steps and corresponding products. |

| | | | |Counter |about numbers in the tables. They use this to predict some |[pic] |

| | | | |Monty |other numbers that would be in the count. | |

| | | | |100 square jigsaw | |A secret sequence has the numbers 13, 15, 17, 19 in it. What|

| | | | | |Sort a set of numbers into those that can be halved exactly |numbers come next in my sequence? What numbers come before? |

| | | | | |and those that cannot. Relate findings to odd and even |What clues did you use to work this out? Give me a number |

| | | | | |numbers. |greater than 40 that is in my secret sequence. How do you |

| | | | | | |know this number is in my sequence? How could you check? |

| | | | | |Find as many ways as possible to complete a missing-digit | |

| | | | | |calculation such as [pic]1 [pic][pic][pic][pic]0, explaining|Choose different criteria for sorting the same set of |

| | | | | |the patterns and relationships in the results. |objects and explain their criteria to others. |

| | | | | | |[pic] |

| | | | | |Which are the even numbers in this list? | |

| | | | | |13, 4, 12, 8, 19, 16, | |

| | | | | |Draw rings around all the multiples of 5. |Describe patterns in the sequences they generate when they |

| | | | | |45, 20, 54, 17, 40 |count on or back from any two- or three-digit number in |

| | | | | | |steps of 1, 2, 3, 5 and 10 |

| | | | | |They identify missing numbers in a 100-square. | |

| | | | | | | |

|Mathematical |Should |I can describe patterns and | | | |

|challenges for able | |relationships involving numbers | | | |

|pupils in Key stages 1| |or shapes, make predictions and | | | |

|and 2 | |test these with examples | | | |

| | | | | | |

|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 | | | | | |

| |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 |Springboard materials: |Look at this calculation: [pic]5[pic]8 [pic][pic][pic]. |Enter the numbers 1 to 20 onto a Venn diagram and answer |

| | |patterns and |Unit 8; unit 9 |Write a digit in each box so that the calculation is |questions such as: |

| | |relationships | |correct. How else can you do it? What patterns do you |Which numbers are multiples of 5 but not even? |

| | |involving numbers or |Unit plans |notice? |Explain why the number 17 is not in either ring. |

| | |shapes, make |Spring unit 8 |Repeat with [pic]2[pic]7 [pic][pic][pic]. | |

| | |predictions and test |Summer unit 8 | |What measurement is shown on these scales? Explain how you |

| | |these with examples | |What is the largest multiple of 10 you can add to 38 if your|worked this out. |

| | | |Nrich multiple pack |answer must be smaller than 100? |What is each division on this scale worth? How did you work |

| | | | | |this out? How could you check that you are right? |

| | | |ICT files | | |

| | | | | |recognise patterns of similar calculations , such as |

| | | |Problem solving materials: | |25[pic]20 [pic]45, 45[pic]20 [pic]65, 65[pic]20 [pic]85. |

| | | |Spaceships |Explain the relationship between adding 3 to 4 and adding 30|Continue the sequence and suggest other sequences of |

| | | |Suzie snake |to 40 and 300 to 400. |calculations that follow similar patterns. |

| | | |Stamps | | |

| | | |Maisie mouse |9[pic]3[pic]6. What is 90[pic]30, and 900[pic]600? How do |What are the missing numbers in these patterns? How did you |

| | | |Kieron’s Cats |you know? |find them? |

| | | |Fireworks | |83, 78,[pic], 68, 63, 58,[pic] |

| | | |Sheepdog trials |count on and back in steps of 1, 2, 3, 4, 5, 6 and 10 from |1, 7, 13, 19, [pic], [pic]; |

| | | |Number puzzle |zero and then from any given number |[pic], 26, 22, [pic], [pic], 10, 6, 2 |

| | | |Farm problem | | |

| | | |Three rings |keep subtracting 6 from 49, what is the smallest number you |Sam says: 'When you count from zero in fours, every number |

| | | |Simple sudoku |get? |is even.' Is he right? How do you know? |

| | | |Shape puzzle | | |

| | | |Colour coded digit mystery |recognise the relationships between counting in: 2s and 4s; |Investigate general statements such as: When you count in |

| | | |Venn and Carroll diagram |3s and 6s; 5s and 10s |fives, the units digits form a pattern |

