1. Goals for this presentation
Learn how the philosophical shift in the way we teach math affects the way we teach basic facts
Learn some effective strategies for teaching basic facts to students

2. Philosophical shift Focus on number sense
Focus on mental math and estimation

3. The Nature of Mathematics
Number Sense
Rote Memory
versus
committing isolated facts to memory one after another
drill and practice
Automaticity
relies on thinking, using relationships among the facts
focusing on relationships

4. What are the basic facts?
The Alberta Program of Studies defines them as:
Addition and Subtraction to 18
Multiplication and Division to 81

5. The Power of Thinking Strategies+ 1 2 3 4 5 6 7 8 9
1+1
1+2
1+3
1+4
1+5
1+6
1+7
1+8
1+9
2+1
2+2
2+3
2+4
2+5
2+6
2+7
2+8
2+9
3+1
3+2
3+3
3+4
3+5
3+6
3+7
3+8
3+9
4+1
4+2
4+3
4+4
4+5
4+6
4+7
4+8
4+9
5+1
5+2
5+3
5+4
5+5
5+6
5+7
5+8
5+9
6+1
6+2
6+3
6+4
6+5
6+6
6+7
6+8
6+9
7+1
7+2
7+3
7+4
7+5
7+6
7+7
7+8
7+9
8+1
8+2
8+3
8+4
8+5
8+6
8+7
8+8
8+9
9+1
9+2
9+3
9+4
9+5
9+6
9+7
9+8
9+9
The Power of Thinking Strategies

6. + 1 2 3 4 5 6 7 8 9
1+1
1+2
1+3
1+4
1+5
1+6
1+7
1+8
1+9
2+1
2+2
2+3
2+4
2+5
2+6
2+7
2+8
2+9
3+1
3+2
3+3
3+4
3+5
3+6
3+7
3+8
3+9
4+1
4+2
4+3
4+4
4+5
4+6
4+7
4+8
4+9
5+1
5+2
5+3
5+4
5+5
5+6
5+7
5+8
5+9
6+1
6+2
6+3
6+4
6+5
6+6
6+7
6+8
6+9
7+1
7+2
7+3
7+4
7+5
7+6
7+7
7+8
7+9
8+1
8+2
8+3
8+4
8+5
8+6
8+7
8+8
8+9
9+1
9+2
9+3
9+4
9+5
9+6
9+7
9+8
9+9
Count On

7. + 1 2 3 4 5 6 7 8 9 Doubles Count On 1+1 1+2 1+3 1+4 1+5 1+6 1+7 1+8
1+9
2+1
2+2
2+3
2+4
2+5
2+6
2+7
2+8
2+9
3+1
3+2
3+3
3+4
3+5
3+6
3+7
3+8
3+9
4+1
4+2
4+3
4+4
4+5
4+6
4+7
4+8
4+9
5+1
5+2
5+3
5+4
5+5
5+6
5+7
5+8
5+9
6+1
6+2
6+3
6+4
6+5
6+6
6+7
6+8
6+9
7+1
7+2
7+3
7+4
7+5
7+6
7+7
7+8
7+9
8+1
8+2
8+3
8+4
8+5
8+6
8+7
8+8
8+9
9+1
9+2
9+3
9+4
9+5
9+6
9+7
9+8
9+9
Count On
Doubles

8. + 1 2 3 4 5 6 7 8 9 Doubles Near Doubles Count On 1+1 1+2 1+3 1+4 1+5
1+6
1+7
1+8
1+9
2+1
2+2
2+3
2+4
2+5
2+6
2+7
2+8
2+9
3+1
3+2
3+3
3+4
3+5
3+6
3+7
3+8
3+9
4+1
4+2
4+3
4+4
4+5
4+6
4+7
4+8
4+9
5+1
5+2
5+3
5+4
5+5
5+6
5+7
5+8
5+9
6+1
6+2
6+3
6+4
6+5
6+6
6+7
6+8
6+9
7+1
7+2
7+3
7+4
7+5
7+6
7+7
7+8
7+9
8+1
8+2
8+3
8+4
8+5
8+6
8+7
8+8
8+9
9+1
9+2
9+3
9+4
9+5
9+6
9+7
9+8
9+9
Count On
Doubles
Near Doubles

9. + 1 2 3 4 5 6 7 8 9 Doubles Near Doubles Names of 10 Count On 1+1 1+2
1+3
1+4
1+5
1+6
1+7
1+8
1+9
2+1
2+2
2+3
2+4
2+5
2+6
2+7
2+8
2+9
3+1
3+2
3+3
3+4
3+5
3+6
3+7
3+8
3+9
4+1
4+2
4+3
4+4
4+5
4+6
4+7
4+8
4+9
5+1
5+2
5+3
5+4
5+5
5+6
5+7
5+8
5+9
6+1
6+2
6+3
6+4
6+5
6+6
6+7
6+8
6+9
7+1
7+2
7+3
7+4
7+5
7+6
7+7
7+8
7+9
8+1
8+2
8+3
8+4
8+5
8+6
8+7
8+8
8+9
9+1
9+2
9+3
9+4
9+5
9+6
9+7
9+8
9+9
Count On
Doubles
Near Doubles
Names of 10

