Download Chapter 6 Guided Problem Solving

Name
Class
Date
6-1 • Guided Problem Solving
GPS
Student Page 181, Exercise 33:
Astronomy When the sun emits a solar flare, the blast wave can travel
through space at 3 3 106 km/h. Use the formula d 5 rt to find how far
the wave will travel in 30 min.
Understand
1. What does each of the variables stand for in the formula?
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2. What are being asked to find?
Plan and Carry Out
3. Which variable are you solving for in the formula?
4.To write the rate in standard form, which way and how many places
will you move the decimal point? What is the rate in standard form?
5. Convert 30 minutes to hours.
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6.Substitute what you know into the formula and solve.
7. Write the distance back into scientific notation. Which way will
you move the decimal point and how many places?
Check
8. How can you check to see if your answer is reasonable?
Solve Another Problem
9. A state animal shelter had 4.2 3 104 unwanted animals dropped
off last year. If the goal of the shelter is to decrease the number
by one-sixth this year, how many fewer animals will enter the
shelter? Write your answer in scientific notation.
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Course 3 Lesson 6-1
Guided Problem Solving
10/10/12 4:39 PM
Name
Class
Date
6-2 • Guided Problem Solving
GPS
Student Page 187, Exercise 34:
Geometry The formula for the area of a square is A 5 s2.
What is the area of a square whose sides are 3x2 cm?
Understand
1. What are you being asked to do?
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2. What do you know?
Plan and Carry Out
3. Write the formula for the area of the square as a multiplication sentence.
4. Substitute the side length of the square for s in the formula you wrote
in Problem 3.
5.Rewrite the formula by using the Commutative Property of Multiplication
to group numbers and to group variables that have the same base.
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6.How do you multiply numbers or variables that have the same base?
7. What is the area of the square in simplest form?
Check
8. How can you check your answer?
Solve Another Problem
9. What is the area of a rectangle whose length is 5x ft and whose width is 8x2 ft?
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Course 3 Lesson 6-2
Guided Problem Solving
10/10/12 4:39 PM
Name
Class
Date
6-3 • Guided Problem Solving
GPS
Student Page 191, Exercise 20:
Geography The Sahara is a desert of about 3.5 million square miles.
There are about 2.79 3 107 square feet in a square mile. About how
many square feet does the Sahara cover? Write your answer in
scientific notation.
Understand
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1. What are you being asked to do?
2. What form will your answer be in? Plan and Carry Out
3. Write 3.5 million in standard form.
4. Write 3.5 million in scientific notation.
5. To convert from square miles to square feet, what operation will
you use?
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6. Write the conversion for square feet to square miles.
7. Convert the square miles of the Sahara to square feet.
Check
8. Use another method to solve the problem. Does your answer check?
Solve Another Problem
9. The human body contains about 3.2 3 104 microliters of blood
per pound of body weight. How many microliters of blood would
a 185-pound man have circulating in his body? Write your
answer in scientific notation.
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Course 3 Lesson 6-3
Guided Problem Solving
10/10/12 4:39 PM
Name
Class
Date
6-4 • Guided Problem Solving
GPS
Student Page 197, Exercise 24:
Earth Science Earth’s crust is divided into large pieces called tectonic
plates. The Pacific tectonic plate is moving northwest at a rate of about
422 m each year. At this rate, how long will it take the plate to move
46 m (about 2.5 miles)?
1. The equation d 5 rt represents the relationship between distance d, rate r,
and time t. What measurements are given in the problem?
2. What measurement are you asked to find?
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Understand
Plan and Carry Out
3. Solve the equation d 5 rt for t.
5. What is the common base?
6. When dividing powers with the same base, what do you do to the exponents?
7. Solve the equation for t.
Check
8. Solve the problem by writing the numbers in standard form. Does your
answer check?
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4. Substitute the values that are known into the equation for t.
Solve Another Problem
9. A rectangular plot of land covers an area of 213 square feet. You measure
the length of the plot to be 27 feet. What is the width?
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Course 3 Lesson 6-4
Guided Problem Solving
10/10/12 4:40 PM
Name
Class
Date
6-5 • Guided Problem Solving
GPS
Student Page 205, Exercise 19:
The sun’s diameter is 1.39 3 106 kilometers. Earth’s diameter is
1.28 3 104 kilometers. How many times greater is the sun’s diameter
than Earth’s diameter?
Understand
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1. Which diameter is larger?
2. What are you being asked to find?
Plan and Carry Out
3. The diameters are in scientific notation, and the numbers 1.28
and 1.39 are close in value, so what do you need to compare?
4. When dividing powers with the same base, what do you do to the
exponents?
5. Subtract the exponents and write the power in standard form.
6. How many times greater is the sun’s diameter than Earth’s?
Check
7. What strategy could you use to check your answer?
Solve Another Problem
8. When you donate a pint of blood, you lose about 2.3 3 1012 red blood cells.
If your body can produce about 2 3 106 red blood cells per second, about
how many seconds would it take for your body to replenish the red blood
cells lost through donation? Write your answer in standard form.
© Pearson Education, Inc., publishing as Pearson Prentice Hall.
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Course 3 Lesson 6-5
Guided Problem Solving
10/10/12 4:40 PM