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How we teach Maths in school Parents’ Information Evening 2014 Aims To discuss a range of mental and written calculation methods that your child will be taught while they progress through St. Leonard’s To show you some of the types of recording that your child will be introduced to in order to support their written calculation methods. To show you some possible activities and resources that you may be able to make/use to support your child/children at home. Year 3 Year 4 • Number line • Number square • Counters • Online games • Place value cards • Unifix sticks Resources Place Value • We use place value cards in combination with unifix cubes and 100 squares to recognize values of numbers. i.e. make the number 245 Step 1: separate the number into its value 2 hundreds, 4 tens and 5 units Step 2: make that number with either cubes or a value card. Mental calculations 1) 2) 3) 4) 5) 6) 7) 8) 9) 1 more / 1 less 3 + 5 number bonds 10 more/ 10 less 6 + 6 doubles 6 + 7 near doubles 26 + 9 add 10 subtract 1 26 + 57 add to the nearest ten and adjust 48 + 25 partitioning counting on/back Written methods: 7 + 4 +1 7 +1 8 +1 9 +1 10 11 This relates to putting a number into your head and count on Written methods: 32 + 23 + 10 32 + 10 42 +3 52 55 By counting on or back in tens the hundred square is used The temperature is -80C. It increases by 150. What is the temperature now? T.U.B Method • • • • • 25 + 33= 58 Step 1: partition numbers ( tens 20 + 30) (units 5+3) Step 2: add up the Tens (T) ( 20 + 30 = 50) Step 3: add up the Units (U) ( 5+ 3 = 8) Step 4: add both (B) (50 + 8= 58) • 55 + 26 ( T 50 + 20= 70) (U 5+6= 11) • 70 + 11 = ( T70 +10= 80 ) (U 0+1=1) • 80+1=81 Now try these! 73+24= 87+21= 44+37= Subtraction Mental methods: 35 - 22 a) as ‘take away’ − 10 −1 −1 13 − 10 14 15 25 35 b) as ‘difference’ +8 22 +5 30 35 Using complements to 10, 100 Subtraction towards formal written methods No ‘breaking down’ needed: 95 − 41 − 90 40 50 Leading to: and and and 95 − 41 54 5 1 4 ‘Exchange’ ‘83 − 47’ 80 and − 40 and 3 7 Re-written as: − 70 and 13 40 and 7 30 and 6 Now try these! 63-24= 87-23= 54-31= Vertical calculation for subtraction can create real difficulties for both children and teachers. It’s easy to think that teaching children to remember a process, perhaps developed through the use of place value resources, will work. Some children may be able to remember this, but, even if they do, learning without understanding is never a basis for future development. The following method, which can be used if you decide you have to teach a vertical method, is still mathematically ‘transparent’. There are no tricks, there is no need to swap 10 ones for a ten or 10 tens for a hundred and it’s possible to keep track of the number you are subtracting from all the way through. Having said that, don’t move to this method unless children have a thorough grasp of subtraction with decimals on a number line and a real understanding of place value. For the first time it’s possible, and necessary, to use partitioning for subtraction. Multiplication as repeated addition 2+2+2+2=8 4 pairs of socks is 8 socks 4 groups of 2 is 8 (4 × 2 = 8) Or show as 4 hops of 2 on a number line (2 × 4 = 8) 2 multiplied by 4 is 8 0 1 2 3 4 5 6 7 8 Multiplication as describing an array 5 x 7 = 35 7 x 5 = 35 Multiplying numbers by 10 and 100 If you can multiply by 1, then you can multiply by 10, 100 etc. When multiplying by 10 we move the digits one place to the left and add a zero if necessary hundreds tens units hundreds tens 1 3 × 10 hundreds tens units 7 × 100 units 1 3 0 hundreds tens units 7 0 0 The grid method 23 × 8 =184 × 20 8 160 3 24 We had to know that 8 × 20 is the same as 8 × 2 × 10. Add the numbers in the boxes together: 160 + 24 =184 We can extend this grid method to larger numbers. From informal to formal methods 23 x 8 (20 x 8) 160 ( 3 x 8) 24 184 23 x 8 ( 3 x 8) 24 (20 x 8) 160 184 23 x 8 184 2 Larger numbers can also be developed in this way. These will eventually be extended to numbers with 2 decimal places. Example 7.24 m × 14 (eg “12 ÷ 4”) Division EQUAL SHARES: “12 sweets between 4 children” GROUPING: “12 sweets into groups of 4” Written methods: 12÷4 -4 0 1 2 -4 3 4 5 6 -4 7 8 9 10 11 12 This relates to grouping (chunking) or how many 4’s go into 12? 145 ÷ 6 = ? Using a number line to divide (with remainders) 60 (10 × 6) 24 (4 × 6 ) 25 1 145 ÷ 6 = 24 r 1 85 145 120 (20 × 6 ) 24 (4 × 6 ) 1 60 (10 × 6) 25 145 Using a number line to divide (with remainders) The progression in written calculations Establish mental methods, based on a good understanding of place value in numbers. Use number lines, and grid methods for multiplication. Show the children how to set out written calculations vertically, initially using expanded layouts. Gradually refine the written method into a more compact standard method. Extend to larger numbers and decimals. Online games Children love games to engage their learning.