Module 1 Ratios and Proportional Relationships Lessons 15 19 Lesson #15 You need: pencil, calculator and binder. Do Now: 1. The table gives pairs of values for the variables x and y. x 1 2 3 y 3 6 9 Determine whether the values in the table form a proportional relationship by finding the ratio of each y value to its corresponding x value. 2. The table gives pairs of values for the variables a and b, which are in a proportional relationship. a 1 2 3 b 5 10 15 Find the constant of proportionality and write an equation that represents the table by comparing each b value to its corresponding a value. 1
Notes: Scale Drawings Scale Drawings and Scale Models are drawings or models that can either be a of an actual item, or an of an actual item. Examples of scale drawings/models that are reductions of the original: 2
Examples of scale drawings/models that are enlargements of the original: 3
Try It! CW: 1 15 #1 3 1. original scale drawing 2cm 5cm 4 cm original dimensions scale drawing 10 cm What is the constant of proportionality? In a scale drawing/model, the constant of proportionality is known as the scale factor. Multiply the original dimensions by the scale factor to get the scale drawing/model dimensions. 4
2. original scale drawing 20 ft 10 ft 12 ft 10 ft 5 ft 6 ft original dimensions scale drawing What is the scale factor (constant of proportionality)? 5
3. original 12 in. 10 in. 16 in. 15 in. original dimensions scale drawing Is this a true scale drawing? How do you know? What is the scale factor (constant of proportionality)? 6
Homework HW: 1 15 #1 5 1. Bob made a sketch of a rectangular logo for a video game he created that measures 1 1 2 inches long by 2 1 2 inches wide. Sketch 1 1 2 in 2 1 2 in Next, he wants to enlarge the logo for the website. Here are the new dimensions. 4 1 2 in. 7 1 2 in. Complete the table to decide if this is a true scale drawing: original dimensions scale drawing 7
2. Bob made a sketch of a rectangular logo for a video game he created that measures 4 inches long by 8 inches wide. Draw the rectangle with your ruler. Bob now wants to REDUCE the sketch so that it fits on the video game disc itself. He is going to use a scale factor of 1/4. Find the new dimensions and draw the scale drawing. original dimensions scale drawing 8
3. Make a scale drawing using a scale factor of 3. Make a scale drawing using a scale factor of 1 2 9
4. What will be the size of the portrait on your phone? 5. 35 mm If the diameter of this circle is 35 mm, and you want to reduce the size of the circle using a scale factor of 3 5 what is the length of the new diameter? 10
Lesson #16 You need: pencil, calculator and binder. Do Now: Find the constant of proportionality. 1. A bicycle rental at the beach costs $36 for 3 days. 2. An engine is turning at the rate of 2800 revolutions in 4 minutes. Determine whether the lengths of the corresponding sides of the figures form a proportional relationship. 3. 12 in. A 10 in. B 16 in. 15 in. 4. 6 ft. 9 ft. 12 ft. 8 ft. 12 ft. 16 ft. Correct HW 1 15 11
Notes: Scale Drawings A scale drawing is a of an object. The of a drawing is the constant ratio of each actual length to its corresponding length in the drawing. This scale can be expressed in a single value as the. A scale drawing and the object it represents are. Similar figures are proportional figures that have the same shape but not necessarily the same size. You can set up and solve proportions to find missing lengths in similar figures. 12
The art class is planning to paint a mural on an outside wall. This figure is a scale drawing of the wall. What is the area of the actual wall? 28 in. 11 in. 2 in. : 3 ft. STEP 1: Find the number of feet represented by 1 inch in the drawing. STEP 2: Find the height of the actual wall labeled 11 inches in the drawing. STEP 3: Find the length of the actual wall labeled 28 inches in the drawing. STEP 4: Since area is length times width, find the area of the actual wall. What is the scale written as a unit rate? Write the ratio of the area of the drawing to the area of the actual mural. 13
