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Introduction WEBSITES www.counton.org www.learn.co.uk www.bbc.co.uk/schools http://nrich.maths.org www.woodlands-junior.kent.sch.uk/maths www.ixl.com/math www.coolmath4kids.com www.mathplayground.com/games.html www.maths-games.org The information in this booklet is to help you to help your child with maths. It explains some of the different strategies we use for recording calculations in school. The written methods we use are progressive ie each method builds on the previous. All the methods are efficient in their own right and can be used with numbers of all sizes, including decimals. The key is that the children have a method which they understand and with which they can experience success. Once a child has mastered one method they will be introduced to the next stage as it may become more efficient for them but they are always given the opportunity to select the method they feel more comfortable with. For each stage there are two strategies listed, the first being the method taught and encouraged. The other is an alternative offered to those who find the first method difficult to understand and apply. In addition to the above, the booklet includes some everyday mathematical activities which you could involve your child in and some websites which they may find interesting. 1 Stages 1-3 allow children to carry out addition calculations with smaller numbers and supported with the use of practical apparatus. STAGE 4 Partitioning 26 + 37 20 + 30 = 50 6 + 7 = 13 50 + 13 = 63 Alternative - Number lines: 86 + 57 (most or least significant first) (A hundred grid could be used to support this recording) + 50 +4 86 136 +3 140 Pizza please! 143 Your pizza costs £3.60. Cut it into six equal slices. How much does each slice cost? The answer is that each slice costs 60p. STAGE 5 Partitioning As above – with 3-digt numbers. Introduce to column form of recording: (significant and insignificant digits first) 754 + 96 597 + 475 700 140 10 12 160 900 Number lines (as above) 850 754 + 40 804 How much is half a slice? How much do two slices cost? How much does half (1/2) of the whole pizza cost? What if you cut your pizza into four equal slices (quarters)? 1072 754 + 96 + 50 Calculator costs Use a calculator to find the cost of one sweet: Clues: 1. Enter the cost of the packet of sweets on the calculator display, for example 35 (pence). 2. Press the divide ÷ button 3. Count the number of sweets in the packet, and enter this number on the calculator, for example 42 (sweets). 4. Press the equals = button 5. The answer is 0.833 (pence), which is less than 1p for each sweet. Now use your calculator to find the cost of: One stick of chewing gum; One finger of a chocolate bar; One segment of a tangerine; One mint; and so on. How much does one slice (1/4) cost now? How much does half cost now? Is it the same, more or less than above? +6 844 850 2 11 MEASUREMENT STAGE 6 Calculating distances in a journey e.g. how much further? Calculating heights of family members – who is the tallest? How much taller is dad than you? Measuring weights of ingredients for baking. Reading the scale on weighing machines and calculating the intervals. 7648 + 1486 27.54 +1 6.7 9134 11 44.24 11 Weigh your child on the bathroom scales. Weigh them again while they are holding the family pet. Can they work out how much heavy the pet is? Time Calculating how long a journey will take looking at train/bus/airline timetables. Using TV guide to calculate the length of programmes. Programming the video or the microwave. Setting an alarm clock. Planning the evenings TV viewing, ‘How long will the programme last?’ 10 3 How you can help your child at home Stages 1-3 allow children to carry out subtraction calculations with smaller numbers and supported with the use of practical apparatus. STAGE 4 Number lines Counting on 84-56=28 +4 +20 +4 56 60 80 84 Counting back 84 – 56 = 28 +4 28 Here are some examples of how you can include mathematics at home: SHOPPING -50 34 STAGE 5 Column: Counting on 754 - 86 14 (100) 600 (700) 54 (754) It is most important that you talk & listen to your child about their work in maths. It will help your child if they have to explain to you. Share the maths activity with your child and discuss it with them. Be positive about maths, even if you don’t feel confident about it yourself. Remember, you are not expected to teach your child maths, but please share, talk and listen to your child. If your child cannot do their homework do let the teacher know by either writing a note on the piece of homework or telling the teacher. A lot of maths can be done using everyday situations and will not need pencil and paper methods. Play games and have fun with maths! £ £ 84 £ STAGE 6 £ £ 5 13 1 6467 - 2684 £ Looking at prices Calculating change – which coins, different combinations. Weighing fruit and vegetables in the supermarket and calculating the cost. Counting pocket money. Estimating the final bill at the end of shopping while waiting at the cash out. Calculating the cost of the family going to the cinema, swimming baths, etc. 3783 668 4 9 STAGE 6 Still using Number Lines as above Stages 1-3 allow children to carry out multiplication calculations with smaller numbers supported with the use of practical apparatus or drawings ie arrays or groups of. Some may move onto:Chunking: 256 ÷ 7 256 - 70 (10 x 7) 186 - 140 (20 x 7) 46 - 42 (6 x 7) 4 Answer is 36 remainder 4 Describing arrays: 4x2=8 2x4=8 Diagrams X X 2 X X + 2 X X + 2 3 groups of 2 Repeated addition: 5 + 5 + 5 = 3 lots of 5 STAGE 4 Grid method (TU x U) : 23 x 8 = 20 8 8 160 24 3 = 184 5 STAGE 5 As with multiplication, stages 1-3 allow children to carry out division calculations with smaller numbers supported with the use of practical apparatus or drawings ie groups of. Throughout we look to develop children’s understanding of the relationship between multiplication and division and seeing division as ‘grouping’ as well as ‘sharing’. Grid method (HTU x U, TU x TU and U.t x U) : 72 x 38 = 70 2100 60 30 560 8 4.9 x 3 3 4.0 0.9 12 2.7 560 2 16 = 2736 Pictorial representations: Grouping: 12 + 2.7 = 14.7 How many twos make 6? Share 6 sweets between 2 boys. Sharing: 16 STAGE 6 Grid method (ThHTU x U; HTU x TU and decimals – up to 2 dp) As above plus: 372 x 24 = 300 70 STAGE 4 2 Number lines: 6000 1400 40 20 1200 4 1x2 280 8 = 8928 12.62 x 8 = 8 10 2 80 16 0.6 4.8 0 1x2 2 6 1x2 8 10 Counting on - 72 ÷ 5 = 14 r 2 10 x 5 Long Multiplication: 352 X 27 2464 7040 9504 4 1x2 STAGE 5 0.16 = 80 + 16 + 4.8 + 0.16 = 100.96 234 1x2 0.02 Leading to Short Multiplication: 4346 X 8 34768 10 ÷ 2 = 5 4x5 0 50 Counting back - 72 ÷ 5 = 14 r 2 -4x5 6 0 2 70 72 - 10 x 5 22 72 7