Domain: Operations and Algebraic Thinking Standard Code: 1.0A.2 Teacher Name: Westside Teachers 1st Grade

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:
OA.2-Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20.
*Develop an understanding of addition of more than one number
*counting on-strategy
*Commutative Property (numbers can be added in any order)
·  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
* counting all & counting from larger number (using tools ex. number line, pictures, counters, Rek-en-Rek etc.)
* using known facts & derived facts (doubles fact plus one, combination of ten, expanded notation)
Background Knowledge:
Students should be able to do the addition of two numbers
Tools:
·  linking cubes
·  number line
·  two colored counters
·  rek-en-rek
·  white board and marker
·  journal and pen or pencil (pictures)
·  beans
-Students will work independently at first to solve the problem. Then students will pair share with their partner and lastly they will discuss and share their strategies as a class.
-Students will record their work in their math journal and then report to a partner. The teacher will select students to report during the discuss phase of the lesson.
How will you introduce students to the activity so as to provide access to all
students while maintaining the cognitive demands of the task? / Your sister went to an ice cream shop. She decided she wanted 3 different toppings on her ice cream sundae. She decided to put 8 chocolate chips, 3 sprinkles and 2 nuts on top. How many toppings total did she put on her ice cream?
Low: Students pick out two toppings which sum is 10
Average: 3 toppings to 10
High: 3 toppings to 20
Literature Connection: The Sundae Scoop by: Stuart J. Murphy
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? / Starting-
How are you going to get started?
What are you trying to figure out?
Show me what numbers you know
What happened next?
What tools can you use?
Focus-
What two numbers did you add first?
Why did you choose those numbers?
Can you add two different numbers first?
What are you trying to find out?
Assess-
How did you get there?
How do you know? Are you sure?
What does that mean?
Will you explain that to me?
Advance-
Show me a different way?
Are there other combinations that you could add first?
What other combinations of numbers or toppings can you add first?
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
Actual toppings to use when counting
Can you show with your fingers?
What if you draw a picture?
Look on your number line? How could you use that to help you?
What does your partner think?
Extensions:
-Have students make (draw) their own ice cream sundae. Have them decide what toppings and
how many they will put on their sundae and then add up how many toppings they had.
-Have students pull out new toppings and amounts of toppings and solve the problem again. See if
they can solve it another way.
-Have students make a math book where you can lift the flap (open door or window etc.) and show
your work or answer.
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 Paths:
* Counting All starting at 1
* Picture representations
* Counting On from the larger number
* Tally marks
* Known facts (combinations of ten: 8+2=10)
* Derived facts (doubles plus one)
* Finding different combinations to add first
* Number line, putting the objects on to the line
Misconceptions:
*That you can only add the numbers in the order in which it is listed
*That they are trying to make them all equal shares
*That they may be adding the wrong numbers
*Starting on the wrong number on the number line
*Counting the ice cream as one of the toppings
Specific Questions:
*What do your drawings show?
*Explain your thinking.
*How do you know this?
*Can you explain it to your partner?
*Is there another way you could mix up your toppings?
Know they Understood:
*Illustration will match the number sentence.