Middle School Mathematics Initiative

1. Middle School Mathematics Initiative Linda Lucey, Ph.D Senior Associate International Center for Leadership in Education

2. Gold Seal Lesson Agenda • 1. Creating a Gold Seal Lesson • 2. Process of Editing a Gold Seal Lesson • 3. Performance Task • 4. You become the content editor! • 5. Review your lessons

3. Steps to Create a Gold Seal Lesson • Review the Rigor/Relevance Framework • Begin with a Big Idea • Find an idea • Brainstorm real-world situations • Research the idea • Develop the lesson

4. A GOLD-SEAL LESSON HAS: RIGOR AND RELEVANCE

5. THAT SOUNDS INTERESTING, BUT MY STUDENTS NEED TO PASS THE FCAT!!

6. MY KIDS TAKE SO MUCH CLASS TIME JUST TO MASTER THE BASIC CONCEPTS!!

7. IF I MAKE MY LESSONS MORE RIGOROUS, MY STUDENTS WILL ALL FAIL!!

8. BESIDES, MAKING GOLD-SEAL LESSONS SOUNDS HARD!! USING THE TEXTBOOK IS EASIER.

9. PRESSURES: • TIME • DIVERSE LEARNERS • EMPHASIS ON TESTING • REMEDIATION • LITERACY • NUMERACY

10. BENEFITS: • INCREASE UNDERSTANDING • MAXIMIZE TIME ON TASK • MINIMIZE RE-TEACHING

11. RIGOR MEANS FRAMING LESSONS AT THE HIGH END OF THE KNOWLEDGE TAXONOMY. EVALUATION SYNTHESIS ANALYSIS APPLICATION COMPREHENSION KNOWLEDGE

12. A LESSON WITH RIGOR ASKS STUDENTS TO: EXAMINE PRODUCE CLASSIFY DEDUCE GENERATE ASSESS PRIORITIZE CREATE SCRUTINIZE DECIDE

13. Math Teachers Beware! • Let x= 4 and y = 3 10x – 2xy Evaluate

14. RELEVANCE IS THE PURPOSE OF THE LEARNING: ACQUIRE KNOWLEDGE APPLY KNOWLEDGE INTERDISCIPLINARY REAL WORLD PREDICTABLE REAL WORLD UNPREDICTABLE

15. A LESSON WITH RELEVANCE ASKS STUDENTS TO: USE THEIR KNOWLEDGE TO TACKLE REAL-WORLD PROBLEMS THAT HAVE MORE THAN ONE SOLUTION.

16. A PROCESS FOR EDITING A GOLD-SEAL LESSON PERFORMANCE TASK — Overview 1.a. Plot the following points on your coordinate system. Remember that the first coordinate of the pair names a position going right or left in the horizontal direction, and the second coordinate names a position going up or down in the vertical direction. (1,1), (5,1),(6,2),(7.2),(7,1)(8,1),(9,2) (9,4),(7,4),(6,5),(5,5),(1,3),(0,3),(1,1) b. Connect the points in the order they are shown in 1a. What is the result? c. Add -10 to the first coordinate of each point. What happens? Add 2 to the first coordinate and add -5 to the second coordinate of each point. What happens? e. What should you do to the coordinates if you want to move the drawing up three units and to the right five units?

17. A PROCESS FOR EDITING A GOLD-SEAL LESSON REVIEW THE LESSON IDEA – Plot a picture with given coordinates. Add the same number to the x-coordinate and re-plot the figure. Observe the translation effect.

18. A PROCESS FOR EDITING A GOLD-SEAL LESSON BRAINSTORM REAL-LIFE SITUATIONS THAT USE TRANSLATION. SEARCH THE INTERNET FOR IDEAS. Marching band formations? Flip book animation?

20. What Is Cartoon Rendering? Cartoon rendering (sometimes referred to as cel-shading) has two major constituents: painting and inking. In the traditional sense, painting is filling a cartoon object with areas of color. A simple cartoon will use solid colors for different objects (flat-shading), but more complex cartoons use two or even three colors for each material. This is often called stepped-shading because the color "steps" dramatically from the shadow color to the highlight color. The stepped-shading effect looks quite different from realistic rendering techniques as there isn't a smooth gradient between the shadowed and highlighted areas of an object.

