Domain: Math Standard Code: 1.OA.2 Teacher Name: Jackie Hull, Katie Althoff

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
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?) / Mathematical Goal
Students will be able to add 3 whole numbers with a sum that is less than or equal to 20.
Background Knowledge counting, making a set, one to one correspondence, addition of two numbers
·  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? / Strategies Tools
* counting all * story problem on paper, pencil
(w/number line, tally marks, counters, R-en-R, etc.) * arcade tickets
* counting on from each larger number * number line
(w/number line, tally marks, counters, R-en-R, etc.) * Rek-en-Reks (create one with 3 rows of 10)
* using known facts & derived facts * interlocking cubes or color tiles
(doubles fact plus one 5+6, combination of ten 6+4
expanded notation 10+5) Future Lesson Tools
* more story problems (Solidify)
Books * triples dot cubes (Practice)
Ten Friends by: Bruce Goldstone * spinners (spin 3 times for Practice)
The Masloppy Family by: Cathy Fosnot * recording sheet for “Roll/Spin 3” (Practice)
Students will work independently at first, pair share, then discuss as a class.
Students will record their work on the story problem paper and report to a partner. The teacher will select students to report during the discuss phase of the lesson. Other students will respond to and question each other.
How will you introduce students to the activity so as to provide access to all
students while maintaining the cognitive demands of the task? / Mathematical Task (Develop Lesson)
Miss Althoff (substitute own name) went to the Nickelcade and earned tickets from three different games. She earned _6__ from ski ball, 4 from basketball, and __5__ from whack-a-mole. How many tickets does she have? Use numbers, words, and/or pictures to show your work.
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? / Launch Questions:
Who has been to the Nickelcade or played a video game? What are some games that you’ve played? What do the machines give you when you do well? What do you do with those tickets? Tell the story of going to the Nickelcade last night. Here are the games I played… You get to find out how many tickets I earned all together. I’m so exited to go back today and take my tickets to the prize counter. Can you help me figure this out?
Clarifying Task Questions:
What do you know? What are you trying to figure out? How can you get started? What tools can you use?
Focus Questions:
How do you know? What two numbers did you add first? Why did you add those first? Can you try another way? Can you add two other numbers first? Can you tell me more about it?
Assessing Questions:
Are you sure? How can you prove that to me? Will you explain that to me? What does that mean? How can you use labels to show your thinking?, 5 Star Rubric for Assessment
Advanced Questions:
Are there other combinations that you could add first? What other combinations of numbers/tickets can you add first? Can you prove your first strategy with a second strategy?
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? / Support for Struggling Students:
* Smaller number choices
* Pre-made number sentence/equation with blanks or other pre-made organizer
* Actual tickets in three groups (Different colored tickets would be ideal for grouping.)
* Specific number of counters
Extensions:
* Prize counter questions- What can I buy with my tickets? Do I have enough for ______?
* Have students create a mock prize counter.
* Give students their own tickets. Predetermine number choices based on informal assessment of original task. Have students add up their own tickets. Ask students to try other ways besides counting. Remember some of the strategies you used in the original task and see if it works for this task.
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? / Solution Path:
Strategies-
* Counting All starting at 1 (tickets, picture, number line, counters, cubes, Rek-en-Rek)
* Picture representations
* Counting On from the larger number (tickets, picture, number line, counters, cubes, R-n-R)
* Tally marks
* Known facts (combinations of ten: 6+4=10)
* Derived facts (doubles plus one)
* Compensation (decompose and re-compose)
* Finding different combinations to add first
Specific Questions:
* Talk Moves- restate, agree or disagree?, etc.
* Questions & Compliments for student reporting
* Would this work for all groups of numbers?
* How is this strategy similar or different from your strategy?
* Which strategy is most efficient (quick and smart)?
What will you see or hear?
* Pre-selected students show work on the document camera.
* Students questioning, commenting, and complimenting to create mathematical arguments
* Students examining strategies and proving them to determine accuracy.
Misconceptions:
* adding two numbers and forgetting the third number
* putting numbers together as a place value (645)
* adding the first two numbers and sticking the other number on the end
* counting the starting number on the number line as part of the “jumps”

Miss Althoff went to the Nickelcade and earned tickets from three different games. She earned 6 tickets from Ski Ball, 4 tickets from Basketball, and 5 tickets from Whack-a-Mole. How many tickets does she have? Use numbers, words, and/or pictures to show your work.

Adding 3 Numbers

______+ ______+ ______= ______

______+ ______+ ______= ______