1. Goals for the session 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. Alberta Program of Studies 2007 By decreasing emphasis on rote calculation, drill and practice, and the size of numbers used in paper and pencil calculations, more time is available for concept development.

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

4. What do you think? Are basic facts important? Should we be having our students memorize them?

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

6. Why is this a topic of interest? The pendulum goes back and forth The discussion about memorizing versus fluency

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

8. +123456789 1 1+11+21+31+41+51+61+71+81+9 2 2+12+22+32+42+52+62+72+82+9 3 3+13+23+33+43+53+63+73+83+9 4 4+14+24+34+44+54+64+74+84+9 5 5+15+25+35+45+55+65+75+85+9 6 6+16+26+36+46+56+66+76+86+9 7 7+17+27+37+47+57+67+77+87+9 8 8+18+28+38+48+58+68+78+88+9 9 9+19+29+39+49+59+69+79+89+9 The Power of Thinking Strategies

9. +123456789 1 1+11+21+31+41+51+61+71+81+9 2 2+12+22+32+42+52+62+72+82+9 3 3+13+23+33+43+53+63+73+83+9 4 4+14+24+34+44+54+64+74+84+9 5 5+15+25+35+45+55+65+75+85+9 6 6+16+26+36+46+56+66+76+86+9 7 7+17+27+37+47+57+67+77+87+9 8 8+18+28+38+48+58+68+78+88+9 9 9+19+29+39+49+59+69+79+89+9 Count On

10. +123456789 1 1+11+21+31+41+51+61+71+81+9 2 2+12+22+32+42+52+62+72+82+9 3 3+13+23+33+43+53+63+73+83+9 4 4+14+24+34+44+54+64+74+84+9 5 5+15+25+35+45+55+65+75+85+9 6 6+16+26+36+46+56+66+76+86+9 7 7+17+27+37+47+57+67+77+87+9 8 8+18+28+38+48+58+68+78+88+9 9 9+19+29+39+49+59+69+79+89+9 Count On Doubles

11. +123456789 1 1+11+21+31+41+51+61+71+81+9 2 2+12+22+32+42+52+62+72+82+9 3 3+13+23+33+43+53+63+73+83+9 4 4+14+24+34+44+54+64+74+84+9 5 5+15+25+35+45+55+65+75+85+9 6 6+16+26+36+46+56+66+76+86+9 7 7+17+27+37+47+57+67+77+87+9 8 8+18+28+38+48+58+68+78+88+9 9 9+19+29+39+49+59+69+79+89+9 Count On Doubles Near Doubles

12. +123456789 1 1+11+21+31+41+51+61+71+81+9 2 2+12+22+32+42+52+62+72+82+9 3 3+13+23+33+43+53+63+73+83+9 4 4+14+24+34+44+54+64+74+84+9 5 5+15+25+35+45+55+65+75+85+9 6 6+16+26+36+46+56+66+76+86+9 7 7+17+27+37+47+57+67+77+87+9 8 8+18+28+38+48+58+68+78+88+9 9 9+19+29+39+49+59+69+79+89+9 Count On Doubles Near Doubles Names of 10

13. +123456789 1 1+11+21+31+41+51+61+71+81+9 2 2+12+22+32+42+52+62+72+82+9 3 3+13+23+33+43+53+63+73+83+9 4 4+14+24+34+44+54+64+74+84+9 5 5+15+25+35+45+55+65+75+85+9 6 6+16+26+36+46+56+66+76+86+9 7 7+17+27+37+47+57+67+77+87+9 8 8+18+28+38+48+58+68+78+88+9 9 9+19+29+39+49+59+69+79+89+9 Count On Doubles Near Doubles Names of 10 Names of 5

14. +123456789 1 1+11+21+31+41+51+61+71+81+9 2 2+12+22+32+42+52+62+72+82+9 3 3+13+23+33+43+53+63+73+83+9 4 4+14+24+34+44+54+64+74+84+9 5 5+15+25+35+45+55+65+75+85+9 6 6+16+26+36+46+56+66+76+86+9 7 7+17+27+37+47+57+67+77+87+9 8 8+18+28+38+48+58+68+78+88+9 9 9+19+29+39+49+59+69+79+89+9 Count On Doubles Near Doubles Names of 10 Nine strategies

