Domain: Math
Standard Code: 1 .N BT 3
Teacher Name: V. Galloway
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
Compare two digit numbers based on meanings of the tens and ones digits, recording the results of
What are your mathematical goals for
comparisons with the correct symbols for greater than, less than and equal to.(<, >, =)
the lesson? (i.e., what do you want
students to know and understand about Strategies include:
 Reading numbers
mathematics as a result of this lesson?)
 Modeling numbers with base ten blocks on a mat
 Compare two numbers
 Write the correct symbol when comparing two numbers
 What are your expectations for
Students will be expected to work cooperatively with their partner in comparing numbers. They will be
students as they work on and
expected to explain their recorded answers.
complete this task?
Tools needed : bags with number cards, base ten blocks, mats and recording sheet. (one for each pair)
 What resources or tools will
students have to use in their
Students will work with a partner on the same ability level. The bags of numbers will be handed out so
work that will give them
the numbers will match their ability level.
entry into, and help them
reason through, the task?
Partners will have one recording sheet. They will take turns being the recorder.
 How will the students work—
independently, in small groups, or
Partners will team up to share their work.
in pairs—to explore this task?
 How will students record and
Radom students will be chosen to explain one of their problems with the class.
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?
Launch:
I will give two students the numbers 35 and 78. They will come to the Smartboard and model their
numbers with the base ten blocks.
Next, 35, 78 and < cards will be given to three different students. They will arrange themselves in front
of the class to make the correct comparison.
PART 2: SUPPORTING STUDENTS’ EXPLORATION OF THE TASK
Have the lower students meet at the table. Get them started on the problems while the remainder
As students work independently or in
of the class self starts. Once lower group has started and is confident go around the room having
small groups, what questions will you
mini conferences with the class. Use the following questions for conferencing:
ask to—
 help a group get started or make Getting Started Questions:
What do you know about your number? How can you use the base ten blocks to show your
progress on the task?
number? How many ones? How many tens?
 focus students’ thinking on the
Focus
Questions:
key mathematical ideas in the
How do you know? How does that work? How did you get there? What else can you do? Tell
task?
 assess students’ understanding of me more about this? Is there another way?
key mathematical ideas, problem- Assessing Questions:
Will you explain that to me? How did you come to that answer? How are you sure? What does
solving strategies, or the
that mean?
representations?
 advance students’ understanding Advanced Questions:
Is there another way to show your answer? Is there a different way to organize your work? Can
of the mathematical ideas?
you show another way?
Assistance:
How will you ensure that students
remain engaged in the task?
 Change their number to one digit.
 What assistance will you give or
 Have their partner assist them.
what questions will you ask a
 Start a strategy and have them finish.
student (or group) who becomes
quickly frustrated and requests
Extensions:
more direction and guidance is
 Give them three numbers to compare.
solving the task?
 Show their work in a different way.
 What will you do if a student (or
 Give higher numbers.
group) finishes the task almost
immediately? How will you
extend the task so as to provide
additional challenge?
PART 3: SHARING AND DISCUSSING THE TASK
Solution Path
How will you orchestrate the class
discussion so that you accomplish your
 Two groups of partners will get together and each one of them will explain one of their
mathematical goals?
comparisons.
 Which solution paths do you want
 Invite students you have selected to share come up. Using the document camera
to have shared during the
students present their work, using base ten blocks, number cards and symbol cards.
class discussion? In what order will
the solutions be presented? Why?
Use some of the questions that follow:
 What specific questions will you ask
so that students will—
 Is there a different way you can compare these numbers?
1. make sense of the
 What do you notice when both of your numbers have the same number of ones?
mathematical ideas that you
 What do you notice when both numbers have the same number of tens?
want them to learn?
2. expand on, debate, and question
What will you see and hear?
the solutions being shared?
 They were accurate in their work.
3. make connections among the
 They could come up with a different way to compare their numbers.
different strategies that are
 Discussion between partners and groups.
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?