8 th Grade EOG Review Sandra Davidson Ma

8 th Grade EOG Review Sandra Davidson, Ma. Ed NBCT EA Math Lakeshore Middle School

Measurement • Perimeter, Area, and Volume • Changing Dimensions • Indirect Measurement Page 2 9/16/2020

Measurement of a Triangle What is the value of x in the following triangle? Page 3 The sum of the measures of the interior angle equals 180°. Write an equation and solve for x: 32 + 100 + x = 180 132 + x = 180 -132 x = 48° 9/16/2020

Perimeter and Circumference P = S 1 + S 2 + S 3 + S 4 + S 5 C=πd Perimeter is the distance around the outside of a plane figure. This distance is called the circumference when the figure is a circle. Page 4 9/16/2020

Area – the measure of square units inside a plane figure. A = ½ bh A = bh Page 5 A = bh A = π r 2 9/16/2020

Practice – Area, Perimeter and Circumference 1. Paul want to build a rectangular dog pen. He has 24 ft. of fencing in 1 -ft. sections. What are the dimensions of the best dog pen he can build? ( 6 ft. x 6 ft. ) 2. Paul decides to use a wall of the house as one side of the rectangular dog pen. If he uses the 24 ft. of fencing for the other 3 sides, what are the dimensions of the best dog pen he can build? ( 8 ft. X 8 ft. ) Page 6 3. Carlos bought a pizza that had an area of 201 in 2. He paid $8. 99 for the pizza. Tameka bought two pizzas, each of which had an area of 133 in 2. She paid a total of $10. 99 for the two pizzas. What is the approximate diameter of each pizza? ( d = 16 in. and 13 in. ) Which pizza is the better buy based on the number of square inches per pizza? (Tameka, $0. 04/sq. in. - while Carlos, $0. 05/sq. in. ) 9/16/2020

Practice – Area, Perimeter and Circumference 1. Paul want to build a rectangular dog pen. He has 24 ft. of fencing in 1 -ft. sections. What are the dimensions of the best dog pen he can build? 2. Paul decides to use a wall of the house as one side of the rectangular dog pen. If he uses the 24 ft. of fencing for the other 3 sides, what are the dimensions of the best dog pen he can build? Page 7 3. Carlos bought a pizza that had an area of 201 in 2. He paid $8. 99 for the pizza. Tameka bought two pizzas, each of which had an area of 133 in 2. She paid a total of $10. 99 for the two pizzas. What is the approximate diameter of each pizza? Which pizza is the better buy based on the number of square inches per pizza? 9/16/2020

Volume - the measure of cubic units inside a 3 -D figure. What is the volume of this rectangular prism? V = Bh V=lxwxh V = 2. 5 x 1. 6 V = 6 m 2 Page 8 9/16/2020

Surface Area – the measure of square units of the outside “wrapping” of a 3 -D figure. What is the surface area? Find the area of the front: front 2. 5 x 1. 6 = 4 and area of the right side: 1. 5 x 1. 6 = 2. 4 and the area of the top: top 2. 5 x 1. 5 = 3. 75 Add these and multiply by 2: 2 2(4 + 2. 4 + 3. 75) 3. 75 = 20. 3 m 2 Page 9 9/16/2020

Practice - Volume and Surface Area What is the volume of this rectangular prism? V = Bh V=lxwxh V=8 x 8 x 7 V = 448 m 3 What is the surface area? area front: 8 x 7 = 56 side: 8 x 7 = 56 top: 8 x 8 = 64 2(56 + 64) 64 = 352 m 2 Page 10 9/16/2020

Practice - Volume and Surface Area What is the volume of this cylinder? V = Bh V = π r 2 x h V = 3. 14 x 22 x 16 V = 200. 96 in 3 (or 64π) What is the surface area? area top: 3. 14 x 22 = 12. 56 bottom: 3. 14 x 22 = 12. 56 label: C x 16 (circumference x 16) πd x 16 3. 14 x 16 = 200. 96 in 2 12. 56 + 200. 96 = 226. 08 in 2 Page 11 9/16/2020