21. Game Programming Beginners Guideby Dave Astle I often get asked how someone with little or no programming experience can get started in game development. I will walk you through the things you need to do to get to the point that you can make your own games. The first thing you will need to do is to choose a language to program in. You have a lot of choices, including Basic, Pascal, C, C++, Java, etc. I'm going to recommend starting with C and C++. Some people will say that those languages are too advanced for beginners, but because I started with C++ myself, I tend to disagree. In addition, C/C++ is the most widely used language today, so you will beable to find a wealth of resources and help.

22. A PROCESS FOR EDITING A GOLD-SEAL LESSON USE THE VERB LIST TO FRAME AN ACTIVITY THAT IS HIGH IN RIGOR. Create, judge, evaluate, generate, examine, decide, produce, assess, prioritize, classify . . .

23. A PROCESS FOR EDITING A GOLD-SEAL LESSON THINK OF AN ACTIVITY THAT IS INTERDISCIPLINARY OR BASED ON THE REAL WORLD AND HAS MORE THAN A SINGLE SOLUTION. Make sure it relates to the learning standard!!

24. A PROCESS FOR EDITING A GOLD-SEAL LESSON USE AN ASSESSMENT METHOD THAT IS BASED ON EVIDENCE OF STUDENT LEARNING. Often, this means to create a rubric.

25. OPERATIONS & COORDINATES Plot the following points on your coordinate system. Remember that the first coordinate of the pair names a position going right or left in the horizontal direction, and the second coordinate names a position going up or down in the vertical direction. Connect the points in the order shown. You should see a picture of a wooden shoe. (1,1) (5,1) (6,2) (7,2) (7,1) (8,1) (9,2) (9,4) (7,4) (6,5) (5,5) (1,3) (0,3) (1,1) 1. KNOWLEDGE Add -10 to the first coordinate of each point in the list shown in a. Write the coordinates, then plot the figure on the same set of axes as used for “a”. Use a different colored pencil.

26. FLIP BOOKS

27. FLIP BOOK ANIMATION Learn how mathematics can be used to animate cartoon figures – it’s all about translation! • First you must learn a little about the mathematics involved. On a sheet of graph paper, draw a large set of coordinate axes. Label the x and y-axes and label some points. • a) Plot the following points on your coordinate system. Remember that the first coordinate of the pair names a position going right or left in the horizontal direction, and the second coordinate names a position going up or down in the vertical direction. Connect the points in the order shown. You should see a picture of a wooden shoe. • (1,1) (5,1) (6,2) (7,2) (7,1) (8,1) (9,2) (9,4) (7,4) (6,5) (5,5) (1,3) (0,3) (1,1) 1. KNOWLEDGE

28. FLIP BOOK ANIMATION Learn how mathematics can be used to animate cartoon figures – it’s all about translation! 2. EXPLAIN b) Add -10 to the first coordinate of each point in the list shown in a. Write the coordinates, then plot the figure on the same set of axes as used for “a”. Use a different colored pencil. Write a sentence or two to describe what happened to the wooden shoe image:

29. FLIP BOOK ANIMATION Learn how mathematics can be used to animate cartoon figures – it’s all about translation! • Add 2 to the first coordinate and add -5 to the second coordinate of each point. Write the new coordinates on the lines below, then plot the points on the same set of axes, using a third colored pencil. • Write a sentence or two to describe what happened to the original wooden shoe image:

30. FLIP BOOK ANIMATION Learn how mathematics can be used to animate cartoon figures – it’s all about translation! 3. RELATE d) How should the coordinates be changed if you want to move the drawing up three units and to the right five units?

31. FLIP BOOK ANIMATION Learn how mathematics can be used to animate cartoon figures – it’s all about translation! 5. DEVELOP e) Work with a partner to clearly write a set of just three rules that a person could use to translate a figure vertically, horizontally or diagonally.

