POWERS EXPONENTS ERROR ANALYSIS. Write and Evaluate Powers Product and Quotient of Powers Power of a Power Negative Exponents. Name (s) Class Date

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1 POWERS Name (s) Class Date & EXPONENTS ERROR ANALYSIS Write and Evaluate Powers Product and Quotient of Powers Power of a Power Negative Exponents Exceeding the CORE Question # 0

2 A playground has an area of square feet. What is the area of the playground? ft 2 The area of the playground is 180 ft 2. Exceeding the CORE Question # 1

3 The table shows the weights of two dogs. What is the weight of each dog? Rottweiler (2 2 2) =80 German Shepard 2 6 (6 6)=36 The Rottweiler weighs 80 pounds and the German Shepard weighs 36 pounds. Dog Average Weight(lb.) Rottweiler German Shepard 2 6 Exceeding the CORE Question # 2

4 The table shows the number of students at Fortran College studying a certain language. How many times as many students study Spanish than French? = = or 27 The number of students that study Spanish is 3 3 or 27 times the number that speak French. Language Total Students Spanish 3 6 French 3 2 Exceeding the CORE Question # 3

5 Michelle s video game system has a processing speed of 10 9 instructions per second. Gregory s video game system has a processing speed that is 10 3 times as fast. How many instructions per second can Gregory s video game process? 10 9 = = 10 6 Gregory s video game has a processing speed of 10 6 or 1,000,000 instructions per second. Exceeding the CORE Question # 4

6 Read the word problem. Look at the students work and solution. Identify th32e error and describe it. Solve the problem correctly. Then The screen on Brian s cellular phone is in the shape of a rectangle with a length of 5x 2 feet and a width of 6x 8 feet. Brian wants to cover the screen with a plastic shield to prevent it from scratching. Find the area of the screen. (5x 2 )(6x 8 ) (5 6)(x 2 8 ) 30x 16 The area of the screen is 30x 16 ft 2. Exceeding the CORE Question # 5

7 The floor of the art room at Laurelton Middle School is in the shape of a square with side lengths of q 2 r 3 feet. New tile is going to be put on the floor of the art room. Find the area of the floor. A = s 2 Area of a square = (q 2 r 3 ) 2 = (q 2 ) 2 (r 3 ) 2 = q 4 r 9 The area of the floor in the art room is q 4 r 69 ft 2. Exceeding the CORE Question # 6

8 Tamara is shipping some clothing in a box the shape of a cube like the one shown. Find the volume of the box. V=s 3 Volume of a cube = (4w 3 ) 3 = 4w 3 3 = 4w 9 The volume of the box is 4w 9 units 3. 4w 3 Exceeding the CORE Question # 7

9 Justin has four pieces of floor mats in the shape of a square like the one shown. He wants to use them together to cover a portion of his garage. What is the area of the space he can cover with the floor mats? 4(3x 2 ) =3x 2 +3x 2 + 3x 2 + 3x 2 3x 2 yards =12x 2 The floor mats will cover 12x 2 yd 2. Exceeding the CORE Question # 8

10 Cheryl is making a bracelet using beads that are about inch in diameter. What is the diameter of the bead as a power of 10? = = =10-2 The bead is about 10-2 inch in diameter. Exceeding the CORE Question # 9

11 A blood cell is very small and is estimated to have a diameter of about 5 5 inches. Evaluate 5 5. Write the estimated diameter of a blood cell using a positive exponent and as a fraction. 5 5 = 55 1 = 55 = 3, The estimated diameter of a blood cell is 55 or 1 3,125 inches. 1 Exceeding the CORE Question # 10

12 Answer Key Error Correct Sample Work Correct Answer 1. The base for each power is incorrectly multiplied to the exponent. The exponent tells how many times the base ,250 ft 2 number is used as a factor. 2. The exponent is used as the factor instead of the base. Rottweiler =90 German Shepard 2 6 =64 Irish Wolfhound 2 3 x 5=40 3. The exponents are divided. When dividing powers with the same base subtract the exponents = or 81 times The area of the playground is 2,250 ft 2. The Rottweiler weighs 90 pounds and the German Shepard weighs 64 pounds The number of students that study Spanish is 3 4 or 81 times the number that speak French. 4. The powers are divided instead of multiplied = Gregory s video game has a processing speed of or 1,000,000,000,000 instructions per second. Exceeding the CORE Question # 11

13 5. The exponents are multiplied. When multiplying powers with the same base add the exponents. 6. The exponents are used as factors. It should be multiplied to the exponent of the power. 7. The base, 4, should also be raised to the 3 rd power. 8. The area of one floor mat needs to be found. 9. The decimal is converted to the wrong fraction. 10. The positive power is placed in the numerator instead of the denominator of the fraction. (5x 2 )(6x 8 ) 30x 10 (q 2 r 3 ) 2 q 2 2 r 3 2 q 4 r 6 = (4w 3 ) 3 = (4 3 ) 3 (w 3 ) 3 = 64w 9 (3x 2 ) 2 (3x 2 ) (3x 2 )=9x 4 Area of 1 floor mat 4(9x 4 )=36x 4 Area of 4 floor mats = 1,000 = = = = = 1 3,125 The area of the screen is 30x 10 ft 2. The area of the floor in the art room is q 4 r 6 ft 2. The volume of the box is 64w 9 units 3 The floor mats will cover 36x 4 yd 2. The bead is about 10-3 inch in diameter. The estimated diameter of a blood cell is or 1 3,125 inch. Exceeding the CORE Question # 12

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