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Into Math Grade 7 Module 1 Lesson 6 Answer Key Practice Proportional Reasoning with Scale Drawings
We included H MH Into Math Grade 7 Answer Key PDF Module 1 Lesson 6 Practice Proportional Reasoning with Scale Drawings to make students experts in learning maths.
HMH Into Math Grade 7 Module 1 Lesson 6 Answer Key Practice Proportional Reasoning with Scale Drawings
I Can make scale drawings and use them to find actual dimensions.
Step It Out The scale on a scale drawing can be shown in the same unit or in different units.
Connect to Vocabulary A scale is a ratio between two sets of measurements. A scale drawing is a proportional two dimensional drawing of an object.
B. What is the scale of the drawing in inches to feet? ________________________ Answer: 1 feet = 12 inches Actual length = 12 feet Convert from feet to inches 12 × 12 = 144 inch The scale is 0.6 : 144 Divide by 0.6 to find the scale length 0.6:144 = 1:240 So, the scale of the drawing in inches to feet is 1:240
C. Write an equation for the proportional relationship between the actual length in feet x and the drawing length in inches y. ____________ Answer: x = 12y
D. Use your equation from Part C to find the actual length represented by a scale drawing length of 1.5 inches, and to find the scale drawing length that represents an actual length of 70 feet. ____ = \(\frac{1}{20}\)x, so x = ___ 1.5 inches represents an actual length of ___ feet. y = \(\frac{1}{20}\) _______ = _______ 70 feet represents a drawing length of _______ inches. Answer: 1.5 = \(\frac{1}{20}\)x x = 30 y = \(\frac{1}{20}\) 30
B. Show how to find the length and width of the actual court. _____________________ Answer: Scale = 1:20 ft Length = 4.2 × 20 = 84 ft Width = 2.5 × 20 = 50 ft
C. What is the area of the actual basketball court? Show your work. _____________________ Answer: Length = 84 ft Width = 50 ft Area = 84 × 50 = 4200 sq. ft
D. Is the ratio of actual area to drawing area the same as the ratio of actual lengths to drawing lengths? Explain. _____________________ _____________________ _____________________ Answer: No, the ratio of actual area to drawing area is the same as the ratio of actual lengths to drawing lengths.
Turn and Talk Is there a relationship between the scale for area and the scale for length? If so, describe the relationship.
B. Use the equation you wrote in Part A to find the scale drawing lengths. Then make the scale drawing. _____________________ _____________________
Turn and Talk How could you write an equation for the drawing length y based on an actual length x?
B. Each side of the new drawing will be (longer / shorter) than the corresponding side of the original drawing. C. Draw the rectangle for the new scale.
Turn and Talk What is another way you could have found the dimensions of your new scale drawing?
Check Understanding
Question 1. The dimensions of an Olympic swimming pool are shown. A scale drawing of the swimming pool has dimensions of 50 centimeters by 100 centimeters and a diagonal that is about 112 centimeters long. A. What is the scale of the drawing in centimeters to meters?_____ Answer: 100cm/50m = 2cm/m
Question 2. A different scale drawing of the same Olympic pool uses a scale of \(\frac{5 \mathrm{~cm}}{1 \mathrm{~m}}\). What are the dimensions of the drawing? _______________ Answer: If the scale is \(\frac{5 \mathrm{~cm}}{1 \mathrm{~m}}\), the dimensions of the drawing is 125 cm by 250 centimeters. 125/250 = 1/2
On Your Own
B. What is the ratio between the actual length and the drawing length as a unit rate? _____________________ Answer: Every 1 inch in the picture represents 5 ft of the actual length The ratio between the actual length and the drawing length as a unit rate is 5:1.
C. Write an equation for the proportional relationship between the drawing lengths and the court lengths, where x is length in the drawing in inches and y is length on the court in feet. _____________________ Answer: y = 5x where, x is the length in the drawing in inches and y is the length on the court in feet.
