1. Virginia Birch MFNERC Numeracy Specialist
Mental Math Strategies
Grade 1 to 4
Virginia Birch
MFNERC Numeracy Specialist

2. Overview Mental Math… what is it? Grade 1 to 3 Strategies
Indicators from the Provincial Report Card

3. Mental Math… what is it
Conceptual strategies that enhance flexible thinking and number sense and number skills (critical numeracy)
calculating mentally without the use of external memory aids.
provides a cornerstone for all estimation processes offering a variety of alternate algorithms and non-standard techniques for finding answers
K - Gr 8 Manitoba Curriculum Framework of Outcomes 2013
K - Gr 8 Manitoba Curriculum Framework of Outcomes 2013

4. K - Gr 8 Manitoba Curriculum Framework of Outcomes 2013
Mental Math… what is it
developing mental math skills and recalling math facts automatically
Facts become automatic for students through repeated exposure and practice.
When facts are automatic, students are no longer using strategies to retrieve them from memory.
K - Gr 8 Manitoba Curriculum Framework of Outcomes 2013

5. Mental Math… what is it
One of the Math Competencies for the Grade 3 and Grade 7 Math Assessment
(see report templates)

6. Mental Math:
Should not be timed. Students differ on the amount of time they need to process concepts.
Can be done daily approximately five minutes for a daily math routine.
Can be practiced with math games or learning centers where students can practice the strategies.
Create a Mental Math Bulletin Board
Create an Estimation Bulletin Board

7. The development of mental math strategies is greatly enhanced by sharing and discussion. Students should be given the freedom to adapt, combine, and invent their own strategies.

8. Math Tools you can use… Ten Frames Array Cards Base 10 Blocks Dominoes
100 – Chart
Finger Patterns
Number Line
Linking cubes
Going from concrete to pictorial to abstract…

9. Counting On – Grade 1
Concept: Addition Meaning: Students begin with a number and count on to get the sum. Students should begin to recognize that beginning with the larger of the two addends is generally most efficient. Example: for think is 8; think 5, 6, 7, 8

10. Practising the strategy…
2+7=
9+3=
3+12=

11. Counting Back – Grade 1
Concept: Subtraction Meaning: Students begin with the minuend and count back to find the difference. Example: for 6 – 2 think 6 – 1 – 1 is 4; think 6, 5, 4

12. Practising the Strategy
9-2= 10-3= 7-1=

13. Using One More – Gr 1, 2 Concept: Addition
Meaning: Starting from a known fact and adding one more.
Example:
for if you know is 12 and one more is 13

14. Practising the Strategy
5+6= 6+7= 8+9=

15. Using One Less - Gr 1, 2 Concept: Addition
Meaning: Starting from a known fact and taking one away.
Example:
for if you know
8 + 7 is 15 and one less is 14

16. Practising the strategy
7+6= 9+8= 6+5=

17. Making 10 – Gr 1, 2 Concept: Addition, Subtraction
Meaning: Students use combinations that add up to ten and can extend this to multiples of ten in later grades.
Example:
4 + ____ is 10
7 + ____ is 10;
so 23 + ____ is 30

18. Practising the strategy
28 +___ = ___= ___= 40

19. Starting from Known Doubles – Gr 1
Concept: Addition, Subtraction
Meaning:
Students need to work to know their doubles facts.
Example: is 4 and 4 – 2 is 2

20. Practising the strategy
3+3=__ , so ___-3=___ 9+9=__ , so ___-9=___ 8+8=__ , so ___-8=___

21. Using Addition to Subtract – Gr 1, 2, 3
Concept: Subtraction
Meaning:
This is a form of part-part-whole representation. Thinking of addition as:
part + part = whole
Thinking of subtraction as:
whole – part = part
Example: for 12 – 5
think 5 + ____ = 12
so 12 – 5 is 7

22. Practising the Strategy
13-7= ? , think 7 +___= = ? , think 6 +___= = ? , think 7+___= 15

23. The Zero Property of Addition – Gr 2
Concept: Addition, Subtraction
Meaning:
Knowing that adding 0 to an addend does not change its value, and taking 0 from a minuend does not change the value.
Example:
0 + 5 = 5;
11 – 0 = 11

24. Using Doubles – Gr 2, 3
Concept: Addition, Subtraction Meaning: Students learn doubles, and use this to extend facts: using doubles doubles plus one (or two) doubles minus one (or two) Example: for think is 12; think is 12 think – 2 is 12

25. Practising the strategy
for 6+ 8,think doubles for 6 + 8, think double 6 plus two for 6 + 8, think double 8 minus two

26. Building on Known Doubles – Gr 2, 3
Concept: Addition, Subtraction
Meaning: Students learn doubles, and use this to extend facts.
Example:
for 7 + 8
think is 14
so is is 15

27. Practising the Strategy
3+4= 7+6= 8+9=

28. Adding from Left to Right – Gr 3
Concept: Addition
Meaning: Using place value understanding to add 2-digit numerals.
Example: for
think and is or 58

29. Practising the Strategy
17+22= 26+21= 45+34=

30. Making 10 – Gr 3 Concept: Addition, Subtraction
Meaning: Students use combinations that add up to ten to calculate other math facts and can extend this to multiples of ten in later grades.
Example: for 8 + 5
think is
or 13

