GRADE 7 MATHEMATICS (7.4) Patterns, relationships, and algebraic thinking. The student represents a relationship in numerical, geometric, verbal, and symbolic form. The student is expected to: (A) generate formulas involving conversions, perimeter, area, circumference, volume, and scaling. (B) graph data to demonstrate relationships in familiar concepts such as conversions, perimeter, area, circumference, volume, and scaling
1 inch to represent 3 feet in a scale drawing of a new library. 2 One room of the library where microfilm will be stored is 15 feet by 18 feet. Another room where videos are stored is 12 feet by 24 feet. What will be the dimensions of these two rooms on the blue print? Show your work.
A blueprint uses a scale of
Microfilm room:
Video room: The entire library will be 120 feet by 150 feet. What are the dimensions on the blue print of the library? What is the scale factor used for the scale drawing? Remember the dimensions need to be in the same unit to find the scale factor.
1. What mathematical concepts and vocabulary do I need to know to be able to work this problem?
2. Will the Grade 7 Mathematics Formula Chart be helpful on this problem? Why or why not?
3. What problem-solving strategy or strategies will I use to help solve this problem?
4. Extension (7.9A): Calculate the area of the library and the area of the library on the blueprint. Show your work.
TEKSING TOWARD TAKS © 2006
Page 1
GRADE 7 MATHEMATICS (7.4) Patterns, relationships, and algebraic thinking. The student represents a relationship in numerical, geometric, verbal, and symbolic form. The student is expected to: (A) generate formulas involving conversions, perimeter, area, circumference, volume, and scaling. (B) graph data to demonstrate relationships in familiar concepts such as conversions, perimeter, area, circumference, volume, and scaling
A blueprint uses a scale of 1 inch to represent 3 feet in a 2 scale drawing of a new library. One room of the library where microfilm will be stored is 15 feet by 18 feet. Another room where videos are stored is 12 feet by 24 feet. What will be the dimensions of these two rooms on the blue print? Show your work. Microfilm room:
Video room:
The entire library will be 120 feet by 150 feet. What are the dimensions on the blue print of the library?
What is the scale factor used for the scale drawing? Remember the dimensions need to be in the same unit to find the scale factor.
TEKSING TOWARD TAKS © 2006
Page 2
GRADE 7 MATHEMATICS (7.4) Patterns, relationships, and algebraic thinking. The student represents a relationship in numerical, geometric, verbal, and symbolic form. The student is expected to: (A) generate formulas involving conversions, perimeter, area, circumference, volume, and scaling. (B) graph data to demonstrate relationships in familiar concepts such as conversions, perimeter, area, circumference, volume, and scaling
Smith Architects needs to make a scale drawing of a building. If they use a scale of 1 cm equals 5 feet, what will be the scale dimensions of a rectangular room that is x feet wide and y feet long? A
width: 5x cm length: 5y cm
B
width: x + 5 cm length: y + 5 cm
C
width: x 5 cm length: y 5 cm
D
width: x cm length: y cm
A triangle has side lengths of 4, 8, and 10. Which of the following side lengths belong to a triangle that is not similar to the given triangle? A
4 2, 8 2, 10 2
B
4 a, 8 a, 10 a; a > 0
C
4 0.5, 8 0.5, 10 0.2
D
4 2, 8 2, 10 2
The local department store is offering an “early bird” sale that begins at 6 a.m. on Saturday. The following table shows the regular and sale prices for several items being offered at this sale. Item
A scale drawing uses a scale of 2 centimeters represents 5 feet. What expression can be used to find the dimension on the drawing of an actual length of 23 feet?
Towels Washcloths Sheets Place Mats
Regular Price, R $12.00 $3.00 $30.00 $7.50
Sale Price, S $9.60 $2.40 $24.00 $6.00
A
(23 2) 5
B
(23 2) 5
Which formula can be used to calculate the sale price?
C
(23 2) 5
A
S R 0.8
D
5 (23 2)
B
S R 0.8
C
S R 0.8
D
S R 0.2
A triangle has side lengths of 5, 8, and 10. Which of the following side lengths belong to a triangle that is similar to the given triangle?
ABC is similar to DEF . AB : DE = 3:2. If BC = 10, what is the length of segment EF?
A
10, 16, 30
A
15
B
8, 11, 13
B
7.3
C
15, 24, 30
C
16
D
2.5, 4, 6
D
6.7
TEKSING TOWARD TAKS © 2006
Page 3
GRADE 7 MATHEMATICS (7.4) Patterns, relationships, and algebraic thinking. The student represents a relationship in numerical, geometric, verbal, and symbolic form. The student is expected to: (A) generate formulas involving conversions, perimeter, area, circumference, volume, and scaling. (B) graph data to demonstrate relationships in familiar concepts such as conversions, perimeter, area, circumference, volume, and scaling
Actual Dimensions (ft)
The following graph shows the relationship between the dimensions of a scale drawing and an actual object. 18 16 14 12 10 8 6 4 2 0 1
2
3
4
5
6
7
8
9
Scale Drawing Dimensions (cm) Identify the scale used for the scale drawing. _______cm represents ______feet. Using the information on the graph, determine the actual dimension that is represented by 5.5 cm. ________ft. Mark that point on the graph.