10. + 1 2 3 4 5 6 7 8 9 Doubles Near Doubles Names of 10 Names of 5
1+1
1+2
1+3
1+4
1+5
1+6
1+7
1+8
1+9
2+1
2+2
2+3
2+4
2+5
2+6
2+7
2+8
2+9
3+1
3+2
3+3
3+4
3+5
3+6
3+7
3+8
3+9
4+1
4+2
4+3
4+4
4+5
4+6
4+7
4+8
4+9
5+1
5+2
5+3
5+4
5+5
5+6
5+7
5+8
5+9
6+1
6+2
6+3
6+4
6+5
6+6
6+7
6+8
6+9
7+1
7+2
7+3
7+4
7+5
7+6
7+7
7+8
7+9
8+1
8+2
8+3
8+4
8+5
8+6
8+7
8+8
8+9
9+1
9+2
9+3
9+4
9+5
9+6
9+7
9+8
9+9
Count On
Doubles
Near Doubles
Names of 10
Names of 5

11. + 1 2 3 4 5 6 7 8 9 Doubles Near Doubles Names of 10 Nine strategies
1+1
1+2
1+3
1+4
1+5
1+6
1+7
1+8
1+9
2+1
2+2
2+3
2+4
2+5
2+6
2+7
2+8
2+9
3+1
3+2
3+3
3+4
3+5
3+6
3+7
3+8
3+9
4+1
4+2
4+3
4+4
4+5
4+6
4+7
4+8
4+9
5+1
5+2
5+3
5+4
5+5
5+6
5+7
5+8
5+9
6+1
6+2
6+3
6+4
6+5
6+6
6+7
6+8
6+9
7+1
7+2
7+3
7+4
7+5
7+6
7+7
7+8
7+9
8+1
8+2
8+3
8+4
8+5
8+6
8+7
8+8
8+9
9+1
9+2
9+3
9+4
9+5
9+6
9+7
9+8
9+9
Count On
Doubles
Near Doubles
Names of 10
Nine strategies

12. + 1 2 3 4 5 6 7 8 9 Doubles Near Doubles Names of 10 Nine strategies
1+1
1+2
1+3
1+4
1+5
1+6
1+7
1+8
1+9
2+1
2+2
2+3
2+4
2+5
2+6
2+7
2+8
2+9
3+1
3+2
3+3
3+4
3+5
3+6
3+7
3+8
3+9
4+1
4+2
4+3
4+4
4+5
4+6
4+7
4+8
4+9
5+1
5+2
5+3
5+4
5+5
5+6
5+7
5+8
5+9
6+1
6+2
6+3
6+4
6+5
6+6
6+7
6+8
6+9
7+1
7+2
7+3
7+4
7+5
7+6
7+7
7+8
7+9
8+1
8+2
8+3
8+4
8+5
8+6
8+7
8+8
8+9
9+1
9+2
9+3
9+4
9+5
9+6
9+7
9+8
9+9
Count On
Doubles
Near Doubles
Names of 10
Nine strategies
Making 10

13. + 1 2 3 4 5 6 7 8 9 Doubles Near Doubles Names of 10 Nine strategies
1+1
1+2
1+3
1+4
1+5
1+6
1+7
1+8
1+9
2+1
2+2
2+3
2+4
2+5
2+6
2+7
2+8
2+9
3+1
3+2
3+3
3+4
3+5
3+6
3+7
3+8
3+9
4+1
4+2
4+3
4+4
4+5
4+6
4+7
4+8
4+9
5+1
5+2
5+3
5+4
5+5
5+6
5+7
5+8
5+9
6+1
6+2
6+3
6+4
6+5
6+6
6+7
6+8
6+9
7+1
7+2
7+3
7+4
7+5
7+6
7+7
7+8
7+9
8+1
8+2
8+3
8+4
8+5
8+6
8+7
8+8
8+9
9+1
9+2
9+3
9+4
9+5
9+6
9+7
9+8
9+9
Count On
Doubles
Near Doubles
Names of 10
Nine strategies
Making 10
Skip count by 2