32. Florida Middle School Mathematics Initiative | International Center for Leadership in Education Integrate the web Lesson 1: The Infernal Bouncing Ball.NOTE: I wrote this tutorial in 2000, and intended it for students learning traditional, hand-drawn animation. Nevertheless, the principles can be adapted to Flash or 3D animation. The main tutorial page is here (there's a walk cycle tutorial, and I'll be adding Flash lessons soon).This exercise will teach you the most important principles of animation, namely: Arcs.Timing/Spacing.Squash and Stretch.Volume. This is the first lesson taught to any animation student. You can pay through the nose to learn it at a school, but I am giving it to you for free, so behold! Look at the bouncing ball scene below:

33. 2a) Now you will be making a FLIP BOOK to animate a point. The point will look like it is rolling across a table and falling off of the edge onto the floor. Once you learn how to animate a simple shape like a point, you will be able to use this technique to animate more complicated figures. There are two websites that do a good job of explaining the first lesson that a beginning animator is taught. Visit these websites before you begin your own animation experiment in 2b: http://www.idleworm.com/how/anm/01b/bball.shtml http://www.cartoonster.com/ We will be using translation to animate our “ball”. The websites referenced above did not use our strict mathematical definition of translation to animate their balls. Write two reasons why the previous sentence is a true statement. 4. INSPECT

34. (7, 0) (7, 0) (6, 1) (5.5, 0) (5.5, 1) (5.5, 1.8) GIVE STUDENTS A WORKSHEET ABOUT ANIMATING A BALL USING GIVEN COORDINATES.

36. ASSIGNMENT: • Create a flip book that uses one or more transformations to animate an object. • Show your flip book to your group. Explain the transformations used. • The group judges whether the animation actually used that transformation. 5. CREATE REAL-WORLD UNPREDICTABLE 2. EXPLAIN 6. JUDGE

37. ASSESSMENT: RUBRIC Score each of the following characteristics on a scale of 4 to 0, where 4 = surpasses expectations; 3 = high quality performance; 2 = satisfactory performance; 1 = minimum quality performance; 0 = does not meet expectations.

38. ASSESSMENT: RUBRIC • The student is able to accurately plot points in the coordinate plane. • Evidence shows that the first wooden shoe was plotted correctly. • Evidence shows that the second and third wooden shoes were plotted correctly.

39. ASSESSMENT: RUBRIC • The student can describe the relationship between translating a point and the changing coordinates of the point. • Evidence of this is provided in the answer to 1d. • Evidence of this is provided in the answer to 1e

40. ASSESSMENT: RUBRIC • The student can apply transformation concepts to animate a shape using a flip book. • The flip book is complete and done on time. • The flip book actually does animate a figure using transformation.

41. Performance Task • Includes an overview and a description. • The overview is a description of how a student is expected to demonstrate learning (understanding, knowledge and skills). The task may be a product, performance of extended writing that requires rigorous thinking and relevant application. It is usually written in the third person describing the learning to other educators. • The description is the teacher procedures, including instructional strategies, and literacy strategies.

42. The overview includes: • Student work that will be produced or performed • Specific learning context • Whether group or individual • Resources students will be provided or have to acquire • Setting where students will complete the work • Conditions (often real-world) under which the work will be done • The overview does not include: • Assessment. It implies but does not specify • Specific direction to the student • Specific equipment list • Homework or reading assignments

43. Florida Middle School Mathematics Initiative | International Center for Leadership in Education Sample Overview Students will create a flip book animation. Students will work individually and in pairs to search the internet for animation instructions, use graph paper and a teacher generated template. Flip book animations will include the translation of images on a coordinate plane.

44. Student Work Students will create a flip book animation. Students will work individually and in pairs to search the internet for animation instructions, use graph paper and a teacher generated template. Flip book animations will include the translation of images on a coordinate plane.

45. Student Work Specific Context Students will create aflipbookanimation. Students will work individually and in pairs to search the internet for animation instructions, use graph paper and a teacher generated template. Flip book animations will include the translation of images on a coordinate plane.

46. Student Work Specific Context Students will create aflipbookanimation. Students will work individually and in pairs to search the internet for animation instructions, use graph paper and a teacher generated template. Flip book animations will include the translation of images on a coordinate plane. How

47. Student Work Specific Context Students will create aflipbookanimation. Students will work individually and in pairs to search the internet for animation instructions, use graph paper and a teacher generated template. Flip book animations will include the translation of images on a coordinate plane. How Resources

48. Student Work Specific Context Students will create aflipbookanimation. Students will work individually and in pairs to search the internet for animation instructions, use graph paper and a teacher generated template. Flip book animations will include the translation of images on a coordinate plane. How Resources Conditions

49. Lesson Components • 1. Instructional Focus Statements • 2. Student Learning: what students will be doing during the lesson (the math) • 3. Essential Skills (from International Center List) • 4. Scoring Guide • 5. Handouts • 6. Standards

50. Performance Task Handout