Domain/Standard Code: 1.0A Author Name: Dilworth and Bell Page 1
Title of Task: Jaun’s Car Collection
Adapted from: Smith, Margaret Schwan, Victoria Bill, and Elizabeth K. Hughes. “Thinking Through a Lesson Protocol: Successfully Implementing High-Level Tasks.”
Mathematics Teaching in the Middle School 14 (October 2008): 132-138.
PART 1: SELECTING AND SETTING UP A MATHEMATICAL TASK (PREPARE)What are your mathematical goals for the lesson? (i.e., what do you want
students to know and understand about mathematics as a result of this lesson?) / Determine the unknown whole number in addition or subtraction equations, relating three whole numbers to twelve.
Strategies include:
· Using manipulatives
· Counting on
· Decomposing a number
· Using relationships between addition and subtraction
.
· What are your expectations for students as they work on and complete this task?
· What resources or tools will students have to use in their work that will give them entry into, and help them reason through, the task?
· How will the students work—
independently, in small groups, or in pairs—to explore this task?
· How will students record and report their work? / Tool Needed:
· Paper pencil
· Unifix cubes
· Number line
· Counters
· Bag of cards showing various numbers of cars from 0 to 11for each color such as 5 blue, 3 blue, 4 red or 2 red etc.
Students will work independently or in assigned pairs (Assign pairs for extra scaffolding as needed.)
Students will record their work on paper or journals making sure they have equations equaling twelve.
How will you introduce students to the activity so as to provide access to all
students while maintaining the cognitive demands of the task? / LAUNCH
Jaun has a box for his toy car collection. The box has twelve spaces. Jaun already owns some cars but he wants all the cars in the box to be the same color. Your job is to help Jaun decide how many more cars of each color he will need. You will each have a bag of numbers of cars. You will need to reach into the bag and remove one card. On the card you will find a number and a color. Your job it to find out how many more of that color of car Jaun will need to fill the spaces in his collection box.
Domain/Standard Code: 1.0A Author Name: Dilworth and Bell Page 1
Title of Task: Jaun’s Car Collection
PART 2: SUPPORTING STUDENTS’ EXPLORATION OF THE TASK (EXPLORE)As students work independently or in small groups, what questions will you ask to—
· help a group get started or make progress on the task?
· focus students’ thinking on the
key mathematical ideas in the task?
· assess students’ understanding of
key mathematical ideas, problem- solving strategies, or the representations?
· advance students’ understanding
of the mathematical ideas? / Make sure that students who may require extra help are working with a partner.
Getting started questions: How are you going to figure this out? What information do you have?
What strategy can you use? What tools can you use? What can you use that you already know?
Focus Questions: How do you know? How does that work? How did you get there? What else can you d0? Tell me more about this. Is there another way? What does that mean? Can you use subtraction to help you?
Assessing Questions: Will you explain that to me? How did you come to that answer? How are you sure that works? What does that mean? How does that work? What did you use to come to that answer? Can you read your equation to me?
Advanced Questions: Is there another way to come up with an answer? What if there were x more cars, how would that change your problem? What if Jaun decided to put more than one color in the box?
How will you ensure that students remain engaged in the task?
· What assistance will you give or what questions will you ask a
student (or group) who becomes
quickly frustrated and requests more direction and guidance is
solving the task?
· What will you do if a student (or group) finishes the task almost
immediately? How will you
extend the task so as to provide additional challenge? / Assistance:
· Make the box smaller,
· Use lower numbers on the card pictures
· Provide an egg carton as the model of the box.
· Start the strategy and have them finish.
Extentions:
· Ask them to write the related subtraction facts to their problems, or equations.
· What if Jaun had two collection boxes?
· What if Jaun had two or three colors in the same box?
Domain/Standard Code: 1.0A Author Name: Dilworth and Bell Page 1
Title of Task: Jaun’s Car Collection
PART 3: SHARING AND DISCUSSING THE TASK (DISCUSS/DEBRIEF)How will you orchestrate the class discussion so that you accomplish your mathematical goals?
· Which solution paths do you want to have shared during the
class discussion? In what order will the solutions be presented? Why?
· What specific questions will you ask so that students will—
1. make sense of the
mathematical ideas that you want them to learn?
2. expand on, debate, and question the solutions being shared?
3. make connections among the different strategies that are presented?
4. look for patterns?
5. begin to form generalizations?
What will you see or hear that lets you know that all students in the class
understand the mathematical ideas that
you intended for them to learn? / Solution Path:
After students have solved three or four equations invite students you have selected to share their thinking.
Specific Questions:
· What else do you notice?
· Why does that work?
· Can you explain your thinking?
· Ask the class: Can you explain the thinking of the presenter?
What will you see or hear?
· Their equations are accurate
· Their work is clear and precise
· Students will be sharing work with the class and partners.
· There will be multiple strategies used.
· Students try to use different strategies.
After each student shares ask a class member to use their own words to summarize the strategy just presented. Have a discussion with the class and the presenter to solidify the strategy used. Do this after the launch and explore.
Domain/Standard Code: 1.0A Author Name: Dilworth and Bell Page 1
Title of Task: Jaun’s Car Collection