Stage 1: Desired Results
| |Quarter: 2 |Unit number: 2 | |Unit title: Ratios and Proportional | |
| | | | |Relationships | |
| |Academic Course: |Grade: 9 |School: Fenger |
| |Algebra | | |
| |Created by: Christopher D. McFarland/Astrid Rodrigues |Date: 7/27/13 | | |
| |Taught by: Christopher D. McFarland |Unit length: 6 | | |
| | |weeks | | |
|Stage 1: Desired Results |
|Established Goals |
|Thinking Process in Unit 2 is Decision Making with a focus on real life scenarios like sales, ratios in cooking and nutrition, ratios found in art art, nature and |
|architecture as examples. In this unit students will receive a series of weekly problems where they will have to compare and decide which item is a better deal. In|
|order to deduce effectively they must begin to master fractions and manipulate ratios so as to compare ratios effectively. Students will learn that a ratio |
|expresses the comparison between 2 quantities. Students will apply (CCCS 6.RP.A.2 & CCCS 6.RP.3) to understand unit rate and how it relates to ratios. Student will|
|begin this unit by reviewing (CCCS 3.F) fractions, representing them on a number line and generating simple equivalent fractions. Students will apply these |
|principles to real-world contexts like pricing and constant speed. Students will then use rate language to describe ratio relationships between two quantities. |
|Although procedural skill and fluency should be improved through this unit, conceptual understanding will be the basis for discovery and instruction. Student |
|understanding of content and thinking processes utilized will be determined by their performance on the transfer task which will also include a written narrative. |
|Transfer |
|Students will be able to independently use their learning to… |
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|Plan a recipe, using ratios to find the quantities, unit rates and cost of ingredients for different number of servings. |
|Meaning |
|Enduring Understandings |Essential Questions |
|Students will understand that… |Students will keep considering… |
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|Numbers |What does a fraction describe in different scenarios? |
|- A fraction describes the division of a whole region into equal parts. | |
| |How are the addition and subtraction of whole numbers similar to the addition and |
|- A fraction is relative to the size of the whole or unit. |subtraction of fractions? |
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|- The real-world actions for addition and subtraction of whole numbers are the |How can fractions be ordered from smallest to largest or largest to smallest when |
|same for operations with fractions. |the denominators are not the same? |
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|Equivalence, Proportionality, Comparison |How can proportions be used to solve real-world problems? |
|- A ratio is a multiplicative comparison of quantities. | |
| |What proportion is needed to produce equivalence given in a real-world scenario? |
|- Ratios give the relative sizes of the quantities being compared, not | |
|necessarily the actual sizes. |How are ratios compared to determine which is larger or smaller? |
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|- Proportions can be used to solve real-world problems. |Do we need to know the actual sizes to compare different quantities? |
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|The equal sign can indicate that two expressions are equivalent. |Why is it sufficient to know the relative sizes of quantities being compared? |
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| |What is unit rate and how is it determined? |
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| |What can unit rate tell us when making comparisons? |
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| |How are ratios, proportions and unit rate related? |
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|Acquisition of knowledge and skills |
| Students will know… |Students will be able to… |
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|The meaning of denominator, numerator, equivalent, ratio, unit rate, |CCCS 3.F |
|proportion(al). |Understand two fractions as equivalent (equal) if they are the same size, or the |
| |same point on a number line. |
|To represent fractions on a number line diagram. | |
| |Recognize and generate simple equivalent fractions, e.g., 1/2=2/4, 4/6=2/3. |
|To reduce a fraction by finding a common factor. |Explain why the fractions are equivalent, e.g., by using a visual fraction model. |
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|That two fractions are equal if they are the same size. |Express whole numbers as fractions, and recognize fractions that are equivalent to|
| |whole numbers. |
|To recognize and generate simple equivalent fractions. | |
| |CCCS 6.RP – Ratios & Proportions |
