Best Buy on Cat Food and The Price of Birdseed 6th Grade Math Focus 2: Rates, including percent Standards: 6.RP.2, 6.RP3b, 6.RP.3c Resource: Fosnot- Best Buys, Ratios, and Rates Addition and Subtraction of Fractions Best Buy on Cat Food and The Price of Birdseed

DAY ONE: Part 1 Students investigate, develop strategies, draft “proofs,” and create a poster clearly displaying their understanding

Today’s Learning Target Students will be able to understand proportional reasoning, fractions, and equivalence by determining the unit prices or comparing the costs of buying more cans/items in a group.

Today’s Learning Target Scale 4 I understand ratio, rates, and proportions thoroughly. I can confidently use what I have learned. I can help others understand it. 3 I am able to understand proportional reasoning, fractions, and equivalence by determining the unit prices or comparing the costs of buying more cans/items in a group  2 I have a basic understanding of ratios, rates, and proportions. I’ve identified a few questions that I’ll need to have answered before I use what I have learned. 1 I have some understanding of some parts of ratios, rates, and proportions. I have many questions that I’ll need to have answered before I can use what I have learned. I do not understand ratios, rates, and proportions. I do not know where to begin.

TEACHER ONLY! Lesson Overview Day One: Best Buy on Cat Food Recommended Needed Materials: Bob’s Best Buy poster and Maria’s Pet Emporium poster Drawing Paper- a few sheets per pair of students Large chart paper- one sheet per pair of students Markers Overview: Support the development of several big ideas related to proportional reasoning, fractions, and equivalence. Working with partners, students explore two stores’ pricing for cat food to determine which store has the better price. They may consider unit prices, or compare the costs of buying more cans in a group. Day One Outline: Developing the Context: introduce and discuss the cat food context and ask students to investigate which store has the better price Supporting the Investigation: as students work, encourage proportional reasoning and keep students grounded in the context to help them understand what the numbers represent Preparing for the Math Congress: ask students to make posters depicting their work on the investigation, sort the posters by strategy in preparation for the math congress to be held on Day Two. Then plan to arrange each small group to include students who used a variety of strategies.

TEACHER ONLY! Lesson Prep You may want to hang the posters side by side on the board so you don’t need to go back and forth with the slides. Introduce and discuss the cat food context/posters and ask students to investigate which store has the better price.

Bob’s Best Buys

Maria’s Pet Emporium

These are pictures of two pet stores These are pictures of two pet stores. As you can see, both stores are having a sale on cat food. Bob’s ad reads, “This week only: 12 cans of KittenGourmet for $15.” Maria’s ad read, “Super Sale: 20 cans of KittenGourmet for $23.” Both stores are offering the same brand of cat food but are pricing it differently! Advertising is often confusing, isn’t it? Each store wants you to think that it has the best sale price. 1. Which store has the better price? 2. How do you know?

Which store has the better sale price on KittenGourmet? Working with your partner, investigate the problem and develop a strategy to solve the questions below. Which store has the better sale price on KittenGourmet? How do you know? Explain your “proof” in your math workbook (3-5 sentences) and be prepared to share your proof with another pair of students.

TEACHER ONLY! Guided Support Support and challenge their investigation BIG IDEA! The unit price (price of one can) is the result of division which is the heart of proportional reasoning in rate problems. Students may not find the unit price but consider the pricing for other numbers of cans like price for 20 cans, 10 cans, or 5 cans. As students work, encourage proportional reasoning and keep students grounded in the context to help them understand what the numbers represent. Possible strategies: division with reminders, distributive property and making partial quotients, using a ratio table, using multiplication to find the price of 60 cans at each store.

DAY ONE: Part 2 Creating Clear and Concise Strategy & “Proof” Posters to Prepare for the Math Congress

TEACHER ONLY! Strategy and “Proof” Posters Needed Materials: large paper (butcher paper) one piece per pair, markers, push pins or masking tape to hang around the room when completed After a sufficient amount of time has been devoted to the investigation Ask students to make posters in preparation for the Math Congress One large sheet of paper to each pair of students and make markers available Explain that the posters should NOT be students’ draft notes copied over!!! They should be CONCISE, CLEAR presentations of the important ideas and strategies students want to present. As part of the solving strategy, students should include their CONVINCING, ELEGANT “proof” or argument justifying their logic and develop the ability to communicate their ideas to others.

TEACHER ONLY! As the Pairs Complete their Posters Plan on structuring three or four small-group discussions This will allow ample student discussions on the variety of strategies used and the connections between them Sort the student work by strategy- look specifically for unit pricing and proportional reasoning Also examine how the remainders have been treated Then arrange each group to include students who used a variety of the different strategies

TEACHER ONLY! Reflections on the Day Several BIG IDEAS about division and equivalence of fractions were explored today as students investigated the best buy situation Some students used division to find and compare unit prices Some students used proportional reasoning and repeated divisions to find and compare unit prices Some students compared prices for different numbers of cans or compared the numbers 3 12 𝑎𝑛𝑑 3 20 to determine which store offered the better buy. As students generalize these ideas, their proportional reasoning will develop During the math congress on Day Two, you can introduce the ratio table and its value in examining equivalence!