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					Layered targets for Mathematics
                                                        Properties of Number

Notes

These targets are drawn from the following strands of the Renewed Framework for Mathematics:
-Secure knowledge of number facts that can be recalled quickly and used and applied appropriately
-Count, compare and order numbers, and describe relationships between them.

The Year 3 target below appears in Year 2 in the Renewed Framework, but as schools have not yet implemented the renewed
framework, it needs to be a focus for Year 3 children, so that this particular group don’t miss out on it.

Similarly the Year 1 target below appears in Foundation Stage in the Renewed Framework, but as schools have not yet
implemented the renewed framework, it needs to be a focus for Year 1 children, so that this particular group don’t miss out on it.

The Year 4 target is based on ‘Use knowledge of rounding, number operations and inverses to check calculations’ (Secure
knowledge of number facts strand) and ‘Use knowledge of numbers and shapes to identify patterns, properties and
relationships, and apply them to unfamiliar situations; investigate a statement involving numbers and test it with examples’ (Use
and Apply Mathematics strand) from the Renewed Framework, but relates specifically to multiplicative properties so that
progression through the school is clear and so that the target is appropriately specific.

Foundation Stage
         Differentiated Pupil              Key Questions to support planning, teaching and                      Success Criteria
                 Targets                                       assessment
     I can join in with number         The practitioner will…                                              The children will:
     rhymes and songs                  Use stories and rhymes to develop understanding of number
                                                                                                           Show enjoyment and join in
        I can count actions or         Provide opportunities for children as a group to join in reciting   Confidently with number
        objects that cannot be         the number names in order                                           rhymes and songs
        moved
                                       Encourage counting of things that cannot be touched (eg             Be able to reliably count
        I can talk about, recognise    jumps)                                                              irregular arrangements of
        and recreate simple                                                                                objects
        patterns                       Encourage children to talk about and extend patterns
                                                                                                           Be able to repeat a pattern
                                                                                                           with 2 or more components
Key Stage One: Properties of Number
Year      Differentiated Pupil            Key Questions to support planning, teaching and                                Success Criteria
                Targets                             assessment (of ‘should’ target)
 Y1   Must:                        Can you carry on counting…                                                      The children will:
      I can count up to 10 objects 5, 6, 7, 8, …     18, 17, 16 15, … 2, 4, 6, 8, … etc?
                                                                                                                   Join in with number rhymes and
      or sounds or hops or skips   Look at this number track:                                                      songs, predicting the next number
                                                       6     7      8                                              correctly
       Should:                         Where would 11 go? Where would 4 go?
       I can count on and then                                                                                     Be able to continue counting in a
       back in steps of 1, 2, 5 and    Freddy the frog jumps on along the number line in 2s. He starts at 3. Can   given pattern
                                       you circle the numbers that he lands on?
       10                                                                                                          Be able to describe whether a
                                       Can you make a number pattern which counts back in 2s?                      given number pattern has been
       Could:                                                                                                      made by counting on or back in
       I can recognise odd and         Find the number 10 on the hundred square. Can you point to the numbers      1s, 2s, 5s, or 10s
       even numbers, and use this      as we count up in 10s?
                                       What if we start with the number 7? Will we say 47? Will we say 52?         Be able to say whether a given
       to help me solve problems                                                                                   number appears in a number
                                       What is the pattern when I count ’25, 20, 15, 10…’?                         pattern by counting using the
                                       What number will come next?                                                 pattern to check
 Y2    Must:                           There are 15 Multilink cubes here. Do you think we will be                  The children will:
       I can count on from and         able to make them into 2 equal towers? What if we had 16?
       then back in steps of 1, 2, 5                                                                               Be able to use the
       and 10                          Is 12 an even number? How do you know?                                      vocabulary ‘odd’ and ‘even’
                                       What about 15? What about 97?                                               to describe numbers
       Should:
       I can recognise odd and         What is the next even number after 6?                                       Be able to identify whether
       even numbers, and use this      What is the odd number that comes before 17?                                a number is odd or even
       to help me solve problems
                                       Show me how you can count these objects (eg 15 acorns) by                   Be able to explain whether
       Could:                          counting in 2s                                                              a given set of objects can
       I can recognise numbers                                                                                     be split into 2 equal parts by
       which can be split into         Can I share 16 Smarties equally between me and my friend?                   referring to whether there is
       groups of 2s, 5s or 10s, and                                                                                an odd or an even number
       use this to help me solve    I got 9 socks out of the washing machine. Will I be able to put     of objects
       problems                     them all in pairs?