D. Use your equation from Part C to find the actual length represented by a scale drawing length of 3.5 inches. _____________________ Answer: If drawing length = 3.5 inch then actual length = 3.5 × 5 = 17.5 feet
E. Use your equation from Part C to find the scale drawing length that represents an actual length of 40 feet. _____________________ Answer: The ratio of the actual length and the drawing length as a unit rate is 5:1. 40/5 = 8 So, the drawing length = 8 in.
A. Show how to find the area of the scale drawing of the tennis court. Answer: Given, Length = 15.6 in width = 7.2 in Area = 15.6 × 7.2 = 112.32 sq. in/
B. Show how to find the length and width of the actual court. Answer: The ratio is 1 in : 5 ft Length = 15.6 × 5 = 78 ft Width = 7.2 × 5 = 36 ft
C. Show how to find the area of the actual tennis court. Answer: 78 × 36 = 2808 sq. ft Thus the area of the actual tennis court is 2808 sq. ft
D. Attend to Precision What is the ratio of the area of the actual court to the area of the drawing (as a unit rate)? Is it the same as the ratio of the length of the actual court to the length of the drawing? How do you know? __________________________ __________________________ __________________________ __________________________ Answer: The ratio of the area of the actual court to the area of the drawing is equal 78:36 = 15.6:7.2
B. Model with Mathematics Write an equation that relates x and y. The diagonal of the scale drawing is approximately 6.3 units. Estimate the length of the diagonal of the mural. _____________________ Answer: y = 7.5x The diagonal of the scale drawing is approx 6.3 units The length of the diagonal of the mural is 47.25 ft y = 7.5 × 6.3 = 47.25
Question 6. The students at Suzanne’s school are also going to paint a smaller mural inside the building. A scale drawing of the mural is shown on the grid.
B. How many grid units are there for every 3 feet of mural in the original scale? How many grid units are there for every 3 feet of mural in the new scale? Answer: There is 1 grid unit for every 3 feet of mural in the original scale.
Lesson 6.5 More Practice/Homework
Question 1. Model with Mathematics Martine’s town is building a volleyball court based on a scale drawing that is 40 centimeters by 80 centimeters and uses the scale 1 cm:22.5 cm. A. Write an equation for the proportional relationship between drawing court lengths x in centimeters and court lengths y in centimeters. Answer: y = 22.5x
B. What are the length and width in meters of the actual court? Show your work. ____________________________ ____________________________ Answer: Given, Martine’s town is building a volleyball court based on a scale drawing that is 40 centimeters by 80 centimeters and uses the scale 1 cm:22.5 cm. y = 22.5x y = 80 × 22.5 = 1800 cm x = 40 × 22.5 = 900 cm
C. Write the ratio of the area of the actual court to the area of the court in the scale drawing. ____________________________ Answer: 40:80 = 1:2 900:1800 = 1:2 Thus the ratio of the area of the actual court to the area of the court in the scale drawing is 1:2
Question 2. The students in Roberto’s school are painting a mural that will be 8 feet by 15 feet. First they make a scale drawing of the mural with a scale of 2 feet:5 feet. A. Write an equation for the proportional relationship between drawing mural lengths x in feet and mural lengths y in feet. _______________________ Answer: Given, The students in Roberto’s school are painting a mural that will be 8 feet by 15 feet. y = 15 ft x = 8 ft So, y = 2x – 1
B. What are the length and width of the scale drawing in feet? Show your work. _______________________ Answer: Scale is 2ft : 5 ft 2 ft represents 5 ft So, the length is 8 ft which will be represented by 2/5 × 8 = 3.2 ft width is 15 ft represented by 6 feet.
C. Open Ended Choose a different scale and use it to make a scale drawing of the mural that will fit on a piece of graph paper. _______________________ Answer:
Question 3. Geography A map has a scale of 1 in.:10 mi. Find the distance on the map between two cities that lie 147 miles apart. Show your work. _______________________ Answer: Given, A map has a scale of 1 in.:10 mi. 147 ÷ 10 = 14.7
B. The equation w = (4)(40) can be used to find the width of the scale model.
C. The width of the scale model is 10 inches.
D The length of the scale model is 240 inches.
