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Mathematics

“Many people think that some students can work to high levels and some cannot because of the brains they are born with, but this idea has been resoundingly disproved. Study after study has shown the incredible capacity of brains to grow and change within a remarkably short period of time”.

Professor Jo Boaler, Stanford University- Growth Mindset Maths(youcubed)

Mathematics introduces children to concepts, skills and thinking strategies that are essential in everyday life and support learning across the curriculum.  It helps children make sense of the numbers, patterns and shapes they see in the world around them, offers ways of handling data in an increasingly digital world and makes a crucial contribution to their development as successful learners.

Children enjoy using mathematics to solve a problem, especially when it leads to an unexpected discovery or new connections.  As their confidence grows, they look for patterns, use logical reasoning, suggest solutions and try out different approaches to problems.

Mathematics offers children a powerful way of communicating.  They learn to explore and explain their ideas using symbols, diagrams and spoken and written language.  They start to discover how mathematics has developed over time and contributes to our economy, society and culture. Studying mathematics stimulates curiosity, fosters creativity and equips children with the skills they need in life beyond school.

Mastery Approach

New Pasture Lane staff care passionately about maths and have adopted (with the help of ‘Hamilton trust’ and ‘White Rose’) a ‘teaching for mastery’ approach, which has proven to have a positive impact upon children’s learning. Staff use a variety of sources to help them on their journey. Each term the children are assessed using a suite of standardised maths tests (PUMA), which then enables the school to track progress, predict future performance and ‘fill in’ any knowledge gaps.

Furthermore as the children progress through the school, they are constantly challenged and provided with many opportunities to express themselves. Therefore they may find themselves participating in Tute interactive online lessons, the UK’s ‘Primary Maths Challenge’ or even competing in the World Class Maths Arena.

Y5/6 Pupils who completed the Primary Maths Challenge in Nov 2019.

Foundation

 By the end of Foundation all children should be able to confidently:

  •  Count forwards to 100 in unison with other children.
  • Count backwards from at least 20.
  •  Know the next number for any number up to 12, e.g. eight, ____.
  • Match one-to-one in counting e.g. one counter, two counters …
  • Subitise numbers up to and including 6: do children recognise arrays, e.g. 6 dots on a dice, without counting?
  •  Match numbers to fingers, e.g. hold up 7 fingers (without counting each finger).
  •  Begin to compare numbers, e.g. knowing that 6 is bigger than 4.
  •  Know the story of 6 (3 + 3, 2 + 4, 1 + 5, 6 + 0), and the stories of 5 and of 4 and of 3…
  •  Recognise some 2-digit numbers related to their own experiences. E.g. Daddy is 34, I live at number 56, etc.
  • Recognise the difference between ‘flat’ and ‘solid’ shapes and describe shapes by mentioning a property, e.g. this one rolls, this one has corners…
  •  Spot and continue patterns
  •  Compare the size of things using mathematical language, e.g. Tom is taller than me.
Year One

 By the end of Year One all children should be able to confidently:

  • Count on and back in ones to and from 100 and from any single-digit or 2-digit number.
  •  Count on and back in tens from any 1-digit or 2-digit number, e.g. 23, 33, 43, 53… Continue to just over 100.
  • Locate any number on a 1-100 grid or a beaded line 0-100.
  •  Know number bonds to 10, e.g. 5 + 5, 6 + 4, etc. Also know what is left if objects are taken from 10, e.g. 10 fingers, fold down 4, leaves 6 standing.
  • Begin to be aware of unit patterns.
  •  Recognise the + and – and = signs, and use these to read and write simple additions and subtractions.
  • Add small numbers by counting on and subtract small numbers by counting back
  •  Recognise doubles to double 6 and find related halves (half even numbers ≤12).
  • Recognise the difference between 2-D and 3-D shapes; identify and describe common 2-D and 3-D shapes.
  • Recognise and compare objects according to height or length, weight or capacity, using appropriate mathematical language. e.g. the tree is taller than the bush, the bag is heavier than the shoes, the teapot holds more than the jug.
  • Tell the time to the half hour on analogue and digital clocks.
  • Sort items into lists or tables.
Year Two

