Domain/Standard Code: K.OA.3 Author Name: Maria Aagard Page 2
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Title of Task: _
Riding in a Parade______
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?) / Students will decompose the number nine into pairs and find more than one way to solve the task.
· 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? / Expectations: Use manipulatives if needed, discover solutions, draw pictures, share with others.
Resources: Manipulatives available for counting (cubes, discs, etc.)
Paper and pencils, crayons if desired
Work: Students will work independently at first, share solutions with a partner, and some students will be chosen to share with the class. As a class we will see how many solutions we can find.
Product/Accountability: Student will independently draw pictures showing solutions to the task and explain his/her thinking to a partner. Students not able to express themselves in writing can show solutions with manipulatives and explain them to a partner and teacher.
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
We have 9 children who want to be in a parade.
A bike holds 1 child.
Wagons hold 2 children.
How many bikes and wagons will we need?
Background Knowledge:
· One to one correspondence
· Counting to 9
Domain/Standard Code: K.OA.3 Author Name: Maria Aagard Page 2
jj
Title of Task: _
Riding in a Parade______
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? / Work Time: Teacher will present the task to the class at the rug, distribute papers or have children locate math journals.
Available manipulatives for acting out solutions on their tables will be presented.
Questions to get started:
· Do you want to use counters to act it out or do you want to start drawing pictures?
· How many children want to be in the parade?
· Do you want to start with bikes or wagons?
· Let’s think of an easy way to draw a child on a bike and two in a wagon.
Teacher will circulate in the room and observe how children are approaching the task, offering encouragement as needed, and giving students opportunities to explain their thinking. Students will work independently in their own areas. Students will be encouraged to find more than one solution. Teacher will be looking for different solutions to be shared with the class.
Students will be encouraged to explain their thinking as they share their findings with a partner and compare solutions.
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? / Engaging Students
· How many children can fit in a wagon? How will you decide how many wagons to use?
· Does your solution include both bikes and wagons?
· Does your solution have a total of nine children? How do you know?
· What is the highest number of wagons you could use in your solution? How do you know?
· Do you think everyone will have the same number of wagons as you do? The same number of bikes? Finish your solution and find someone to compare with.
Fast Finishers:
· Have you shared your solution with a partner and explained your thinking? Find a different partner.
· How many different ways can you solve this task?
· What if small floats were available to ride on for the parade and four children could sit on a float? What would a new solution be that includes bikes, wagons and floats?
· Change the number of children to 14. Show a new solution!
· Let’s change it to 14 children want to be in the parade. Show your solution.
·
·
Domain/Standard Code: K.OA.3 Author Name: Maria Aagard Page 2
jj
Title of Task: _
Riding in a Parade______
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? / Class Discussion:
Students will bring their solutions and gather at the rug with the teacher, who has pre-selected a few students to share their solutions paths. The first child selected may be one who used nine counters first and acted it out at their desk. (This may encourage students to involve manipulatives in solving future problems which may be more challenging for them.)
Another student who has the same answer but drew a picture may be chosen to come up next and compare.
Solution paths showing different amounts of wagons and bikes will also be shared.
Questions:
· How many of you had the same number of wagons as ______did? Hold it up.
· How many of you had a different amount of wagons than ______did? Hold it up.
(May repeat for number of bikes.)
· Does this solution show nine children total? How do you know?
· Who has a solution different than any of the ones shown?
· Let’s count how many solutions our class came up with.
· Do you think there are any other ways we didn’t think of yet? How do we know?
(Note: If students already have drawn three solutions on their page, they will have to choose which one they are comparing to the child sharing.)
The different solution paths children created could be written on a chart:
3 wagons and 3 bikes
2 wagons and 5 bikes
1 wagon and 7 bikes
Students could be asked to look for number patterns and explain their findings.
A demonstration using manipulatives or a pictorial representation that totals 9 children, using bikes and wagons, will show students have understanding of decomposing the number nine into pairs.
Domain/Standard Code: K.OA.3 Author Name: Maria Aagard Page 2
jj
Title of Task: _
Riding in a Parade______