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Mental Computation

Mental Computation. Adapted from Bern Long and Angela Rogers presentation , 2013 K . Chiodi. What is mental computation?. Discuss with the person next to you what you think mental computation involves? When should mental computation be taught?. What is mental computation?.

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Mental Computation

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  1. Mental Computation Adapted from Bern Long and Angela Rogers presentation, 2013 K. Chiodi

  2. What is mental computation? • Discuss with the person next to you what you think mental computation involves? • When should mental computation be taught?

  3. What is mental computation? • Mental computation is a calculation performed entirely in the head, with only the answer being written (McIntosh, 2005) • Reading: Mental Computation and Estimation Read and then discuss at your table Victoria Department of Education and Early Childhood Development, 2009 • Resource: Mental Computation: A Strategies Approach Alistair McIntosh, 2004

  4. How are you teaching mental computation in your classroom?

  5. Mental Computation Vs. Mental Arithmetic • Mental computation is based on understanding. • Mental arithmetic is based on speed and accuracy related to memory. Research by Biggs (1967) revealed that: “Allocation of time to mental arithmetic bore no relation to attainment” “In other words, these daily speed and accuracy tests did not make the children noticeably more competent, but it did make them slightly more neurotic about numbers” (McIntosh, 2004, 1)

  6. Mental Computation Vs. Mental Arithmetic • Warm Up activity using the Westwood Addition and Subtraction test.

  7. How do we teach mental computation? • Introduce and make explicit the strategies we use to help us complete mental computations. • Memorisation of some basic facts required. • It is certainly desirable for children to know the addition facts to 20. • Mental computation strategies must be efficient and always allow us to arrive at the correct answer. • Strategies are necessary because they allow students not only to calculate simple 1-digit facts but also to calculate much bigger equations e.g. 6 + 4 …….. 66 + 24

  8. Mental Computation in the National Curriculum

  9. The Addition and Subtraction strategies to be taught F – 6

  10. 2. Count on 0, 1, 2, 3 You can use your fingers to count on 0, 1, 2, 3 • 3+0=3 • 3+1=4 • 3+2=5 • 3+3=6 (also a double)

  11. Count on 1, 2, 3Using the single digit strategies year 3-6 move to: • Add 1,2,3 to a multi digit no. e.g. 3+35= • Add 10, 20, 30 to a multiple of 10 up to 90. e.g. 80+30= • Add 10, 20, 30 to a multi digit number e.g. 34+30= • Add 100, 200, 300 to a hundreds number • E.g. 500+200= • Add 100, 200, 300 to a multi digit number e.g. 34+300 • Add 1000, 2000, 3000 to a single digit number • E.g. 3 000+9= • Add 1000, 2000, 3000 to a multi digit number e.g. 41+2 000=

  12. 3. Spin Arounds (commutativity) • If you spin around addition equations you get the same answer. • This shows children the commutativity of addition equations 2 + 4 =6 4 + 2 = 6

  13. 3. Spin AroundsYear 3-6 move to: • Single digit with multi-digit • E.g. 4+64=64+4 • Multi-digit with multi-digit • E.g. 97+123=123+97

  14. 4. Doubles • Start with real world • We need to learn these doubles. • 1+1=2 6+6=12 • 2+2=4 7+7=14 • 3+3=6 8+8=16 • 4+4=8 9+9=18 • 5+5=10 10+10=20

  15. Doubles Using single digit strategiesyear 3-6 move to: • Double multiples of 10 up to 90 e.g. 50+50 Think… 5 tens+5 tens= 10 tens= 100 • Double multiples of 100 up to 900 e.g. 600+600= Think… 6 hundred+6 hundred= 12 hundred= 1 200 • Double multiples of 1 000 up to 9 000 e.g. 6 000+6 000 Think… 6 thousand+6 thousand=12 thousand= 12 00

  16. Doubles Using single digit strategiesyear 3-6 move to: • Use doubles strategy with multi-digit and single digit numbers e.g. 64+4 • Use doubles strategy when adding multi-digit with multi-digit 64+24 356+36

  17. 5. Near Doubles • If we remember the doubles, we can work out these sums. • 6+7=13 • 5+6=11 • 4+3=7 • 9+8=17