15. +123456789 1 1+11+21+31+41+51+61+71+81+9 2 2+12+22+32+42+52+62+72+82+9 3 3+13+23+33+43+53+63+73+83+9 4 4+14+24+34+44+54+64+74+84+9 5 5+15+25+35+45+55+65+75+85+9 6 6+16+26+36+46+56+66+76+86+9 7 7+17+27+37+47+57+67+77+87+9 8 8+18+28+38+48+58+68+78+88+9 9 9+19+29+39+49+59+69+79+89+9 Count On Doubles Near Doubles Names of 10 Nine strategies Making 10

16. +123456789 1 1+11+21+31+41+51+61+71+81+9 2 2+12+22+32+42+52+62+72+82+9 3 3+13+23+33+43+53+63+73+83+9 4 4+14+24+34+44+54+64+74+84+9 5 5+15+25+35+45+55+65+75+85+9 6 6+16+26+36+46+56+66+76+86+9 7 7+17+27+37+47+57+67+77+87+9 8 8+18+28+38+48+58+68+78+88+9 9 9+19+29+39+49+59+69+79+89+9 Count On Doubles Near Doubles Names of 10 Nine strategies Making 10 Skip count by 2

17. +123456789 1 1+11+21+31+41+51+61+71+81+9 2 2+12+22+32+42+52+62+72+82+9 3 3+13+23+33+43+53+63+73+83+9 4 4+14+24+34+44+54+64+74+84+9 5 5+15+25+35+45+55+65+75+85+9 6 6+16+26+36+46+56+66+76+86+9 7 7+17+27+37+47+57+67+77+87+9 8 8+18+28+38+48+58+68+78+88+9 9 9+19+29+39+49+59+69+79+89+9 Count On Doubles Near Doubles Names of 10 Nine strategies Making 10 Skip count by 2 Number in Middle

18. +123456789 1 1+11+21+31+41+51+61+71+81+9 2 2+12+22+32+42+52+62+72+82+9 3 3+13+23+33+43+53+63+73+83+9 4 4+14+24+34+44+54+64+74+84+9 5 5+15+25+35+45+55+65+75+85+9 6 6+16+26+36+46+56+66+76+86+9 7 7+17+27+37+47+57+67+77+87+9 8 8+18+28+38+48+58+68+78+88+9 9 9+19+29+39+49+59+69+79+89+9 Count On Doubles Near Doubles Names of 10 Nine strategies Making 10 Skip count by 2 Number in Middle Commutativity

19. +123456789 1 1+11+21+31+41+51+61+71+81+9 2 2+12+22+32+42+52+62+72+82+9 3 3+13+23+33+43+53+63+73+83+9 4 4+14+24+34+44+54+64+74+84+9 5 5+15+25+35+45+55+65+75+85+9 6 6+16+26+36+46+56+66+76+86+9 7 7+17+27+37+47+57+67+77+87+9 8 8+18+28+38+48+58+68+78+88+9 9 9+19+29+39+49+59+69+79+89+9 Count On Doubles Near Doubles Names of 10 Nine strategies Making 10 Skip count by 2 Number in Middle Commutativity

20. Your thoughts….

21. 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

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

23. x012345678910 0 000000 1 0 2 0 3 0 4 0 5 0 6 7 8 9 Zero groups of

24. x012345678910 0 000000 1 012345 2 02 3 03 4 04 5 05 6 7 8 9 Zero groups of 1 group of

25. x012345678910 0 000000 1 012345 2 02 3 0315 4 0420 5 0510152025 6 7 8 9 10 Zero groups of 1 group of Counting by 5’s

26. x012345678910 0 000000 1 012345 2 02468 3 03615 4 04820 5 0510152025 6 7 8 9 10 Zero groups of 1 group of Counting by 5’s Counting by 2’s

27. x012345678910 0 000000 1 012345 2 02468 3 036915 4 0481620 5 0510152025 6 7 8 9 10 Zero groups of 1 group of Counting by 5’s Counting by 2’s Doubles

28. x012345678910 0 000000 1 012345 2 02468 3 03691215 4 048121620 5 0510152025 6 7 8 9 10 Zero groups of 1 group of Counting by 5’s Counting by 2’s Doubles Families

29. Important to remember Teach through families 2 x 3 = 6 3 x 2 = 6 6 ÷ 3 = 26 ÷ 2 = 3 Work the teaching of division right into the teaching of the multiplication….

