2. 1 Mental Math in Math Essentials 10 David McKillop Coordinator of Math CCRSB

3. 2 Why Mental Math? Most widely used form of computation in everyday life Makes one alert to the reasonableness of answers generated by technology by estimating answers Is empowering Facilitates the development of other math concepts

4. 3 What mental math in Essentials 10?  Double facts in addition extended to 10s, 100s, and 1000s; corresponding subtraction facts ;multiplication by 2; division by 2; finding one half of; and finding 50% of  All addition facts and their extensions to 10s, 100s, and 100s  Finding 1%, 10%,15%, and 50% of “nice” numbers  Finding estimates of sums, differences, products, quotients, and percents as applications of the mental math strategies learned

5. 4 Double Addition Facts (By Association) 1 + 1 2 + 2 3 + 3 4 + 4 5 + 5 6 + 6 7 + 7 8 + 8 9 + 9

6. 5 Double Addition Facts Extended to 10s, 100s, and 1000s 1000 + 1000 200 + 200 3000 + 3000 40 + 40 5000 + 5000 600 + 600 70 + 70 8000 + 8000 900 + 900

7. 6 Double Addition Facts Applied to Estimation $3.89 + $3.99 $29.75 + $30.59 $499 + $489 $78 + $79 5800 km + 5900 km

8. 7 Double Addition Facts Used to Find Some Differences 14 - 7 8 - 4 16 - 8 18 - 9 1200 - 600 400 - 200 10 000 - 5000 60 - 30

9. 8 Double Addition Facts Used to Find Products Involving a Factor of 2 2 x 6 2 x 8 2 x 4 7 x 2 9 x 2 3 x 2 2 x 300 2 x 5000 2 x 60 80 x 2 700 x 2

10. 9 Double Addition Facts Used to Find Some Quotients with Divisors of 2 18  2 12  2 8  2 60  2 140  2 800  2 4000  2 16 000  2 1000  2 1800  2

11. 10 Double Addition Facts Used to Find Some Products Involving One-half ½ x 12 ½ x 6 ½ x 14 ½ x 18 ½ x 1000 ½ x 1600 ½ x 12 000 ½ x 180

12. 11 Double Addition Facts Used to Find Some Products Involving 50% 50% x 16 50% x 8 x 12 50% x 18 50% x 1400 50% x 600 50% x 180 50% x 16 000

13. 12 Double Addition Facts Used to Find A Variety of Estimates 50% x $17.89 50% x $1190 2 x $799 2 x $6.93 ½ x 7.9 km ½ x $15.89 $15 990  2 $38.99  2

14. 13 Add 0 Facts (No Change Strategy) 0 + 0 1 + 0; 0 + 1 2 + 0; 0 + 2 3 + 0; 0 + 3 4 + 0; 0 + 4 5 + 0; 0 + 5 6 + 0; 0 + 6 7 + 0; 0 + 7 8 + 0; 0 + 8 9 + 0; 0 + 9

15. 14 Add 1 Facts (By Association to Next Number) 2 + 1; 1 + 2 3 + 1; 1 + 3 4 + 1; 1 + 4 5 + 1; 1 + 5 6 + 1; 1 + 6 7 + 1; 1 + 7 8 + 1; 1 + 8 9 + 1; 1 + 9

16. 15 Add 1 Facts (Applied to 10s, 100s, 1000s and Estimation) 200 + 100 5000 + 1000 60 + 10 100 + 700 1000 + 9000 5.97 + 0.98 3.921 + 0.95 29.6 + 9.9 296 + 111

17. 16 1-Apart Facts (Double  1 Strategy) 2 + 3; 2 + 3 3 + 4; 4 + 3 4 + 5; 5 + 4 5 + 6; 6 + 5 6 + 7; 7 + 6 7 + 8; 8 + 7 8 + 9; 9 + 8

18. 17 1-Apart Facts (Applied to 10s, 100s, 1000s, and Estimation) 20 + 30 300 + 400 4000 + 5000 800 + 700 60 + 50 $6.03 + $7.06 $7.98 + $6.95 81.2 + 70.25 $199 + $298

19. 18 Add 2 Facts (Next Even/Odd Strategy) 4 + 2; 2 + 4 5 + 2; 2 + 5 6 + 2; 2 + 6 7 + 2; 2 + 7 8 + 2; 2 + 8 9 + 2; 2 + 9 1 + 2; 2 + 1 2 + 2 2 + 3; 3 + 2

