Transcript (a + b) 2
I think of a number and add 6. My answer is negative 7, what number did I start with? Sums and Things for Parents Negative 13 Well done Lucie. How did you think that through? The story so far ………. children’s recall of number facts has become more accurate and faster children are more aware of the strategies they use to calculate they use vocabulary correctly they are more confident about maths maths is more fun! What can a numerate child do? By the age of 11 they should : have a sense of the size of number and where it fits into the number system know by heart addition and subtraction facts to 20, multiplication and division facts to 10x10, doubles and halves, complements to 100, multiply and divide by 10 and 100 use what they know to figure out answers mentally What can a numerate child do? (cont.) calculate accurately and efficiently, both mentally and on paper, using a range of strategies recognise when it is appropriate to use a calculator- and when it is not- and be able to use one effectively explain their methods and reasoning using correct mathematical terms judge whether their answers are reasonable and have strategies for checking them where necessary The aim The aim is for children to do mathematics in their heads, and if the numbers are too large, to use pencil and paper to avoid losing track. To do this children need to learn quick and efficient methods, including appropriate written methods. Learning written methods is not the ultimate aim. Mathematics is foremost an activity of the mind, and written calculations are an aid to that mental activity. The Numeracy Strategy aims to develop children’s mental strategies and then written methods that derive from and support mental methods. We want children to ask themselves: Can I do this in my head? Can I do this in my head using drawings or jottings? Do I need to use an expanded/compact written method? Do I need a calculator? How do you add and subtract? 61 + 45 7800 – 5600 5735 + 3657 5735 + 3990 83 – 68 5002 – 4996 538 - 295 267 + 267 2.5 + 2.7 5.1 - 2.78 Mistakes children make: 1 16 - 9 …….and more: 643 6 10 13 803 + 274 - 526 8117 187 Addition 76 + 47 = +10 76 +10 86 +10 96 +10 106 +7 116 + 40 76 123 +7 116 123 Addition 358 + 473 = 358 358 + 473 + 473 11 8+3 120 50 + 70 700 300 + 400 831 831 1 1 Have a go!!! • I have £257 in one bank account and £468 in another. How much is this altogether? • A sunflower measures 1.94m. By Friday it has grown 38cm. How tall is it now? Subtraction Imran has 43 conkers; he gives 24 away to his friends. How many does he have left? 43 – 24 = 19 20 -1 19 conkers 23 -3 33 -10 43 -10 Subtraction Sam has saved 93p, Amy has 55p. How much more money does Sam have than Amy? 93 – 55 = +5 55 38p more +30 60 +3 90 93 Subtraction 8.23 – 4.55 = +0.45 4.55 3.68 5.00 +3 +0.23 8.00 8.23 Subtraction A sports stadium holds 9010 spectators. 5643 people attend a football match. How many empty seats are there? + 57 5643 5700 +300 +3010 6000 9010 5643 3367 empty seats 5700 6000 9010 57 +300 +3010 3367 Have a go!!! • There are 83 children on the playground. 37 go in for their lunch. How many are left outside? • There are 7000 spaces in the car park. 3756 cars go in. How many spaces are empty? • 6.35 – 3.49 = How do you multiply and divide? 57 x 2 78 ÷ 2 43 x 50 742 ÷ 2 36 x 25 700 ÷ 4 18 x 15 65.5 10 8 x 19 17 ÷ 5 34 x 7 5.4 ÷ 6 Mistakes children make: 76 67 8 x 54 5648 268 x 335 101 r 5 7 847 603 Multiplication 47 x 8 = x 8 40 320 7 56 30 1200 180 7 280 42 376 37 x 46 = x 40 6 1480 222 1702 Have a go!!! How many legs do 36 spiders have? 82 x 43 ……… leading to algebra at KS3 (a + b) 2 = (a + b) x (a + b) x a b a 2 a ab b ab 2 b 2 a + ab 2 ab + b 2 a + 2ab + b (a + b) 2 2 = a + 2ab + b 2 2 Division 47 8 375 43 8 47 43 375 …or ‘chunking’ First using partitioning 84 ÷ 7 = First we partition the 84 into a convenient multiple of 7 + the rest 84 70 10 + + 14 2 = 12 First using partitioning 840 ÷ 7 = First we partition the 840 into a convenient multiple of 7 + the rest 840 700 100 + 140 + 20 = 120 First using partitioning 93 ÷ 7 = First we partition the 93 into a convenient multiple of 7 + the rest 93 70 10 + + 23 3r2 = 13 r 2 First using partitioning 168 ÷ 7 = First we partition the 168 into a convenient multiple of 7 + the rest 168 140 20 + 28 + 4 = 24 First using partitioning 9.8 ÷ 7 = First we partition the into a convenient multiple of 7 + the rest 9.8 7 + 2.8 1 + 0.4 = 1.4 First using partitioning 173 ÷ 15 = First we partition the 173 into a convenient multiple of 15 + the rest 173 150 10 + + 23 1r8 = 11 r 8 Have a go!!! 72 children in Year 4 were put into teams of 6 for sports day. How many teams were there? 168 and 19 children are going on a school trip. Each mini bus holds 15 passengers, how many buses will be needed? How can you help? Talk about how you do maths Give praise and encouragement Be positive Ask your child to explain Make sure maths is fun!