1. 1 Overview of Class #13 Final Exam – questions & comments 1 ¾ ÷ ½ Long division Course evaluations/Break Basic Facts Closing

2. 2 Final Exam Exam questions –8 questions in the study guide –Actual exam questions (4 - 5) drawn from these, or parts of these –Numbers will vary –1-2 oral questions Thursday, December 11, 10 am - 12 pm, our classroom –Time is not an issue. –Room will be available from 9 - 1. (Optional) Study sessions –Thursday, December 4 (tonight), 7 - 10 pm –Sunday, December 7, 4 - 6 pm –Tuesday, December 9, 7 - 9 pm

3. 3 Study Guide Questions 8 questions in the study guide: 1.Model computation with materials 2.Represent multiplication with area model 3.Write or evaluate story problems for meaning 4.Compare manipulatives 5.Analyze student error and design what to do next 6.Choose numerical examples for particular topic –– easy, medium, difficult 7.Analyze video segment from classroom lesson 8.Reflect on own professional growth using work samples

4. 4 Practice with Meaning of Division –– Fraction Division 1. Calculate the answer. 2. Write a story problem, or describe a situation, that corresponds to 1 3/4 ÷ 1/2.

5. 5 I have two pizzas. My friend eats one quarter of one of the pizzas. I have one and three quarters pizzas left. Then I split it evenly between two of my other friends. Each person gets three and a half pieces of pizza. 1. What is wrong with this? 2. Write a story problem that correctly represents the division.

6. 6 Long Division Transition to dividing large numbers 1.Division as repeated subtraction 2.Using place value to make repeated subtraction more efficient 3.Recording The long division algorithm 1.Modeling meaning 2.Recording 3.Becoming efficient and fluent

7. 7 119 - 9 1 110 - 9 2 101 - 9 3 92 - 9 4 83 - 9 5 74 - 9 6 65 - 9 7 56 - 9 8 47 - 9 9 38 - 9 10 29 - 9 11 20 - 9 12 11 - 9 13 2 Division as Repeated Subtraction 119 ÷ 9 Subtract 9 repeatedly Result: 13 9s can be subtracted with 2 left over Measurement interpretation of division

8. 8 Division as Repeated Subtraction 94 ÷ 6 –work with partner –start with 94 unifix cubes –method of recording subtractions 346 ÷ 8 –Becoming more efficient by removing groups of the divisor

9. 9 Learning Basic Facts Why this is important What to avoid and be careful about What to do more of What to explore

10. 10 Why Basic Facts are Important With our place value numeration system (how we write numbers in terms of sums of multiples of powers of ten), all computation is reduced to operations with basic facts.

11. 11 Avoid: Competition Public displays of progress Equating mastery of math facts with general competence in math Prohibiting counting on fingers or using manipulatives Single expectation for entire class Assessment as instruction; using timing as the major mode of “training” Abandoning instruction

12. 12 Increase Use of: Strategic ways of analyzing and learning facts; use of patterns Individualized pacing for memorizing facts Naturalized, repetitive practice in games where use of math facts is authentic Drill that is engaging Situated problems that happen to make use of math facts Make use of inverses and “number families”

13. 13 Possibly Explore, with Caution: Mnemonic devices for memorization Use of songs, rap, poetry for memorizing Activities that students can do outside of class (e.g., flash cards) Computer drill activities

14. 14 Wrap Up: Questions or comments? Not collecting notebooks today --- will collect everyone’s after final Staying in touch Thanks for a great semester!