Year 2 Mathematics

Maths Maths is magic! Unfortunate because with Maths iit is usually like sprouts at xmas you either hate it or love it! We want our children to love it! You will be glad to know there are only a few slides for me! Step1: Think of a number below 10. Step2: Double the number you have thought. Step3: Add 6 with the getting result. Step4: Half the answer, that is divide it by 2. Step5: Take away the number you have thought from the answer, that is, subtract the answer from the number you have thought. Answer: 3 Numicon-who has a 2 shape, who has an odd number, who has 1 more than 6, who 6 subtract 2, who has a multiple of 2. model the difference-number pairs, multiplaction, place value

The Knowledge Led Curriculum 3 Forms of Knowledge: I know that … I know how… I know why … The Yearly Programmes Of Study - Factual - Procedural - Conceptual

National Curriculum Structure Fluency Reason Mathematically Solve Problems Programmes of Study for Each Year Group Number Place Value + / - X / ÷ FDP Measurement Geometry Properties of Shape Position & Direction Statistics (Y2 – Y6) Fractions, decimals, percentages

Expectations of Mathematics in the National Curriculum Close the gap and raise attainment Providing access to mathematical concepts for all children Pupils should make connections in mathematics Use representations to support learning Deep rather than superficial learning Calculating with confidence More and longer time on fewer topics

Problem Solving

Deep Over Superficial…

Using and Applying So broaden rather than lengthen Apply maths skills to problem solving Cover all areas of problem solving: Word problems Logic problems Finding all possibilities Visual problems Rules and Patterns

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Long Term Plan townlaneinfantschool.eschools.co.uk

NCETM https://www.ncetm.org.uk/ Free to sign up Responsible for running the day-to-day mathematics curriculum for the government Examples of questions to meet each maths N.C objective Progression maps for all maths topics Progression maps for reasoning skills

Fluency

Curriculum Balance Procedural Conceptual Efficiency Understanding - make links - reason - depth & breadth - fluency - representations - procedures - fluency - not ‘getting lost’ - accuracy - select & check

Mental Mathematics Targets

Number Bonds By the end of Year One, children should be recalling all number bonds to 20. In Year Two, the children should be using these facts to derive related facts to 100.

+ 1 2 3 4 5 6 7 8 9 10 Y1 facts Y2 facts Adding 1 and 2 Bonds to 10 Bridging/ compensating Y1 facts Y2 facts Doubles Adding 0 Near doubles + 1 2 3 4 5 6 7 8 9 10 0 + 0 0 + 1 0 + 2 0 + 3 0 + 4 0 + 5 0 + 6 0 + 7 0 + 8 0 + 9 0 + 10 1 + 0 1 + 1 1 + 2 1 + 3 1 + 4 1 + 5 1 + 6 1 + 7 1 + 8 1 + 9 1 + 10 2 + 0 2 + 1 2 + 2 2 + 3 2 + 4 2 + 5 2 + 6 2 + 7 2 + 8 2 + 9 2 + 10 3 + 0 3 + 1 3 + 2 3 + 3 3 + 4 3 + 5 3 + 6 3 + 7 3 + 8 3 + 9 3 + 10 4 + 0 4 + 1 4 + 2 4 + 3 4 + 4 4 + 5 4 + 6 4 + 7 4 + 8 4 + 9 4 + 10 5 + 0 5 + 1 5 + 2 5 + 3 5 + 4 5 + 5 5 + 6 5 + 7 5 + 8 5 + 9 5 + 10 6 + 0 6 + 1 6 + 2 6 + 3 6 + 4 6 + 5 6 + 6 6 + 7 6 + 8 6 + 9 6 + 10 7 + 0 7 + 1 7 + 2 7 + 3 7 + 4 7 + 5 7 + 6 7 + 7 7 + 8 7 + 9 7 + 10 8 + 0 8 + 1 8 + 2 8 + 3 8 + 4 8 + 5 8 + 6 8 + 7 8 + 8 8 + 9 8 + 10 9 + 0 9 + 1 9 + 2 9 + 3 9 + 4 9 + 5 9 + 6 9 + 7 9 + 8 9 + 9 9 + 10 10 + 0 10 + 1 10 + 2 10 + 3 10 + 4 10 + 5 10 + 6 10 + 7 10 + 8 10 + 9 10 + 10 Music-number fun

