## Japanese Lesson Study Summary

### Monday - Friday, July 19-23, 2004

All four days this week were dedicated to writing and revising our lesson plan. The best record of the week is the change shown in the progress of the lesson. Here are the daily electronic versions of the lesson.

Monday:

To facilitate participation and progress, we formed two smaller groups and thereby, came up with two different visions of the lesson. Megan and Remy submitted the following drafts:

Megan Taylor

Subject: Draft #1 of the Big Question

LESSON STUDY WORKING GROUP INFORMATION

The new Gamecube game, "Superhero City," has just come out in stores. To win the game you need a certain number of points. At the beginning of the game you must choose a character. Guinevere starts with 5 points in Level 1 and every level she wins 5 more points. Harry Potter starts with 1 point in Level 1, and wins the square of the level number he is on. Spiderman also starts with 1 point in Level 1, but his points double every new level. When Guinevere beats a level, she adds her new points to her score. However, Harry Potter and Spiderman do not.

1. How many points would each character have at the end of Level 5?
2. Choose one character and graph his/her score from Level 1 to Level 8.
3. Which character would you choose?

Remy's group

PCMI Lesson Study Group 1 Plan (draft)

Over arching goals:

• Lesson will set the stage for development of the meaning of coefficients and variables
• Lesson will focus on conceptual versus procedural understanding
• Lesson will convey some necessity, importance, beauty of math

Essential questions:

How can change be represented graphically?

Launch:

• Ask students about what does it mean for something to change, e. g. give examples about something that changes in their life
• Provide time for students to write about their thought

(Need to think of situations that are relevant to students)

Activity 1: Blow a balloon for students to observe change

1. First balloon just to observe
2. Blow a second balloon for students to draw a picture of change from their observation
• Ask students what is changing as they see the balloon being blown up
• Provide individual thinking time in regards to what is changing before they write down their observation
• Have students discuss with partner or in small group

As students are writing about "change," facilitator walks around the room to make sure who will be called on to get a range of answer and let them share in the order that will lead to what we want.

What if student draws the change of balloon without using a graph, what questions can we ask them? (How can we represent change graphically?)

Talk about how would they represent change and how one variable relate to another.

Activity 2:

• Students in each group pick a scenario of "change" that they had shared and graph them
• Exchange the graph with another group to see whether they will be able to match the scenario

Conclusion:

• Justification of how graph match with scenario
• Debrief about using graph representation

Tuesday: Megan took over the typing and combining of the two plans

As you can see, there is a great deal to do in reconciling these two versions. Megan thoughtfully (and expertly) took over the task of compiling the two and with the use of a projector, the lesson study group began combining ideas. The result was this version of the lesson.

Subject: Lesson Study Group TOPIC

PCMI Japanese Lesson Study
July 12 - July 31, 2004

Overall Theme: Translation between Math and Real Life

Overall Goals:

• Emphasize the meaning of coefficients and variables
• Lesson will convey some necessity, importance, beauty of Math
• Lesson will focus on conceptual versus procedural understanding

Content Theme: Modeling Change

Overall Goals/ Essential Question(s):

#1

• Students can understand the difference between 2x, x2 and 2x. "Understanding" means being able to compare the contrast the functions algebraically, being able to create a table and graph for each function and being able to describe each with a real-life example.
• Students understand the increase in mathematical complexity as you move from a linear to exponential model.

vs.

#2

• How can some change be represented graphically?
• Students should understand how change can be represented graphically. Students can create a real-life scenario for a given graph. Students can use a description of a situation to sketch a representative graph.

The three groups came back together and with fantastic work by Megan, we patched the three together and started revising.

Thursday Author: Megan Taylor
Subject: Notes from Lesson Study - 7/19

Thursday:

Megan continues to type revisions for us and this is the version we had on Thursday.

Overall Theme: Translation between Math and Real Life

Overall Goals:

• Lesson will emphasize the meaning of coefficients and variables.
• Lesson will convey some necessity, importance, beauty of Math.
• Lesson will focus on conceptual versus procedural understanding.

Content Theme: Modeling Change

The Essential Question(s):

How can change be represented graphically?