Try It! CW: 1 16 #1 4 1. The scale of a room in a blueprint is 3in.: 5ft. A wall in the same blueprint is 18 in. Complete the table. Blueprint length (in) 3 Actual length (ft) a) How long is the actual wall? b) A window in the room has an actual width of 2.5 feet. Find the width of the window in the blueprint. 2. Marie has a small copy of Rene Magritte's famous painting, The Schoolmaster. Her copy has dimensions 2 inches by 1.5 inches. The scale of the copy is 1 in.:40 cm. a) Find the dimensions of the original painting. b) Find the area of the original painting. c) Since 1 inch = 2.54 centimeters, find the dimensions of the original painting in inches. d) Find the area of the original painting in square inches. 14
3. A game room has a floor that is 120 feet by 75 feet. A scale drawing of the floor on grid paper uses a scale of 1 unit:5 feet. What are the dimensions of the scale drawing? 4. A scale for a drawing is 10 cm:1 mm. Which is larger, the actual object or the scale drawing? Explain. 15
Homework HW: 1 16 #1 9 16
Lesson #17 You need: pencil, calculator and binder. Correct HW 1 16 Do Now: Try It! CW: 1 17 #1 11 1. Francisco's bedroom has a width of 12 feet and a length of 15 feet. What is the length to width ratio of his bedroom? Write the length to width ratio. Simplify: 1 1 2 6 2. Katie walks mile in hour. What is her unit rate of speed? Write the ratio as a complex fraction. Divide to find the unit rate. 1 2 3. Sarah uses 5 cups of flour for every 2 loaves of bread she bakes. What is the unit rate per loaf? 17
4. The values in the table represent equivalent ratios. Find another equivalent ratio for this table. First Term 2 3 4? Second Term 6 9 12? 5. A motorboat travels 196 meters in 20 seconds. What is the motorboat's unit rate of speed? 6. If 6 cans of tomatoes cost $9, how much would it cost to buy 8 cans? 7. The distance a truck travels is directly proportional to the time, in hours, that it has been driven, as shown in the chart. Write an equation to represent this relationship. Then determine how far the truck will have traveled after driving for 5 hours at that rate. Time, t (hours) 0 1 2 5 Distance, d (miles) 0 50 50? 18
8. The equation y = 6.50x relates the number of tickets purchased for the school play and the total cost, in dollars. Use the equation to complete the table. Number of Tickets, x Cost in Dollars, y 1 2 3 4 5 6 9. The table shows the relationship between the side lengths of a regular pentagon and its perimeter. Side Length, s 1 2 3 4 5 6 Perimeter, P 5 10 15 20 25? a) Use words to describe the relationship between a side length, s, and the perimeter, P. b) What is the constant of proportionality for this relationship? 19
10. The graph shows how much money Neil earns depending on the number of hours he works. Neil's Earnings a) How do you know that this is a directly proportional relationship? b) What does the point (1,12) represent in this problem situation? Total Earnings ($) 120 108 96 84 72 60 48 36 24 12 1 2 3 4 5 6 7 8 9 Number of Hours Worked c) Write an equation in the form y = kx to represent this situation. 20
11. Peppers at a farm stand are being sold at a cost of $2 per pound. Complete the table below to show this proportional relationship. Number of pounds (x) Cost in dollars (y) 1 2 3 4 5 6 Create a graph to show the values in the table. Costs of Peppers Total Cost ($) Number of Pounds 21
Homework HW: 1 17 #1 8 Take Home Quiz 22
Lesson #18 You need: pencil, calculator and binder. Do Now: Review for Mid Module 1 Test Correct HW 1 17 23
Homework HW: 1 18 #1 14, AD #1 17 24
Lesson #19 You need: pencil, calculator and binder. Do Now: Review for Mid Module 1 Test Homework: STUDY FOR TEST 25
Lesson #20: Module 1 Test DO NOW: study for Module 1 Test You have two days to complete the test. CW: Module 1 Test HW: study 26
Lesson #20A: Module 1 Test DO NOW: study for Module 1 Test You have only today to complete the test. CW: Module 1 Test HW: extra credit worksheet 27