1. Mental Math in Math Essentials 11
David McKillop, Presenter

2. Mental Math Outcomes B1 Know the multiplication and division facts
B2 Extend multiplication and division facts to products of tens, hundreds, and thousands by single-digit factors
B3 Estimate sums and differences
B4 Estimate products and quotients

3. Mental Math Outcomes
B5 Mentally calculate 25%, 33⅓%, and 66⅔% of quantities compatible with these percents
B6 Estimate percents of quantities

4. Why should students learn number facts?
They are the basis of all mental math strategies, and mental math is the most widely used form of computation in everyday life
Knowing facts is empowering
Facilitates the development of other math concepts

5. How is fact learning different from when I learned facts?
1. Facts are clustered in groups that can be retrieved by the same strategy.
Students can remember 6 to 8 strategies rather than 100 discrete facts.
3. Students achieve mastery of a group of facts employing one strategy before moving on to another group.

6. General Approach
Introduce a strategy using association, patterning, contexts, concrete materials, pictures – whatever it takes so students understand the logic of the strategy
Practice the facts that relate to this strategy, reducing wait time until a time of 3 seconds, or less, is achieved. Constantly discuss answers and strategies.
Integrate these facts with others learned by other strategies.
IT WILL TAKE TIME!

7. Facts with 2s: 2 x ? and ? X 2
Strategy: Connect to Doubles in Addition (Math Essentials 10)
Start with 2 x ?
Relate ? X 2 to 2 x ?

8. 17 facts

9. Practice the Facts
Webs
Dice games
Card games
Flash cards

10. Facts with 9s: ? X 9 and 9 x ?
Nifty Nines Strategy: Two Patterns -Decade of answer is one less than the number of 9s and the two digits of the answer sum to 9
9 x 9 = 81
8 x 9 = 72
7 x 9 = 63
6 x 9 = 54
5 x 9 = 45
4 x 9 = 36
3 x 9 = 27

11. 13 facts
30 Total

12. Practice the Facts
Calculator

13. Extend Nifty Nines To 10s, 100s, 1000s 4 x 90 9 x 60 5 x 900 9 x 700
To estimating
6.9 x $9
9 x $4.97
3.1 x $8.92
7 x $91.25
9 x $199
4 x $889
8.9 x $898.50

14. Extend Nifty Nines To division: 36 ÷ 9 54 ÷ 9 63 ÷ 9 27 ÷ 3 81 ÷ 9
45 ÷ 5

15. Facts with 5s
The Clock Strategy: The number of 5s is like the minute hand on the clock – it points to the answer. For example, for 4 x 5, the minute hand on 4 means 20 minutes; therefore, 4 x 5 = 20.

16. 13 new facts
43 Total

17. Practice Strategy Selection
Which facts can use The Clock Strategy?
Which facts can use the Nifty Nines Strategy?
Which facts can use the Doubles Strategy?
3 x 5
5 x 9
8 x 2
9 x 7
9 x 2
2 x 5
7 x 5
6 x 9

18. Extend Clock Facts To 10s, 100s, 1000s 5 x 80 7 x 50 5 x 400 6 x 500
To estimating
4.9 x $5
3 x $4.97
3.89 x $50
5 x $61.25
7 x $499
5 x $399
4.9 x $702.50

19. Extend Clock Facts To division: 25 ÷ 5 45 ÷ 5 30 ÷ 5 20 ÷ 4 15 ÷ 3
35 ÷ 5

20. Facts with 0s
The Tricky Zeros: All facts with a zero factor have a zero product.
(Often confused with addition facts with 0s)
If you have 6 plates with 0 cookies on each plate, how many cookies do you have?

21. 19 facts
62 Total

22. Facts with 1s
The No Change Facts: Facts with 1 as a factor have a product equal to the other factor.
If you have 3 plates with 1 cookie on each plate OR 1 plate with 3 cookies on it, you have 3 cookies.

23. 13 new facts
75 Total

24. Facts with 3s
The Double and One More Set Strategy. For example, for 3 x 6, think: 2 x 6 is 12 plus one more 6 is 18.