Key Stage Two: Properties of Number
Year      Differentiated Pupil         Key Questions to support planning, teaching and                       Success Criteria
                 Targets                                    assessment
 Y3   Must:                                                                                             Children can…
      I can recognise odd and        5             6              3             2            7
      even numbers, and use this Use these number cards to make as many different even                  Recognise whether a given
      to help me solve problems    numbers as you can.                                                  number is a multiple of 2, 5
                                   Which numbers can you use in the units column? Why?                  or 10, and say why
      Should:                      Which numbers can you use in the tens column? Why?
      I can recognise numbers                                                                           Be able to use their
      which can be split into      When I add 23 and 65, will the answer be odd or even?                knowledge of odd and even
      groups of 2s, 5s or 10s, and What about when I add 36 and 68?                                     numbers to explain whether
      use this to help me solve                                                                         the answer is odd or even
      problems                     On your hundred square, find some numbers that can be:               when two odd or two even
                                      - both grouped into fives, and into twos (eg 20)                  numbers are added
      Could:                          - grouped into fives, but not into twos (eg 15)                   together
      I can use my knowledge of       - grouped into twos but not into fives (eg 18)
      multiplication facts to help What patterns can you see?                                           Explain how a given number
      me solve number problems                                                                          could be grouped into 2s, 5s
                                   Can you count this set of 47 objects by grouping them in 5s?         or 10s, and say how many
                                   How many groups of 5 will we be able to make?                        would be left over in each
                                   How many do you think will be left after we have made as             case
                                   many groups of 5 as we can?
                                   Why do you think so?

                                    I am thinking of a number between 10 and 20. When I
                                    organise it into groups of 5, I have 3 left over. When I organise
                                    it into groups of 2, I have 1 left over. What might my number
                                    be?

                                    When you count back in 10s from 84 to 34, how many tens
                                    did you count?
Look at this sequence: 2, 7, 12, 17 …
What is the pattern?
What will the next three numbers in the sequence be?
Key Stage Two

Year       Differentiated Pupil             Key Questions to support planning, teaching and                    Success Criteria
                  Targets                                      assessment
 Y4    Must:                             What do you notice when you count on from zero in:               The children will:
       I can recognise numbers                          Twos      Fours       Eights
       which can be split into                            2          4           8                        Be able to describe the
       groups of 2s, 5s or 10s, and                       4          8          16                        relationship between
       use this to help me solve                          6         12          24                        different multiplication
       problems                                           8         16          32                        tables

       Should:                           If you make a sequence by counting in 4s from 0, will 44 be in   Be able to identify which
       I can use my knowledge of         your sequence?                                                   numbers will be included in
       multiplication facts to help      What about 52?                                                   a sequence which follows a
       me solve number problems          How do you know?                                                 given rule

       Could:                            Circle the numbers in the box that divide exactly by 4.          Be able to use information
       I can identify pairs of factors               3 8 20 27 34 36 48 50                                about how a number can be
       of two-digit numbers, and         Which numbers in the box are divisible by both 5 and 2?          grouped to identify what the
       use this to help me solve                                                                          number could be
       problems                          When I colour the multiples of 3 on a hundred square, what
                                         kind of pattern will they make? (vertical or diagonal?)          Be able to identify what will
                                         Can you suggest some numbers whose multiples will make           happen when a given
                                         vertical patterns?                                               number is grouped- how
                                                                                                          many groups there will be,
                                            5            3           4           1             0          and how many would be left
                                         Use these number cards to make a number that can be              over
                                         grouped in 3s, 5s and 2s.
                                         Can you make a number that can be grouped in 3s and 5s but
                                         not in 2s?