 By the end of year two children should be able to confidently:

  •  Locate any 2-digit number on a landmarked line and use this to compare numbers; record comparisons using crocodile signs, e.g. 56 > 39.
  •  Identify any number on the 1-100 number grid; understand that each number is a multiple of ten and some ones, e.g. 54 is 50 and 4 more.
  •  Know securely number pairs for all the numbers up to and including 12, e.g. pairs which make 8 (4+4, 5+3, 6+2, 7+1, 8+0) and bonds to 10 (1+9, 2+8, 3+7, 4+6, 5+5).
  •  Recognise that addition and subtraction are inverse operations and understand that 10 – 4 = 6 as well as 6 + 4 = 10.
  •  Count in steps of 2, 5, and 10 from 0.
  •  Count in halves e.g. ½, 1, 1½, 2, 2½, 3…
  •  Know different unit patterns when not crossing a ten, e.g. 4 + 3 = 7         14 + 3 = 14              24 + 3 = 27, etc.
  •  Begin to recognise unit patterns when crossing a ten, e.g. 5 + 6 = 11      15 + 6 = 21                 25 + 6 = 31, etc.
  •  Add two single digit numbers (8 + 7) by counting up; add two 2-digit numbers which total less than 100 by counting on in tens and ones, e.g. 54 + 37 as 54 + 30 + 7.
  •  Count back in ones or tens to take away, e.g. 27 – 3 = or 54 – 20 =.
  • Begin to count up to find a difference between two numbers with a small gap (42 – 38).
  •  Know the 2X, 5X and 10X tables and begin to say how many 10s are in 40 or how many 5s are in 30; use X sign correctly and begin to use ÷ sign.
  • Understand the concept of one half, one quarter and three quarters as numbers (½, ¼, ¾) and as operators (½ of 6 is…?) in a practical context, e.g. on a fraction strip or with smarties on a cake.
  •  Compare and order objects according to their lengths, weights and capacities using suitable units.
  •  Identify and describe, with reference to relevant properties, 4 or more common 2-D and 3-D shapes.
  • Tell the time on digital and analogue clocks to the nearest quarter of an hour.
Year 3

By the end of year 3 children should be able to confidently:

  • Locate any 3-digit number on a landmarked line from 0-1000 and use this to order and compare numbers.
  • Understand place value in 3-digit numbers; add and subtract 1s, 10s or 100s without difficulty; use this to add and subtract multiples of 1, 10, 100 to/from 3-digit numbers.
  •  Know securely number pairs for all the numbers up to and including 20, e.g. pairs which make 15 (7+8, 6+9, 5+10, 4+11, 3+12, 2+13, 1+14, 0+15)
  •  Round to the nearest ten and hundred, e.g. 34 to the nearest ten is 30, 276 to the nearest hundred is 300.
  •  Mentally add or subtract any pair of 2 digit numbers, e.g. 75 + 58 or 75 – 58
  •  Recognise that there are two ways of completing subtractions, either by counting up or by counting back, e.g. 54 – 27 (counting up)         54 – 21 (counting back)
  •  Subtract larger numbers with confidence, counting up, e.g. 302 – 288
  •  Understand that multiplication is commutative, e.g. 4 x 8 is the same as 8 x 4.
  •  Know the 2x, 3x, 5x and 10x times tables. All tables need to be learned to 12th multiple. Include division facts (important). So we know how many 3s in 36, i.e. 36 ÷ 3 = 12, as well as knowing 12 x 3 = 36.
  •  Multiply any 2-digit number by 10 or a single-digit number by 100; divide any multiple of 10 or 100 by 10 or 100. Understand the effect of multiplying and dividing whole numbers by 10 and 100.
  • Multiply a 1 digit number by a 2 digit number starting to use the grid
Year 4:

By the end of year 4, children should be able to confidently:

