1. Math Talk Today’s exit card! Choose one of the examples below. Give an example of how you can help your students develop algebraic reasoning. 1. Use a variety of representations to show that… --even + even  _____? --odd + odd  _____? --odd + even  _____? 2. Use a variety of representations to show the Additive Properties— What happens when …. --You add zero to a number (identity) --You double a number (doubles) --You know fact family relationships (commutative) --You rearrange the order of the numbers to add (associative)

2. Math Talk: Homework Discussion What should a mathematical investigation involve? Give a specific example of an activity in the article that is related to helping students develop algebraic thinking.

3. Teaching Patterns, Functions, and Algebraic Thinking in Grades K-2 EDUC 226.3 Class 3: Linking Algebraic Representations October 14, 2013 Priscilla Nelson Andrienne Setorie

4. Today’s Agenda Homework Review-Developing Algebra-’Rithmetic in the Elementary Grades -Exit Cards -Blog Reminders -Teacher Voices -Ice Breaker-How Many Outfits? Teacher Share Presentations Math Talk: Representations from Van de Walle Math Stations: Playing with Squares- Grades: 1 & 2 Melting snow and ice- Grade: 1 [functions w/o formulas]

5. Remember our Class Norms No sidebars Cell phones on “silence” Be prepared We will start on time and end on time

6. Teachers’ Voices Excerpts from Exit Card #2 Children should be able to explain “why” or “how” to discuss answers. Getting the correct answer isn’t the most important thing. Learners are creators of their own learning. Students should have discussions about math and not just do problems and worksheets alone. Teachers should resist always evaluating children’s answers and allow them to make sense of the math. Students need to be able to generalize their thinking.

7. Ice Breaker How Many Outfits? You have 3 shirts: red, blue, and green; and 3 pairs of pants: red, blue, and green. Work with your number partner. Find all of the possible clothing combinations of shirts and pants. Use a variety of representations to show your work!

8. Teacher Share Technology Presentations Gladys Inoa http://www.arcademics.comhttp://www.arcademics.com Veronica Ikeda www.Mathplayground.com. Jeanette Spann http://www.softschools.com/ Elizabeth Dela Rosa www.k-5mathteachingresources.comwww.k-5mathteachingresources.com Chandra Alexander www.AAAMath.comwww.AAAMath.com Nicole Daniels http://www.abcya.comhttp://www.abcya.com

9. Linking Representations How might the representations from one activity apply to the representations in other activities?

10. Theory and Tools by Kat Meints Models are mental maps that help us to understand and represent our world by showing relationships (Fosnot & Jacob, 2007). Students need repeated opportunities to construct models. Action in the situation Representations of the situation Symbolic Representations Models

11. Math Talk: Van de Walle  Group 1RepresentationsPages 21-22  Group 2Manipulatives Pages 23-24  Group 3Invented StrategiesPages 210-212  Group 4Graphical RepresentationsPages 342- 348

12. Station 1:Playing With Squares 1.Your task is to build growing squares. -Start with one tile as your first square. -Continue building growing squares. -Represent your work in at least 2 ways. -State your observations. 2. Now build a square with one tile in the center. -Add more tiles around it. What do you notice? -Add another “layer” of tiles around it. What do you notice? -Represent your work in at least 2 different ways. and state your observations

13. Task 1: Growing Squares 11 24 39 416 525 Rule: x 2 Task 2: Growing Squares with a Tile in the Center Rule: (s+ s -1) 2

14. Students conducted an experiment comparing the rates at which packed snow, loose snow and crushed ice melt. They collected data every 30 minutes from 10:00 AM until 12noon. One group used loose snow, another group used packed snow and another group used ice. Each group started with 50 ml of ice/snow. After 30 minutes, loose snow was 20 mL, packed was 40 mL and ice was 35 mL/. 30 minutes later, loose snow was 15 mL, packed was 31mL and ice was 30 mL. 30 minutes later, loose was 14 mL, packed was 31 mL, and ice was 30 mL. At the final 30 minutes, loose was 14 mL, packed was 31 mL and ice was 30mL. Melting Snow and Ice (Graded)

15. Melting Snow and Ice Your task is to compare the rates at which snow and ice melts by representing the data in at least 2 different ways. Use at least 2 different representations. Write a statement analyzing the data.

16. Melting Snow and Ice TIMELoosePackedIce 10:00 a.m.50 mL 10:30 a.m.20 mL40 mL35 mL 11:00 a.m.15 mL31 mL30 mL 11:30 a.m.14 mL31 mL30 mL 12:00a.m.14 mL31 mL30 mL Use at least 2 different representations. Write a statement analyzing the data.

17. Instructional Strategies for Teaching Algebra in Elementary School (TCM May 2008)

18. Reflections: Points to Ponder 1.How do I help my students extend their understanding of patterns and the relationships among the elements of a pattern? 2. What learning experiences can I provide so that the students have experience exploring change? 3.What would be the greatest challenges for my students? How do I meet these challenges? 4.How do I know if my students have learned the concepts? What do I do if they have not learned? 5.What mathematical concepts did we use today?

19. BLOG: Questions to Ponder: 1.What did you encounter in the mathematics ? 2.What do you think your students will encounter? 3.What are the benefits of your students using a variety of representations to show their work? 4.Are there any drawbacks of using these representations?

20. Graded Work BLOG- 5 points REFLECTION- 10 points -Article: Instructional Strategies for Teaching Algebra in Elementary School (TCM May, 2008) Attendance and Participation- 5 points Math Classwork- 5 points

21. Math Solutions Math Talk Videoclip http://www.mathsolutions.com/index.cfm?pa ge=wp10&crid=553 http://www.mathsolutions.com/index.cfm?pa ge=wp10&crid=553 (Multiple Ways to Solve and Represent Problems video clip)

22. Technology Teacher Share Our October 21, 2013 Technology Teacher-Share Presenters are: Angelica, Claudia, June, Connie, Mitzie, Diane, Brittney, Lisa DID YOU REMEMBER TO… Sign up for your Teacher Share ? Turn in your EXIT Card Reflections ? Turn in your classwork ? See you next week for… Manipulatives and Technology!