E. The scale means that 1 inch in the model represents 4 feet in the house. Answer: Option A, E, C 1 in = 4 ft x in = 60 ft 60 = 4x x = 60/4 x = 15 1 in = 4 ft y = 40 ft 4y = 40 y = 40/4 = 10 in Thus Option A, C and E are correct statements.
Question 5. A scale drawing of an elephant shows the animal as 6 inches high and 10.8 inches long. The scale used for the drawing was 3 in.:5 ft. What are the height and length of the actual elephant? Height: ___ feet Length: ____ feet Answer: Given, A scale drawing of an elephant shows the animal as 6 inches high and 10.8 inches long. The scale used for the drawing was 3 in.:5 ft. 6/3 = 2 in 2 × 5in = 10 ft First find out how many times 3 fits into 10.8, which is 3.6 times. 3.6 × 5 = 18 ft Thus length is 10 ft and the height is 18 ft.
Question 6. Town planners are planning a 500-foot by 700-foot parking lot by making a scale drawing that is 90 inches by 126 inches. What is the scale of inches in the drawing to inches in the actual object? A. 3:200 B. 1:300 C. 2:30 D. 1:200 Answer: Given, Town planners are planning a 500-foot by 700-foot parking lot by making a scale drawing that is 90 inches by 126 inches. convert from feet to inches 500 × 12 = 6000 inch 90:6000 = 3:200 126: (700 × 12) 126:8400 21:1400 3:200 Thus option A is the correct answer.
Spiral Review
B. Is the relationship between the number of teams and the number of jerseys proportional? Explain. Answer: The ratio is 3:36 = 1:12 y = 12x So, yes the relationship between the number of teams and the number of jerseys is proportional.
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Chapter 6, Lesson 8: Scale Drawings
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Chapter 6, Lesson 8: Scale Drawings
- Extra Examples
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- Personal Tutor
- Self-Check Quizzes
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cal. is 15 inches = 1 yard? or 36 12. 15. A barn is 50 feet wide by 80 feet long. Make a scale drawing of the barn t. has a scale of − 1 i. ch = 10 feet.2Check students' drawings. The wid. h i. 2.5 inches and the length is 4 inches.16. A. an in a photograph is 1.5 inches in height. I. ta.
8. 9. 10. 12. length. length. height: height: length. 19ft 56 ft; height: 2 ft 300 ft 6 in. 40 ft 9.75 in. ; height: 4.125 .n. 11. 1:95 13. 193 nches 150 miles
The scale of a drawing is 1 in. 4 15 ft. Find the actual measurement. 2 in. 3. 14 in. 4. 15 i 540 ft 720 ft 840 ft 900 ft The scale is 2 cm 25 m. Find the length each measurement would be on a scale drawing. 5. 150 m 6. 475 m 7. 350 m 8. 500 m 12 cm 38 cm 28 cm 40 cm Tell whether each scale reduces, enlarges, or preserves the size of an actual ...
1 an open shape made up of one or more curves. 3 a closed shape that is not a polygon made entirely of segments. 5 a concave hexagon with two pairs of congruent sides. 2 a concave quadrilateral with an acute angle and exactly two congruent sides. 4 a convex pentagon with two parallel sides and two perpendicular sides.
A scale drawing is a diagram of an object in which the dimensions are in proportion to the actual dimensions of the object. The scale on a scale drawing tells how the drawing's dimensions and the actual dimensions are related. The scale "1 in. : 12 ft" means that 1 inch in the floor plan represents an actual distance of 12 feet. W H Y ?
Practice A 5-8 Scale Drawings and Scale Models 1. A drawing is 10 in. and the actual measurement is 20 ft. What is the scale? 1 in. 2 ft 2. A model of a planned baseball stadium is 2 ft wide. The actual stadium will be 200 yd wide. What is the scale?