31. Practising the strategy
8+7= 7+9= 5+7=

32. Compensation – Gr 3
Concept: Addition, Subtraction Meaning: Using other known math facts and compensating. For example, adding 2 to an addend and taking 2 away from the sum. Example: for think – 2 is 60 – 2 or 58

33. Practising the strategy
47+22= 18+15= 39+17=

34. Commutative Property – Gr 3
Concept: Addition
Meaning:
Switching the order of the two numbers being added will not affect the sum.
Example:
4 + 3 is the same as
3 + 4

35. Compatible Numbers – Gr 3, 4
Concept: Addition, Subtraction
Meaning: Compatible numbers are friendly numbers (often associated with compatible numbers to 5 or 10).
Example: for students may think is 5 and 2 more makes 7

36. Practising the Strategy
4+7= 9+8= 7+8=

37. Array – Gr 3 Concept: Multiplication, Division
Meaning: Using an ordered arrangement to show multiplication or division (similar to area).
Example: for 3 x 4 think

for 12 ÷3 think

38. Practising the strategy
5x5= 3x4= 4x2=

39. Commutative Property – Gr 3
Concept: Multiplication
Meaning: Switching the order or the two numbers being multiplied will not affect the product.
Example:
4 x 5 is the same as
5 x 4

40. Skip Counting – Gr 3 Concept: Multiplication
Meaning: Using the concept of multiplication as a series of equal grouping to determine a product.
Example:
for 4 x 2
think 2, 4, 6, 8
so 4 x 2 is 8

41. Practising the Strategy
2x5= 3x4= 5x4=

42. Zero Property of Multiplication– Gr 4
Concept: Multiplication
Meaning: Multiplying a factor by zero will always result in zero.
Example: 30 x 0 is 0
0 x 15 is 0

43. Multiplicative Identity– Gr 4
Concept: Multiplication Meaning: Multiplying a factor by one will not change its value. Dividing a dividend by one will not change its value. Example: 1 x 12 is ÷ 1 is 21

44. Skip-Counting from a Known Fact– Gr 4, 5
Concept: Multiplication, Division
Meaning: Similar to the counting on strategy for addition. Using a known fact and skip counting forward or backward to determine the answer.
Example: for 3 x 8
think 3 x 5 is 15 and skip count by threes 15, 18, 21, 24

45. Practising the Strategy
4 x 7 =
6 x 8=
8 x 7=
9 x 8=

46. Doubling or Halving– Gr 4, 5
Concept: Multiplication, Division
Meaning: Using known facts and doubling or halving them to determine the answer.
Example: for 7 x 4,
think the double of 7 x 2 is 28
for 48 ÷ 6,
think the double of 24 ÷ 6 is 8

47. Practising the Strategy
8 x 4 = think double 8 x 2 = ___ 32 ÷ 4 = think double 16 ÷ 4 = ____

48. Using the Pattern for 9s- Gr 4
Concept: Multiplication, Division
Meaning: Knowing the first digit of the answer is one less than the non-nine factor and the sum of the product’s digits is nine.
Example: for 7 x 9
think one less than 7 is 6
and 6 plus 3 is nine,
so 7 x 9 is 63

49. Practising the Strategy
4 x 9 = 36
5 x 9 = 45
6 x 9 = 54
7 x 9 = 63
8 x 9 = 72

50. Repeated Doubling– Gr 4, 5 think 3 x 2 is 6, 6 x 2 is 12, 12 x 2 is 24
Concept: Multiplication
Meaning: Continually doubling to get to an answer.
Example: for 3 x 8,
think 3 x 2 is 6,
6 x 2 is 12,
12 x 2 is 24

51. Practising the Strategy
To find 8 X 8, first find 2 X 8, then double, then double again. 2 X 8 = 16 4 X 8 is double 2 X = 32 so, 4 X 8 = 32 8 X 8 is double 4 X = 64 so, 8 X 8 = 64

52. Using multiplication to divide - Gr 4
Concept: Division
Meaning: This is a form of part-part-whole representation. Thinking of addition as:
part x part = whole
Thinking of subtraction as:
whole ÷ part = part
Example: for 35 ÷ 7
think 7 x ____ = 35
so 35 ÷ 7 is 5

53. Practising the Strategy
36 ÷ 6 = Think 6 x ___ = ÷ 7 = Think 7 x ___ = 42

54. Distributive property – Gr 4, 5
Concept: Multiplication
Meaning: In arithmetic or algebra, when you distribute a factor across the brackets:
a x (b + c) = a x b + a x c
(a + b) x (c + d) = ac + ad + bc + bd
Example: for 2 x 154
think 2 x 100 plus 2 x 50 plus 2 x 4 is
or 308

55. Place a straw between two columns.
What does it now show?
a x (b + c) = a x b + a x c
Record it as 3 x 7 = 3 x x 5

56. 13 x 12 = (10 + 3) x (10 + 2) = (10 x 10) + (10 x 2) + (3 x 10) + (3 x 2)
(a + b) x (c + d) = ac + ad + bc + bd

57. How do you assess for mental math strategies?
Use checklists
Observe strategies students are using through games
Make anecdotal notes while conversing with a student
Collect student sample work

58. Indicators from the Provincial Report Card (Gr 1 to 8)
Determines an answer using multiple mental math strategies
Applies mental math strategies that are efficient, accurate, and flexible
Makes a reasonable estimate of value or quantity using benchmarks and referents.
Uses estimation to make mathematical judgments in daily life.
Provincial Report Card Document Pg. 43