Thinking Through a Lesson Protocol (TTLP) Template s10

Domain: Geometry Standard Code: G2 Name:

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 G2 – Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the the lesson? (i.e., what do you want whole. (fractions of 1/2,1/3,1/4,1/6,1/8) students to know and understand about mathematics as a result of this lesson?)

 What are your expectations for  Students share with table partners about their pet. Draw a diagram of the cages and write the students as they work on and fraction for it. complete this task?  What resources or tools will  Graph paper, pencil, ruler, cm cubes or square tiles, 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—  Small groups/tables independently, in small groups, or in pairs—to explore this task?  Draw and label pictures, and share with the class what fraction of the kennel was used.  How will students record and report their work? How will you introduce students to the Questions for introduction: How many of you have a pet? Have you ever had to leave your dog? activity so as to provide access to all students while maintaining the Your family is going on a vacation. You need to leave your dog in the dog care center. You have a cognitive demands of the task? building that is 12 by 18 feet. Create a kennel with equal-sized cages. What does it look like? Draw your kennel. What fraction of the area does your dog stay in?

How many people at your table have a dog? If each of you had a dog, what fraction of the kennel is open?

The kennel has 3 different areas of 12 x 18 each. Each of the 3 areas has different sized cages. Which size cage would your dog need and what fraction of that area would that be? PART 3: SHARING AND DISCUSSING THE TASK How will you orchestrate the class discussion so that you accomplish your mathematical goals? Are the parts equal? PART 2:W hSUPich PsoORlutionTING p aStThsU DdENTS’o you w EXanPtL ORA TI DidON you OF have THE the TA sameSK as someone else? As studteon hats vweo sharedrk inde dpuernidnegn thetly or in How is your kennel the same or different to other tables? small grclassoups, d iscussion?what quest Iionsn w hwatill o yrdouer will Does the shape of your kennel determine the fraction? ask to—the solutions be presented? Why? Are youWhat using was thethe entiremost importantspace? idea you had to create your kennels?  Whelphat a s gprecoupific g qetuest staironsted worill ma youke ask Is each What piece fractional equal? part would give you the most cages? sopr othatgress stu onde thents twill—ask? Is the What size reasonable? roadblocks did you encounter while working?

 f1oc. umas stuked seennsets’ thinkingof the on the Can you explain that to me? keymathematical mathematical i iddeeaass that in the you Why did you divide it that way? Extension questions: taskw?ant them to learn? Why did you choose (fourths)? What size kennel is the most economical for a kennel to have?  ass2. eexpass stundd eon,nts’ d eunbadterstae, andn dqiuestng ofion Show me and explain your picture. the solutions being shared? Would How you would mind thesharing size ofyour the ideas? dog change your kennel design? key mathematical ideas, problem- Is there a cost difference for the different size cages and what would it be? 3sol. vmaingk strate conengectionsies, or the am ong the reprdesiffeerentntations? strategies that are  advpanrescee stuntedde?nts’ understanding 4of. the loo mak forthemat patteircalns? ideas? 5. begin to form generalizations?

What will you see or hear that lets you Pictures show equal parts, know that all students in the class How will you ensure that students understand the mathematical ideas that On-task students more engaged remain engaged in the task? you intended for them to learn? Use the vocabulary of “geometry and fractions”  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 Early finishers: what is the area of your cages? group) finishes the task almost immediately? How will you extend the task so as to provide additional challenge?