14. + 1 2 3 4 5 6 7 8 9 Doubles Near Doubles Names of 10 Nine strategies
1+1
1+2
1+3
1+4
1+5
1+6
1+7
1+8
1+9
2+1
2+2
2+3
2+4
2+5
2+6
2+7
2+8
2+9
3+1
3+2
3+3
3+4
3+5
3+6
3+7
3+8
3+9
4+1
4+2
4+3
4+4
4+5
4+6
4+7
4+8
4+9
5+1
5+2
5+3
5+4
5+5
5+6
5+7
5+8
5+9
6+1
6+2
6+3
6+4
6+5
6+6
6+7
6+8
6+9
7+1
7+2
7+3
7+4
7+5
7+6
7+7
7+8
7+9
8+1
8+2
8+3
8+4
8+5
8+6
8+7
8+8
8+9
9+1
9+2
9+3
9+4
9+5
9+6
9+7
9+8
9+9
Count On
Doubles
Near Doubles
Names of 10
Nine strategies
Making 10
Skip count by 2
Number in Middle

15. + 1 2 3 4 5 6 7 8 9 Doubles Near Doubles Names of 10 Nine strategies
1+1
1+2
1+3
1+4
1+5
1+6
1+7
1+8
1+9
2+1
2+2
2+3
2+4
2+5
2+6
2+7
2+8
2+9
3+1
3+2
3+3
3+4
3+5
3+6
3+7
3+8
3+9
4+1
4+2
4+3
4+4
4+5
4+6
4+7
4+8
4+9
5+1
5+2
5+3
5+4
5+5
5+6
5+7
5+8
5+9
6+1
6+2
6+3
6+4
6+5
6+6
6+7
6+8
6+9
7+1
7+2
7+3
7+4
7+5
7+6
7+7
7+8
7+9
8+1
8+2
8+3
8+4
8+5
8+6
8+7
8+8
8+9
9+1
9+2
9+3
9+4
9+5
9+6
9+7
9+8
9+9
Count On
Doubles
Near Doubles
Names of 10
Nine strategies
Making 10
Skip count by 2
Number in Middle
Commutativity

16. + 1 2 3 4 5 6 7 8 9 Doubles Near Doubles Names of 10 Nine strategies
1+1
1+2
1+3
1+4
1+5
1+6
1+7
1+8
1+9
2+1
2+2
2+3
2+4
2+5
2+6
2+7
2+8
2+9
3+1
3+2
3+3
3+4
3+5
3+6
3+7
3+8
3+9
4+1
4+2
4+3
4+4
4+5
4+6
4+7
4+8
4+9
5+1
5+2
5+3
5+4
5+5
5+6
5+7
5+8
5+9
6+1
6+2
6+3
6+4
6+5
6+6
6+7
6+8
6+9
7+1
7+2
7+3
7+4
7+5
7+6
7+7
7+8
7+9
8+1
8+2
8+3
8+4
8+5
8+6
8+7
8+8
8+9
9+1
9+2
9+3
9+4
9+5
9+6
9+7
9+8
9+9
Count On
Doubles
Near Doubles
Names of 10
Nine strategies
Making 10
Skip count by 2
Number in Middle
Commutativity

17. Multiplication Talk about ‘groups of ‘ Talk about ‘families’
Give strategies for when we don’t know what to do
There is NOT an endless supply of basic facts

18. Start in grade 3 Learn up to 5 x 5
What do we already know?
Start in grade 3 Learn up to 5 x 5

19. x 1 2 3 4 5 6 7 8 9 10
Zero groups of

20. x 1 2 3 4 5 6 7 8 9 10
Zero groups of
1 group of

21. x 1 2 3 4 5 6 7 8 9 10 15 20 25 Zero groups of 1 group of1 2 3 4 5 6 7 8 9 10 15 20 25
Zero groups of
1 group of
Counting by 5’s

22. x 1 2 3 4 5 6 7 8 9 10 15 20 25 Zero groups of 1 group of1 2 3 4 5 6 7 8 9 10 15 20 25
Zero groups of
1 group of
Counting by 5’s
Counting by 2’s

23. x 1 2 3 4 5 6 7 8 9 10 15 16 20 25 Zero groups of 1 group of1 2 3 4 5 6 7 8 9 10 15 16 20 25
Zero groups of
1 group of
Counting by 5’s
Counting by 2’s
Doubles

24. x 1 2 3 4 5 6 7 8 9 10 12 15 16 20 25 Zero groups of 1 group of1 2 3 4 5 6 7 8 9 10 12 15 16 20 25
Zero groups of
1 group of
Counting by 5’s
Counting by 2’s
Doubles
Families

25. Important to remember Teach through families 2 x 3 = 6 3 x 2 = 6
6 ÷ 3 = ÷ 2 = 3
Work the teaching of division right into the teaching of the multiplication….

26. So that is it for Grade 3
Let’s move on to grade 4…… Coming Later!