1 / 38

Numeracy Methods at SMA

Numeracy Methods at SMA. How , what and why we teach what we teach. Four cornerstones to effective numeracy learning. A sense of number Times tables Place value Patterns. A sense of number. What is ten?. Times Tables. MUST be learnt! Increase confidence

marcell-connor
Télécharger la présentation

Numeracy Methods at SMA

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Numeracy Methods at SMA How , what and why we teach what we teach

  2. Four cornerstones to effective numeracy learning • A sense of number • Times tables • Place value • Patterns

  3. A sense of number • What is ten?

  4. Times Tables • MUST be learnt! • Increase confidence • Form the foundation of many other skills (division)

  5. Place value • What do the numbers mean? • Includes a knowledge of multiplying and dividing by 10, 100, 1000 etc.

  6. Place Value • Place value allows children to partition, which is an essential skill needed in the development of techniques to solve all four number operations • 34 = 30 +4 • 456= 400 + 50 + 6 • 3456= 3000 + 400 + 50 + 6

  7. Place Value • X 10 DOES NOT simply mean add a zero! • X 10 means move to the left • ÷ 10 DOES NOT mean remove a zero! • ÷ 10 means move to the right!

  8. Patterns • Patterns in sequences and tables and shape • An ability to see patterns makes a lot of numeracy more accessible and indeed more enjoyable! • Fibonnaci sequence; patterns between tables, within tables

  9. Lots of methods and techniques • Idea is to provide children with a tool box of methods that also ensure children maintain a sense of number and place value • By year five, children should be able to choose from these ‘tools’ and to choose their EAR method • Efficient Appropriate Reliable • The only correct method is the one that gets the right answer • No point slaving at a technique if a child does not understand it and gets the wrong answer!

  10. Only one answer • Whilst making mistakes and discussing mistakes and misconceptions is essential to the learning process, the right answer is essential! • ‘I was almost right!’ is not good enough • An engineer who miscalculates the width of a bridge is no use to anyone!

  11. Attitude of parents is essential if children are to become effective learners in numeracy • http://www.nationalnumeracy.org.uk/why-are-attitudes-important/index.html

  12. The four operations

  13. Addition

  14. Mental Strategies for Addition Secure mental addition requires the ability to: • recall key number facts instantly (number bonds to 10, 20 & 100, doubles etc) and to apply these to similar calculations • recognise that addition can be done in any order and use this to add mentally different combinations of one and two digit numbers • partition two-digit numbers in different ways, including adding the tens and units separately before recombining • understand the language of addition including more than, sum, plus, greater than, total, altogether etc)

  15. Addition – Year 5 • Consolidate and use an effective written method when adding: Expanded form of addition, starting with the hundreds column first, then moving on to ones.. Using the words 'carry ten' or 'carry one hundred', not 'carry one‘ 369 369 + 138+ 138 400 17 90 90 + 17+ 400 507 507

  16. Addition – Year 5 • Consolidate and use an effective written method when adding. Moving onto compacted form of addition, where addition is started in the ones column and the carried number is shown at the top. Moving up to adding whole numbers with up to 5 digits. Using the words 'carry ten' or 'carry one hundred', not 'carry one‘ 1 1 1 47 369 + 59 + 138 106 507 These same strategies can be used when adding decimals, lining up all columns and the decimal point.

  17. Subtraction

  18. Subtraction – Year 5

  19. Subtraction – Year 5 • Consolidate written methods of subtraction: Moving onto compacted form of subtraction, where subtraction is started in the ones column and the borrowed number is shown at the top. Moving up to subtracting whole numbers with up to 5 digits. 60 + 14 6 14 70 + 4 70 + 4 74 - 20 + 7 - 20 + 7- 27 40 + 7 47 These same strategies can be used when subtracting decimals, lining up all columns and the decimal point.

  20. Multiplication

  21. Multiplication – Year 5 • Factors of numbers Children understand that the factors of a number are all the numbers that divide it exactly giving no remainder. For example, 4 is a factor of 12 because 12 can be divided by 4 with no remainder. The other factors of 12 are 1, 2, 3, 6 and 12. All the pairs of numbers that give the product 60. Take feedback. Establish that 60 has 12 factors:

  22. Multiplication – Year 5 • Multiplication/Division. ‘Buy one – get three free’ • Children rehearse multiplication facts to 12 × 12 and the related division facts. They discuss the facts that they can recall rapidly and strategies to help them derive those they struggle to recall, for example doubling 4 times-table facts to work out 8 times table facts. They respond to questions such as: The product of Two numbers is 24. What could the numbers be?

