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8 th Grade EOG Review

8 th Grade EOG Review. Sandra Davidson, MaEd NBCT EA Math Lakeshore Middle School. Measurement. Perimeter, Area, and Volume Changing Dimensions Indirect Measurement. Measurement of a Triangle. The sum of the measures of the interior angle equals 180 ° .

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8 th Grade EOG Review

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  1. 8th Grade EOG Review Sandra Davidson, MaEd NBCT EA Math Lakeshore Middle School

  2. Measurement • Perimeter, Area, and Volume • Changing Dimensions • Indirect Measurement

  3. Measurement of a Triangle 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 -132 x = 48° What is the value of xin the following triangle?

  4. Perimeter and Circumference Perimeter is the distance around the outside of a plane figure. This distance is called the circumference when the figure is a circle. P = S1 + S2 + S3 + S4 + S5 C = πd

  5. Area– the measure of square units inside a plane figure. A = ½ bh A = bh A = bh A = πr2

  6. 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? 3. Carlos bought a pizza that had an area of 201 in2. He paid $8.99 for the pizza. Tameka bought two pizzas, each of which had an area of 133 in2. 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? Practice – Area, Perimeter and Circumference ( 6 ft. x 6 ft.) ( d = 16 in. and 13 in.) (Tameka, $0.04/sq. in. - while Carlos, $0.05/sq. in.) ( 8 ft. X 8 ft.)

  7. 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? 3. Carlos bought a pizza that had an area of 201 in2. He paid $8.99 for the pizza. Tameka bought two pizzas, each of which had an area of 133 in2. 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? Practice – Area, Perimeter and Circumference

  8. Volume - the measure of cubic units inside a 3-D figure. What is the volume of this rectangular prism? V = Bh V = l x w x h V = 2.5 x 1.5 x 1.6 V = 6 m2

  9. 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: 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: 2.5 x 1.5 = 3.75 Add these and multiply by 2: 2(4 + 2.4 + 3.75) = 20.3m2

  10. Practice - Volume and Surface Area What is the volume of this rectangular prism? V = Bh V = l x w x h V = 8 x 8 x 7 V = 448 m3 What is the surface area? front: 8 x 7 = 56 side: 8 x 7 = 56 top: 8 x 8 =64 2(56 + 56 + 64) = 352 m2

  11. Practice - Volume and Surface Area What is the volume of this cylinder? V = Bh V = π r2xh V = 3.14 x22 x 16 V = 200.96 in3 (or 64π) What is the surface area? top: 3.14 x 22 = 12.56 bottom: 3.14 x 22 = 12.56 label: C x 16 (circumference x 16) πdx 16 3.14 x 4 x 16 = 200.96 in2 12.56 + 12.56 + 200.96 = 226.08 in2

  12. 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 ft3 What is the surface area? top/bottom: ½ (6 x 4) = 12 3 rect. sides: 3(6 x 8) = 144 12 + 12+ 144= 168 ft2

  13. Changing DimensionsPerimeter and Area (Rectangles, Triangles, and Circles) When both the dimensions double, the perimeter or circumference doubles, and the area becomes 4 times greater. When both the dimensions triple, the perimeter or circumference triples, and the area becomes 9 times greater.

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

  15. Practice - Changing Dimensions 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?

  16. Practice - Changing Dimensions 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? ( P= 116 m ) ( A= 810 ft2 )

  17. 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 m2. 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? 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 in2. A large pizza has a radius that is triple the radius of a small pizza. What is the area of a large pizza? Practice - Changing Dimensions

  18. 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 m2. 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? 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 in2. A large pizza has a radius that is triple the radius of a small pizza. What is the area of a large pizza? Practice - Changing Dimensions ( C = 52 cm.) ( P = 24 ft.) ( A = 8 m2 ) ( A = 261 in2 )

  19. Practice - Changing Dimensions 8. Claire’s old aquarium has a volume of 27,000 cm3. 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 yd3. 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 )

  20. Practice - Changing Dimensions 8. Claire’s old aquarium has a volume of 27,000 cm3. 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 yd3. The city is going to make the length of the pool twice as long. What will be the volume of the new pool? ( V = 675,000 cm3 ) 7. If the length, width, and height of the rectangular prism are tripled, what will be the volume? ( V = 1512 m3 ) ( V = 1600 yd3 ) Practice: Buckle Down ( pp. 160 – 162 )

  21. 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?

  22. 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? ( 48 ft.)

  23. 1. If the length of a rectangle is doubled, what will happen to its area? A. the area will be the same B. the area will double. C. the area will triple. D. the area will quadruple. 2. 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 3. 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. EOG Grade 8 Math – Sample Items-Goal 1(released by NC DPI)

  24. 1. If the length of a rectangle is doubled, what will happen to its area? A. the area will be the same B. the area will double. C. the area will triple. D. the area will quadruple. 2. 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 3. 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. EOG Grade 8 Math – Sample Items-Goal 1(released by NC DPI) 1. (B) 2. (C) 3. (B)

  25. 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 1 ½ times the original B. the volume will be twice the original C. the volume will be three times the original D. the volume will be four times the original

  26. 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 1 ½ times the original B. the volume will be twice the original C. the volume will be three times the original D. the volume will be four times the original 4. (D)

  27. 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 approximatelength of the pond? A. 25 ft. B. 19 ft. C. 18 ft. D. 13 ft.

  28. 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 approximatelength of the pond? A. 25 ft. B. 19 ft. C. 18 ft. D. 13 ft. 4. (D)

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