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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.

Martha created a parallelogram using two congruent trapezoids. Generate a formula she could use to find the area of parallelogram ABCD. Show your work. 12 cm

A

B

10 cm D

6 cm

C

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. Do I need to add more labeling to the given sketch? If so, what?

4. What problem-solving strategy or strategies will I use to help solve this problem?

5. Extension (7.4A): Generate a formula to find the area of the parallelogram if the bases are b 1 and b 2 and the height is h.

TEKSING TOWARD TAKS Š 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.

Martha created a parallelogram using two congruent trapezoids. Generate a formula she could use to find the area of parallelogram ABCD. Show your work. 12 cm

A

B

10 cm D

TEKSING TOWARD TAKS Š 2006

6 cm

C

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.

You must calculate the shaded area below created when four circles are inscribed in a square. The side of the square is 20 units. Which of the following formulas will correctly calculate the shaded area, A?

A composite figure is shown below. The figure has a rectangular center and two sets of congruent isosceles triangles attached to the four sides of the rectangle.

c units

n units

A

A = 20 20 20 3.14

B

A = 20 20 5 3.14 4

C

A = 20 20 10 3.14

D

A = 52 3.14 4 10 10

2

2

The following table shows the surface area of cubes. The surface area is the total of the area of all six faces. Surface Area (in square units) 6 13.5 24 37.5 54 73.5 96

Length of an Edge 1 1.5 2 2.5 3 3.5 4

Which formula can be used to find the perimeter, P, of the figure? A

P 4 c 4 n

B

P 3 c 3 n

C

P 2 c 2 n

D

P 4 c n

If the pattern continues, which of the following would be the next two rows in the table? A

4.5 5

120 160

B

4.5 5

136 150

C

4.5 5

121.5 150

D

4.5 5

132.5 180

TEKSING TOWARD TAKS © 2006

A rectangle has a length of 2 x 3 and a length of 8. Which expression can be used to represent the perimeter of the rectangle? A

P 2 x 3 8

B

P 2(2 x 3) 8

C

P 8 (2 x 3)

D

P 2(2 x 3) 2(8)

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: (B) graph data to demonstrate relationships in familiar concepts such as conversions, perimeter, area, circumference, volume, and scaling.

The relationship of the perimeter of a family of rectangles with a constant width is shown in the graph below. 36 32

Perimeter

28 24 20 16 12 8 4 0

1

2

3

4

5

6

Length

Predict the perimeter of a rectangle in this family that has a length of 5.5 units. Predict the area of a rectangle in this family that has a length of 5 units.

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. Would a picture or diagram be helpful on this problem? If so, how?

4. What problem-solving strategy or strategies will I use to help solve this problem?

5. Extension (7.13A): If a rectangle in this family had an area of 24 square units, find the length of the rectangle.

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: (B) graph data to demonstrate relationships in familiar concepts such as conversions, perimeter, area, circumference, volume, and scaling.

The relationship of the perimeter of a family of rectangles with a constant width is shown in the graph below. 36 32

Perimeter

28 24 20 16 12 8 4 0

1

2

3

4

5

6

Length

Predict the perimeter of a rectangle in this family that has a length of 5.5 units. Predict the area of a rectangle in this family that has a length of 5 units. 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: (B) graph data to demonstrate relationships in familiar concepts such as conversions, perimeter, area, circumference, volume, and scaling.

The table and the graph show the relationship between the length of 1 side of a regular polygon and its perimeter.

Regular Polygon Length of Side (inches) 1.5 3 4 5 6

Perimeter (inches) 7.5 15 20 25 30

Which of the following graphs best represents the data in the table?

y

40

35

35

30

30

25

C

20

20 15

10

10

5

5 x 1 2 3 4 Length of Side y

Perimeter

25

15

0

B

Perimeter

40

5

6

0

7

40

40

35

35

30

30

25

D

20

10

10

5

5 x 2

3

4

Length of Side

TEKSING TOWARD TAKS Š 2006

5

6

7

3

4

5

6

7

x

Length of Side

20 15

1

2

25

15

0

1 y

Perimeter

A

Perimeter

y

0

1

2

3

4

5

6

7

x

Length of Side

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: (B) graph data to demonstrate relationships in familiar concepts such as conversions, perimeter, area, circumference, volume, and scaling.

The table and the graph show the relationship between the length of a side of a regular polygon and its perimeter.

The relationship of the area of a family of rectangles with a constant width is shown in the graph below.

Regular Polygon Perimeter (inches) 6 12 16 20 24

32 28 24 Area

Length of Side (inches) 1.5 3 4 5 6

36

20 16 12 8

24

4

Perimeter

21 0

18

1

2

3

4

5

6

Length

15 12

Using the graph predict the area of the rectangle that belongs to this family that would have a length of 9 units.

9 6

A

28

3

B

32

C

36

D

40

0 1

2

3

4

5

6

Length of a Side Which regular polygon is represented by the data? A

Triangle

B

Square

C

Hexagon

D

Octagon

TEKSING TOWARD TAKS Š 2006

Page 7


05-7.4A and 7.4B