|To recognize fractions that are equivalent to whole numbers and that they |Understand the concept of a ratio and use ratio language to describe a ratio |
|represent division. |relationship between two quantities. |
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|The difference between a fraction and a ratio. |CCSS.Math.Content.6.RP.A.2 Understand the concept of a unit rate a/b associated |
| |with a ratio a:b with b ≠ 0, and use rate language in the context of a ratio |
|The unit rate is when one of the two quantities is 1. |relationship. For example, “This recipe has a ratio of 3 cups of flour to 4 cups |
| |of sugar, so there is 3/4 cup of flour for each cup of sugar.” “We paid $75 for 15|
|To use ration language to describe relationship between two quantities. |hamburgers, which is a rate of $5 per hamburger.”1 |
| |CCSS.Math.Content.6.RP.A.3a Make tables of equivalent ratios relating quantities |
|Understand unit rate and use rate language to describe ration relationships. |with whole-number measurements, find missing values in the tables, and plot the |
| |pairs of values on the coordinate plane. Use tables to compare ratios. |
|Make tables of equivalent rations, find missing values in the tables and use |CCSS.Math.Content.6.RP.A.3b Solve unit rate problems including those involving |
|tables to compare ratios. |unit pricing and constant speed. For example, if it took 7 hours to mow 4 lawns, |
| |then at that rate, how many lawns could be mowed in 35 hours? At what rate were |
|Solve unit rate problems. |lawns being mowed? |
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|How to use proportional relationships to solve real-world problems. | |
| |----------------------------------------------------------------------------- |
| |Re-teaching Plan: Students will be able to….. |
|Stage 2: Assessment Evidence |
|Performance Task |Other Evidence |
| |Bell Ringer |
|Students will plan a recipe, using ratios to find the quantities, unit rates and|Exit Tickets |
|costs of ingredients for different number of servings. |Class work |
| |Weekly Quizzes |
|Tittle: Pizza Champions |Ratio Quiz |
|For this performance task, students will assume the role of school cafeteria |Rates and Unit Rates assessment |
|chef to create a pizza recipe and plan ingredients to make pizza for 12, 60 and |Group Assignments |
|240 students. Students compute unit pries for the ingredients, prepare a budget,|Narrative writing / rigorous writing tasks |
|and calculate the cost to feed varying number of people. Using ratio/rate |Individual and whole class questioning |
|language, each students writes a proposal to persuade the cafeteria manager to | |
|use the recipe. | |
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|List of Large-Scale Tasks | |
|Task I : Cost of make 1 pizza | |
|Task II: Cost to feed 12,60, 240 students | |
|Task III: Proposal to the Cafeteria Manager | |
|Stage 3: Learning Plan |
|Learning Activities – Integrate Re-teaching Plan activities into the learning sequence and indicate with an asterisk* |
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|Week 1: Review / re-teach fractions and equivalent fractions |
|Comparing fractions: |
|Snow Day |
|Comparing Pizzas: |
|Money in the piggy bank: |
|Making cookies: |
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|Week 2 and 3: Ratios – Introduction to ratios, writing ratios, solving math and real-life problems with ratios |
|Variety of teaching videos at learnalberta.ca which focus on definition of ratio and the ways that a ratio can be expressed |
|Spy Guy video – |
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|watch?v=eT1yYqmjHPY or watch?v=yztq_ELjfSw&feature=related |
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|Writing ratios: |
|Interactive site where students learn how to use blocks to model ratio problems |
|ThinkingBlocks_Ratios/ TB_Ratio_Main.html |
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|Find ratios using a cup of beans: |
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|Practice sheets to help students explore ratio relationships: math-.Ratios/ |
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|Table of equivalent ratios |
|Week 4: Unit Rate and Proportions – Understanding rates and unit rates, solving problems with unit rates, using rates / unit rates to make good consumer decisions |
|Buying gas: |
|Anna in D.C: |
|Gotham City Taxis: |
|Music Companis: |
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|Grocery Store Flyer Scavenger Hunt: Students are provided with a worksheet that lists various grocery items. They find the unit rate for each item on the list. |
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|Assessment: |
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|Pizza Party: Justin is organizing a pizza party. He needs to buy 4 pizzas for the party. He found 3 ads in his local newspaper: |
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|Rosa's Pizza |
|Pizza Mart |
|Collins Pizza |
