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Ratios & Rates Unit

Ratios & Rates Unit. DAY 1. Ratio Introduction. Today’s Lesson; I can write a ratio in multiple forms. I can identify the parts and whole of a ratio. Engage. Count the number of each shape in the bag you are given. Questions: How can you compare the types of shapes in your bag?

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Ratios & Rates Unit

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  1. Ratios & Rates Unit

  2. DAY 1 Ratio Introduction

  3. Today’s Lesson; I can write a ratio in multiple forms. I can identify the parts and whole of a ratio.

  4. Engage • Count the number of each shape in the bag you are given. • Questions: • How can you compare the types of shapes in your bag? • Are there other ways to compare the types of shapes in your bag? • How would you write these comparisons?

  5. ExplainWhat is a ratio?How do you write a ratio? • RATIO: expresses the relationship between two quantities. Ratios compare two measures of the same types of things. The order of the numbers in a ratio is important. • Ways to write ratios…. • 1 to 1 - use the word “to” • 1 : 1 – use a colon “:” • 1/1 – write as a fraction (top number is 1st number in ratio)

  6. ExplainRatio RelationshipsA class has 30 total students. 20 of the students are boys and 10 of the students are girls. Part to Part: boys to girls Part to Whole: girls to class Whole to part: class to boys

  7. Explain Ratios in Real Life Builders and Contractors • As a contractor or builder, it would be imperative to know how many pounds of weight each beam could support and to make sure that buildings are made to code. • Codes or regulations include ratios like: thickness to height ratios; occupancy to area; and height to length (the slope) of ramps. • Contractors also need to understand ratios so that they can order the correct number of parts or estimate additional costs. If every additional wall requires 3 sheets of plywood and 84 nails (3 sheets: 84 nails reduces to 1 sheet: 28 nails), you could find the quantities and costs of the project. 

  8. Explain Ratios in Real LifePower Outages 9/11/17 What is the ratio of customers affected to customers served in the Duluth Area? Screen clipping from www.gapower.com – Georgia Power outage map on day of school closure 9-11-17.

  9. Math Mystery: The Cajun Chili Caper

  10. Evaluate • On an index card… 1.) Write the Ratio of to 3 DIFFERENT WAYS ? 2.) What is the Ratio of to ? 3.) What is the ratio of to All of the shapes?

  11. Day 2 Equivalent Ratios

  12. Today’s Lesson; I can write equivalent ratios.

  13. ENGAGE: Video: Equal Ratios | All Those Different Size Screens PBSMathClub https://www.youtube.com/watch?v=VyhRv_MuxvA

  14. = Explain: Equivalent Ratios • Equivalent ratios are tworatios that express the same relationship between numbers • Equivalent ratios are similar to equivalent fractions. • You can use a ratio table to help you find equivalent ratios. • Continue the pattern below using multiples.

  15. Explain: MULTIPLY to find Equivalent Ratios To make 1 box of pasta salad, you add 3 tablespoons of vegetable oil and 1 tablespoon of water to the cooked pasta. If you want to make 6 boxes of pasta, how many tablespoons of vegetable oil will you need? X 6 X 6

  16. Explain: DIVIDE to find Equivalent Ratios 12 cans of green beans can be purchased for $6. How many cans can you purchase for $2? ÷ 3 ÷ 3

  17. Explain: PRACTICE finding Equivalent Ratios - multiply It takes 6 eggs to bake 5 chocolate cakes. Jim wants to bake 10 chocolate cakes. How many eggs will he need?

  18. Explain: PRACTICE finding Equivalent Ratios - multiply It takes 6 eggs to bake 5 chocolate cakes. Jim wants to bake 10 chocolate cakes. How many eggs will he need? ANSWER

  19. Explain: PRACTICE finding Equivalent Ratios - divide To make sweet tea, you need 4 cups of sugar for every 8 cups of tea. How many cups of sugar will you need for 24 cups of tea?

  20. Explain: PRACTICE finding Equivalent Ratios - divide To make sweet tea, you need 4 cups of sugar for every 8 cups of tea. How many cups of sugar will you need for 24 cups of tea? ANSWER

  21. Explain: SCALING to find Equivalent Ratios Sometimes you have to do a combination of multiplication and division to find equivalent ratios. Packages of gum are on sale at 10 for $4. Find the cost of 15 packages of gum. Scale back by dividing by 2, then scale forward by multiplying by 3. x 3 ÷ 2 ÷ 2 x 3

  22. Explain: SCALING to find Equivalent Ratios Sometimes you have to do a combination of multiplication and division to find equivalent ratios. Thomas edits videos to earn extra money. He edited 8 videos in 14 hours last weekend. How many videos could he edit in 49 hours if he works at this same pace? Scale back by dividing by 2, then scale forward by multiplying by 7. x 7 ÷ 2 ÷ 2 x 7

  23. Explain: PRACTICE SCALING to find Equivalent Ratios Sometimes you have to do a combination of multiplication and division to find equivalent ratios. Kimora works at a manufacturing plant. For every 25 products she uses 10 gallons of paint. How many gallons of paint will she need to produce 55 products?

