Worksheet both sides, ratio and rate quiz Thursday Homework Worksheet both sides, ratio and rate quiz Thursday

Warm Up - convert each rate to a unit rate. 42 miles in 7 hours 2) 108 sit ups in 6 minutes 27 𝑜𝑢𝑛𝑐𝑒𝑠 0.35 𝑠𝑒𝑐𝑜𝑛𝑑𝑠 4) 4.5 gallons in ⅝ minutes State if the two ratios form a proportion. 5) 6 9 18 27 6) 5.5 8.6 22 34.4 7) 5 8 45 64

Homework questions

Learning Objective Students will learn how to interpret tables and graph proportional ratios. CCSS: CCSS: 7.RP.2

CCSS: 7.RP.2

You can determine if a relationship is proportional by looking at a table of values or the graph. How? Table If all the ratios of numbers in the table are equivalent, the relationship is proportional. Graph If the graph of the numbers forms a straight line through the origin (0,0), the relationship is proportional.

Next, find the simplified ratios and compare them. Are they the same? Example 1. On a field trip, every chaperone is assigned 12 students. Is the student to chaperone ratio proportional? If you use a table to demonstrate, you would need several ratios to start. Next, find the simplified ratios and compare them. Are they the same? The relationship is proportional. Chaperones 1 2 3 4 5 Students 12 24 36 48 60

Example 2 Try this: The local pizza place sells a plain pie for $10. Each topping costs an additional $1.50. Is the cost of pizza proportional to the number of toppings purchased? Toppings 1 2 3 4 Cost ($) 11.50 13.00 14.50 16.00 cost toppings Ratios: Since the ratios are not equivalent, the relationship is not proportional.

Is the relationship shown in the table proportional? Ex 3) Is the relationship shown in the table proportional? Yes No Year 1 2 4 5 Income $22,000 $44,000 $88,000 $110,000 Answer: Yes

Is the relationship shown in the table proportional? Ex 4) Is the relationship shown in the table proportional? Yes No x 2 5 6 9 y 7 17.5 21 34.5 Answer: No

Is the relationship shown in the table proportional? 38 Is the relationship shown in the table proportional? Yes No x 1 2 6 9 y 5 11 31 46 Answer: No

Is the relationship shown in the table proportional? 5. Is the relationship shown in the table proportional? Yes No x 1 2 4 7 y 8 16 35 Answer: No

Is the relationship shown in the table proportional? 6. Is the relationship shown in the table proportional? Yes No x 2 4 6 8 y -3 -10 -15 -20 Answer: No

Ex 6. Does the diagram represent a proportional relationship Ex 6. Does the diagram represent a proportional relationship? If so, identify the constant of proportionality. 1 2 3 4 5 10 20 30 40 50

Ex 7. Does the diagram represent a proportional relationship Ex 7. Does the diagram represent a proportional relationship? If so, identify the constant of proportionality. 1 2 3 4 5 6 7 8 9 10

Remember: Table If all the ratios of numbers in the table are equivalent, the relationship is proportional. Graph If the graph of the numbers forms a straight line through the origin (0,0), the relationship is proportional.

Example 8. On a field trip, every chaperone is assigned 12 students. Is the student to chaperone ratio proportional? (x) Chaperones 1 2 3 4 5 Students 12 24 36 48 60 (y) Chaperones Students 0 1 2 3 4 5 6 7 8 9 10 6 12 18 24 30 36 42 48 54 60 Connected points form a straight line Line crosses through the origin Since the graph is a straight line through the origin, the relationship is proportional.

Example 9. Draw a graph to represent the relationship. Is the relationship proportional? 10 9 8 X Y 1 5.5 2 7 3 8.5 4 10 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 10

Is the relationship shown in the graph proportional? 10 Yes No Hours Salary ($) 0 1 2 3 4 5 6 7 8 9 10 5 10 15 20 25 30 35 40 45 50 Answer: Yes

Is the relationship shown in the graph proportional? 11. Yes No 50 45 Cost ($) 40 35 30 25 20 15 10 Answer: No 5 0 1 2 3 4 5 6 7 8 9 10 Toppings

Is the relationship shown in the graph proportional? 12. Yes No Text Messages Cost ($) 0 1 2 3 4 5 6 7 8 9 10 5 10 15 20 25 30 35 40 45 50 Answer: No

Is the relationship shown in the graph proportional? 13. Yes No Teachers Students 0 1 2 3 4 5 6 7 8 9 10 5 10 15 20 25 30 35 40 45 50 Answer: Yes

The constant of proportionality is a constant ratio (unit rate) in any proportional relationship. We use the letter k to represent the constant of proportionality. Equations: y = kx or k = y x “x” is your independent variable “y” is your dependent variable “y” will depend on what you do to “x”. Whatever you do to “y over x” you will get k the constant. Unit rate is the relationship between the y and the x. When the x value is 1, y will be the unit rate.

In a table, simplify any one of the ratios. We can find the constant of proportionality from a table of values, equation and a graph. In a table, simplify any one of the ratios. (x) Chaperones 1 2 3 4 5 Students 12 24 36 48 60 (y)

Ex 14) Find the constant of proportionality: Apples (lbs) 2 2.5 3 3.5 4 Cost ($) 3.96 4.95 5.94 6.93 7.92 (y) Click

Ex15) Find the constant of proportionality: 3 4.5 4 6 5 7.5 8 12 9 13.5 Click

Find the constant of proportionality. Ex 16 Find the constant of proportionality. X Y 2 1.5 5 3.75 10 7.5 12 9 Answer: k = 0.75

Find the constant of proportionality. 17 X Y 2 2.5 3 3.75 4 5 9 11.25 Answer: k = 1.25

In an equation, what does k equal. Example 18: Click Click Click

Find the constant of proportionality: (click to reveal)

In a graph, choose a point (x, y) to find and simplify the ratio. (2, 24) Find the unit rate. Chaperones Students 0 1 2 3 4 5 6 7 8 9 10 6 12 18 24 30 36 42 48 54 60

Ex 19) Find the constant of proportionality. 0 2 4 6 8 10 12 14 16 18 20 2 4 6 8 10 12 14 16 18 20 Click

Find the constant of proportionality. Find the unit rate. Ex 20) 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 4 8 12 16 20 24 28 32 36 40 Answer: k = 8

Learning Objective Can you interpret tables and graph proportional ratios? If not, please schedule a math clinic session! CCSS: CCSS: 7.RP.2

Homework Worksheet: Representing Proportional Relations Quiz 7-1, 7-2 & Proportional Relationships