Geometry 7 th Grade Math https://www.teacherspayteachers.com/Store/Math-Maker Justify: Apply: Create: Compute:
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Geometry 7th Grade Math�
https://www.teacherspayteachers.com/Store/Math-Maker
Justify:
Apply: Create:
Compute:
Compute…. Justify….
Create…. Apply….
CCSS.MATH.CONTENT.7.G.A.1 Solve problems involving scale drawings of geometric figures, including compuDng actual lengths and areas from a scale
drawing and reproducing a scale drawing at a different scale.
1.)
2.) A scale drawing for a construcDon project uses a scale of 1 inch = 4 feet. The dimensions of the rectangular family room on the sale drawing are 7.5 inches by 12 inches. What will be the actual area of the floor of the family room aPer the construcDon?
Using a ruler and graph paper, create a scale drawing of a city center. Use the informaDon below to create your drawing. -‐ The scale for your drawing is 1 inch = 2 miles. -‐ Use dots to represent the buildings on your map. -‐ Place city hall in the center of the town. -‐ Draw two streets north of city hall that are parallel to each other. -‐ Draw a street perpendicular to the parallel streets to the leP of city hall, and a street perpendicular to the parallel streets to the right of city hall. -‐ Place the post office two miles away from city hall, and the police staDon 3.5 miles from city hall. -‐ Add a school, park, and hospital to your map, and create a table that displays the distance in miles between each of the buildings in city hall.
1.) ΔABC ~ ΔDEF: Find the measure of side DE
2.) Paula has an 80:1 scale –drawing of the floor plan of her house. On the floor plan, the dimensions of her living room are 1 ⅞ inches by 2 ½ inches. What is the area of her real living room in square feet?
Triangle ABC ~ Triangle DEF. Find the value of x and the value of y. Use the words in the word bank below to jusDfy your answer.
Word Bank: Scale Factor, Corresponding Sides, Similar Figures
A
B
C
D
E
F
The two hexagons are similar figures. Find the value of “x” and the value of “y”
45 in
20 in
5x -‐ 25 2x -‐ 8
128° 3y + 8
Compute…. Justify….
Create…. Apply….
CCSS.MATH.CONTENT.7.G.A.2 Draw (freehand, with ruler and protractor, and with
technology) geometric shapes with given condiDons. Focus on construcDng triangles from three measures of angles or sides, noDcing when the condiDons determine a unique triangle,
more than one triangle, or no triangle.
Joe uses metal rods to make triangular frameworks in which each side has a different length. He buys metal rods which have lengths of 1 meter, 2 meters, 3 meters etc and he always keeps one rod of each length in stock.
The diagram shows one of Joe’s triangular frameworks. a, b, and c are all integers and c > b > a. How many different triangular frameworks can Joe make which have a longest side of 7 meters long? Justify your answer
Investigate this situation for other values of c. What generalizations can you make?
1.) The side measures of triangle ABC are 14 inches, 17 inches, and 20 inches. Using the given angle measurements, place the side measures on the correct sides.
2.) The angle measures of Triangle JKL are 50°, 80° and 100°. Using the given side lengths, label the angles correctly.
1.) Decide whether each set of three measures could be the three side lengths of a triangle. Label each set with a “y” for yes, or a “n” for no.
____ 3, 5, 7 _____ 2, 6, 9 _____ 5, 6, 11
____ 4, 9, 15 _____ 12, 15, 30 _____ 1.5, 3.1, 4.55
2.) Decide whether each set of three measures could be the three angle measures of a triangle. Label each set with a “y” or “n”.
____ 40°, 50°, 90° _____ 25°, 85°, 60°
____ 51°, 69°, 80° _____ 18°, 72°, 80°
Create a list of possible whole number values for x.. Do not assume that any one side is the longest.
Which two figures below would have the same shape cross-‐secDon parallel to the base?
Which two figures below would have the same shape cross-‐secDon perpendicular to the base?
1.) Draw a 3-‐D shape that has a circular cross-‐secDon parallel to the base, and a triangular cross-‐secDon perpendicular to the base.
2.) Draw a 3-‐D figure that has a triangular cross-‐secDon parallel to the base, and a triangular cross-‐secDon perpendicular to the base.
Compute…. Justify….
Create…. Apply…. CCSS.MATH.CONTENT.7.G.A.3
Describe the two-‐dimensional figures that result from slicing three-‐dimensional figures, as in plane secDons of right rectangular prisms and right rectangular pyramids.
Match each 3-‐D shape with the cross secDon that would form if the shape was sliced parallel to the base:
A B C D E
cross-‐secDon: ____ _____ _____ ______ ______
1.) Sara sliced the cylinder and cone, and formed congruent cross-‐secDons. Was her slice parallel to the base, or perpendicular to the base? Explain..
2.) Katherine sliced the two pyramids, and formed congruent cross-‐secDons. Was her slice parallel to the base, or perpendicular to the base? Explain
Compute…. Justify….
Create…. Apply…. CCSS.MATH.CONTENT.7.G.B.4
Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivaDon of
the relaDonship between the circumference and area of a circle.
1.) Consider a circle that has a circumference of 28π cm. What is the exact area of the circle?
2.) Consider a circle that has an area of 49π in2. What is the exact circumference of the circle?
3.) Find the approximate area and circumference of the circle below. Use 3.14 to represent pi.