Using the information on the graph, determine the scale drawing dimension that represents an actual length of 17 feet. Mark that point on the graph. 1. What mathematical concepts and vocabulary do I need to know to be able to work this problem? 2. Will the Grade 7 Mathematics Formula Chart be helpful on this problem? Why or why not?
3. What problem-solving strategy or strategies will I use to help solve this problem?
4. Extension (7.2F): How would you represent a room that is 20.5 feet long and 25 feet wide on the scale drawing? Show the proportions you would use to solve this problem.
TEKSING TOWARD TAKS © 2006
Page 4
GRADE 7 MATHEMATICS (7.4) Patterns, relationships, and algebraic thinking. The student represents a relationship in numerical, geometric, verbal, and symbolic form. The student is expected to: (A) generate formulas involving conversions, perimeter, area, circumference, volume, and scaling. (B) graph data to demonstrate relationships in familiar concepts such as conversions, perimeter, area, circumference, volume, and scaling
The following graph shows the relationship between the dimensions of a scale drawing and an actual object.
Actual Dimensions (ft)
18 16 14 12 10 8 6 4 2 0 1
2
3
4
5
6
7
8
9
Scale Drawing Dimensions (cm)
Identify the scale used for the scale drawing. _______cm represents ______feet. Using the information on the graph, determine the actual dimension that is represented by 5.5 cm. ________ft. Mark that point on the graph. Using the information on the graph, determine the scale drawing dimension that represents an actual length of 17 feet. Mark that point on the graph. TEKSING TOWARD TAKS © 2006
Page 5
GRADE 7 MATHEMATICS (7.4) Patterns, relationships, and algebraic thinking. The student represents a relationship in numerical, geometric, verbal, and symbolic form. The student is expected to: (A) generate formulas involving conversions, perimeter, area, circumference, volume, and scaling. (B) graph data to demonstrate relationships in familiar concepts such as conversions, perimeter, area, circumference, volume, and scaling
Mary wants to draw a graph that shows a scale of 0.5 inch represents 5 feet. Which of the following correctly represents the scale Mary wants to use?
y
100 90 80 70 60
C
50 40 30 20 10 0
Actual Dimensions (feet)
A
Actual Dimensions (feet)
y
x 0 1 2
3
4
5 6
7
100 90 80 70 60 50 40 30 20 10 0
8 9 10
x 0 1 2
Scale Drawing (inches)
5 6
7
8 9 10
y
90 80 70
D
60 50 40 30 20 10 0
x 0 1 2
3
4
5 6
7
8 9 10
Scale Drawing (inches)
TEKSING TOWARD TAKS Š 2006
Actual Dimensions (feet)
100
Actual Dimensions (feet)
4
Scale Drawing (inches)
y
B
3
100 90 80 70 60 50 40 30 20 10 0
x 0 1 2
3
4
5 6
7
8 9 10
Scale Drawing (inches)
Page 6
GRADE 7 MATHEMATICS (7.4) Patterns, relationships, and algebraic thinking. The student represents a relationship in numerical, geometric, verbal, and symbolic form. The student is expected to: (A) generate formulas involving conversions, perimeter, area, circumference, volume, and scaling. (B) graph data to demonstrate relationships in familiar concepts such as conversions, perimeter, area, circumference, volume, and scaling
Lambert wants to draw a graph that shows a scale of 2 centimeters represents 7 meters. Which of the following correctly represents the scale Lambert wants to use? y
100 90 80 70 60
C
50 40 30 20 10 0
x 0 1 2
3
4
5 6
7
Actual Dimensions (meters)
A
Ac tual Dimensions (meters)
y 100 90 80 70 60 50 40 30 20 10 0
8 9 10
x 0 1 2
Scale Drawing (cm)
5 6
7
8 9 10
y
100 90 80 70 60
D
50 40 30 20 10 0
x 0 1 2
3
4
5 6
7
8 9 10
Scale Drawing (cm)
TEKSING TOWARD TAKS Š 2006
Actual Dimensions (meters)
Actual Dimensions (meters)
4
Scale Drawing (cm)
y
B
3
100 90 80 70 60 50 40 30 20 10 0
x 0 1 2
3
4
5 6
7
8 9 10
Scale Drawing (cm)
Page 7
GRADE 7 MATHEMATICS (7.4) Patterns, relationships, and algebraic thinking. The student represents a relationship in numerical, geometric, verbal, and symbolic form. The student is expected to: (A) generate formulas involving conversions, perimeter, area, circumference, volume, and scaling. (B) graph data to demonstrate relationships in familiar concepts such as conversions, perimeter, area, circumference, volume, and scaling
The drawings below show the dimensions of a scale drawing of a room and the actual room. 6 inches
15 feet 4 inches
Scale Drawing Dimensions
10 feet
Actual Room Dimensions
18
18
16
16
14
14
12
12
10
C
8
Feet
A
Feet
Which graph shows the scale used in the drawing?
10 8
6
6
4
4
2
2
0
1
2
3
4
5
0
6
1
2
18
18
16
16
14
14
12
12
10
D
8
4
4
2
2 2
3
4
Inches TEKSING TOWARD TAKS Š 2006
5
6
8 6
1
4
10
6
0
3
Inches
Feet
B
Feet
Inches
5
6
0
1
2
3
4
5
6
Inches Page 8