Lesson 4. Is it a proportion?

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1 Learning Target Ratios and Proportional Relationships Lesson 4 Is it a proportion? Analyze proportional relationships and use them to solve real world and mathematical problems. CCSS.Math.Content.7.RP.A.2 Recognize and represent proportional relationships between quantitie CCSS.Math.Content.7.RP.A.2a Decide whether two quantities are in a proportional relationship e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin. CCSS.Math.Content.7.RP.A.2b Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships. CCSS.Math.Content.7.RP.A.2c Represent proportional relationships by equations. For example if total cost t is proportional to the number n of items purchased at a constant price p, the relationship between the total cost and the number of items can be expressed as t = pn. Duration: 3 days Common Core Grade 7 Proportions Lesson 4 page

NOTES Is it a proportion? We can make a table to represent the relationship between the amounts of red and yellow paint that would make the same shade of orange.

Remember that a table represents a proportional situation if it satisfies two requirements: Criteria : There is a constant factor that the x column can be multiplied by that results in the number in

2 NOTES Is it a proportion? We can make a table to represent the relationship between the amounts of red and yellow paint that would make the same shade of orange. Red Yellow Does this table represent a proportional relationship? Remember that a table represents a proportional situation if it satisfies two requirements: Criteria : There is a constant factor that the x column can be multiplied by that results in the number in the y column. This number is called k. An easy way to find the k for a table is to divide y by x. Criteria 2: If x = 0 then y = 0 or if y = 0 then x = 0. Let s expand the table above to find the value of k. x Red k y Yellow To find k we need to think The number in the x column times what number equals the number in the y column? Specifically, let s look a the first row and think 4 times what number equals 6? As a number sentence it would look like 4 [? ] = 6 To find this number we would divide 6 by 4 and that would gives us the value of k. k = 6 4 = 3 2 =.5 Even if we use the row where x = 0, the value of k is still 3 2. k = 5 0 = 3 2 =.5 A completed table would look like this... Since k is 3 2 for every row, the table satisfies Criteria. Criteria 2 is satisfied because if 0 cups of red paint are used, then obviously 0 cups of yellow paint is also used. Common Core Grade 7 Proportions Lesson 4 page 2

3 Therefore, this is a proportional relationship. Now that we know this is a proportional relationship, we can write the equation as x = y or more traditionally, it would be y = x For any table that represents a proportional relationship, you can find k by dividing y x. k = x y All proportional relationships can be expressed by the equation y = kx Common Core Grade 7 Proportions Lesson 4 page 3

4 CLASS PRACTICE Is it a proportion? Table A Table A represents a proportional relationship. a. Find the constant of proportionality, k, that relates the two columns. b. Write the equation for this proportion. Table B Table B represents a proportional relationship. a. Find the constant of proportionality, k, that relates the two columns. b. Write the equation for this proportion. Table C Table C does not represent a proportional relationship. Explain how you can tell. Table D Table D does not represent a proportional relationship. Explain how you can tell. Common Core Grade 7 Proportions Lesson 4 page 4

5 Common Core Grade 7 Proportions Lesson 4 page 5

6 HOMEWORK Is it a proportion? Below are two tables, but they are not complete. So far, the x and y values are identical.. Complete Table A so that it represents a proportional relationship and describe a real life situation the table could represent. Say what is represented in the table by the x variable, y variable, and the constant of proportionality. 2. Complete Table B so that it represents a relationship that is not proportional and describe a situation that the table could represent. Say what the values in the table represent. Table A 0 0 Situation: Table B 0 0 Situation: Common Core Grade 7 Proportions Lesson 4 page 6

CLASS PRACTICE Is it a proportion? (Part 2) Analyze each of the following tables. If the table is a proportion, find y = kx. If the table is not proportion, say how you can tell.

7 CLASS PRACTICE Is it a proportion? (Part 2) Analyze each of the following tables. If the table is a proportion, find y = kx. If the table is not proportion, say how you can tell. Table A k and write the equation in the form Table B Table C Table D Look at each graph. Determine whether the graph is proportional. Tell how you know. Common Core Grade 7 Proportions Lesson 4 page 7

HOMEWORK Is it a proportion? (Part 2) Problem For every minute that a particular water pump runs, it pumps a certain amount of water from one tank into another.

8 HOMEWORK Is it a proportion? (Part 2) Problem For every minute that a particular water pump runs, it pumps a certain amount of water from one tank into another. Fill in the following table showing the time the pump runs and the amount of water it pumps. x Minutes y Gallons. Is this situation a proportion? Explain how you can tell If this is a proportional relationship, what is the constant o proportionality (k)? What is the equation for this situation? 6 Problem 2 Chairs are placed around a table. The number of chairs is directly related to the number of tables. Fill in the following table showing the number of chairs and the number of tables. x Tables y Chairs. Is this situation a proportion? Explain how you can tell If this is a proportional relationship, what is the constant of proportionality (k)? What is the equation for this situation? 0 Common Core Grade 7 Proportions Lesson 4 page 8

miles per hour, equivalently 2 miles per hour.

miles per hour, equivalently 2 miles per hour. Content Standard MAFS.7.RP Ratios and Proportional Relationships. Assessment Limits Calculator Context MAFS.7.RP.1 Analyze proportional relationships and use them to solve real-world and mathematical problems.