Domain: Operations and Algebraic Thinking
Standard Code: 3.OA.1,2
Teacher Name:
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
Interpret products of whole numbers e.g., interpret 5 x 7 as the total number of objects in 5 groups of 7
What are your mathematical goals for
objects each.
the lesson? (i.e., what do you want
students to know and understand about
Interpret whole-number quotients of whole numbers, e.g. interpret 56 ÷ 8 as the number of objects in
mathematics as a result of this lesson?)
each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56
objects are partitioned into equal shares of 8 objects each.
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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?
How will you introduce students to the
activity so as to provide access to all
students while maintaining the
cognitive demands of the task?
Expectations: Students will multiple and divide to solve a real world problem.
Tools: Counters, paper, pencil, recipe
Grouping: partners/independent/ small or large groups, etc.
How will they report?
1. chalkboard, poster, document camera, white board, models, verbal explanations, table
representatives, etc.
Jessie is excited about his trip to Arizona. He’s going hiking with four friends and found this recipe for a snack.
Nature Mix
2 cups almonds
1 cup cashews
How many batches will Jessie need to make if each of the boys
3 cups dried pineapple
wants 2 cups of mix?
4 cups oats
What if they each want 4 cups?
1.Mix ingredients in bowl.
2. Scoop a serving into a plastic bag
If he makes 6 batches, how many cups will each boy get?
3. Eat and enjoy on your next outdoor trip.
How many batches will Jessie need to make if each of the boys wants 2 cups of mix?
What if they each want 4 cups?
PART 2: SUPPORTING STUDENTS’ EXPLORATION OF THE TASK
Started: What do you know? How would you start? What do you need to know?
As students work independently or in
small groups, what questions will you
Focus: Can you explain this to me (picture/thinking)? Can you show me a picture? How many
ask to—
people need trail mix?
 help a group get started or make
progress on the task?
Assess: What challenges have you found. Describe, explain, tell, show……
 focus students’ thinking on the
key mathematical ideas in the
Advance:
task?
 assess students’ understanding of Is there another way you can do that? How do you know? What have you discovered?
key mathematical ideas, problem- What other choices do you have? How are these similar? How are these different?
Where can you find that answer? What do you find difficult or challenging?
solving strategies, or the
Describe…….
Explain……
Tell……….
List……..
representations?
Restate-“Can
you
tell
me
what
he
said?”
 advance students’ understanding
of the mathematical ideas?
The Frustrated Student: Remind them not to over think, but just to follow the given guidelines.
How will you ensure that students
What materials could you use to get started? Can you circle the important information? What is
remain engaged in the task?
the question asking you to do? What do you know? Can you draw a picture of the ingredients?
 What assistance will you give or
what questions will you ask a
student (or group) who becomes The Early Finishers
--Jessie really like peanuts, so he adds some to his original mix. Now how many cups of the mix
quickly frustrated and requests
will each boy get?
more direction and guidance is
--On the way to Arizona, a raccoon gets in the car and eats half of the mix. How much is left?
solving the task?
--While hiking, they meet a friend and decide to share with him. Now how much will each person
 What will you do if a student (or
get?
group) finishes the task almost
immediately? How will you
Describe the task
extend the task so as to provide
“Tell me which of these ideas were yours.”
additional challenge?
Restate-“Can you tell me what he said?”
See Above
PART 3: SHARING AND DISCUSSING THE TASK
What are the students doing? What is the teacher doing?
How will you orchestrate the class
-Students: Think/pair/share and then have select students come to the front to share their
discussion so that you accomplish your
strategy.
mathematical goals?
-Teacher: Facility sharing, asking questions
 Which solution paths do you want
to have shared during the
Ways of Comparing:
class discussion? In what order will
the solutions be presented? Why?
Gallery Walk with post it notes
 What specific questions will you ask
Group shares
so that students will—
Combine like ideas
1. make sense of the
Discuss differing or “unlike” ideas
mathematical ideas that you
Defending procedures
want them to learn?
Finding Patterns
2. expand on, debate, and question
Variety of answers
the solutions being shared?
3. make connections among the
different strategies that are
presented?
4. look for patterns?
Responses:
5. begin to form generalizations?
Varied responses, energized conversation, assessment, model, journals,
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?
How will you know they “got it”? Facial expressions, assessment, discussion,
Demonstration, presentation, positive energy,
Nature Mix Division
Jessie is excited about his trip to Arizona. He’s going hiking with four
friends and found this recipe for a snack.
 How many batches will Jessie need to make if each of the boys
wants 2 cups of mix?
 What if they each want 4 cups?
 If he makes 6 batches, how many cups will each boy get?
Extensions:
 Jessie really like peanuts, so he adds some to his original mix.
Now how many cups of the mix will each boy get?
 On the way to Arizona, a raccoon gets in the car and eats half of
the mix. How much is left?
 While hiking, they meet a friend and decide to share with him.
Now how much will each person get?