DEVELOPING UNDERSTANDING OF ADDITION AND SUBTRACTION Year 1 Objectives read, and interpret mathematical statements involving addition (+), subtraction (-) and equals (=) signs represent and use number and related subtraction facts within 20 add and subtract one-digit and numbers to 20, including zero Recall of Facts = + If we know 4 + 5 = 9 We also know: , 5+4=9 9-4=5 14 + 5 = 19 19 - 14 = 5, etc Work with all numbers up to 20. Mental Jottings with representations Immerse children in practical opportunities to develop understanding of addition and subtraction. Link practical representations on a number track on a beadstring to recording on a number line. By the end of Year 1 children should be able to recall and use facts within and to 20. Children need to be secure with Using and Applying these skills in unfamiliar contexts before moving into the Year 2 objectives. 4
Year 2 Objectives: Show that addition of two numbers can be done in any order and subtraction cannot. Recall and use addition and subtraction facts to 20 fluently and derive and use related facts up to 100. Add and subtract numbers concrete objects, pictorial presentations and mentally including: 2 digit number and ones 2 digit number and tens Two 2 digit numbers Add three 1 digit numbers Solve problems with addition and subtraction: • using concrete objects and pictorial representations, including those involving numbers, quantities and measures • applying their increasing knowledge of mental and written methods Recall/Jottings: Using known facts If I know: 2+3 = 5 I also know: 3+2 = 5 20 + 30 = 50 30 + 20 = 50 50—30 = 20 = 30 Bridge through 10 26 + 7 = 26 + 4 + 3 26 + 4 = 30 30 + 3 = 33 Counting on/back in10s 26 + 20 = 67-20 Partitioning 23 + 34 = 46—25 Special Strategy Rounding and adjusting + 9—9 +11—11 Bonds to 10 2+7+8=8+2+7 Finding the difference between two numbers. 71 - 37: Partitioning numbers in different ways in preparation for subtracting using decomposition: 90 + 2 80 + 12 (I have subtracted a ten and added it onto the ones) Continue to record mental jottings as outlined in Year 2 with increasingly larger numbers. Use suitable resources as required (See models and images page). Children that have not achieved the age related expectations for Year 2 should not move onto formal written methods until they are secure with mental recall/jottings. Written Methods with representations Recording addition and subtraction in columns supports place value and prepares for formal written methods. Tens Ones Tens Ones Encourage children to recognise this can be completed mentally: 42 40 + 2 30 + 12 42 - 15 = 27 -15 10 + 5 10 + 5 20 + 7 5
Year 5 Objectives: Add and subtract whole numbers with more than 4 digits, including using formal written methods (columnar addition and subtraction) Add and subtract numbers mentally with increasingly large numbers Use rounding to answers to calculations Mental Recall/Jottings: 12 462 - 2300 Use knowledge of place value to calculate mentally with increasingly larger numbers. Employ a range of special strategies to develop confidence in calculating mentally. E.g. 2364 + 1999 = 2364 + 2000 = 4364 = Written Methods: 800 + 640 = 1440 900 - 500 = 400 900 - 500 = 400 and determine, in the context of a problem, 13484 + 2400 = 13000 + 2000 = 15000 Is your estimate close to the answer you have calculated? levels of accuracy Solve addition and subtraction multi-step problems in contexts, deciding which operations and methods to use and why. 484 + 400 = 884 15000 + 884 = 15884 4 = 2001—1997 1997 2000 13486—5000 13486—3000 = 10486 10486—2000 = 8486 2001 + 346.28 becomes: Estimate: 25 + 350 = 375 25.356 +346.28 371.636 1 1 9.076 - 3.142 becomes: Estimate: 9-3=6 89.1076 3. 142 5. 934 8
Year 1 Objective count, read and write numbers to 100 in numerals; count in multiples of twos, fives and tens Double numbers to 20 Examples Use of visual models to support counting in 2, 5, 10 Ensure children begin to see the patterns of counting in 2, 5, 10. numbers up to: 10 + 10 = 10 x 2 20 - 10 = 20 ÷ 2 Children do not need to record number sentences using the symbols. Develop the vocabulary by encouraging children to explain what they are doing. Representations Grouping and sharing How many legs will 3 teddies have? Arrays 11
Year 4 Objective count in multiples of 6, 7, 9, 25 and 1 000 (copied from Number and Place Value) Mental Methods If the children know multiplication and division facts for: 2/5/10/3/4/8/ they now need to learn. Written Methods with representations These are the methods from the appendix of the National Curriculum. Schools should agree the methods that they are going to use. 6x6 7x7 9 x 9 11 x 11 recall multiplication and 7x6 9 x 7 11 x 9 12 x 11 division facts for multiplication tables up to 12 × 12 use place value, known and derived facts to multiply and divide mentally, including: multiplying by and 1; dividing by 1; multiplying together three numbers. recognise and use factor pairs and commutativity in mental calculations (appears also in Properties of Numbers) multiply two-digit and three-digit numbers by a one-digit number using formal written layout 9 x 6 11 x 7 12 x 9 12 x 12 11 x 6 12 x 7 12 x 6 Explore what happens when we divide by 1 and 0. To solve 24 x 3 Use knowledge of factor 8 x 3 x3 6 x 4 x3 In measuring and scaling contexts, (for example, four times as high, eight times as long etc.) and correspondence problems in which m objects are connected to n objects (for example, 3 hats and 4 coats, how many different outfits?; 12 sweets shared equally between 4 children; 4 cakes shared equally between 8 children). 14
DEVELOPING UNDERSTANDING OF FRACTIONS/DECIMALS AND PERCENTAGES Year Objectives Examples Models and Images Year 1 Year 2 find and name a half as one of two equal parts of an object, shape or quantity Recognise, find and name a quarter as one of four equal parts of an object, shape or quantity Recognise, find, name and write fractions , , and of a length, shape, set of objects or quantity Write simple fractions for example, of 6 = 3 and recognise the equivalence of and . Children use their knowledge of fractions of shape to find fractions of quantities. Children should be give practical apparatus to find halves and quarters of quantities within 20. Record work pictorially. Children use their knowledge of unit and non-unit fractions of shapes to find fractions of quantities. They relate this to find fractions of a length e.g. 2/4 of 1m = Children need to relate finding a quarter to halving and halving Pupils should count in fractions up to 10, starting from any number and using the1/2 and 2/4 equivalence on the number line (Non Statutory Guidance) If I can see ¼ how many quarters can you see? If I can see 2/3 how many thirds can you see? 19