Times Tables x 2 3 4 5 6 7 8 9 10 11 12 14 16 18 20 22 24 15 21 27 30 33 36 28 32 40 44 48 25 35 45 50 55 60 42 54 66 72 49 56 63 70 77 84 64 80 88 96 81 90 99 108 100 110 120 121 132 144 Year Two Year Three Year Four Year Two 30 facts 2, 5 and 10 times tables

Nrich Investigation/Reasoning Pupil One puts in a secret number into the calculator and asks pupil Two, "What do you want to multiply it by?" Pupil Two replies, "Multiply it by 5  ." Pupil One puts in 'times' and '5  ' and hands the calculator to Pupil Two. When Pupil Two presses the 'equals' button the calculator shows '35’.

NCETM/Topmarks

Resources Websites Topmarks.co.uk NCETM Nrich BBC Documents National Curriculum https://www.gov.uk/government/collections/national-curriculum

Solve addition and subtraction problems 30+20 = 50 4 + 3 = 7 34 + 23 = 57 30 + 20 = 50 4 + 3 = 7 = 57 100 40 5 7 60 300 222 + 145 = In order to order chldren need to understand the value of numbers-we do lots of work on place value usng practical equipment such as arrow cards and dienes equipment to partition a number. Once children understand how to partition numbers we can then move onto using an empty number lne to support mental calculations of addition and subtraction. Why? What does the column method teach them??????????????????

Assessment Interim teacher assessment frameworks at the end of key stage 1 Key principles: The interim framework does not include full coverage of the content of the national curriculum and focuses on key aspects for assessment. Pupils achieving the different standards within this interim framework will be able to demonstrate a broader range of skills than those being assessed. Teachers must base their teacher assessment judgement on a broad range of evidence from across the curriculum for each pupil. The evidence used must include the key stage 1 mathematics test, which does not focus solely on the key aspects listed in this interim framework.

Working towards the expected standard The pupil can demonstrate an understanding of place value, though may still need to use apparatus to support them (e.g. by stating the difference in the tens and ones between 2 numbers i.e. 77 and 33 has a difference of 40 for the tens and a difference of 4 for the ones; by writing number statements such as 35 < 53 and 42 > 36). The pupil can count in twos, fives and tens from 0 and use counting strategies to solve problems (e.g. count the number of chairs in a diagram when the chairs are organised in 7 rows of 5 by counting in fives). The pupil can read and write numbers correctly in numerals up to 100 (e.g. can write the numbers 14 and 41 correctly). The pupil can use number bonds and related subtraction facts within 20 (e.g. 18 = 9 + ?; 15 = 6 + ?). The pupil can add and subtract a two-digit number and ones and a two-digit number and tens where no regrouping is required (e.g. 23 + 5; 46 + 20), they can demonstrate their method using concrete apparatus or pictorial representations. The pupil can recall doubles and halves to 20 (e.g. pupil knows that double 2 is 4, double 5 is 10 and half of 18 is 9). The pupil can recognise and name triangles, rectangles, squares, circles, cuboids, cubes, pyramids and spheres from a group of shapes or from pictures of the shapes.

Working at the expected standard The pupil can partition two-digit numbers into different combinations of tens and ones. This may include using apparatus (e.g. 23 is the same as 2 tens and 3 ones which is the same as 1 ten and 13 ones). The pupil can add 2 two-digit numbers within 100 (e.g. 48 + 35) and can demonstrate their method using concrete apparatus or pictorial representations. The pupil can use estimation to check that their answers to a calculation are reasonable (e.g. knowing that 48 + 35 will be less than 100). The pupil can subtract mentally a two-digit number from another two-digit number when there is no regrouping required (e.g. 74 − 33). The pupil can recognise the inverse relationships between addition and subtraction and use this to check calculations and work out missing number problems (e.g. Δ − 14 = 28). The pupil can recall and use multiplication and division facts for the 2, 5 and 10 multiplication tables to solve simple problems, demonstrating an understanding of commutativity as necessary (e.g. knowing they can make 7 groups of 5 from 35 blocks and writing 35 ÷ 5 = 7; sharing 40 cherries between 10 people and writing 40 ÷ 10 = 4; stating the total value of six 5p coins). The pupil can identify 1/3 , 1/4 , 1/2 , 2/4 , 3/4 and knows that all parts must be equal parts of the whole. The pupil can use different coins to make the same amount (e.g. pupil uses coins to make 50p in different ways; pupil can work out how many £2 coins are needed to exchange for a £20 note). • The pupil can read scales in divisions of ones, twos, fives and tens in a practical situation where all numbers on the scale are given (e.g. pupil reads the temperature on a thermometer or measures capacities using a measuring jug). • The pupil can read the time on the clock to the nearest 15 minutes. • The pupil can describe properties of 2-D and 3-D shapes (e.g. the pupil describes a triangle: it has 3 sides, 3 vertices and 1 line of symmetry; the pupil describes a pyramid: it has 8 edges, 5 faces, 4 of which are triangles and one is a square).