| | | |templates1 | | |

| | | |Venn diagram number sort |locate and position multiples of 10 or 100 on a number line |Can 113 be a multiple of 5? How do you know? |

| | | |Carroll diagram number sort | |Can a multiple of 4 ever end in a 7? |

| | | |Caterpillar sequences |Sort the numbers 1-20 into two groups: | |

| | | |Function machine |Multiples of 5 |Start at 93 and count back in tens. What will be the |

| | | |Excel files |Not multiples of 5 |smallest number that you reach on a 100-square? |

| | | |Zids and zods | | |

| | | |Pentabods and bipods | |Classify objects, numbers or shapes according to one |

| | | |Duck sequencing game | |criterion, progressing to two criteria, and display this |

| | | |Counter | |work on a Carroll diagram |

| | | |Monty |What do you notice? Tell me a number greater than 100 that | |

| | | | |would go in each group. |Recognise simple patterns and relationships, for example to |

| | | | | |find a pair of numbers with a sum of 17 and a product of 70 |

| | | | |Identify numbers to 1000 that are multiples of 2, 5 or 10 |Children partition two- and three-digit numbers in different|

| | | | | |ways. For example, they continue the patterns: |

| | | | |Sort a set of numbers using criteria such as: 'These numbers|72 [pic]70 [pic]2 |

| | | | |are multiples of 5', or: 'These numbers are in the 6 |853 [pic]800 [pic]53 |

| | | | |times-table'' | |

| | | | | |72 [pic]60 [pic]12 |

| | | | |Find the number of edges of assorted prisms to investigate |853 [pic]700 [pic]153 |

| | | | |the general statement : The number of edges of a prism is | |

| | | | |always a multiple of 3. |72 =50 + 22 |

| | | | | |853 = 600 + 253 |

| | | | |One of these shapes is in the wrong place on the diagram. | |

| | | | |Which one? | |

|Mathematical challenges for |Should |I can solve problems | | | |

|able pupils in Key stages 1 and| |by Identifying | | | |

|2 | |patterns and | | | |

| | |relationships | | | |

|Finding rules and describing | |involving numbers or | | | |

|patterns problem solving pack | |shapes. | | | |

| | | | | | |

|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 | | | | | |

| | | | | | |

| | | | | | |

| |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 |Springboard materials: |Count on in eights from zero. Now count back to zero. This |Write the two missing numbers in this sequence. |

| | |by Identifying |Unit 6; |time, count on seven eights from zero. |[pic] |

| | |patterns and | |Show me seven hops of eight from zero on the number line. | |

| | |relationships |Autumn: unit 4 |How can you work out the 8 times-table from the 4 times-table? |Sean counts his books in fours. He has one left over. He |

| | |involving numbers or |Spring unit 8 |Or the 9 times-table from the 3 times-table? |then counts his books in fives. He has three left over. |

| | |shapes. |Summer unit 8 | |How many books has Sean? |

| | | | |Predict numbers that will occur in the sequence, and answer | |

| | | |Nrich multiple pack |questions such as: If I keep on subtracting 3 from 10 will -13 |count in fractions along a number line from 0 to 1, for |

| | | | |be in my sequence? |example, in tenths |

| | | |ICT files | | |

| | | | |use the constant function on a calculator to check their |Count in steps of 50p in a sequence such as [pic]0.50, |

| | | |Problem solving materials: |predictions |[pic]1.00, [pic]1.50, [pic]2.00, or in steps of 25 cm in |

| | | | | |a sequence like 1.25 m, 1.5 m, 1.75 m. |

| | | |Row of coins |Tell me some numbers that will divide exactly by 2, by 5, by | |

| | | |Row of numbers |10. How do you know? |What would my sequence look like if I counted in steps of|

| | | |Shape coordinates | |20p from [pic]1.10? |

| | | |Stickers |Tell me a number that will divide exactly by 4. How do you know| |

| | | |Footsteps in snow |that a number will divide exactly by 4? |Complete an equation such as [pic][pic]- 47 [pic][pic]9, |

| | | |Esmareldas coins | |and find the largest and smallest possible differences. |

| | | |Ski lift |Continue this number sequence in both directions. | |

| | | |Function machine |[pic] |Lisa went on holiday. In 5 days she made 80 sandcastles. |

