Domain: Operations and Algebraic Thinking Standard Code: 1.0A1 Teacher: Penny Gardner/Apryl Beck
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?) / Use addition and subtraction within 20 to solve word problems.
Involving situations of:
· Adding to
· Taking from
· Putting together
· Taking apart
· Comparing unknowns in all positions
· 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 record their answers in their math journal using words, pictures and drawings. Several students will be chosen to share various strategies.
Various manipulatives (i.e. counters, linking cubes, buttons)
Number line
100 chart
pencil/paper
chart paper
Students will work independently recording their work in their math journals. Students will solve various word problems that are posted around the room on chart paper. Different levels of problems are posted. Students will solve their "color" of problems.
Students will record their thinking in their math journals.
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: Read aloud the book One Too Many by Gianna Marino. Help the children discovery and count the animals.
Let the students help you write a word problem using the numbers 1-20.
Examples- There are 3 sheep, 1 flea and 6 bunnies. How many total animals are in the barn? (adding to) There are 4 cows and 9 horses. How many animals are there? (putting together) There are 20 animals in the barn. It was too crowded so 8 ducks decided to leave. How many animals are in the barn now? (taking from) There are 15 animals in the barn. There are 5 pigs and some goats. If there are 15 total animals how many goats are in the barn? (comparing with unknowns)
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? / Explore:
Students will go to their assigned color of word problems posted around the room. They will solve the various problems in their math journals. (colors are based on skill level)
Blue Group-There are 20 animals in the barn. Some are geese, some are pigs and some are chickens. How many of each animal could you have? Solve using more than one strategy.
__+__+__=20
Green Group-There are 15 animals in the barn. There are 7 bunnies, some chickens and some geese. How many chickens and geese do you need to have a total of 15 animals in the barn? Solve using more than one strategy.
7+___+___=15
Purple Group-There are 9 animals in the barn. There are 5 mice and some fireflies. How many fireflies are there? Solve the problem using a strategy that you already know.
5+___=9
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? / Teacher will walk around asking specific questions to students while they are solving the word problems. Focus on those students who might be frustrated and clarify any misunderstandings.
Getting Started Questions:
What information do you have? What tools would help you? What strategy can you use that you already know?
Focus Questions:
How do you know? Explain your work. Is there another way?
Extension: Have students write and solve their own animal word problem in their math journal.
Select several students to share who have used different strategies.
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? / Bring students to the rug. Using the document camera student's present strategies in the order that you have selected.
Specific questions to the student sharing
· Can you explain your thinking?
· Is there another way?
· What else did you notice?
Turn and Talk
· What strategy did you notice "Amber" using?
· Is there a connection that you had to "Amber's" problem?
Teacher focuses students on key mathematical ideas and helps connect prior knowledge in order to extend students' thinking.
Key mathematical ideas: Solve word problems using an unknown number to represent the problem.