25. 9 new facts
84 Total

26. Extend Threes Facts To 10s, 100s, 1000s 5 x 80 7 x 50 5 x 400 6 x 500
To estimating
4.9 x $5
3 x $4.97
3.89 x $50
5 x $61.25
7 x $499
5 x $399
4.9 x $702.50

27. Extend Threes Facts To division: 18 ÷ 3 15 ÷ 3 12 ÷ 3 9 ÷ 3 21 ÷ 3
18 ÷ 6

28. Facts with 4s The Double-Double Strategy.
For example, for 4 x 6, think: double 6 is 12 and double 12 is 24.

29. 7 facts
91 Total

30. Extend Fours Facts To 10s, 100s, 1000s 4 x 40 7 x 40 8 x 400 4 x 600
To estimating
3.9 x $4
6 x $3.97
3.89 x $80
4 x $41.25
7 x $399
4 x $599
5.9 x $402.50

31. Extend Fours Facts To division: 16 ÷ 4 28 ÷ 4 20 ÷ 4 32 ÷ 4 12 ÷ 4
28 ÷ 7

32. The Last Nine Facts Using helping facts: 6 x 6 = 5 x 6 + 6
7 x 6 = 5 x x 6
6 x 8 = 5 x 8 + 8
7 x 8 = 5 x x 8
8 x 8 = 4 x 8 x 2
Some know 8 x 8 is 64 because of a chess board
What about 7 x 7?
6 x 6
6 x 7 and 7 x 6
6 x 8 and 8 x 6
7 x 7
7 x 8 and 8 x 7
8 x 8

33. The 100 Facts

34. Extend Last 9 Facts To 10s, 100s, 1000s 6 x 60 7 x 80 6 x 700 7 x 700
To estimating
6.8 x $7
6 x $5.97
7.89 x $80
7 x $61.25
6 x $799
8 x $699
5.9 x $702.50

35. Extend Last 9 Facts To division: 36 ÷ 6 42 ÷ 7 64 ÷ 8 49 ÷ 7 56 ÷ 8
42 ÷ 6

36. Practice the Facts Flash cards Bingo Dice Games Card Games Fact Bee
Calculators

37. B3 Estimate sums and differences
Using a front-end estimation strategy prior to using a calculator would enable students to get a “ball-park” solutions so they can be alert to the reasonableness of the calculator solutions.
Example: $ $ would have a “ball-park” estimate of $ $ or $

38. B3 Estimate sums and differences
In other situations, especially where exact answers will not be found, rounding to the highest place value and combining those rounded values would produce a good estimate.
Example: $ $ would be rounded to $ $ to get an estimate of $

39. About how many people live in the Maritime provinces
About how many people live in the Maritime provinces? In the Atlantic provinces? About how many more people live in Nova than in New Brunswick?
Nova Scotia
Prince Edward Island
Saskatchewan
Newfoundland
New Brunswick

40. Percents
B5 Mentally calculate 25%, 33 ⅓%, and 66 2/3% of quantities compatible with these percents
B6 Estimate percents of quantities

41. Visualization of Percent
Find 3% of $800.
Think: If $800 is distributed evenly in these 100 cells, each cell would have $8 – this is 1%. Therefore, there is 3 x $8 or $24 in 3 cells (3%).

42. Visualization of 25 Percent
Find 25% of $800.
Think: If $800 is distributed evenly in these 4 quadrants, each quadrant would have $800 ÷ 4 or $200. Therefore, 25% of $800 is $200.

43. Estmating Percent Estimate: 25% of $35 25% of $597 26% of $48

44. Visualization of 33⅓% Percent
Find 33⅓% of $69.
Think: $69 shared among three equal parts would be $69 ÷ 3 or $23. Therefore, 33⅓% of $69 is $23.

45. Visualization of Percent
Find 33⅓% of:
$96
$45
$120
$339
$930
$6309

46. Estimating Percent Estimate: 33⅓% of $67 33⅓% of $91 33% of $180

47. Visualization of 66⅔ Percent
Find 66⅔% of $36.
Think: $36 divided by 3 is $12, so each one-third is $12, Therefore, 2-thirds is $24, so 66⅔% of $36 is $24.

48. Visualization of 66⅔ Percent
Find 66⅔% of:
$24
$60
$120
$360
$660

49. Estimating Percent Estimate: 67% of $27 65% of $90 68% of $116

50. Parting words… It will take time. Build on successes.
Always discuss strategies.
Use mental math/estimation during all classes whenever you can.
Model estimation before every calculation you make!