Thinking Through a Lesson Protocol (TTLP) Template s9

Domain: Unit Rate Standard Code: RP. 3b Teacher 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 Solve a real world problem using unit rate in pricing. the lesson? (i.e., what do you want students to know and understand about mathematics as a result of this lesson?)

 What are your expectations for Students will be able to interpret data to calculate the unit rate of various priced items while students as they work on and comparing. complete this task?  What resources or tools will Use grocery ads with prices and ounces listed. Have the students find items to compare between students have to use in their different stores (ads). They can have the same price, but different ounces, generic vs. name brand, etc. work that will give them Use any manipulatives you have, Unifix cubes, tape diagrams, etc... entry into, and help them reason through, the task? Work in independent groups, pairs and groups. This will ensure all ideas are included.  How will the students work— independently, in small groups, or Use math journals to record and show work. Include pictures and calculations (no erasing allowed). in pairs—to explore this task?  How will students record and report their work?

How will you introduce students to the Initial questions/displays, written and verbal instructions. activity so as to provide access to all Set up same cereal but different ounce amounts. Each box has a price tag. Ask the student which box students while maintaining the of cereal would you buy? Why? Explain your answer (draw pictures/calculations) cognitive demands of the task? Better Buys PART 3: SHARING AND DISCUSSING THE TASK How will you orchestrate the class Look for some that used estimation and have them explain their methods. discussion so that you accomplish your mathematical goals? Next, have groups that calculated explain their methods. PART 2:W ShUPichP soORlutionTING p aStThsU DdENTS’o you EXPLORATION OF THE TASK As studwenatsnt wtoo hark vine dsharedepend ednutlyring Have students decide when each method would be appropriate. or inthe small groups, what Bring students together and ask them which they would choose before having them questionsclass w illd yiscussion?ou ask to— In whatdiscussAsk studentsas a group other (record factors votes that on they board). might consider (ie. What if you only needed  helporder a g wroupill theget st solutionsarted or be one box of cereal? Is there a time you might not buy the better ounce?) mapreske nptreodgr? essWhy on? the task? As groups of 3 or 4 they must decide which is the best deal and why. They must Look at individual work to help evaluate student understanding.  fWochuats stuspecdeifnicts’ q uestthinkingions wonill defend and justify their answer, theyou ask so that students will— Provide follow up problems and check answers. k1ey. ma maktehemat senseical of theideas Bring students back together as a whole group to discuss group choices and in themathematical task? ideas that reasoning. Hamburger is $4 for 5 lbs, how much is it per pound?  asseyssou stu wadnetn tts’hem to learn? und2ersta. expandinndg on,of debate, and Students will record work in math journals and individual/group votes can be keyq muestathemation theical solutions ideas, recorded on a white board/smart board. being shared? problem- solving strategies, Resources: or3. the ma rkeep conresennectionstations? among the different strategies that News article about pricing scams. Good to show students to check unit pricing.  advance students’ are presented? http://lifehacker.com/5813854/what-not-to-buy-at-the-warehouse-club understanding 4. look for patterns? of the mathematical ideas? 5. begin to form Worksheet on unit rate generalizations? http://www.edhelper.com/math/ratios217.htm How will you ensure that Questions to ask/ that will help: students remain engaged in What strategy did you use/ Show me what you did or what you pictures mean? What the task? made you choose that size? What were you most concerned with size or price? What What will you see or hear that lets  What assistance will you did you do to be able to compare the different products? you know that all students in the give or what questions class will you ask a Frustration: understand the mathematical ideas that student (or group) who Give simple examples (ie. Hamburger is $4 for 4 lbs, how much would 1 lb. be? you intended for them to learn? becomes quickly frustrated and Extensions: requests more direction Have students figure cost with coupons. and guidance is Give students a recipe, cost, budget, etc… See if they can purchase all the ingredients solving the task? for less the budgeted amount. Have a contest between students to see who can save  What will you do if a the most (use coupons/price comparing) student (or group) finishes the task almost 1. Smiths has Tillamook cheese for $3.99 for 2 lbs. Maceys has their cheese 2 for $6 for 8 oz. Which one is the better deal? Show your work and justify your answer in complete sentences. 2. Fresh Market has a sale that if you buy 5 boxes of cereal you get $5.00 off. The Mini Wheats are 15.8 oz and start at $2.49 per box. What would you pay per ounce if you were to buy only one box, 2 boxes or 5 boxes?

Allen’s Mini Wheats are 4 for $10 and the boxes are 18 ounces. How much would you pay per ounce?

Which Mini Wheats are the better deal? Allen’s or Fresh Market’s? Justify your answer using pictures and write complete sentences.

3. Dan’s grocery store is selling Cheetos for 3 for $5 and they are 9.75 ounces and Walmart is selling their Cheetos for $1.50 per bag and you get to choose the size of the bags which are 9.5 ounces and 9.75 ounces. Which Cheetos are the better buy? After you find your answer develop a formula that would work when comparing ounces. (Prices are altered from the ad below to fit this particular question. You could change the price to fit the ad.)