6 cm
Mr. Burns has a paDo in the shape of a trapezoid. A round fountain having a circumference of 14π is placed in the corner as shown in the diagram. Approximately how much of the paDo’s area is NOT taken up by the fountain?
1.) Use your ruler, and a compass to draw a circle that has an area of 4π in2. Explain how you know that the circle has that area.
2.) Use your ruler and a compass to draw a circle that has a circumference of 3π in. Explain how you know that the circle has that circumference.
1.) Square ABCD has a perimeter of 48 inches. What percent of the square’s area is taken up by the four circles? Use 3.14 for pi. JusDfy your answer.
2.)How many Dmes larger is the area of the outer circle, than the area of the inner circle? JusDfy your answer.
Compute…. Justify….
Create…. Apply….
CCSS.MATH.CONTENT.7.G.B.5 Use facts about supplementary, complementary, verDcal, and adjacent angles in a mulD-‐step problem to write and solve
simple equaDons for an unknown angle in a figure.
1.) The three angles in a triangle have a sum of 180°. What is the value of x? JusDfy your answer.
Find the value of x for each angle relaDonship.
1)
4) 3)
2)
2.) If the measure of angle CGD is 51°, what is the measure of angle FGE? JusDfy your answer.
1.) Use a protractor to draw a pair of adjacent supplementary angles, in which one of the angles is three Dmes larger than the other angle. Name the larger angle ∠ABC, and the smaller angle ∠CBD. Give the measure of each angle.
2.) Use a protractor to draw a pair of complementary angles, in which one of the angles is 9 more than two Dmes the other angle. Name the larger angle ∠XYZ, and the smaller angle ∠ZYW. Give the measure of each angle.
1.) The measures of two complementary angles are 12q-‐9 and 8q+14. Find the measures of the angles.
2.) Two angles are complementary. One angle is 15 degrees more than 2 Dmes the other. Find the measure of both angles.
3.) When scissors are opened, they form verDcal angles. If m∠4 = 38°, find the measures of the other 5 angles.
Compute…. Justify….
Create…. Apply….
CCSS.MATH.CONTENT.7.G.B.6 Solve real-‐world and mathemaDcal problems involving area, volume and surface area of two-‐ and three-‐dimensional
objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.
A movie theater designs two bags to each hold 96 cubic inches of popcorn. Calculate the height of both bags, then write a lewer to the owner of the theater explaining which bag is more eco-‐friendly by using less paper.
Tino designs tents for a sporDng goods store. To manufacture the tent it costs $0.25 per square foot. The store then charges the customer $0.30 per cubic feet of capacity. a. How much of a profit will the store make off of each one of Tino’s
tents? b. Is it more profitable for Tino to increase the surface area of the
tent, or the volume of the tent? explain.
Find the area of each polygon below:
Find the volume of each 3-‐D figure:
A school currently uses the locker shown to the right for students in PE. They are looking to replace these lockers with new ones, that will give the students more storage space, but will have a smaller surface area. Design a locker that meets this criteria.
http://www.teacherspayteachers.com/Store/Math-Maker
15 in
48 in
Answer Key:
Slide One: Compute: 1.) 2.25 cm 2.) 8.64 cm JusDfy: y = 2.9 cm x = 23.2 cm The scale factor from triangle ABC to DEF is 0.25. x corresponds to side EF, and y corresponds to
side AB. Apply: 1) x = 14 y = 40 2) 1,440 sq feet Create: answers will vary
Slide Two: Compute: 1.) Top: Y, N, N Bowom: N, Y, N 2) Top: Y, N Bowom: N, Y JusDfy: 10 possible triangles
Apply: 1.) Side AB = 20 in, Side AC = 14 in, Side BC = 17in. 2.) Angle J = 100° Angle K = 50° Angle L = 80° Create: x could equal: 0, 1, 2, 3, 4, 5, and 6
Slide Three:
Compute: C, E, B, A, D JusDfy: 1) Parallel to the base. Parallel cross-‐ secDons will be circles for both. 2) Perpendicular to the base. These cross-‐secDons
will both be triangles.
Apply: 1.) The cone and the cylinder 2.) The Pentagonal prism and the triangular prism. Create: 1.) 2)
Slide Four: Compute: 1.) 196π cm1 2.) 14π 3.) c= 73.68 cm a = 113.04 cm2
Justify: 1.) 78.5 percent of the square’s area is filled with circles. 2.) The outer circle is 16 times larger. Apply: 321.5 ft2 of patio Create: Answers will vary
Slide Five: Compute : 1) x = 37 2.) x = 15 3) x = 19 4.) x = 7
JusDfy: 1.) x = 67° 2.) 39° Apply: 1.) q = 4 2.) 55° and 125° 3.) angle 2 = 38° angle 1 and 3 = 142° Create: Answers will vary
Slide Six: Compute: Trapezoid: 18m2 Triangle: 60in2 Parallelogram: 75 cm2 Rectangular Prism: 120 in3 Triangular Prism: 1250 cm3
JusDfy: Bag A has a height of 8 in, and will require 124 in2 of paper to make. Bag B has a height of 6 in, and will require 112 in2 of paper to make. Bag B is more eco friendly.
Apply: The store will profit $104 for every tent sold. It is more profitable to increase the volume, and decrease the surface area. Create: Answers will vary
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