Thinking Through a Lesson Protocol (TTLP) Template s27

Domain: Operations &Algebraic Thinking Standard Code: #7 Teacher Name: Jody K. Coy

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 Students will understand the meaning of equal. Students will also recognize and understand the the lesson? (i.e., what do you want meaning of the equal sign, and determine if equations involving addition and subtraction are true or students to know and understand about false. For example, which of the following equations are true and which are false? 6 = 6, 7 = 8-1, mathematics as a result of this lesson?) 5+2 = 2+5, 4+1 = 5+2. involving addition and subtraction.

 What are your expectations for Counters students as they work on and Linking Cubes complete this task? Coins  What resources or tools will Ten Frames students have to use in their Sorting circles work that will give them Paper entry into, and help them Pencil, markers reason through, the task? Small White Boards or Cardstock in Sheet Protector per student  How will the students work— True/False Cards for each student independently, in small groups, or in pairs—to explore this Students will work whole group at first and transition into pair groupings and finally they will work task? independently  How will students record and Students will report their work using a math journal/notebook and document camera or a large piece of report their work? paper and markers. How will you introduce students to the Write 3+2=5 Stating, “Is three plus two equal to five.” How about 4+3= 7 or 6-4= 2 (discuss). What activity so as to provide access to all about 7=7 (discuss). We now agree that these are equal. Is two plus six equal to 9? Is seven take away students while maintaining the two equal to five? (Students can hold up True/False Cards or White Boards to show answer). cognitive demands of the task? *Tasks If Ben has 6______and Pat has 4 how many more does Pat need to have the same amount? Show it concretely with choice of manipulative. Then show it symbolically with numbers and the equal sign. If Ben has (any number) ______how many does Pat need to have the same amount? Show it concretely with choice of manipulative. Then show it symbolically with numbers and the equal sign. I would recommend changing the way the numbers look somehow. You could use wingdings or some other crazy font or something to disguise the

PART 3: SHARING AND DISCUSSING THE TASK How will you orchestrate the class Solution Path: discussion so that you accomplish your Using counters or other manipulative mathematical goals? Using Ten Frames PART 2:W hSUPich PsoORlutionTING p aStThsU DdENTS’o you w EXanPtL ORAPictureTION O representations.F THE TASK As studteon hats vweo sharedrk inde dpuernidnegn thetly or in AskNumerically questions such and as: Symbolically small grclassoups, d iscussion?what quest Iionsn w hwatill o yrdouer willGetting Started Questions: ask to—the solutions be presented? Why? How many does Ben have+? How many does Pat need?  Whelphat a s gprecoupific g qetuest staironsted worill ma youke ask CanSpecific you write Questions: the numbers for that? sopr othatgress stu onde thents twill—ask? WhatHow do couldyou know? you show What this are another you trying way? to find out? How can you start? What tools can you What else do you notice?  f1oc. umas stuked seennsets’ thinkingof the on the use? keymathematical mathematical i iddeeaass that in the you taskw?ant them to learn? Focus Questions: What will you see or hear?  ass2. eexpass stundd eon,nts’ d eunbadterstae, andn dqiuestng ofion How do you know? How did you get there? What else can you do? They were accurate in their work showing equal amounts and values concretely. keythe ma tsolutionshematical b eidingea s,sha prrobleed? m- 3. make connections among the AssessingThey respond Questions: accurately with True/False Cards or White Boards solving strategies, or the They came up with multiple accurate combinations symbolically. reprdesiffeerentntations? strategies that are Will you explain that to me? How did you come to that answer? How are you sure?  advpanrescee stuntedde?nts’ understanding What does that mean? (It’s the same on both sides). 4of. the loo mak forthemat patteircalns? ideas? 5. begin to form generalizations? Advanced Questions: What do you notice? Is there a different way to organize your work? Can you show another way? What will you see or hear that lets you What else do you notice? know that all students in the class How will you ensure that students Assistance: understand the mathematical ideas that remain engaged in the task? Reduce the number given. you intended for them to learn?  What assistance will you give or Give students examples of equal and not equal groups using manipulatives, pictures, or number what questions will you ask a representations. student (or group) who becomes Give students sorting circles or graphic organizer with dashes for numbers. quickly frustrated and requests Assign them a partner early. more direction and guidance is solving the task? Extensions:  What will you do if a student (or Add number sentences. group) finishes the task almost Have them use a different manipulative (i.e. Money) immediately? How will you Have them show it a different way. extend the task so as to provide additional challenge? numbers. Here are the numbers 1-10 changed to the wingding font.



You could set up equations like:

2 + 3 = 5

5= 2 + 3 to look like:





You could leave the symbols the same like this:

+=

=+

You can build on the idea to then make other properties of being equal such as fact families. You could put a bonus challenge of figuring out the value of each symbol (they can do this if you do something that adds to 10). The true of false cards would be a quick assessment way but then you’d have to find someone with a similar or opposite sign and explain WHY you think it is true or false. I think that would make it perhaps more 1st grade level of fun than just standing up saying what you did in the front.

I think the task of asking what would you Pat need to equal Ben will be all the more powerful after having struggled to understand the value of the symbols or while still trying to remember the relationship.

Let me know what you think.