Working at greater depth within the expected standard The pupil can reason about addition (e.g. pupil can reason that the sum of 3 odd numbers will always be odd). The pupil can use multiplication facts to make deductions outside known multiplication facts (e.g. a pupil knows that multiples of 5 have one digit of 0 or 5 and uses this to reason that 18 × 5 cannot be 92 as it is not a multiple of 5). The pupil can work out mental calculations where regrouping is required (e.g. 52 − 27; 91 – 73). The pupil can solve more complex missing number problems (e.g. 14 + – 3 = 17; 14 + Δ = 15 + 27). The pupil can determine remainders given known facts (e.g. given 15 ÷ 5 = 3 and has a remainder of 0, pupil recognises that 16 ÷ 5 will have a remainder of 1; knowing that 2 × 7 = 14 and 2 × 8 = 16, pupil explains that making pairs of socks from 15 identical socks will give 7 pairs and one sock will be left). The pupil can solve word problems that involve more than one step (e.g. which has the most biscuits, 4 packets of biscuits with 5 in each packet or 3 packets of biscuits with 10 in each packet?). The pupil can recognise the relationships between addition and subtraction and can rewrite addition statements as simplified multiplication statements (e.g. 10 + 10 + 10 + 5 + 5 = 3 × 10 + 2 × 5 = 4 × 10). The pupil can find and compare fractions of amounts (e.g. 14 of £20 = £5 and 12 of £8 = £4 so 14 of £20 is greater than 12 of £8). The pupil can read the time on the clock to the nearest 5 minutes. The pupil can read scales in divisions of ones, twos, fives and tens in a practical situation where not all numbers on the scale are given. The pupil can describe similarities and differences of shape properties (e.g. finds 2 different 2-D shapes that only have one line of symmetry; that a cube and a cuboid have the same number of edges, faces and vertices but can describe what is different about them).

KS1 Mathematics 2016 https://www.gov.uk/government/collections/national-curriculum-assessments-2016-sample-materials 2016 tests will be made of 2 components 1. Fluency in calculation 2. Application & reasoning Test will reflect each of the domains within the PoS A new test and mark scheme will be developed each year. Marked internally by teachers. Both papers will be timed and contain a ‘grid’ on which to show workings (reflecting a square maths book).

Paper 1 – Arithmetic Paper The guidance time for this test is 20 mins. Questions are context free. Focus is speed and accuracy – ‘recall and use known facts’, encourages pupils to use efficient calculation strategies. NO apparatus can be used to support pupils to access questions. Marks will not be awarded for working out. Every question is worth one mark.

Paper 2 - Application and Reasoning The guidance time for this test is 35 minutes. There are 5 aural questions and after these there should be approximately 30 minutes. Reflects current KS1 test question ‘style’ with raised expectations in line with current National Curriculum. This paper will contain ‘working mark’ questions – 1 mark for appropriate working but incorrect answer. The test will contain a mixture of contextualised and context-free questions, and real life and abstract problems. Language will be appropriate to key stage 1 and questions can be read to the children; word length will be kept to a minimum for accessibility reasons. The only apparatus that can be used to support the children are spelling aids.

KS1 Mathematics 2016

Paper Two – Range of methods

“If you want to take part in tomorrow’s world, you’ll need mathematics and statistics just as much as grammar and syntax” Professor Robert Worcester, Chairman, Market Opinion Research International I like to have the last word!