| | | |Money grids | |Each day she made 4 fewer castles than the day before. |

| | | |Multiplication jigsaw |Use these four digit cards. |How many sandcastles did she make each day?' |

| | | |Venn diagram number sort |[pic] | |

| | | |Carroll diagram number sort |Use each of the digits once to make a total that is a multiple |Name a multiple of 6 that is also a multiple of 9. |

| | | |Shape puzzle |of 5. | |

| | | |Spaceships |[pic] |What colour is each shape? Write it on the shape. |

| | | |Suzie snake | |Clues |

| | | |Stamps |Here is part of a number square. The shaded numbers are part of|Red is not next to grey. |

| | | |Maisie mouse |a sequence. Explain the rule for the sequence. |Blue is between white and grey. |

| | | |Kieron’s Cats | |Green is not a square. |

| | | |Fireworks |Explain what you did to get your answer to the problem. |Blue is on the right of pink. |

| | | |Sheepdog trials | | |

| | | |Number puzzle |count in steps of 6 from zero and investigate the patterns of |What are the missing numbers in this sequence? |

| | | |Farm problem |multiples in the 100-square. |[pic] |

| | | |Three rings | | |

| | | |Colour coded digit mystery |classify polygons, using Carroll or Venn diagrams |Complete the number pattern. |

| | | |Venn and Carroll diagram | |[pic] |

| | | |templates |If 7 [pic]9 [pic]63, what is 63 [pic]7? What other facts do you| |

| | | |Caterpillar sequences |know? |Explore a number sequence arising from a given rule, for |

| | | |Function machine | |example 'double the last number and subtract 1' (2, 3, 5,|

| | | |Weakest link template |Are there any multiples of 7 that are also multiples of 8? |9, ...). What are the gaps between the numbers? and What |

| | | |Blockbusters template | |if the rule were double and add 1? |

| | | |fraction mysteries |Draw an arrow on the number line to show 1 [pic]. | |

| | | |multiplication mystery |[pic] |Count on and back in halves, quarters, fifths and tenths |

| | | |subtraction mystery | | |

| | | |Duck sequencing game | |Rosie spent [pic]2 on 10p and 20p stamps. She bought |

| | | |Counter | |three times as many 10p stamps as 20p stamps. How many of|

| | | |Monty | |each stamp did she buy? |

|Mathematical challenges for |Should |I can complete | | | |

|able pupils in Key stages 1 and| |sequences by following| | | |

|2 | |simple rules and | | | |

| | |investigate statements| | | |

|Finding rules and describing | |by identifying and | | | |

|patterns problem solving pack | |using patterns, | | | |

| | |relationships and | | | |

|Guidance booklet | |properties of numbers | | | |

| | |or shapes. | | | |

|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 | | | | | |

| |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 |Autumn: unit 8; unit 12 |Create a sequence that includes the number -5. Describe your |Simon's birthday is on August 20th. Tina's birthday is on |

| | |sequences by following|Spring: unit 2 unit 11 |sequence to the class. |September 9th. On what day of the week was her birthday in |

| | |simple rules and |Summer: unit 6b unit 12 | |1998? |

| | |investigate statements| |Here is part of a sequence: [pic], -9, -5, -1, [pic]. | |

| | |by identifying and |ICT files |Explain how to find the missing numbers. Explain how you |What is the next number in this sequence: 0, 0.2, 0.4, 0.6, |

| | |using patterns, | |would find the missing numbers in this sequence: 10, [pic], |0.8? |

| | |relationships and |Problem solving materials: |4, 1, [pic], -5, [pic] |What is the rule for this sequence: 3, 2.7, 2.4,...? |

| | |properties of numbers |Arithmagons 2 |What is the 'rule' for the sequence? |Suggest some other numbers that will be in the sequence. |

| | |or shapes. |Age old problems | |Write in the missing number on this number line. |

| | | |Zids and Zods |Put a ring around the numbers that are factors of 30: 4 5 6 | |

| | | |Jacks book |20 60 90 |Find two numbers between 3 and 4 that total 7.36. Use a |

| | | |A bit fishy | |written method to check your answer. |

| | | |Eggs (excel eggs) |Create sequences by counting on and back from any start | |