30. Other strategies up to this point?

31. So that is it for Grade 3 Let’s move on to grade 4…… Expand what they already know

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33. x012345678910 0 00000000000 1 0123456789 2 02468 3 03691215 4 048121620 5 0510152025 6 06 7 07 8 08 9 09 10 0 Zero groups of 1 group of

34. x012345678910 0 00000000000 1 0123456789 2 02468 3 03691215 4 048121620 5 05101520253035404550 6 0630 7 0735 8 0840 9 0945 10 0 50 Zero groups of 1 group of Counting by 5’s

35. x012345678910 0 00000000000 1 0123456789 2 02468 1214161820 3 03691215 4 048121620 5 05101520253035404550 6 061230 7 071435 8 081640 9 091845 10 0 2050 Zero groups of 1 group of Counting by 5’s Counting by 2’s

36. x012345678910 0 00000000000 1 0123456789 2 02468 1214161820 3 0369121530 4 04812162040 5 05101520253035404550 6 06123060 7 07143570 8 08164080 9 09184590 10 0 2030405060708090100 Zero groups of 1 group of Counting by 5’s Counting by 2’s 10’s

37. A side note about tens 10 X 6 100 X 7 1000 X 8 10 x 5 30 x 5 40 x 7

38. Working with 9’s What do you know?

39. x012345678910 0 00000000000 1 0123456789 2 02468 1214161820 3 036912152730 4 0481216203640 5 05101520253035404550 6 0612305460 7 0714356370 8 0816407280 9 09182736455463728190 10 0 2030405060708090100 Zero groups of 1 group of Counting by 5’s Counting by 2’s 10’s 9’s

40. 09 18 27 36 45 54 63 72 81 90

41. The fours… Relate the 4’s to the 2’s… 2x1 2x24x1 2x3 2x44x2 – families here 2x5 2x64x3 2x7 2x84x4 2x9 2x104x5

42. x012345678910 0 00000000000 1 0123456789 2 02468 1214161820 3 036912152730 4 0481216202428323640 5 05101520253035404550 6 061224305460 7 071428356370 8 081632407280 9 09182736455463728190 10 0 2030405060708090100 Zero groups of 1 group of Counting by 5’s Counting by 2’s 10’s 9’s 4’s

43. x012345678910 0 00000000000 1 0123456789 2 02468 1214161820 3 036912152730 4 0481216202428323640 5 05101520253035404550 6 061224305460 7 071428356370 8 081632407280 9 09182736455463728190 10 0 2030405060708090100 Zero groups of 1 group of Counting by 5’s Counting by 2’s 10’s 9’s 4’s

44. x012345678910 0 00000000000 1 0123456789 2 02468 1214161820 3 036912152730 4 0481216202428323640 5 05101520253035404550 6 06122430365460 7 07142835496370 8 08163240647280 9 09182736455463728190 10 0 2030405060708090100 Zero groups of 1 group of Counting by 5’s Counting by 2’s 10’s 9’s 4’s Doubles

45. x012345678910 0 00000000000 1 0123456789 2 02468 1214161820 3 036912151821242730 4 0481216202428323640 5 05101520253035404550 6 06121824303642485460 7 07142128354249566370 8 08162432404856647280 9 09182736455463728190 10 0 2030405060708090100 Zero groups of 1 group of Counting by 5’s Counting by 2’s 10’s 9’s 4’s Doubles Families

46. x012345678910 0 00000000000 1 0123456789 2 02468 1214161820 3 036912151821242730 4 0481216202428323640 5 05101520253035404550 6 06121824303642485460 7 07142128354249566370 8 08162432404856647280 9 09182736455463728190 10 0 2030405060708090100 Zero groups of 1 group of Counting by 5’s Counting by 2’s 10’s 9’s 4’s Doubles Families

47. Questions?