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These are the different strands of mathematics • • • • • • • Using and applying Counting and understanding number Knowing and using number facts Calculating Understanding shape Measuring Understanding data Objectives: • To know the methods of calculation that the children use in order to be able to support them at home • To learn some of the mathematical language we use at school • To understand the order in which we teach calculations Resources On each table is a variety of resources you are free to use. Calculation policy which shows the methods used will be available on the website along with feedback from this evening’s session and a copy of this powerpoint. A copy of the calculation skills through the year groups is on a handout for you to take home! Long multiplication and long division This is how I used to do it at school • Children need to be introduced to the processes of calculation through practical, oral and mental activities • As children begin to understand the underlying ideas they develop ways of recording to support their thinking and calculation methods Foundation stage • Begin to relate addition to combining two groups of objects and subtraction to ‘taking away’ • In practical activities and discussion begin to use the vocabulary involved in adding and subtracting • Count repeated groups of the same size • Share objects into equal groups and count how many in each group Year 1 • Relate addition to counting on; recognise that addition can be done in any order; use practical and informal written methods to support the addition of a one-digit number or a multiple of 10 to a one-digit or two-digit number • Understand subtraction as ‘take away’ and find a ‘difference’ by counting up; use practical and informal written methods to support the subtraction of a one-digit number from a one digit or two-digit number and a multiple of 10 from a two-digit number • Use the vocabulary related to addition and subtraction and symbols to describe and record addition and subtraction number sentences • Solve practical problems that involve combining groups of 2, 5 or 10, or sharing into equal groups What is an informal written method of recording? Year 2 Add or subtract mentally a one-digit number or a multiple of 10 to or from any two-digit number; use practical and informal written methods to add and subtract two-digit numbers Understand that subtraction is the inverse of addition and vice versa; use this to derive and record related addition and subtraction number sentences Represent repeated addition and arrays as multiplication, and sharing and repeated subtraction (grouping) as division; use practical and informal written methods and related vocabulary to support multiplication and division, including calculations with remainders Use the symbols +, –, ×, ÷ and = to record and interpret number sentences involving all four operations; calculate the value of an unknown in a number sentence (e.g. □ ÷ 2 = 6, 30 – □ = 24) Year 3 • Add or subtract mentally combinations of one-digit and two-digit numbers • Develop and use written methods to record, support or explain addition and subtraction of two-digit and three-digit numbers • Multiply one-digit and two-digit numbers by 10 or 100, and describe the effect • Use practical and informal written methods to multiply and divide two-digit numbers (e.g. 13 × 3, 50 ÷ 4); round remainders up or down, depending on the context • Understand that division is the inverse of multiplication and vice versa; use this to derive and record related multiplication and division number sentences • Find unit fractions of numbers and quantities(e.g. 1/2, 1/3, 1/4 and 1/6 of 12 litres) • • • • • • Year 4 Add or subtract mentally pairs of two-digit whole numbers (e.g. 47 + 58, 91 – 35) Refine and use efficient written methods to add and subtract two-digit and three-digit whole numbers and £.p Multiply and divide numbers to 1000 by 10 and then 100 (whole-number answers), understanding the effect; relate to scaling up or down Develop and use written methods to record, support and explain multiplication and division of two-digit numbers by a one-digit number, including division with remainders (e.g. 15 × 9, 98 ÷ 6) Find fractions of numbers, quantities or shapes (e.g. 1/5 of 30 plums, 3/8 of a 6 by 4 rectangle) Use a calculator to carry out one-step and two-step calculations involving all four operations; recognise negative numbers in the display, correct mistaken entries and interpret the display correctly in the context of money What is an efficient written method? Year 5 • Extend mental methods for whole-number calculations, for example to multiply a two-digit by a one-digit number (e.g. 12 × 9), to multiply by 25 (e.g. 16 × 25), to subtract one near multiple of 1000 from another (e.g. 6070 – 4097) • Use efficient written methods to add and subtract whole numbers and decimals with up to two places • Use understanding of place value to multiply and divide whole numbers and decimals by 10, 100 or 1000 • Refine and use efficient written methods to multiply and divide HTU × U, TU × TU, U.t × U and HTU ÷ U • Find fractions using division (e.g. / of 5 kg), and percentages of numbers and quantities (e.g. 10%, 5% and 15% of £80) • Use a calculator to solve problems, including those involving decimals or fractions (e.g. find 3/4 of 150 g); interpret the display correctly in the context of measurement 1 100 How do I refine my written method? Year 6 • Calculate mentally with integers and decimals: U.t ± U.t, TU × U, TU ÷ U, U.t × U, U.t ÷ U • Use efficient written methods to add and subtract integers and decimals, to multiply and divide integers and decimals by a one digit integer, and to multiply two-digit and three-digit integers by a two-digit integer • Relate fractions to multiplication and division (e.g. 6 ÷ 2 = 1/2 of 6 = 6 × 1/2); express a quotient as a fraction or decimal (e.g. 67 ÷ 5 = 13.4 or 132/5); find fractions and percentages of whole-number quantities (e.g. 5/8 of 96, 65% of £260) • Use a calculator to solve problems involving multi-step calculations Isn’t using a calculator cheating? • By the end of Year 6, children are equipped with mental, written and calculator methods they understand and can use correctly. • When faced with a calculation, children are able to decide which method is most appropriate and have strategies to check their accuracy. Addition: 1. 2. 3. 4. number lines partitioning extended - horizontal/vertical column ITP Subtraction 1. 2. 3. 4. Number lines – counting on Extended Decomposition column Multiplication 1. 2. 3. 4. ITP Arrays Partitioning Grid method Column Division 1. Grouping and sharing Stand in 3 groups, stand in groups of 3 2. Repeated subtraction 3. Remainders It does not matter which year the child is in. We can only teach children the next step if they have mastered the one before. It does not matter which method children use providing they are confident in its use. We give children a range of strategies so that they can choose which one they are happiest with. It doesn’t matter how they get there, they just need the answer!