  24. Explain: PRACTICE SCALING to find Equivalent Ratios Sometimes you have to do a combination of multiplication and division to find equivalent ratios. Kimora works at a manufacturing plant. For every 25 products she uses 10 gallons of paint. How many gallons of paint will she need to produce 55 products? ANSWER

  25. Math Mystery: The Mystery of Pirate Ringold’s Lost Treasure

  26. EXTEND: Real World ProblemCopy and solve this problem in your math journal.The ratio of Karen’s CDs to the number of Sarah’s CDs is 4:5. If the total number of CDs is 45, how many CDs does Karen and Sarah have?

  27. Day 3 Rates and Unit Rate

  28. Today’s Lesson; I can describe the difference between a rate and a unit rate.

  29. Engage: • I went to Kroger this weekend to purchase Cinnamon Toast Crunch cereal. The Cinnamon Toast Crunch is packaged and sold in 3 different box sizes. Which box do you think I bought, knowing that I like to shop for the best value?

  30. Explain: Rate A rate is a special ratio in which the two terms are in different units. You can buy 5 hamburgers for $15. The rate is $15 for 5. You pay $15 for every 5 hamburgers.

  31. Explain: • Rate: $3.79 for 20.25 ounces • Rate: $3.25 for 16.2 ounces • Rate: $2.98 for 12.2 ounces

  32. 1 Explain: Unit Rate (a special ratio) unit rate A rate that is simplified so that it has a denominator of 1. unit ratio A unit rate where the denominator is one unit. Two options to find unit rate… 1.) Use methods used to find equivalent ratios. OR 2.) Identify the item that is in the denominator that you need to be a 1. Then divide the numerator by the denominator. Examples: What is the price per pound? How far will you travel in 1 hour? How many can you complete in 1 minute? 80 copies in 4 minutes = 20 copies per minute.

  33. Explain: • Rate: $3.79 for 20.25 ounces • Unit Rate: How much for 1 ounce? • Rate: $3.25 for 16.2 ounces • Unit Rate: How much for 1 ounce? • Rate: $2.98 for 12.2 ounces • Unit Rate: How much for 1 ounce?

  34. BEST DEAL Explain: • Rate: $3.79 for 20.25 ounces • Unit Rate: How much for 1 ounce? • Rate: $3.25 for 16.2 ounces • Unit Rate: How much for 1 ounce? • Rate: $2.98 for 12.2 ounces • Unit Rate: How much for 1 ounce?

  35. Solve on Index Card • Karen is building a tiny house. She can buy an 8 pound box of nails for $7.40 or a 4 pound box of the same nails for $5.38. Which is the better buy?

  36. Extend - Golden ratio / golden rectangle

  37. Extend: Golden Ratio/Rectangle in Nature See Notes for Image Credits

  38. Extend: Golden Ratio/Rectangle in Architecture See Notes for Image Credits

  39. Extend: Golden Ratio/Rectangle in Art See Notes for Image Credits

  40. Extend: – Golden Ratio/Rectangle – other uses

  41. Your Turn…. On the 8 ½ x 11 paper provided, use the golden rectangle template to create your own work of art. Your masterpieces will be displayed in our classroom, so do your best to make it visually appealing and neat.

  42. Day 4 Other Ways You May Encounter Ratios Mini Engineering Design Process (EDP) Project

  43. Today’s Lesson; I can find equivalent ratios and graph them.

  44. Engage: Answer the following questions. 1.) What should you do first? a.) cross the street b.) look both ways 2.) What should you do first? a.) jump up and down on the diving board b.) run to the end of the diving board 3.) What should you do first? a.) count up on the y-axis b.) count over on the x-axis

  45. Explain: Other Ways You May See Ratio Problems Vertical Ratio Tables Horizontal Ratio Tables (what we have used most in class)

  46. Explain: Other Ways You May See Ratio Problems Bar Diagrams 45 miles Double Number Lines 0 3.50 7 10.50 14 17.50 21 24.50 7 15 miles Cost Packages 0 1 2 3 4 5 6 7

  47. Explain: Other Ways You May See Ratio Problems Graphs Sam saved the same amount of money each week. She recorded her savings on the graph below. How much money did Sam have in her savings account in week 3? After how many weeks will Sam have saved $90?

  48. Explain: Creating a Ratio Graph Every hour Stefano walks 2 miles. Create a ratio table showing the miles traveled over the course of 5 hours. Then, plot the values on the coordinate plane.

  49. Explain: Creating a Ratio Graph – Your Turn Every hour the city bus travels 20 miles. Create a ratio table showing the miles traveled over the course of 5 hours. Then, plot the values on the coordinate plane.

  50. EXPLORE:Ratio StructuresMini-EDP Project 1. Discuss ideas using protocol (see below) 2. Sketch a drawing of the idea you want to build and have it approved by the Construction Supervisor (your teacher) Your idea should include the ratio of marshmallows to spaghetti you plan on using in your build. 3. Build your idea. During this step, record the ratio of the number of pastel colored marshmallows to the number of white ones used in your build. 4. Test your idea. 5. Revise and Improve your idea. This activity should take about 25-30 minutes from start to finish. PROTOCOL: Silent 1 minute to think. Then each person has 1 minute to share their idea while the other people listen. (see the unit rate there…. 1 person per minute) After all have shared, as a group decide which ideas sound like the best to use for the design. Use the Engineering Design Process to build a structure that will support my apple stress ball. The only materials you may use are the 20 miniature marshmallows and 15 pieces of spaghetti in your bag. You will work with a group of 3-4 students at your table.

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