  23. Multiplication – Year 5 • Use strategies previously taught to help: Children use known multiplication facts and place value to find related facts. For example, they use 8 × 4 = 32 to find the answer to 80 × 4, explaining that 80 is ten times as big as 8 so the answer will be ten times 32, or 320. They predict the answer to 80 × 40, explaining how they worked this out. They find related division facts, e.g. recognising that 3 200 ÷ 400 = 8 because 8 × 400 = 3 200. Children use similar strategies and their understanding of inverse operations to find the missing numbers in calculations= such as: • 20 ×  = 600 • 2800 ÷ 70 =  •  ÷ 50 = 300

  24. Multiplication – Year 5 • Children multiply whole numbers by 10, 100 and 1 000. They answer questions like: How many times bigger than 60 is 6000? What did I multiply 6 by to get 600?

  25. Multiplication – Year 5 • Inverse operations and finding patterns between the operations. Multiplication Division 4 × 80 = 320 320 ÷ 80 = 4 4 × 800 = 3200 3200 ÷ 800 = 4 40 × 8 = 320 320 ÷ 8 = 40 40 × 80 = 3200 3200 ÷ 80 = 40 40 × 800 = 32 000 32 000 ÷ 800 = 40 400 × 8 = 3200 3200 ÷ 8 = 400 400 × 80 = 32 000 32 000 ÷ 80 = 400

  26. Multiplication – Year 5 • Multiply two-digit by one-digit numbers mentally by using partitioning. 26 × 7 = 20 × 7 and 6 × 7 = 140 and 42 = then putting the answers together to get 182. They use factors where appropriate to help them to multiply numbers efficiently, for example calculating 35 × 6 by working out 35 × 2 × 3.

  27. Multiplication – Year 5 • Children develop and refine written methods for multiplication. They move from expanded layouts (such as the grid method) towards a compact layout for HTU × U and TU × TU calculations. They suggest what they expect the approximate answer to be before starting a calculation and use this to check that their Answer sounds sensible. For example, 56 × 27 is approximately 60 × 30 = 1 800.

  28. Multiplication – Year 5 • Develop written methods of Multiplication:HTU × U, TU × TU 1 1 56 56 x 27x 27 1000 50 x 20 = 1000 1120 56 x 20 120 6 x 20 = 120 + 392 56 x 7 350 50 x 7 = 350 1512 42 6 x 7 = 42 1512 x 50 6 7 350 42 = 392

  29. Multiplication – Year 5 • Develop written methods of Multiplication:HTU × U, TU × TU 4 3 2 56 354 x 7x 6 392 2124

  30. Division

  31. Division – Year 5 • Multiplication/Division. Buy one, get three free Children rehearse multiplication facts to 12 × 12 and the related division facts. They discuss the facts that they can recall rapidly and strategies to help them derive those they struggle to recall, for example doubling 4 times-table facts to work out 8 times table facts. They respond to questions such as: The product of Two numbers is 24. What could the numbers be?

  32. Division – Year 5 • Children divide whole numbers by 10, 100 and 1 000. They answer questions like: How many times smaller than 5000 is 5? What did I divide 7 500 by to get 75?

  33. Division – Year 5 • Inverse operations and finding patterns between the operations. Multiplication Division 4 × 80 = 320 320 ÷ 80 = 4 4 × 800 = 3200 3200 ÷ 800 = 4 40 × 8 = 320 320 ÷ 8 = 40 40 × 80 = 3200 3200 ÷ 80 = 40 40 × 800 = 32 000 32 000 ÷ 800 = 40 400 × 8 = 3200 3200 ÷ 8 = 400 400 × 80 = 32 000 32 000 ÷ 80 = 400

  34. Division – Year 5 • Children understand that 6 ÷ 3 gives a different answer from 3 ÷ 6. They divide two-digit by one-digit numbers mentally also by using partitioning, finding 51 ÷ 3 by splitting 51 into 30 and 21, dividing each part by 3 and then putting the answers back together to get 17. They use factors where appropriate; for example, they work out 90 ÷ 6 by dividing 90 by 3 and then dividing the answer by 2..

  35. Division – Year 5 • Children extend their knowledge of division to short division of HTU by U, by repeated subtraction of multiples of the divisor (taking away chunks), aiming to subtract as few chunks as necessary. 84 ÷ 7 96 ÷ 7 84 96 - 70 (7x10) - 70 (7x10) 14 26 - 14 (7x2) - 21 (7 x 3) 0 5 = 12 = 13 R 5

  36. Division – Year 5 7 959 - 700 (7 x 100) 259 - 210 (7 x 30) 49 - 49 (7 x 7) = 137 0

  37. Numeracy at home • Essential that numeracy is seen as something that is happening all the time all around us. • Talking and listening to your child about their work in maths- parents are not expected to teach their child maths but rather be engaged in it with them. • Shopping, time, measurement, money, games and cooking all provide excellent opportunities for maths

  38. Useful websites • www.nationalnumeracy.org.uk • www.maths-games.org • http://resources.woodlands-junior.kent.sch.uk/maths/index.html • http://www.bbc.co.uk/bitesize/ks2/maths/

More Related