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|Each 12-inch pizza: $6.35 |
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|Buy 3 and get 1 free! |
|Each 12 inch pizza: $4.65 |
|Four pack of 12-inch pizzas: $19.60 |
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|Where would Justin get the best deal? |
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|Little Red Riding Hood's Grocery Trip |
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|Week 5: Proportional Relationships |
|Running at constant speed: |
|The escalator: |
|Walk-A-Thon: |
|Art Class: |
|Robot Races: |
|Sore Throats: |
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|Week 6 – Transfer Task – See Below |
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|Task 1: Student Directions: |
|You have created an award-winning recipe for pizza. You must write a proposal to convince the cafeteria manager to use your recipe. The proposal will include the |
|cost to feed 12, 60 and 240 students. To help persuade the manager, you must explain all of the mathematics used to create your budget. |
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|First, you will find the cost to make one pizza using your recipe. |
|Second, you will determine the cost to make pizza for 12, 60 and 240 students. |
|Last you will write a proposal to the cafeteria manager. |
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|Use the price sheet to determine the ingredients for your pizza. |
|You may use a spreadsheet or calculator to perform the computations. |
|Use the template below to make a table showing the cost to make one pizza using your recipe. |
|The first line is partially completed as an example. |
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|Important Information: |
|Your pizza must include dough, sauce, cheese and 3 other ingredients. |
|1 pound (lb) = 16 ounces (oz) |
|One 16-inch pizza serves 4 students. |
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|Award Winning Pizza Recipe |
|(Recipe for 1 pizza) |
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|Ingredient |
|Amount Needed |
|Package Size |
|Price |
|Unit Cost (Cost per ounce) |
|Total Cost for 1 pizza |
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|Dough |
|20 oz. |
|60 oz. |
|$4.20 |
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| Price Sheet |
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|Ingredient |
|Amount Needed |
|Package Size |
|Price |
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|Dough |
|20 oz. |
|60 oz. |
|$4.20 |
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|Pizza Sauce |
|5 oz. |
|15.oz |
|$1.20 |
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|Cheese (Shredded) |
|8 oz. |
|16 oz. |
|$3.36 |
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|Pepperoni |
|4 oz. |
|16 oz. |
|$5.52 |
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|Meatballs |
|8 oz. |
|16 oz. |
|$3.84 |
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|Sausage |
|8 oz. |
|1 lb. |
|$4.16 |
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|Green Bell Peppers |
|8 oz. |
|1 lb |
|$1.44 |
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|Onions |
|8 oz. |
|2 lbs. |
|$2.56 |
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|Mushroons |
|6 oz. |
|24 oz. |
|$4.56 |
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|Tomatoes |
|3 oz. |
|12.oz |
|$2.88 |
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|Black Olives |
|6 oz. |
|6 oz. |
|$1.86 |
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|Task 2: |
|Determine the cost of make pizza for 12, 60 and 240 students. Remember, one 16-inch pizza serves 4 students. Create a table to show the following. |
|The number of students |
|how many pizzas are needed |
|how much of each ingredient is needed |
|the price of each ingredient |
|the unit cost for each ingredient |
|the total cost for each ingredient |
|the total cost (based on unit rate) to feed 12, 60, and 240 students. |
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|You may use a spreadsheet or calculator to perform the computations. |
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|Ingredient |
|Unit Cost for 1 pizza |
|Pizzas needed for 12 students |
|Total Cost for 12 students |
|Pizzas needed for 60 students |
|Total cost for 60 students |
|Pizzas needed for 240 students |
|Total cost for 240 students |
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|Task 3: |
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|Write a proposal to convince the cafeteria manager to add your pizza to the school lunch menu. Your proposal should include the following. |
|The tables you created for task 1 and task 2 |
|an explanation of the information provided in each table |
|an explanation of the mathematics you used to create the information in each table |
|a convincing argument for choosing your recipe. |
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