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Welcome to the Year 6 Numeracy Workshop th 18 Friday February 1 Aims for today. To show you what is expected of children in numeracy in Year 6 To show you how we teach your children a variety of strategies to solve mathematical problems. To provide you with the chance to ask questions and chat with other parents and the teachers. To give you ideas and ways to help your children at home. 2 Multiplication and division • use mental calculation strategies for multiplication and division. • use mental methods for calculations including decimals. • Know when to use mental methods, when to use a written method • Use an efficient written method for multiplication and division • TU x U TU x TU TU ÷ U TU ÷ TU • Solve real life problems 3 Mental test questions 5 seconds Multiply 60 by 10 10 seconds Divide 350 by 100 How would you work these out? 4 How would calculate these mentally? 12 x 10 12 ÷ 10 12 x100 12 ÷100 12 x 1000 12 ÷1000 Must understand place value and the value of each digit in a number and a decimal 5 Th H 1 T U . 1/10 1 2 . 0 2 0 . 0 1 2 . 0 1 . 2 1/100 1/1000 1.2 divided by 10? 1.2 divided by 100? 6 Children manipulate numbers • Multiply move digits to the left • Divide move digits to the right • Decimal point stays constant 7 14 x 10 14 ÷by 10 14 x 100 14 ÷ by 100 8 Calculate 17 × 5 × 4 1 mark How would you work this out in 3 – 5 minutes? 9 Children must know the value of each digit. Partitioning helps them to learn the value of the digits. . Will lead to methods of long multiplication. 10 Higher order mathematicians 17 x (4x 5) = 17 x 20 = 11 To calculate this children must know their tables Must have an efficient method Must be able to check their answers Use partitioning to gain understanding of values 17 x 5 10 x 5 = 50 7 x 5 = 35 50 + 35 = 85 must also be able to add 12 85 x 4 80 x 4 = 320 5 x 4 = 20 (8 x 4 x 10 ) 320 + 20 = 340 17 x 5 x 4 = 340 13 The Grid Method x 10 7 5 14 The Grid Method x 10 7 5 50 35 50 + 35 = 85 15 The Grid Method x 80 5 4 320 20 320 + 20 = 340 16 23 x 16 17 The Grid Method x 20 3 10 200 30 6 120 18 320 48 18 320 + 48 = 368 19 • Use the grid method to calculate • 18 x 6 • 18 x 16 20 Plastic cups are sold in packs of 8 Amir needs 27 cups. How many packs must he buy? _____________ packs How would you work this out in 5 minutes without a calculator? 21 48 ÷ 3 = How many 3s in 48 Share 48 by three Three times table 48 is made from an amount of 3s 3 x _ = 48 22 Using a number line to learn that 48 is made from an amount of 3’s Chunking in multiples along the number line to make this more efficient and quicker to calculate 23 Chunking moving to a formal written method (Subtracting multiples of 3 ) 48 ÷ 3 = 16 48 30 10 x 3 18 18 6 x 3 0 1x3 2x3 5x3 10 x 3 24 Multiplication the inverse of division The Grid Method to check division x 10 6 3 30 18 30 + 18 = 48 25 90 ÷ 6 = 1x6 2x6 5x6 10 x 6 26 27 ÷ 8 = 1x8 2x8 What do we get with this problem? How is that dealt with? 27 Subtraction and addition • Develop and refine written methods for addition and subtraction building on mental methods • Add by partitioning • Add using the column method • Find the difference by counting on on a number line • Subtract using exchanging and decomposition (column method) • Solve real life problems 28 How would I work this out? What do the words mean? What maths is required? What calculations need to be used? A shop sells three types of sunglasses. What is the difference in price between the most expensive and least expensive sunglasses? £ 1 mark 29 Column Subtraction £5.85 - £2.99 £5. 85 £2. 99 Children need to understand place value and exchanging. 30 Use of a number line to find the difference • Giving change in the shop • Count on in amounts £2.99 on £0.01 to £3.00 £3.00 on £2.00 to £5.00 £5.00 on £0.85 to £5.85 £0.01 + £2.00 + £0.85 = £2.86 31 High order mathematicians would use their mental skills • Round £2.99 to £3.00 • Subtract £3.00 from £5.85 • Add back a penny 32 I spend £4.32 on food and £3.62 on drinks How much change to I get from £20.00? Pineapples £1.40 each Grapes are £2.25 for 1KG I buy one pineapple and half a kilogram of grapes. How much change will I get from £5. 33 Add money amounts Subtract answer from £10 Ryan buys the £4.69 sunglasses and a sun hat. How much change does he get from £10? Show your working. You may get a mark. 34 Fractions, Percentages, Decimals Doubling and Halving • ¼ of 600? ¼ of 800 Half and half again Divide by 4 Half of 27? Half of any odd number? Dealing with an odd number and a decimal 27 = 20 and 7 10 + 3.5 = 13.5 35 Applying multiplication and division knowledge and skills - Fractions of quantities • 1/4 of 24 Divide by 4 1/8 of 24 Divide by 8 • 1/6 of 18 • Divide by 6 36 Applying multiplication and division knowledge and skills - Fractions of quantities 2/4 of 24 =12 divide by denominator 4 24÷4 = 6 and multiply by numerator 2 6x2 = 12 3/8 of 24 = 9 24÷8 = 3 3x3=9 37 Percentages • • • • 1 % divide by 100 10% divide by 10 5 % find 10% and half (divide by 2) 20% find 10% and double (multiply by 2) • 61% find 1% (divide by 100) and multiply by 61 38 • Reduce the price of these trainers by 15% • What is the new price? • Trainers cost £26.00 £2.60 + £1.30 = £3.90 £26.00 - £3.90 = 39 • 60 x 10 = • 60 divided by 100 = • 17 x 5 x4 = • 48 ÷ 3 = • You buy two items for £1.75 and £3.62 – What change would you get from £10 ? • What is half of 49? • Find 15% of 400 40 Ways to help • Ensure your child knows their times tables and division facts; then extend this e.g. 30 x 6 420 divided by 7 • Improve their mental addition or subtraction skills by asking them questions on the way to school e.g. 67+43. You can make this fun! • Ensure they do their homework ( remember this will only get more frequent in year 7!) • Encourage them to do their best! • Practising halving and doubling numbers • Talking about real life maths situations – adding and finding the change 41