1. Helping Children Master the Basic Facts Copyright © Allyn and Bacon 2010

2. Developmental Nature of Basic Fact Development Phase 1: Counting Strategies—using object counting Phase 2: Reasoning Strategies—using known information to logically determine an unknown combination Phase 3: Mastery—efficient production of answers

3. Copyright © Allyn and Bacon 2010 Guiding Strategy Development Story problems Reasoning strategies

4. Using Problem Structures P. 146

5. Reasoning Strategies ADDITION One more than and two more than Adding zero Using 5 as an anchor 10 facts Up Over 10 Doubles Near-doubles SUBTRACTION Subtraction as think-addition Down Over 10 Take from the 10

6. Number Sense, Mental Math, and Addition: 1. Use making and breaking apart numbers to find the sums. A. 9 + 5 B. 4 + 8 C. 7 + 6 D. 9 + 7 What are some other strategies for solving these problems?

7. Number Sense, Mental Math, and Addition: Find the sums. Use as many different methods as you can. A. 68 + 14 B. 27 + 49 C. 46 + 38D. 92 + 14 Did you try these? –Add tens, add ones, then combine –Move some to make tens –Add on tens then add ones (Number line) –Use a nice number and compensate

8. Number Sense, Mental Math, and Addition: 1. Use making and breaking apart numbers to find the sums. A. 398 + 99 B. 89 + 298 C. 425 + 199 What are some other strategies for solving these problems?

9. CROSS OUT SINGLES 1.Make a 3 x 3 grid. 2.Roll a die nine times. 3.Each time a number is rolled all players write that number in a square on their chart. 4.When nine squares are filled in, players find the sums of the rows, columns, and diagonal, and record these sums in the circles outside the grid. 5.If a sum appears in only one circle it must be crossed out. 6.The total of the sums that are not crossed out is the player’s score for that round. 342 234 635 © Math Solutions (Burns)

10. How Would You Solve? 1.35-18 = 2.140–35 = 3.298-99 = 4.1000–5 = 5.312-20=

12. Copyright © Allyn and Bacon 2010 Mastering the Basic Facts (Effective Drill) What to Do: Ask students to self- monitor Focus on self-improvement Drill in short segments Work on facts over time Involve families Make drill enjoyable Use technology Emphasize the importance of quick recall of facts What Not to Do: Use lengthy timed tests Use public comparisons of mastery Proceed through facts in order from 0 to 9 Move to memorization too soon Use facts as a barrier to good mathematics

14. Copyright © Allyn and Bacon 2010 Reasoning Strategies (Multiplication) Doubles Zeros and ones Nifty nines Using known facts to derive other facts

16. Multiplication Arrays

17. Copyright © Allyn and Bacon 2010 Fact Remediation 1.Recognize that more drill will not work. 2.Provide hope. 3.Inventory the known and unknown facts for each student in need. 4.Diagnose strengths and weaknesses. 5.Focus on reasoning strategies. 6.Build in success. 7.Provide engaging activities for drill.

18. Contextual Division Problems Ms. Wright has 28 students in her class. She wants to divide them into groups with 4 students in each group. How many groups will she have? Ms. Wright has 28 students in her class. She wants to divide them into 4 groups. How many students will be in each group?

19. Contextual Division Problems How could you distribute 231 M&Ms evenly among 5 containers? How could you evenly distribute 231 gum balls into packages of 5? How many packages could be filled?