  18. Near Doubles Using single digit strategiesyear 3-6 move to: • Near doubles with multiples of 10 up to 90 e.g. 50+60 Think… 5 tens +5tens is tens and 1 more ten is 11 tens=110 • Near doubles with multiples of 100 to 900 e.g. 400+500 • Near doubles with multiples of 1000 up to 9000 e.g. 7000+6000 • Use near doubles strategy with multi-digit and single digit numbers e.g. 64+5 • Use near doubles strategy when adding multi-digit with multi-digit 64+25 356+37

  19. 6. Tens Facts • These equations add to 10. • 1+9=10 9+1=10 • 2+8=10 8+2=10 • 3+7=10 7+3=10 • 4+6=10 6+4=10 • 5+5=10 5+5=10

  20. Tens factsUsing single digit strategiesyear 3-6 move to: • Tens facts with single digits that add to 20 E.g. 6+14 • Tens facts with multiples of 10 that add to 100 E.g. 60+40 • Tens facts with multiples of 100 that add to 1000 E.g. 200+800 • Tens facts with multiples of 1000 that add to 10 000 E.g. 4000+6000 • Tens facts with single digit that add with multi digit numbers E.g. 6+34 • Tens facts with multi digit with multi digit E.g. 64+36 • 129+211

  21. 7. Bridging Ten • Seven, Eight, Nine are close to Ten. • 9+2=11 8+6=14 7+6=13 • 9+3=12 8+7=15 7+5=12 • 9+4=13 8+8=16 7+4=11

  22. Bridging 10Using single digit strategies year 3-6 move to: • Bridging with multiples of 10 e.g. 40+90 think…4 tens +9 tens is 13 tens = 130 400+900 4000+9000 • Bridging single digit numbers with multi digit numbers • E.g. 43+9 • Bridging multi digit numbers with multi-digit numbers e.g. 43+59 256+349

  23. 8. Adding Ten • When we add ten, the ones number stays the same. • 2+10=12 6+10=16 • 3+10=13 7+10=17 • 4+10=14 8+10=18 • 5+10=15 9+10=19

  24. Adding 10Using single digit strategies year 3-6 move to: • Add 10 to multi-digit numbers e.g. 10+25 10+257 • Add 100 to single digit e.g. 100+5 • Add 100 to multi-digit e.g. 100+27 • Add 1000 to single digit e.g. 1 000+6= • Add 1000 to multi-digit e.g. 56+1 000

  25. Important to note! • To teach with understanding all strategies must be taught using visual aids and at any time when students are experiencing difficulties teachers must return to visual aids e.g. tens frames, bead strings, place value cards etc.

  26. Strategy Game Bingo! • 2 dice are rolled • Write the number sentence on your playing board that corresponds with the strategy you used to work out the answer • The player to fill up their playing board first calls ‘Bingo’ and reads out their answers

  27. Subtraction: Basic Facts

  28. 1. Count Back 0, 1, 2, 3 • You can count back 0, 1, 2, 3 using your fingers or in your head • 5-2=3 • 6-1=5

  29. Count down to: • Beginning at the total, count down to the number being taken away. The answer is the number of steps this takes. For example, 18-13 start at 18 and count down to 13, 17, 16, 15, 14, 13= 5 numbers counted back Count up from: • Beginning at the number being taken away, count up to the total. The answer is the number of steps this takes. For example, 21-17 start at 17 and count up to 21. 18, 19, 20, 21 = 4 numbers counted up

  30. Tens Facts • Tens facts can help us work out the answer when we subtract from ten. • E.g.. 10=5=5 • 10-6=4

  31. 3. Doubles • If you know 6+6=12, then you also know 12-6=6 • E.g.: 4+4=8 so 8-4=4 • 10+10=20 so 20-10=10

  32. 4. Subtract 10 • You can take away the ones number and it leaves you with just the tens. • E.g.: 13-3=10 • 25-5=20

  33. 5. Bridging Ten • Count back to the nearest tens number, then its easy to take away what is left. • E.g.. 11-3= • First do 11-1=10 • Then 10-2=8 (tens fact)

  34. 6. Near Doubles • If you know the doubles the near doubles can also help. • E.g.. 12-7= • I know 12-6 (double)=6 • Take one more = 5

  35. While you play… Reflect on these Mental Computation Questions (Brian Tickle)

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