20. 19 Add 2 Facts (Applied to 10s, 100s, 1000s, and Estimation) 400 + 200 5000 + 2000 300 + 200 70 + 20 20 + 80 6000 + 2000 $3.89 + $1.99 $7.92 + $1.98 $29.25 + $19.97 58.9 + 21.2 $698 + $197

21. 20 Add 9 Facts (Make-10 Strategy) 9 + 3; 3 + 9 9 + 4; 4 + 9 9 + 5; 5 + 9 9 + 6; 6 + 9 9 + 7; 7 + 9 9 + 8; 8 + 9 9 + 9

22. 21 Add 9 Facts (Applied to 10s, 100s, 1000s, and Estimation) 90 + 30 900 + 700 9000 + 6000 50 + 90 400 + 900 8.9 km + 4 km $9.03 + $6.99 $89.75 + $30.75 $905 + $495 $8.99 + $3.97

23. 22 Add 8 Facts (Make-10 Strategy) 8 + 3; 3 + 8 8 + 4; 4 + 8 8 + 5; 5 + 8 8 + 6; 6 + 8 7 + 8; 8 + 7

24. 23 Add 8 Facts (Applied to 10s, 100s, 1000s, and Estimation) 800 + 500 80 + 30 4000 + 8000 600 + 800 $8 + $2.97 $7.98 + $4 5.9 km + 7.9 km $789 + $605

25. 24 The Last 12 Facts (A Variety of Strategies) 5 + 3; 3 + 5 6 + 3; 3 + 6 6 + 4; 4 + 6 7 + 3; 3 + 7 7 + 4; 4 + 7 7 + 5; 5 + 7

26. 25 Mental Math: Per cent (The 1% Strategy) When a quantity is distributed equally among the 100 cells in this grid, the amount in each cell is 1% of this quantity. Therefore, divide a quantity by 100 to get 1%.

27. 26 Mental Math: Per cent (The 1% Strategy) For example, to find 1% of $800, divide $800 by 100 to get $8 in each cell which is 1%. So, 1% x $800 = $8. To find 3% of $800, you would just multiply $8 by 3 to get $24. So, 3% x $800 = $24.

28. 27 Mental Math: Per cent (The 1% Strategy) Find: 1% of $600 1% of $1200 3% of $900 4% of $500

29. 28 Mental Math: Per cent Applied to Estimation Estimate: 3% of $395 5% of $880 4.25% of $482 3.75% of $215

30. 29 Mental Math: Per cent (The 10% Strategy) Finding 10% of a quantity is like finding the amount in 10 cells of this grid. Since there are ten rows of 10, 10% can be found by dividing the quantity by 10.

31. 30 Mental Math: Per cent (The 10% Strategy) For example, to find 10% of $150, just divide $150 by 10 to get $15. Therefore, 10% x $150 = $15

32. 31 Mental Math: Per cent (The 10% Strategy) Find: 10% of $70 10% of $300 10% of $250 10% of $1200

33. 32 Mental Math: Per cent (Estimating 10% by rounding to the nearest “nice” number) Estimate: 10% of $38.75 10% of $72.35 10% of $289 10% of $137.89

34. 33 Mental Math: Per cent (The 15% Strategy) Finding 15% of a quantity is like finding the amount in 15 cells of this grid. Since 5% is half of 10%, you can find 15% by finding 10%, taking half of that amount, and adding it to the 10%.

35. 34 Mental Math: Per cent (The 15% Strategy) For example, to find 15% of $400, find 10% of $400 by dividing by 10 to get $40, take half of $40 to get $20, and add the $20 to the $40 to get a total of $60. Therefore, 15% x $400 = $60.

36. 35 Mental Math: Per cent (The 15% Strategy) Find 15% of each of the following: $40 $80 $120 $600

37. 36 Mental Math: Per cent (Estimate using the 15% Strategy) Estimate the 15% tax on each of the following costs: $61.25 $139 $198.75 $789

38. 37 Mental Math: Practising Strategies Short periods of rehearsal Fewer questions with more discussion Focus of “in the head” and not on pencil- and-paper Strategies rehearsed in isolation until mastered and then combined with previously learned strategies