Domain: Operations Standard Code: 2.OA.2 Teacher Name: Susan Stoddard

* Note: Weber School District teachers…. This task goes with Unit 1 lesson 3 Expressions lessons.

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?) / ·  Students will understand that zero added to or subtracted from any number equals the original number.
·  Students will become more fluent at adding and subtracting two one-digit numbers when one of the numbers is a zero.
·  Students will create a mental strategy as they discover the rule for sums and differences that involve zero.
·  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? / Expectations:
·  Students will explore add and subtract equations that contain a zero using the number cards.
·  Students will record the equations they build on a T chart. ( plus sign and minus sign on T chart.)
·  Students will recognize a pattern in the equations as they add and subtract zero to another number.
·  Students will discuss their learning with a partner.
·  Students will formulate and record a rule that explains the sum of equations when zero is present as an addend and the difference of equations when zero is subtracted from any number.
Materials:
·  Number cards 0 through 9 (The set must contain two of each numeral.)
·  Add, subtract, and equal sign cards
·  Math journal with T chart drawn on page. (plus on one side, minus on one side)
Students will work:
·  With a partner
Students will:
·  Record equations, answers, ideas, and their rules in their math journals.
·  Students will share their thinking with other students on their team tables.
How will you introduce students to the activity so as to provide access to all
students while maintaining the cognitive demands of the task? / Wrap a box in an interesting way. Tell students they are going to solve a mystery. They must figure out the mystery of the box. What do you think is in the box? Give students clues until they discover there is nothing in the box. Tell students there is nothing, or zero of anything in the box. Tell them they are going to solve the “mystery of zero.”
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? / ·  Who is the student? Teacher?
·  How many equations have you written?
·  What do you notice as you build the equations and write them down?
·  Is there a pattern?
·  What are you thinking about zero as you build?
·  Can you explain what is happening?
·  What do you need to do next?
·  Do think there could be another way to find the solution to the mystery?
·  Have you written the solution to the mystery?
·  Can you prove that your solution is correct?
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? / All students will be required to complete the T chart. Partnerships that complete the task will receive points for their team. The teacher will circulate around the room and interact will all groups. This is a simple task designed to give students success early in the year.
·  What is the first step? (model if necessary)
·  What is the next step?
·  Look closely at your chart, what pattern can you see?
·  What is your solution? Can you write it?
Extensions:
·  Use your number cards to find a mystery pattern or rule with the number 1.
·  Can you find another mystery pattern using numbers?
·  Write another mystery task for your classmates to solve.
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? / All students will be solving the mystery or finding the rule of zero by recognizing the pattern. Because of this, it is unlikely that there will be many different ways of finding the solutions. Therefore the discussion will need to be whole group. Students could share their thinking processes. Students that complete the extensions could share their discoveries.
·  What is the mystery of zero?
·  Which step of the task were you on when you solved the problem?
·  Do you think that other numbers may have mystery patterns? How would those patterns be different?
·  Can you make any connections to another math activity or game?
·  Did you think the task was difficult? Why?
·  Can you think of a question about number patterns, addition patterns, or subtraction patterns?
·  Evaluate the T charts and solution sentences of each students.
·  Observe students as they build the number sentences and discuss the mystery.
·  Each student will be able to explain, orally, what they were thinking as they discovered the solution to the mystery.
·  Each student will be able to explain which step they were working on when they discovered the pattern.

Task:

You and your partner are going to work together to solve the “mystery of zero.” You will use number and symbol cards to build addition and subtraction equations that contain a 0 in the problem. One of you will be the teacher and one of you will be the student.

(1) The student will build number sentences or equations. The teacher will supervise the student and record the number sentences on his or her “T” chart. The student will build a subtraction number sentence for each number and a zero, and an addition number sentence for each number and a zero.

(2) Next the teacher and the student will switch roles and the new teacher will record on his or her T chart.

(3) After both partners have completed the T chart you will discuss what you have learned about zero.

(4) The last step of the task is to write a sentence or two that explain what you have learned about the number zero. What is the interesting mystery?

*Please keep your solution to the mystery a secret!!

Note:

The teacher should model making a number sentence with the cards, and recording the equation on the T chart.