Domain: Geometry Standard Code: 2.G.2 Teacher Name: __Karen Leavitt

Title: Birthday Candy Bars______

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?) / 2.G.2 Partition a rectangle into rows and columns of same-size squares and count to find the total number of them.
·  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? / ·  Students will make sense of the problem and persevere in solving it.
·  Students will work as a team and use mathematical discourse in solving the task.
·  Students will determine which of the candy bars has the largest area. They will be able to partition a rectangle into rows and columns of same-size squares.
Students will create representations to show their reasoning.
·  Students will be able to use rectangles with the following dimensions: 1 x 8, 2 x 7, 2 x 6, 3 x 6, 4 x 6, 4 x 5, 4 x 4. They may also use a ruler, 1’ tiles, cm cubes, Unifix cubes, graph or plain paper for recording, pencils.
·  Students will work in pairs.
·  Students will record their rectangles on paper, having partitioned them into equal rows and columns, stating which is largest and how they know.
How will you introduce students to the activity so as to provide access to all
students while maintaining the cognitive demands of the task? / Before beginning the task, each pair of students will be given a set of rectangles to arrange from biggest to smallest. They will then predict which is the largest.
They will be shown all the tools they will have available to find how much chocolate each bar has: paper, graph paper, 1” tiles, cm cubes, linking cubes.
The task:
On your birthday at school, your teacher lets you choose a candy bar out of her birthday basket. Because you love chocolate, when it’s your birthday, you want to choose the candy bar with the most chocolate. But the candy bars are all different sizes, so you’re not sure which one is the biggest. How will you know which one to choose? Use the tools and the rectangles to help you decide which candy bar you will pick. Show your work on the paper. Use words and pictures to share which one has the most chocolate.
PART 2: SUPPORTING STUDENTS’ EXPLORATION OF THE TASK
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? / ·  Which candy bar (rectangle) did you predict is largest? Why?
·  What tools might help you?
·  What would be your first (next) step
·  How will you measure all of the chocolate?
·  Explain your process. How do you know that your measurement is accurate?
·  Is there another way to solve this problem?
·  How are you going to show your solution?
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? / Both students in each pair will be required to record their solution. Students will also be engaged in discussion with their partners.
·  Can you tell me what you are trying to find out?
·  What would be a good way to start?
·  What tools might be helpful for you?
Extensions:
·  Can you put all the candy bars (rectangles) in order, from the largest to the smallest?
·  Did your solution match your prediction? What is the difference between your prediction and your solution?
·  Can you find other rectangles that have the same amount of chocolate as the biggest one?
PART 3: SHARING AND DISCUSSING THE TASK
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? / ·  Students who covered the rectangles with colored tiles (because they are 1” and will fit evenly) would be first to share.
·  Then there might be some who have used another unit (cm cubes.Unifix cubes).
·  Then students who used the graph paper to outline the shape and counted the squares.
·  The most difficult solution may be students who have used a ruler to make rows and columns on the rectangles.
·  How did we represent our data differently? What things are similar/different?
·  What connections can you make between your strategy and others’?
·  Did your prediction match your findings? Why do you think it did or didn’t?
·  Students will be able to use words and pictures to explain which rectangle is the largest. Their drawings will represent their thinking.
·  Explanations of solution that match their representations.
·  They will be able to compare their representation with those of others.
·  Students’ written work will allow the teacher to examine each child’s understanding of rows/columns/partitioning/covering the whole area.

Candy Bar Task:

On your birthday at school, your teacher lets you choose a candy bar out of her birthday basket. Because you love chocolate, when it’s your birthday, you want to choose the candy bar with the most chocolate. But the candy bars are all different sizes, so you’re not sure which one is the biggest. How will you know which one to choose? Use the rectangles to help you decide which candy bar you will pick. Show your work on the paper. Use words and pictures to share which one has the most chocolate.