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©Exceeding the CORE www.exceedingthecore.com Question # 0

ERROR ANALYSIS

POWERS &

Write and Evaluate Powers

Product and Quotient of Powers

Power of a Power

Negative Exponents

EXPONENTS

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Name (s) ______________________________________ Class_______________ Date_______________________________


Error Analysis – POWERS & EXPONENTS Read the word problem. Look at the students work and solution. Identify the error and describe it. Solve the problem correctly. Then

share a strategy this student could use to prevent the same error in the future.

A playground has an area of 2 ∙ 32 ∙ 53 square feet. What is the area of the playground?

Incorrect Work/Solution Identify and Explain the Error

2 ∙ 32 ∙ 53

2 ∙ 6 ∙ 15

180 ft2

The area of the playground is 180 ft2.

Correct Work/ Solution Share a Strategy


Name (s) ______________________________________ Class_______________ Date_______________________________




The table shows the weights of two dogs. What is the weight of each dog?


Rottweiler 2 ∙ 32 ∙ 5 2 ∙ (2∙2∙2) ∙ 5 2 ∙ 8 ∙ 5 =80

The Rottweiler weighs 80 pounds and the German Shepard weighs 36 pounds.


Dog Average Weight(lb.)

Rottweiler 2 ∙ 32 ∙ 5

German Shepard 26

German Shepard 26 (6∙6)=36


Name (s) ______________________________________ Class_______________ Date_______________________________




The table shows the number of students at Fortran College studying a certain language. How many times as many students study Spanish than French?

Incorrect Work/Solution Identify and Explain the Error 36

32 = 36÷2 33 = 3 × 3 × 3 or 27 The number of students that study Spanish is 33 or 27 times the number that speak French.


Language Total Students

Spanish 36 French 32


Name (s) ______________________________________ Class_______________ Date_______________________________




Michelle’s video game system has a processing speed of 109 instructions per second. Gregory’s video game system has a processing speed that is 103 times as fast. How many instructions per second can Gregory’s video game process?


109

103 = 109−3 = 106

Gregory’s video game has a processing speed

of 106or 1,000,000 instructions per second.



Name (s) ______________________________________ Class_______________ Date_______________________________


Error Analysis – POWERS & EXPONENTS Read the word problem. Look at the students work and solution. Identify th32e error and describe it. Solve the problem correctly.

Then share a strategy this student could use to prevent the same error in the future.

The screen on Brian’s cellular phone is in the shape of a rectangle with a length of 5𝑥2 feet and a width of 6𝑥8feet. Brian wants to cover the screen with a plastic shield to prevent it from scratching. Find the area of the screen.


(5𝑥2)(6𝑥8)

(5 ∙ 6)(𝑥2∙8)

30𝑥16

The area of the screen is 30𝑥16 ft2.



Name (s) ______________________________________ Class_______________ Date_______________________________




The floor of the art room at Laurelton Middle School is in the shape of a square with side lengths

of 𝒒𝟐𝒓𝟑 feet. New tile is going to be put on the floor of the art room. Find the area of the floor.


𝐴 = 𝑠2 Area of a square = (𝑞2𝑟3)2 = (𝑞2)2(𝑟3)2 = 𝑞4 𝑟9 The area of the floor in the art room is 𝑞4 𝑟69 ft2.



Name (s) ______________________________________ Class_______________ Date_______________________________




Tamara is shipping some clothing in a box the shape of a cube like the one shown. Find the volume of the box.


V=s3 Volume of a cube = (4𝑤3)3 = 4𝑤3×3 = 4𝑤9

The volume of the box is 4𝑤9 units3.


| 4w3 |


Name (s) ______________________________________ Class_______________ Date_______________________________


Error Analysis – POWERS & EXPONENTS Read the word problem. Look at the students work and solution. Identify the error and describe it. Solve the problem correctly. Then share a strategy this student could use to prevent the same error in the future.

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(3x2 )

=3x2 +3x2 + 3x2 + 3x2

=12x2

The floor mats will cover 12x2 yd2.


3x2 yards


Name (s) ______________________________________ Class_______________ Date_______________________________




Cheryl is making a bracelet using beads that are about 0.001 inch in diameter. What is the diameter of the bead as a power of 10?


0.001 = 1

100

= 1

102

=10-2 The bead is about 10-2 inch in diameter.



Name (s) ______________________________________ Class_______________ Date_______________________________




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

1=

3,125

1

The estimated diameter of a blood cell is 55

1 or

3,125

1 inches.



Name (s) ______________________________________ Class_______________ Date_______________________________


Error Analysis – POWERS & EXPONENTS 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 number is used as a factor.

2 ∙ 32 ∙ 53

2 ∙ 9 ∙ 125

2,250 ft2

The area of the playground is 2,250 ft2.

2. The exponent is used as the factor instead of the base. Rottweiler 2 ∙ 32 ∙ 5 =90

German Shepard 26=64 Irish Wolfhound 23 x 5=40

The Rottweiler weighs 90 pounds and the German Shepard weighs 64 pounds

3. The exponents are divided. When dividing powers with the same base subtract the exponents.

36

32= 36−2

34 or 81 times

The number of students that study Spanish is 34 or 81 times the number that speak French.

4. The powers are divided instead of multiplied.

109 × 103 = 109+3

Gregory’s video game has a processing speed of 1012 or 1,000,000,000,000 instructions per second.


Name (s) ______________________________________ Class_______________ Date_______________________________


5. The exponents are multiplied. When multiplying powers with the same base add the exponents.

(5𝑥2)(6𝑥8) 30𝑥10

The area of the screen is 30𝑥10 ft2.

6. The exponents are used as factors. It should be multiplied to the exponent of the power.

(𝑞2𝑟3)2 𝑞2×2 𝑟3×2 𝑞4 𝑟6

The area of the floor in the art room is 𝑞4 𝑟6 ft2.

7. The base, 4, should also be raised to the 3rd power.

= (4𝑤3)3 = (43)3(𝑤3)3 = 64𝑤9

The volume of the box is 64𝑤9 units3

8. The area of one floor mat needs to be found.

(3x2 )2 (3x2 ) (3x2 )=9x4

Area of 1 floor mat 4(9x4)=36x4

Area of 4 floor mats

The floor mats will cover 36x4 yd2.

9. The decimal is converted to the wrong fraction.

0.001 = 1

1,000

=1

103

=10-3

The bead is about 10-3 inch in diameter.

10. The positive power is placed in the numerator instead of the denominator of the fraction.

5−5 = 1

55

= 1

55 =

1

3,125

The estimated diameter

of a blood cell is 1

55 or

1

3,125 inch.


Name (s) ______________________________________ Class_______________ Date_______________________________


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