                                         I have 8 coins in my pocket. Each one is either a 10p or a 5p.
                                         Altogether I have 55p. How many of each coin do I have?
Key Stage Two

Year       Differentiated Pupil             Key Questions to support planning, teaching and                  Success Criteria
                  Targets                                          assessment
 Y5    Must:                             What are all the pairs of factors of 36?                       The children will:
       I can use my knowledge of
       multiplication facts to help      How could you use factors to help you calculate 16 x 12        Be able to identify all the
       me solve number problems          mentally?                                                      pairs of factors of a given
                                         (16 x 12 = 16 x 3 x 2 x 2 = 48 x 2 x 2 = 96 x 2 = 192)         number
       Should:
       I can identify pairs of factors   Is the number 6732 divisible by 2, 4, 5, 10 and 100?           Be able to use tests of
       of two-digit numbers and          How do you know?                                               divisibility to solve number
       use tests of divisibility to                                                                     problems
       help me solve problems            84 chairs are set out in the school hall. The same number of
                                         chairs are put in each row.                                    Be able to recognise the
       Could:                            How many rows of chairs might there be?                        square numbers to 100
       I can explain what prime          How many chairs would be in each row?
       numbers are and give              How many different ways of arranging the chairs can you        Be able to explain how they
       examples                          find?                                                          solved a problem by using
       I can recognise and extend                                                                       their knowledge of factors
       number sequences even             Which number multiplied by itself gives 49?                    and multiples
       where the steps are not a         A square has an area of 64cm squared. What is the length of
       constant size                     each side?

                                         A line of counters is set out in a pattern:
                                         Two white, four blue, two white, four blue…
                                         What colour is the 49th counter?
                                         What position in the line is the 11th blue counter?

                                         My age this year is a multiple of 8.
                                         Next year it will be a multiple of 7.
                                         How old am I? How did you work it out?
Key Stage Two

Year       Differentiated Pupil                Key Questions to support planning, teaching and                   Success Criteria
                  Targets                                          assessment
 Y6    Must:                             Describe and extend this sequence:                                 The children will…
       I can identify pairs of factors   1, 3, 6, 10, 15, 21 …         (triangular numbers)
       of two-digit numbers and          Explain the rule orally and in writing.                            Be able to create and
       use tests of divisibility to                                                                         describe non-linear
       help me solve problems            What are the missing numbers in this sequence?                     sequences
                                         1, 4, , , 25, 36, , ,…
       Should:                                                                                              Be able to use their
       I can explain what prime          Make a sequence where the steps are not a constant size.           knowledge of factors and
       numbers are and give              Explain the rule for your sequence to a partner.                   multiples to solve number
       examples                                                                                             problems
       I can recognise and extend        A line of counters is set out in a pattern:
       number sequences even             Five white, four blue, five white, four blue…                      Be able to describe and
       where the steps are not a         What colour is the 65th counter?                                   identify prime numbers
       constant size                     What position in the line is the 17th blue counter?
                                                                                                            Be able to use their
       Could:                            What whole number should I multiply 7 by to make a number          knowledge of prime
       I can recognise square and        as close as possible to 100?                                       numbers to solve number
       cube numbers and the                                                                                 problems
       corresponding roots               Use a calculator to find the number which, multiplied by itself,
                                         gives 2809. What can you say about the number you are
                                         looking for (eg about the units digit)?

                                         Which of these numbers are prime numbers?
                                         11, 21, 31, 41, 51, 61.

                                         Which of these numbers have more than 2 factors?
                                         How do you know?
                                         35, 172, 39, 63, 100

                                         How many rectangles can I make where the length and width
                                         are whole numbers and the area is 47cm squared?
                                         How do you know?

				
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