HW: Identifying Proportional Relationships Wkst Tuesday, 11/29/16 Write the IC and HW in your planner. IC: Ch. 5 – Day 2 HW: Identifying Proportional Relationships Wkst Materials Pencil & grading pen Marker and eraser Planner p.167 HW

Hint…find the unit rate for each pack!! 1 2 . 8 $2.80 per pack $2.87 per pack $2.55 per pack

Please get out the sheet of paper that you are doing bellwork on all week. Remember, this will help you on Friday when we correct the Equations Test!!

8 3 + 8 = 11ft Bellwork The perimeter of this banner is 30 feet. 4 3 + x 15) Write an equation in simplest form that would represent the perimeter of the banner. What is the measurement across the top of the banner? Show all steps. 3 + x + 4 + 3 + x + 4 = 30 2x + 14 = 30 Equation ______________________ -14 -14 2x + 14 = 30 2x = 16 2 2 1x = ? 1x = 8 3 + 8 = 11ft 4

Proportional Relationships Objective: TSWBAT identify proportional relationships in tables. Identifying Proportional Relationships Definition: Ratios are considered proportional if they are equivalent. NOT Proportional: Proportional:

Unit Rate Example 1: Pay by the Ounce Frozen Yogurt A new self-serve frozen yogurt store opened this summer that sells its yogurt at a price based on the total weight of the yogurt and its toppings in a dish. Each member of Isabelle’s family weighed his dish, and this is what they found. a) Determine if the cost is proportional to the weight. Weight (ounces) Cost ($) 12.5 5 10 4 2 8 3.20 Unit Rate  12.5 $0.40 per ounce  12.5 The cost is ___________________________ to the weight.

Unit Rate Example 1: Pay by the Ounce Frozen Yogurt A new self-serve frozen yogurt store opened this summer that sells its yogurt at a price based on the total weight of the yogurt and its toppings in a dish. Each member of Isabelle’s family weighed his dish, and this is what they found. a) Determine if the cost is proportional to the weight. Weight (ounces) Cost ($) 12.5 5 10 4 2 8 3.20 Unit Rate  10 $0.40 per ounce  10 The cost is ___________________________ to the weight.

Unit Rate Example 1: Pay by the Ounce Frozen Yogurt A new self-serve frozen yogurt store opened this summer that sells its yogurt at a price based on the total weight of the yogurt and its toppings in a dish. Each member of Isabelle’s family weighed his dish, and this is what they found. a) Determine if the cost is proportional to the weight. Weight (ounces) Cost ($) 12.5 5 10 4 2 8 3.20 Unit Rate  5 $0.40 per ounce  5 The cost is ___________________________ to the weight.

Unit Rate Example 1: Pay by the Ounce Frozen Yogurt A new self-serve frozen yogurt store opened this summer that sells its yogurt at a price based on the total weight of the yogurt and its toppings in a dish. Each member of Isabelle’s family weighed his dish, and this is what they found. a) Determine if the cost is proportional to the weight. Weight (ounces) Cost ($) 12.5 5 10 4 2 8 3.20 Unit Rate  8 $0.40 per ounce  8 The cost is ___________________________ to the weight.

proportional Same unit rate every time! Example 1: Pay by the Ounce Frozen Yogurt A new self-serve frozen yogurt store opened this summer that sells its yogurt at a price based on the total weight of the yogurt and its toppings in a dish. Each member of Isabelle’s family weighed his dish, and this is what they found. a) Determine if the cost is proportional to the weight. Since everyone paid the same amount ($0.40 per ounce), we say the amounts are proportional. Weight (ounces) Cost ($) 12.5 5 10 4 2 8 3.20 Same unit rate every time! proportional The cost is ___________________________ to the weight.

Take the # of ounces and multiply it by $0.40 b) Isabelle’s brother takes an extra-long time to create his dish. When he puts it on the scale, it weighs 15 ounces. If everyone pays the same rate in this store, how much will his dish cost? How did you calculate this cost? $0.40 per ounce Take the # of ounces and multiply it by $0.40 $0.40 for 1 ounce $0.80 for 2 ounces 15(0.40) = 6 $1.20 for 3 ounces $ ? for 15 ounces 15 ounces will cost $6.00

c) Write an equation that can be used to find the cost of any weight of yogurt. Unit rate = $0.40 per 1 ounce x y Take weight (x) and mulitply it by $0.40 to get the cost (y). Weight (ounces) Cost ($) 12.5 5 10 4 2 8 3.20 (0.4) = In other words… (0.4) = x(0.4) = y 0.4x = y (0.4) = (0.4) = Unit Rate y = 0.4x Equation: __________________ d) Does this relationship still hold true if you don’t buy any yogurt at all? Explain why or why not. It does hold true because if you don’t buy any yogurt, that’s zero ounces and 0(0.4) = 0 dollars.

