Domain: Counting and Cardnality Standard Code: K. CC5 (also 3 & 4a) Teacher Name: Susan Jorgensen
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 TASKWhat 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 be able to count up to 20 objects arranged in a rectangular array.
They will show 1:1 correspondence and record the numeral correctly.
· 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:
1. Students will arrange up to 20 objects on a double 10 frame.
2. Students will count the number of objects and record the numeral.
3. Students will show 1:1 correspondence when counting
Resources and Tools:
1. Bag with 20 objects inside for each pair of students (not a clear bag)
2. Double 10 frame mat for each pair of students
3. Recording sheet for each student
4. Crayons and pencils
· Students will work in pairs to explore this task & will record and report their work on the recording sheet.
How will you introduce students to the activity so as to provide access to all
students while maintaining the cognitive demands of the task? / The lesson will begin with all students located on the rug, or central meeting area in the classroom. When all students are at the rug, put them into pairs.
Ask the question “I have some bags with counters in them, how can I find out if I have enough for each group?” Guide students in a discussion to figure out if there are enough bags. Brainstorm and list the ideas. Then have them decide what the best method would be and then try it out. (Counting number of pairs and number of bags is one way)
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? / Whole Group Task:
· Introduce activity as a whole group/walk through the process with whole class
· Call up a student to pull out items from a bag
· Using a document cam, Smart Board, or overhead assist the student in placing objects on the double ten frame. Count the objects as a group.
· On chart paper or white board have the student color in a double ten frame to match the object representation. Count the colored square and write the numeral next to the ten frame.
*Repeat process with 2-3 other students.
Independent Practice:
· In pairs students will take turns drawing objects out of the bag and placing them on the double ten frame mat. The partner will record the objects by coloring in boxes on the double ten frame. They will count the objects together and then record the numeral next to the frame.
· Students will do this task 8 times (so each student will have recorded four times)
· Circulate through the classroom and ask these questions.
*How many objects did you put in each box on your mat?
*If you took the objects out of the boxes how many would there be and how do you know?
*Who drew more objects, you or your partner?
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? / · Students who struggle should be paired with a student who understands the concept or can be given a bag with fewer objects.
· Pairs who finish early will be given the task to count the objects and record them without placing them on the ten frame mat. They can explore different ways to arrange their objects to count them.
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? / Discussion Questions:
1. How did you know how many boxes to color in on your recording sheet?
2. How else could you arrange your objects to count?
3. Can you tell who drew the largest number of items by looking at their record sheet?
Assessment
1. Circulate the room and check to make sure students are only placing one object in each box, counting and recording correctly.
2. Check the recording sheet to make sure they have the correct numeral written for the number of boxes colored in.
Magic Bag Recording Sheet
My Number is:______
My Number is:______
My Number is:______
My Number is:______