Practice - Volume and Surface Area What is the volume of this triangular prism? V = Bh V = ½ (b x h ) x h V = ½ (6 x 4) x 8 V = 96 ft 3 What is the surface area? top/bottom: ½ (6 x 4) = 12 3 rect. sides: 3(6 x 8) = 144 12 + 144 = 168 ft 2 Page 12 9/16/2020

Changing Dimensions Perimeter and Area (Rectangles, Triangles, and Circles) When both the dimensions double, double the perimeter or circumference doubles, and the area becomes 4 times greater. When both the dimensions triple, triple the perimeter or circumference triples, and the area becomes 9 times greater. Change (action) Perimeter Area double x 22 = 4 triple are multiplied by n x 3 xn x 32 = 9 x n 2 When both dimensions. . . Page 13 9/16/2020

Changing Dimensions – Volume (Rectangular Prisms) Changing one dimension: when one dimension doubles, doubles the volume doubles. . . 21 = 2 when one dimension triples, triples the volume triples. . . 31 = 3 Changing two dimensions: when two dimensions double, double the volume becomes 4 times greater. . . 22 = 4. 4 when two dimensions triple, triple the volume becomes 9 times greater. . . 32 = 9 Changing three dimensions: when all 3 dimensions double, double the volume becomes 8 times greater. . . 23 = 8 when all 3 dimensions triple, triple the volume becomes 27 times greater. . . 33 = 27 Page 14 9/16/2020

Practice - Changing Dimensions Page 15 1. If the length and width of the following rectangle are doubled, what will be the perimeter? 2. If the base and height of the following triangle are tripled, what will be the area? 9/16/2020

Practice - Changing Dimensions 1. If the length and width of the following rectangle are doubled, what will be the perimeter? ( P= 116 m ) 2. If the base and height of the following triangle are tripled, what will be the area? ( A= 810 ft 2 ) Page 16 9/16/2020

Practice - Changing Dimensions 3. Gary had a triangular dog pen with a perimeter of 12 ft. He made it bigger by doubling the dimensions. What is the perimeter now? 4. Tara has a rectangular table with an area of 2 m 2. She is going to buy another table that has dimensions that are double the first table. What is the area of Tara’s new table? Page 17 5. Kasey drew a circle that has a circumference of 13 cm. If he draws another circle with a radius that is 4 times greater, what will be the circumference? 6. A small pizza at Pete’s Pizza has an area of 29 in 2. A large pizza has a radius that is triple the radius of a small pizza. What is the area of a large pizza? 9/16/2020

Practice - Changing Dimensions 3. Gary had a triangular dog pen with a perimeter of 12 ft. He made it bigger by doubling the dimensions. What is the perimeter now? 5. Kasey drew a circle that has a circumference of 13 cm. If he draws another circle with a radius that is 4 times greater, what will be the circumference? ( C = 52 cm. ) 6. A small pizza at Pete’s Pizza has an area of 29 in 2. A large pizza has a radius that is triple the radius of a small pizza. What is the area of a large pizza? ( P = 24 ft. ) 4. Tara has a rectangular table with an area of 2 m 2. She is going to buy another table that has dimensions that are double the first table. What is the area of Tara’s new table? ( A = 8 m 2 ) Page 18 ( A = 261 in 2 ) 9/16/2020

Practice - Changing Dimensions 8. Claire’s old aquarium has a volume of 27, 000 cm 3. She bought a new aquarium in which the length and width are 5 times those of her old tank. What is the volume of Claire’s new aquarium? 9. The swimming pool at the park is shaped like a rectangular prism. The volume of the pool is 800 yd 3. The city is going to make the length of the pool twice as long. What will be the volume of the new pool? 7. If the length, width, and height of the rectangular prism are tripled, what will be the volume? Practice: Buckle Down ( pp. 160 – 162 ) Page 19 9/16/2020