| | | |Spendthrift |number in equal steps such as 19 or 25 |Write what the four missing digits could be: |

| | | |Handshakes | |[pic][pic][pic][pic]10 [pic]3[pic] |

| | | |addition and subtraction puzzles |Identify the rule for a given sequence. And use this to | |

| | | |Sleigh ride |continue the sequence or identify missing numbers, e.g. |What is the total mass of the apples on the scales? |

| | | |Oranges and lemons |complete- 89, [pic], 71, 62, [pic], |A piece of cheese has a mass of 350 grams. Mark an arrow on |

| | | |Library area | |the scale to show the reading for 350g. |

| | | |Roses for sale |Explore sequences involving negative numbers using a number | |

| | | |Bunches of grapes |line. For example, they continue the sequence -35, -31, -27, |Tell me a number that is both a multiple of 4 and a multiple |

| | | |Ages to ages |... by recognising that the rule is 'add 4'. |of 6. Are there any other possibilities? |

| | | |Ages and ages | | |

| | | |Fruit bowl |Use calculators or the ITP 'Moving digits' to explore the |The sum of two even numbers is a multiple of 4. Is this |

| | | |Arithmagons 3 |effect of repeatedly multiplying/dividing numbers by 10. |sometimes true, always true or never true? Justify your |

| | | |Double scoop ice cream | |answer with examples |

| | | |Nicknames |Place the digits 0 to 9 to make this calculation correct: | |

| | | |Which number where? | |Find different ways to complete: |

| | | |Weakest link template |Two numbers have a total of 1000 and a difference of 246. | |

| | | |Blockbusters template |What are the two numbers? |Two square tiles are placed side by side. How many tiles are |

| | | |Pyramids | |needed to surround them completely? What if there were five |

| | | |More pyramids |The area of a rectangle is 32 cm2. What are the lengths of |tiles? How many tiles would be needed if 100 tiles were laid |

| | | |Leapfrogs |the sides? Are there other possible answers? How did you work|side by side? Explain your answer. |

| | | |Function machine |it out? | |

| | | |Caterpillar sequences | |Identify all the factors of a given number; eg, the factors |

| | | |fraction mysteries |Explain why 81 is a square number. |of 20 are 1, 2, 4, 5, 10 and 20 |

| | | |multiplication mystery | | |

| | | |subtraction mystery |One number is in the wrong place on the sorting diagram. |My age is a multiple of 8. Next year my age will be a |

| | | |Duck sequencing game |Which one is it? |multiple of 7. How old am I? |

| | | |Counter | | |

| | | |Monty |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 | |

|Mathematical challenges for able |Should |When exploring | | | |

|pupils in Key stages 1 and 2 | |patterns, properties | | | |

| | |and relationships I am| | | |

|Finding rules and describing | |able to propose a | | | |

|patterns problem solving pack | |general statement | | | |

| | |involving numbers or | | | |

|Guidance booklet | |shapes; | | | |

| | | | | | |

|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 | | | |

| | |represent and | | | |

| | |interpret sequences, | | | |

| | |patterns and | | | |

| | |relationships in | | | |

| | |different ways, | | | |

| | |including using simple| | | |

| | |expressions and | | | |

| | |formulae in words then| | | |

| | |symbols | | | |

|Year Target |Group Target |Key Resources / |Outcomes |

|Yr 6 |Must |When exploring |Springboard: |Here is a repeating pattern of shapes. Each shape is |Investigate the differences between terms of the sequence of |

| | |patterns, |Unit 21; unit 22; unit 26; unit |numbered. |square numbers 1, 4, 9, 16, ... |

| | |properties and |29; |[pic] |Describe the pattern and use it to continue the sequence. |

| | |relationships I am|Unit plans |The pattern continues in the same way. What will the 35th |Investigate the statement: 'Every square number is the sum of|

| | |able to propose a |Autumn: unit 12 |shape be? Explain how you can tell. |two triangular numbers'. |

| | |general statement |Spring: unit 4 unit 11 | | |

| | |involving numbers |Summer: unit 5; unit 9; unit 10 |Start from a two-digit number with at least six factors, e.g.|Parveen has the same number of 20p and 50p coins. She has |

| | |or shapes; |ICT files |56. How many different multiplication and division facts can |[pic]7.00. How many of each coin does she have? |