Content Goal(s):

Students should understand how change can be represented graphically. "Understanding" means students can explain how graphs represent change and can tell "stories" with graphs. Students can create a real-life scenario for a given graph and conversely can sketch a graph using a description of a situation ("a story"). Students should be able to label graphs and choose quadrants effectively and understand that one graph can describe more than one situation. Finally, students should see graphs as showing relationships between two or more variables.

(5 min.)
Launch: Make a list of things in your life that change.
Describe how one of the things in your list changes.

EX: Money
Growing/ Height
Skin color (being tan)
Gaining/Losing Weight
Friends
Teacher
Classes
Weather

Discussion Questions:
Which of these things will continue to change/are always changing?
What causes the change?
Can you measure change?

(20 min.)
Activity 1: Balloon Observation

• Students observe the teacher blowing up of the balloon.     Teacher blows up a second balloon for students to decide what is changing and how from their observation.
• What is changing about the balloon?
EX: size
shape
air in the balloon
surface area/ volume
color (hue)
• Students discuss lists with partners or in small group.
• As students are writing about the change(s), the teacher walks around the room to make sure who will be called on to share to get a range of answers.
• Students are given a number of graphs relating time and ______ of a balloon.
• Students (in pairs or groups) describe each graph with a story. What does this graph show? What is happening?

(25 min.)
Conclusion: Re-visitation of the idea of change

• Students revisit the lists made previously about change in their lives.
• Describe how you would keep track of this change.
• Describe one of the changes from your list using a graph.
• Students create graphs that describe some of the changes from their lists. Students will not be told explicitly whether to label or not.
• Student pairs/groups switch graphs and must describe what is happening in words. Graphs without labels may be described very differently than intended, which will be a

(3 min.)
Wrap-Up: What is change?

Lesson Planning:

Group A: Instruction to Lesson; Transitions; Wrap-up (Bill, Luis, Megan)
Group B: Balloon Graphs and Activity Overview (Claudia, Cheryl, Susana)
Group C: Re-visitation of Change Lists (Remy, JoAnn, Don) (20 min.)

Activity 1: Balloon Observation

• Students observe the teacher blowing up of the balloon.
I want you to write about changes in the balloon as I blow it up.
Teacher blows up a second balloon, slowly, then quickly, releasing some air, etc... and students are asked to describe what is changing from the observation.
• As students are writing about the change(s), the teacher walks around the room to make sure who will be called on to share to get a range of answers.
• What was changing about the balloon? Teacher calls on volunteers.
EX: size
shape
air in the balloon
surface area/ volume
color (hue)
• Students are given the two situations below and are asked to sketch a graph for each with their partners.
1. A balloon is being blown up quickly (with a helium tank, for example)
2. A balloon is blown up, tied off, then "runs into" a sharp object
• Students (in pairs or groups) describe each graph with a story. What does this graph show? What is happening?

Descriptions ‡ Graphs

Graphs ‡ Descriptions

Friday

On Thursday Claudia agreed to teach the lesson to a group of volunteers from the HSTP next Tuesday and Megan agreed to teach the lesson in Provo to David Wright's group of eighth graders.

Hi to the Hard-core Lesson Study Planners!

I feel like we got a lot done today (in the end) and am glad we cut out the large chunk we did. I have compiled what I gleaned from our discussions this morning into a semi-coherent document. Here are the things, specifically, I think you should be ready to comment on by tomorrow. Yes, you have homework!

1. The "Questions," "Student Response" and "Materials" columns are vastly incomplete. I didn't even try to fill in most of what we need here. Please think about these spaces, especially the "Questions" column, as this will be the most important part of the whole lesson!
2. Where there were holes in the plan, I made stuff up. Yes, not exactly the Lesson Study model, but at least then we'll have less to write from scratch tomorrow. Nothing major of course, for example I made the time divisions sum to 60 and I added a "Wrap-up" at the end of the lesson. Do we want one? I didn't know! So I put it in and we can talk about it.
3. As we probably won't have time for the third activity, where students read situations and have to graph them, I created a *sample* worksheet for it just in case and if we have extra time tomorrow (hahahaha) then we can edit that as well.

Good job everyone!
I decided I should be excited and honored to be able to teach our lesson!

Megan

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