Practice - Changing Dimensions 8. Claire’s old aquarium has a volume of 27, 000 cm 3. She bought a new aquarium in which the length and width are 5 times those of her old tank. What is the volume of Claire’s new aquarium? ( V = 675, 000 cm 3 ) 9. The swimming pool at the park is shaped like a rectangular prism. The volume of the pool is 800 yd 3. The city is going to make the length of the pool twice as long. What will be the volume of the new pool? 7. If the length, width, and height of the rectangular prism are tripled, what will be the volume? ( V = 1512 m 3 ) Practice: Buckle Down ( pp. 160 – 162 ) Page 20 ( V = 1600 yd 3 ) 9/16/2020

Indirect Measurement Apply the concepts of similar figures to find the unknown measurement of an object that is nearly impossible to measure with a common measuring tool. What is the distance across the lake? Page 21 9/16/2020

Indirect Measurement Apply the concepts of similar figures to find the unknown measurement of an object that is nearly impossible to measure with a common measuring tool. ( 48 ft. ) What is the distance across the lake? Page 22 9/16/2020

EOG Grade 8 Math – Sample Items-Goal 1 (released by NC DPI) 1. If the length of a rectangle is doubled, what will happen to its area? A. B. C. D. the the area Page 23 will be the same double. triple. quadruple. 2. 3. The side measurements of a cube are tripled. What is the ratio of the surface area of the original cube to the larger one? A. 1: 3 C. 1: 9 B. 1: 6 D. 1: 12 The shadow of a flagpole is 19 ft. long. The shadow of a 12 ft. wall is 4 ft. What is the height of the flagpole? A. 48 ft. C. 62 ft. B. 57 ft. D. 75 ft. 9/16/2020

EOG Grade 8 Math – Sample Items-Goal 1 (released by NC DPI) 1. If the length of a rectangle is doubled, what will happen to its area? A. B. C. D. the the area 1. (B) Page 24 will 2. (C) be the same double. triple. quadruple. 3. (B) 2. 3. The side measurements of a cube are tripled. What is the ratio of the surface area of the original cube to the larger one? A. 1: 3 C. 1: 9 B. 1: 6 D. 1: 12 The shadow of a flagpole is 19 ft. long. The shadow of a 12 ft. wall is 4 ft. What is the height of the flagpole? A. 48 ft. C. 62 ft. B. 57 ft. D. 75 ft. 9/16/2020

EOG Grade 8 Math – Sample Items-Goal 1 (released by NC DPI) The diagram below shows a company’s current packaging of its plant food. 4. The company doubles the radius but keeps the height the same. What effect will this change have on the volume of the container? A. the volume will be times the original the volume will be times the original B. C. D. Page 25 1½ twice three four 9/16/2020

EOG Grade 8 Math – Sample Items-Goal 1 (released by NC DPI) The diagram below shows a company’s current packaging of its plant food. 4. The company doubles the radius but keeps the height the same. What effect will this change have on the volume of the container? A. the volume will be times the original the volume will be times the original B. C. D. 4. (D) Page 26 1½ twice three four 9/16/2020

EOG Grade 8 Math – Sample Items-Goal 1 (released by NC DPI) 5. Jake wanted to measure the length of the pond, so he drew this diagram of two similar triangles. What is the approximate length of the pond? A. 25 ft. B. 19 ft. C. 18 ft. D. 13 ft. Page 27 9/16/2020

EOG Grade 8 Math – Sample Items-Goal 1 (released by NC DPI) 5. Jake wanted to measure the length of the pond, so he drew this diagram of two similar triangles. What is the approximate length of the pond? A. 25 ft. B. 19 ft. 4. (D) C. 18 ft. D. 13 ft. Page 28 9/16/2020