| | | |Problem solving materials: |you make using what you know about 56? |What multiplication table does this image represent? How do |

| | | |Moneybags | |you know? What other numbers will you see in the boxes |

| | | |Five numbers |John says that every multiple of 4 ends in 2, 4, 6 or 8. |outside? |

| | | |Jacks book |Persuade me that John is wrong. |Find two numbers with a product of 899. |

| | | |Arithmagons 2 | | |

| | | |Age old problems |Convince your partner that 2140 will not be in this sequence.|In a village where all the roads are straight, every time two|

| | | |addition and subtraction puzzles |40 80 120 160 200 ... |streets intersect a street lamp is required. Investigate the |

| | | |Zids and Zods | |number of street lamps required for 2 streets, 3 streets, 4 |

| | | |A bit fishy |Count forwards in jumps of 19 from 7 and backwards in 7s |streets, ... |

| | | |Eggs (excel eggs) |starting at 19 and continuing below zero | |

| | | |Spendthrift | |What is the minimum and maximum number of lamps needed for 5 |

| | | |Handshakes |Count in thirds from 0 using mixed numbers and in steps of |streets? n streets |

| | | |Sleigh ride |0.3 from 0, and backwards in 100s from 21 and 213 | |

| | | |Oranges and lemons | |How many different flights there would be connecting 2, 3 and|

| | | |Library area |Identify the rule for a given sequence. For example, 1, 3, 7,|4 airports if each airport is connected by return flights. |

| | | |Roses for sale |15, 31 |Predict how many flights will be needed for 5, testing their |

| | | |Bunches of grapes | |predictions. They find a general rule and express it in |

| | | |Ages to ages |A number multiplied by itself gives 2809. Find the number |words, then using symbols. |

| | | |Ages and ages | | |

| | | |Fruit bowl |Describe the relationship between terms in this sequence: |The rule for this sequence of numbers is 'add 3 each time'.: |

| | | |Arithmagons 3 | |1, 4, 7, 10, 13, 16 ... The sequence continues in the same |

| | | |Which number where? |2, 3, 8, 63, ... |way. I think that no matter how far you go there will never |

| | | |Tower of Hanoi |Make the ITP '20 cards' generate this sequence of numbers: |be a multiple of 3 in the sequence. Am I correct? Explain how|

| | | |chessboard problem |1, 3, 7, 13, ... |you know. |

| | | |Pyramids | | |

| | | |More pyramids |Explain why a square number always has an odd number of |What is the value of 4x [pic]7 when x [pic]5? Explain how you|

| | | |Leapfrogs |factors. |know. |

| | | |Caterpillar sequences | | |

| | | |Function machine |The first two numbers in this sequence are 2.1 and 2.2. The |Draw the next two terms in this sequence: |

| | | |Investigating consecutive numbers|sequence then follows the rule: 'to get the next number, add |Describe this sequence to a friend using words. Describe it |

| | | |Twelve days of Christmas |the two previous numbers'. What are the missing numbers? |using numbers. How many small squares would there be in the |

| | | |Hexagon pattern |2.1, 2.2, 4.3, 6.5, [pic], [pic] |10th picture? |

| | | |Weakest link template | |I want to know the 100th term in the sequence. Will I have to|

| | | |Blockbusters template |Find two square numbers that total 45. |work out the first 99 terms to be able to do it? Is there a |

| | | |fraction mysteries | |quicker way? How? |

| | | |multiplication mystery |Explore the pattern of primes on a 100-square, explaining why| |

| | | |subtraction mystery |there will never be a prime number in the tenth column and |This sequence of numbers goes up by 40 each time. |

| | | |Square ages |the fourth column. |40 80 120 160 200 ... |

| | | |Sticky triangles | |This sequence continues. Will the number 2140 be in the |

| | | |Duck sequencing game |Convince me that in a number grid starting at 1 with nine |sequence? Explain how you know. |