Classwork: Homework: Extra Practice: Scale Drawings Worksheet Scale Drawing Worksheet (4 problems) Teacher selected Closure 1. A scale drawing is a reduced or enlarged drawing of a actual object. What are some examples of scale drawings? Maps, blueprints, models 2. How do you solve problems involving scales? Set up a proportion. 3.
California Standards Practice (STP) ... Personal Tutor Self-Check Quizzes. Hotmath Homework Help Math Review Math Tools Multilingual Glossary Online Calculators Study to Go. Mathematics. Home > Chapter 4 > Lesson 8. California Mathematics: Concepts, Skills, and Problem Solving, Grade 7. Chapter 4, Lesson 8: Scale Drawings and Models. Extra ...
Lesson 8 of the skills practice focuses on understanding scale drawings and models. In this lesson, students learn how to interpret and create scale drawings and models, which are used to represent real-life objects or places in a reduced or enlarged form.
Practice C: Scale Drawings and Scale Models Identify the scale factor.
Lesson 12 Summary: Units in Scale Drawings. Lesson Practice Problems. Lesson 1: What Are Scaled Copies. Lesson 2: Corresponding Parts and Scale Factor. Lesson 3: Making Scaled Copies. Lesson 4: Scaled Relationships. Lesson 5: The Size of the Scale Factor. Lesson 6: Scaling and Area. Lesson 7: Scale Drawings.
Unit 1, Lesson 8: Scale Drawings and Maps +8>7 97+ 7)'1+ *6';/3-7 84 741:+ 564(1+27
Chapter 6, Lesson 4: Scale Drawings and Models. Extra Examples. Personal Tutor. Self-Check Quizzes.
Our worksheet is designed to provide students with a solid foundation in the principles of scale drawings and models. By including a range of problems and detailed solutions, we ensure that students can independently practice, apply, and master the concepts. This resource empowers educators and parents to support students in building essential math and problem-solving skills.
Find the answer keys for your McGraw Hill Education textbooks and improve your learning outcomes. Access the link below to download the keys in PDF format.
Here, students use a scale and a scale drawing to answer a speed-related question. The task involves at least a couple of steps beyond finding the distance of travel and can be approached in several ways. Minimal scaffolding is given here, allowing students to model with mathematics more independently (MP4).
***UPDATED 2/29/16*** Four half-sheet exit slips are now included! These can be used for extra practice, homework, or as assessments. This set includes 8 pages of interactive notes and practice pages for teaching or reviewing the following: Computing actual lengths from a scale drawing Determining the scale factor when given a scale drawing Calculating the areas of scale drawings Reproducing a ...
Chapter 6, Lesson 8: Scale Drawings Extra Examples Group Activity Cards Personal Tutor Self-Check Quizzes
HMH Into Math Grade 7 Module 1 Lesson 6 Answer Key Practice Proportional Reasoning with Scale Drawings I Can make scale drawings and use them to find actual dimensions.
Homework and Practice Scale Drawings and Maps Use the map to answer the questions. 1. On the map, the distance between Key West and Key Largo is 1 inch. What is the actual distance in miles? 2. On the map, the distance between
Chapter 6, Lesson 6: Scale Drawings and Models. Extra Examples. Personal Tutor. Self-Check Quizzes.
Standardized Test Practice Vocabulary Review Lesson Resources ... Personal Tutor Self-Check Quizzes. Hotmath Homework Help Math Review Math Tools Multilingual eGlossary Visual Vocabulary Cards ... Concepts, Skills, and Problem Solving, Course 2. Chapter 6, Lesson 8: Scale Drawings. Extra Examples; Group Activity Cards; Personal Tutor; Self ...
Standardized Test Practice Vocabulary Review Lesson Resources Extra Examples ... Personal Tutor Self-Check Quizzes. Hotmath Homework Help Math Review Math Tools Multilingual eGlossary Visual Vocabulary Cards ... Skills, and Problem Solving Course 2. Chapter 6, Lesson 8: Scale Drawings. Extra Examples; Group Activity Cards; Personal Tutor; Self ...