Is this a proportional relationship? Ex. 3) The table below gives how far John jogged for different numbers of minutes. Do the numbers in the table represent a proportional relationship and how do you know? Justify your answer in complete sentences. x y Time (minutes) Distance (km) 10 2 15 3 20 4 25 5

Is this a proportional relationship? Ex. 3) The table below gives how far John jogged for different numbers of minutes. Do the numbers in the table represent a proportional relationship and how do you know? Justify your answer in complete sentences. This represents a proportional relationship because all of the ratios are equivalent (1/5) and all levels of the table have the same unit rate. x y Time (minutes) Distance (km) 10 2 15 3 20 4 25 5 (0.2) = (0.2) = (0.2) = How far could he go in 17 minutes? (0.2) = 17(0.2) = 3.4 km x(0.2) = y Equation: ___________________ y = 0.2x 0.2x = y

Is this a proportional relationship? Ex. 4) Jessie has a bakery. The table below shows the amount of flour used for a number of cupcakes. Does the table represent a proportional relationship? Explain and justify your answer in complete sentences. x y # of cupcakes Cups of flour used 4 6 9 8 12 10 18

Is this a proportional relationship? Ex. 4) Jessie has a bakery. The table below shows the amount of flour used for a number of cupcakes. Does the table represent a proportional relationship? Explain and justify your answer in complete sentences. This DOES NOT represent a proportional relationship because the ratios are not equivalent. The last row of the table has a different unit rate. x y # of cupcakes Cups of flour used 4 6 9 8 12 10 18

Not proportional Closure! A student notices in the table below that as the x-value increases by 3, the y-value increases by 4. Because there is a pattern, the student has determined that x is proportional to y. Do you agree with the student’s claim? Why or why not? Not proportional The value of the ratios aren’t equivalent (1/4 ≠ 5/7). There are different unit rates.

Unit Rate Example 2: Cups to Ounces Conversions In the back of a recipe book, a diagram provides easy conversions to use while cooking. 0.5 1.5 x y a) Is the number of ounces proportional to the number of cups? How do you know? y  0.5 ounces Unit Rate x  0.5 cup 8 ounces per cup

Unit Rate Example 2: Cups to Ounces Conversions In the back of a recipe book, a diagram provides easy conversions to use while cooking. 0.5 1.5 x y a) Is the number of ounces proportional to the number of cups? How do you know? y ounces Unit Rate x cup 8 ounces per cup

Unit Rate Example 2: Cups to Ounces Conversions In the back of a recipe book, a diagram provides easy conversions to use while cooking. 0.5 1.5 x y a) Is the number of ounces proportional to the number of cups? How do you know? y  1.5 ounces Unit Rate x  1.5 cup 8 ounces per cup

Unit Rate Example 2: Cups to Ounces Conversions In the back of a recipe book, a diagram provides easy conversions to use while cooking. 0.5 1.5 x y a) Is the number of ounces proportional to the number of cups? How do you know?  2 ounces Unit Rate  2 cup 8 ounces per cup

Example 2: Cups to Ounces Conversions In the back of a recipe book, a diagram provides easy conversions to use while cooking. 0.5 1.5 x y a) Is the number of ounces proportional to the number of cups? How do you know? Yes, the number of ounces is proportional to the number of cups because every ratio has the same unit rate: 8 ounces per cup

5.75 So… 5.75 cups = 46 ounces Example 2: Cups to Ounces Conversions In the back of a recipe book, a diagram provides easy conversions to use while cooking. 0.5 1.5 x y Take the cups (x) and multiply it by 8 to get the number of ounces (y). b) How many ounces are in 5 ¾ cups? 5.75 We know 1 cup = 8 oz (this is the unit rate!) So… 2 cups = 16 oz (just take 2 x 8) 3 cups = 24 oz (just take 3 x 8) So… 5.75 cups = 46 ounces (just take 5.75 x 8)

y = 8x Unit Rate Example 2: Cups to Ounces Conversions In the back of a recipe book, a diagram provides easy conversions to use while cooking. 0.5 1.5 x y c) Write an equation that can be used to find the number of ounces (y) in any amount of cups (x). Take the cups (x) and multiply it by 8 to get the number of ounces (y). y = 8x 8x = y Unit Rate

y = 8x 3.25 cups make 26 ounces 26 = 8x 8 8 3.25 = 1x Example 2: Cups to Ounces Conversions In the back of a recipe book, a diagram provides easy conversions to use while cooking. 0.5 1.5 x y d) How many cups make 26 ounces? y = 8x 3.25 cups make 26 ounces 26 = 8x 8 8 3.25 = 1x

Is this a proportional relationship? Ex. 4) The table below gives how far John jogged for different numbers of minutes. Do the numbers in the table represent a proportional relationship and how do you know? Justify your answer in complete sentences. Time (minutes) Distance (km) 10 2 15 3 20 4 25 5

Is this a proportional relationship? Ex. 5) Jessie has a bakery. The table below shows the amount of flour used for a number of cupcakes. Does the table represent a proportional relationship? Explain and justify your answer in complete sentences. # of cupcakes Cups of flour used 4 6 9 8 12 10 18

Closure! A student notices in the table below that as the x-value increases by 3, the y-value increases by 4. Because there is a pattern, the student has determined that x is proportional to y. Do you agree with the student’s claim? Why or why not?

Total # of flower arrangements Example 3: Slim Jim is back and he is now a florist. The following chart show how many flower arrangements he has sold over the course of a number of days. You could find the unit rate for each row in the table, but since it doesn’t ask what the unit rate is just simplify each fraction and see if they are all the same! x y Days Total # of flower arrangements 6 2 8 4 10 12  2  2  2  2  4  4  4  4 Does this represent a proportional relationship? Explain why or why not. No, it’s NOT proportional. The ratios are not the same.