EduGAINs



OverviewIn this activity students calculate unit rates and use them to make comparisons. They contrast the strategy of calculating unit rates with other strategies used to solve proportion problems.Important Mathematical Ideas A rate is a comparison of two quantities with different units.A unit rate is a rate with a second term of 1.A unit rate can be used for solving proportion problems.Prior KnowledgeUnderstanding that a rate is a comparison, or ratio, of two measurements with different units.Using unit rate to make comparisons (e.g., what's the better deal?)Common MisconceptionsInterpreting cost per item to be the same as number of items per dollar.Units are not necessary for describing unit rates.Lack of understanding that solving a ratio, rate or percent problem always involves determining an equivalent ratio in an appropriate form for the situation.Curriculum NotesAlthough rates were introduced in earlier grades, many students are developing their ability to think proportionally. Solving problems with memorized procedures does not help them to develop this essential thinking skill. (Paying Attention to Proportional Reasoning page 4)Information to Support/ Enhance/ Extend LearningStudents are asked to keep a journal for each unit in the course. It should contain notes of important mathematical ideas with examples and new vocabulary.ePortfolio may be used for these journal entries.Students can make individual choices whether this is a paper or digital personal resource.Consider a variety of formats as alternatives to journal entries (e.g., student note, pair/share, group discussion, exit card, poster, electronic posting).Develop a Word Wall and continue it throughout the unit as new vocabulary and terms arise that require clarification (e.g., rate, unit rate).Minds OnTask 1: Review Rates and Unit RatesReview definitions.Review Rates and Unit Rates at?Math Antics. Show from time 5:12 to end.can be watched as a whole class pausing at key points to discuss learningTask 2: Rate My GroceriesInteractive learning object (ELO1414380) showing how unit rates apply to grocery shopping.Bring in examples of priced grocery items that will help students to understand unit rate, (e.g., two packages of granola bars showing different quantities like 6 and 12, cereal boxes of various sizes).Journal Prompts and Sample ResponsesWhat is a unit rate?A unit rate is a ratio of two measurements with different units and a second term of 1.Why is unit rate important?A good understanding of unit rates can save you money.How can you calculate unit rate?If a rate is given and the quantity in the denominator is not 1, the unit rate is calculated by finding an equal ratio where the denominator is 1.Task 3: Check Your UnderstandingStudents will:solve comparison problemscheck with provided solutions which use a unit rate strategyCan be done with a Think/Pair/Share strategy.Observe to see the variety of strategies (e.g., ratio table, percent, reasoning) and share with the class making connections as appropriate.ActionTask 4: Discussion Prompts and Sample ResponsesGale is shopping for laundry detergent. She examines two brands:Clean and Fresh sells for $5.49 and will do 10 loads of laundry.Colour Safe sells for $11.74 and will do 20 loads of laundry.Determine which brand is the better deal.Sample 1:Clean and Fresh sells for??Colour safe sells for?The unit rate for Clean and Fresh is less, so it is a better deal.Sample 2: I notice that the Colour Safe box does exactly twice as many loads.Clean and Fresh sells for ?The price for 20 loads of Clean and Fresh is less, so it is a better deal.Is calculating unit rates always the best strategy to use when comparing deals?No, in this case it was easier to make the comparison for 20 loads. To use mental math, to double $5.49, I would double $5.50 which is $11.00. This quick mental calculation tells me Clean and Fresh is a better deal.Responses should include:calculations showing the unit rate for each brand of laundry detergentan explanation of which laundry detergent is the better deal using unit ratesan explanation of which laundry detergent is the better deal using a strategy other than unit ratesa comparison of the two strategiesCommon Errors:not including units with unit ratedividing the quantity by the cost and misinterpreting the resultConsolidationTask 5: Check Your UnderstandingStudents will:solve problems using unit rates or another strategycheck their solutions with the sample solutions providedCan be done as a Think/Pair/Share.Discuss the variety of strategies presented. Ask if students might use someone else's strategy another time.Task 6: Journal Prompt and ResponseIn this unit called?Proportional Reasoning, you have used four computational strategies to solve proportion problems: equivalent ratios, ratio tables, percents, and unit rates. Describe what you look for in a problem to help you decide when to use each of these strategies.I would use equivalent ratios if a problem involves a relationship with two quantities with the same units.I would use rate if a problem involves a relationship with two quantities with different units.I would use percent if a percent is given in the question.I would use ratio tables to solve equivalent ratio or percent questions.Consider reserving the Frayer Model Reflection for?Proportional Reasoning for later in the unit. At this time have small groups of students develop a?Frayer Model?for unit rates or consider constructing an?Anchor Chart?on equivalent ratios as a whole-class activity on unit rates.Task 7: Assignment 1: Unit Rates ReportPosted with unit.See sample solution in the Teacher Notes posted on the vLE.Task 8: Student ReflectionStudents are asked to reflect on their understanding of this topic.These reflections can be used as assessment for learning to help determine next steps for individual students. ................
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