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?