  • Locate 4 and 5 digit numbers on a landmarked line and use this to compare and order numbers; round to ten, a hundred and a thousand.
  • Understand the numbers of 1s, 10s, 100s, 1000s and 10,000s in a 5-digit number and the use of zero as a place holder.
  •  Know that one-place decimal numbers represent ones and tenths e.g. 3.7 = 3 ones and 7 tenths.
  •  Count in steps of 2, 4, 5, 10, 50, 100 and 1000.
  • Recognise negative numbers in relation to number lines and temperature.
  • Add multiples of 1, 10, 100, 1000 without difficulty, e.g. 15,347 + 3000, 434 + 300 and 648 – 220
  •  Mentally add and subtract any pair of two digit numbers.
  • Know how to use the written addition: first expanded method, moving onto concise method..
  • Subtract 3 digit numbers from 3 digit numbers
  •  Multiply 1 and 2 digit numbers by 10, 100 and 1000; divide 1 and 2 digit numbers by 10 and 100 to understand place value in decimal numbers with one place.
  •  Know and recite 2x, 3x, 4x, 5x, 9x, 10x times tables incl. division facts up to 12th multiple; include multiplying by 0 (e.g. 5 x 0 = 0, 7 x 0 = 0) or by 1 (e.g. 5 x 1 = 5, ½ x 1 = ½). Pupils in Y4 will be assessessed National on their tables in 2019/20
  •  Multiply 1- digit numbers by 2-digit or friendly 3-digit numbers using grid method.
  •  Know how to use ‘efficient chunking’ for division above the range of the tables’ facts, e.g. 84 ÷ 6 = ? Re-write as  x 6 = 8410 x 6 = 60               = 24 (84 – 60)                4 x 6 = 24
  • Add the red numbers: so 14 x 6 = 84 0 So 84 ÷ 6 = 14
  • Begin to extend this to 3 digit numbers, e.g. 145 ÷ 5 = ?
  •  Write the equivalent fraction for fractions with given denominators or numerators, e.g. ½ = ?/8; reduce a fraction to its simplest form, e.g. 6/12 ≡ ½.
  •  Convert between units of measurement, e.g. cm to m, g to Kg and ml to L; convert between units of time and between analogue and digital times.
  •  Identify acute and obtuse angles, compare and order angles up to 180⁰.
  •  Interpret and present discreet data using bar charts and pictograms.
Year 5

By the end of year 5, children should be able to confidently:

  •  Locate 5 and 6 digit numbers on a landmarked line; use this to compare/order numbers.
  •  Round to ten, a hundred, a thousand or ten thousand.
  •  Begin to read scales of different types
  •  Understand a one-place decimal number as a number of tenths and a two-place decimal number as a number of hundredths.
  •  Understand the effect of multiplying and dividing by 10 and 100 to give 1-place and 2-place decimal answers. E.g. 4.5 x 10 = 45, and 678 ÷ 100 = 6.78 etc.
  • §Add or subtract 0.1 or 0.01 to/from any decimal number with confidence, e.g. 5.83 + 0.01 or 4.83 – 0.1
  •  Add and subtract mentally with confidence – where the numbers are less than 100 or the calculation relies upon simple addition/subtraction and place value. Examples include: 6,723 – 400, 78 + 46, 72 – 46, 8020 + 910, 100 – 64, 5000 + 12,000, etc.
  •  Confidently add 3- and friendly 4-digit numbers together using a secure written method, including adding ‘piles’ of numbers
  •  Subtract larger numbers using expanded column subtraction or by counting up
Year 6

By the end of year 6, children should be able to confidently:

  •  Locate numbers up to 999,999 on a landmarked line; use this to compare/order numbers.
  •  Round to ten, a hundred and a thousand, ten thousand or one hundred thousand.
  •  Read scales with accuracy and confidence
  •  Add and subtract mentally with confidence – where the numbers are less than 100 or the calculation relies upon simple addition/subtraction and place value. Examples include: 6,723 – 400, 78 + 46, 72 – 46, 8020 + 910, 100 – 64, 5000 + 12,000, etc.
  • Add several large numbers using written addition,
  • Add several large or decimal numbers using written addition
  • Subtract large numbers using decomposition or counting up