2. (this is where I started)

3. (this is where I ended)

4.  “The ability to read, listen, think creatively, and communicate about problem situations, mathematical representations, and the validation of solutions will help students to develop and deepen their understanding of mathematics.” ( NCTM Standards)

5. No better way exists to learn mathematics than by attempting “to catch its complexities in the constraining structure of words.”

6.  Online  Books  Curriculum Coordinator  Other Teachers

8. 88-11 = 11 7 7x + 11 = 88 X=11 7x + 11 = 88 - 11 -11 7x = 77 7 7 x = 11 widgets

10. (2, 72) By graphing, I see that the intersection point is (2, 70). So in 2 hours we will have the same amount of cookies made, 70. X = 2 Y= 72 ____(blank)___________ Where the two lines cross. When the two equations are the same. At first you will make more cookies, but at 2 hours you both make 72 cookies. After that your friend will make the most cookies.

11. To write out an explanation or explain what their results mean students must know the vocabulary.

12.  A new term must be used between 6 -14 times before a student will know it.  Word Wall- continually build it and NEVER take any of it down  Flash Cards

13.  Math Vocabulary and Everyday English Vocabulary- NOT all words mean the same › What is the difference between 5 and 12?  12 – 5 = 7  5 is odd and 12 is even.

14. Graphic Organizers provide visual representations of concepts or ideas and can help students organize their thoughts.

15. Frayer Model DefinitionCharacteristics Examples Non-examples

16. Equation Definition A math statement that sets two expressions equal to one another. Characteristics ALWAYS has an = sign Could have numbers or variables and operation symbols Examples B = 3 y = mx + b 3z – 4 = 13 Non-examples 11x > 12 3x + 8 2

17. Problem: Solution: Explanation:

19. FIVESTEPFIVESTEP PROBLEMSOLVINGPROBLEMSOLVING

20. Summarize what you are asked to DO VO cabulary The work yo U do.

21. Part 1

22. Verbally saying what you are thinking when solving a problem

23.  By verbalizing what you are thinking while solving a problem, teachers are modeling how expert thinkers solve problems.  By having students think-aloud while they are solving a problem, teachers can see where the misconceptions lie.

24.  If students can verbally explain what they are doing and why they are doing it, they will be able to write down their explanations.

25.  You may need to begin by having Directed Think-Alouds for the students. You may need to use questions to direct the students if they become stuck or ensure of what to say.

27. Part 2

28. Math Log

29.  They provide a place for students to reflect or write down their thinking on the content covered in class.  They are not a journal, because journals are for personal or private feelings not focused on class content.

30.  They provide practice writing about a concept to let the student evaluate how well they know the concept.  They can be used at any point during a lesson: › Before › During › After

31. › Problematic Situations- Students write or guess potential solutions for the problem. › Yesterday’s News- Students have 5 minutes to write a note to a student explaining one idea from the previous class that they believe is important. › One-liners – Write one sentence about the importance of something they learned in the previous lesson.

32. › Fast Food for Thought- after explaining a concept or process have the students write a question that they still have about the topic and switch papers with their neighbor. Then answer the neighbors question. › Out of This World- You are an alien from another planet, who crashes to earth outside of school. You enter and your first stop is this classroom. Write down your observations of the lesson, teacher, and students in the class.

33. › Read the Instructions- Students write instructions for how to solve a problem or perform a skill they just learned in class. › The Last Word- Students write a letter to the teacher telling what they do not understand or what they need help with in the current unit.

34. Part 3 Take the shapes we used in the beginning of our activity and group them into three different groups. Each shape should fit into ONLY one group.

35. Prop. Terms Equi- angular Equi-lateral4 Sides3 SidesConvexOpp. Sides Par. Pentagon x Square XXXxX Triangle xX Rhombus XXxX Hexagon Regular Polygon XXx Rectangle xxxx

36. Khan Academy