| | | |Counter |columns, there will never be a prime number in the sixth | |

| | | |Monty |column. | |

|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 | | | | | |

| | | | | | |

|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 | | | |

| | |represent and | | | |

| | |interpret | | | |

| | |sequences, | | | |

| | |patterns and | | | |

| | |relationships in | | | |

| | |different ways, | | | |

| | |including using | | | |

| | |simple expressions| | | |

| | |and formulae in | | | |

| | |words then symbols| | | |

| | | | | | |

| |Could |I can use letters | | | |

| | |and symbols to | | | |

| | |represent unknown | | | |

| | |numbers or | | | |

| | |variables and find| | | |

| | |the nth term in a | | | |

| | |sequence | | | |

|Year Target |Group Target |Key Resources / |Outcomes |

|Yr 6 |Could |I can use letters |Springboard: |n stands for a number. Complete this table of values. |Ann makes a pattern of L shapes with sticks. |

| | |and symbols to |Unit 21; unit 22; unit 26; unit | | |

| | |represent unknown |29; | |Ann says : ‘I find the number of sticks for a shape by first |

| | |numbers or | | |multiplying the shape-number by 4, then adding 3.’ |

| | |variables and find|Unit plans |k, m and n each stand for a whole number. They add together |Work out the number of sticks for the shape that has |

| | |the nth term in a |Autumn: unit 12 |to make 1500. |shape-number 10. |

| | |sequence |Spring: unit 4 unit 11 |k + m + n = 1500 |Ann uses 59 sticks to make another L shape in this pattern. |

| | | |Summer: unit 5; unit 9; unit 10 |m is three times as big as n. |What is its shape-number? |

| | | | |k is twice as big as n. | |

| | | |ICT files |Calculate the numbers k, m and n. |The graph shows a straight line. The equation of the line is |

| | | |Problem solving materials: | |y = 3x.. Does the point (25, 75) lie on the straight line y =|

| | | |Patterns and sequences |Debbie has a pack of cards numbered from 1 to 20 She picks |3x? Tick (⎫) Yes or No. Explain how you know. |

| | | |Moneybags |four different number cards. | |

| | | |Five numbers |[pic] | |

| | | |addition and subtraction puzzles |Exactly three of the four numbers are multiples of 5. Exactly|The same number is missing from each box. Write the same |

| | | |Jacks book |three of the four numbers are even |missing number in each box. |

| | | |Arithmagons 2 |numbers. All four of the numbers add up to less than 40. | |

| | | |Age old problems |Write what the numbers could be. Write two further questions |χ × χ × χ = 1331 |

| | | |Square ages |that you could ask about the cards. | |

| | | |Zids and Zods | |Here is a sequence. |

| | | |A bit fishy |30 children are going on a trip. It costs £5 including lunch.|[pic] |

| | | |Eggs (excel eggs) |Some children take their own packed lunch. They pay only £3. |The rule is to add the same amount each time. |

| | | |Spendthrift |The 30 children pay a total of £110. How many children are |Write in the missing numbers. |

| | | |Handshakes |taking their own packed lunch? | |

| | | |Sleigh ride | |The formula for the number of circles (c) |

| | | |Oranges and lemons |A sequence starts at 500 and 80 is subtracted each time. |in shape number (n) is: |

| | | |Library area | |c = 3n – 1 |

| | | |Roses for sale |500 420 340 ... | |

| | | |Bunches of grapes |The sequence continues in the same way. Write the first two |Use the formula to work out the shape number that has 104 |

| | | |Ages to ages |numbers in the sequence which are less than zero. |circles. |

| | | |Ages and ages | | |

| | | |Fruit bowl |Here are five number cards. | |

| | | |Arithmagons 3 |[pic] | |

| | | |Chalk problem; |A and B stand for two different whole numbers. The sum of all| |

| | | |fraction mysteries |the numbers on all five cards is 30. What could be the values| |

| | | |multiplication mystery |of A and B? | |

| | | |subtraction mystery | | |

| | | |Tower of Hanoi |This four digit number is a square number. Write in the | |

| | | |chessboard problem |missing digits. | |

| | | |Which number where? |9 χ χ 9 | |

| | | |Pyramid numbers | | |

| | | |Pyramids |Write the three missing digits: χ χ × χ = 371 | |

| | | |More pyramids | | |

| | | |Leapfrogs | | |

| | | |Function machine | | |

| | | |Caterpillar sequences | | |

| | | |Hexagon pattern | | |

| | | |Squares and circles | | |

| | | |Weakest link template | | |

| | | |Blockbusters template | | |

| | | |Sticky triangles | | |

|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 | | | | | |

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