1. Operations and Numerical Fluency 25 + 25 =   10 + 10 + 5 + 10 + 10 + 5 = 10, 20, 25, 35, 45, 50   20 + 20 + 5 + 5 = 40 + 10 = 50   I just thought of it as 2 quarters and 2 quarters is 50 cents. So, 25 + 25 = 50

2. Goals & Purposes  Increase teacher knowledge regarding the refinements of the TEKS relating to numerical fluency.  Increase teacher knowledge of composing and decomposing numbers.  Increase teacher knowledge of the use of strategies to teach numerical fluency for operations of whole numbers.  Develop an understanding of the use of metacognition in problem solving.

3. Defining Addition, Subtraction, Multiplication, and Division of Whole Numbers  At your table, develop a definition of addition, subtraction, multiplication, and division based on the TEKS for your particular grade level.  Small groups share their answer with the large group.

4. Solve the Following Problem   Mrs. Parks is buying ice-cream bars for the 17 dozen students at her school. The ice cream bars are packaged 10 to a box. What is an estimate of the number of boxes she has to buy so that each student gets at least 1 ice cream bar?

5. What am I supposed to find? Picture Table/Chart/List Number Sentence Explain how you derived your answer(s)? Write down your thought processes as you solve the following problem.

6. Let us come back together and share solutions and strategies with groups.

7. TEKS  Each group will be assigned a grade level.  Identify the TEKS in your grade level (K-5) that students must master in order to have success in solving this 5 th grade problem.  Are there any refinements that need to be identified? Add refined TEKS needed to teach this concept to the poster board.

8. Estimation  Measurement estimation  Quantity estimation  Computational estimation

9. Computational Estimation Computational estimation is the ability to quickly produce an approximate result for a computation that will be adequate for the situation.

10. Computational Estimation  Front-end Approach  Rounding Methods  Compatible Numbers

11. BREAK

13. Addition and Subtraction of Whole Numbers  Amy is 8 years old. She was assigned a school project regarding her family. She did not know the year that her grandmother was born, but did know that she just celebrated her 86 th birthday. How could Amy determine the year her grandmother was born?

14. Double Digit Addition and Subtraction Through the Use of Strategies  Reflect on how you have solved previous problems. Have you always used a traditional algorithm to solve the problem?  Think about how children use inventive strategies to solve problems.  How important is students’ metacognition of solving mathematical problems?

15. Relationships in Multiplication and Division 12 1x12 2x6 3x4 12x1 6x2 4x3

16. Relationships of Operations  Brainstorm at your table all the relationships between the operations of whole numbers.  Walk 7 steps from where you are now and share relationships with someone near you.  Take 7 more steps and repeat this procedure.  Share with the whole group relationships that were found.

17. When to Develop Automaticity  Once you have taught two strategies, drill based on those strategies.  Teach more strategies.  Automaticity is needed ONLY after students have developed a meaningful concept of addition, subtraction, multiplication, or division and they have also developed flexible and useful strategies for those operations.

18. How to Develop Automaticity  The competition is to be developed from within the child (intrinsic motivation), not against other children.  Using time as the goal.  Using number of problems as the goal.

19. BREAK