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					        Problem Solving opportunities in Everyday Mathematics Grade 6
                                    (2004)
       Unit 1
       Draw a line plot that represents data with the following landmarks. Use at
least 10 numbers with a:
       range: 7
       minimum: 6
       median: 10
       modes: 6 and 11



      ––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––                     5
      6       7       8      9      10     11      12      13

      Describe a situation in which the data in the above line plot might occur.
      Give the line plot a title and a unit.
      Title:
      Unit:
      Explain your thinking.

      Mr. Martinez surveyed his health class. He asked the following questions:
            a. About how many hours do you sleep each night?
            b. About how many glasses of milk do you drink per day?
            c. What is your heart rate in beats per minute after exercising for one
      minute?
      Tomas sketched a line plot (see below) of the class results for one of the questions,
      bur he forgot to label his line plot.
                                             X
                                             X            X
                                  X          X            X
                                  X          X            X
      X`    `      X              X          X            X             X
      X            X              X          X            X             X          X
      0            1              2          3            4             5          6

      The minimum of the data is ___. The maximum of the data is ____. The range of
      the data is ___. Which of the questions do you think is represented by his line
      plot? Show and explain how you got your answer.



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Find the median and mean of each of the following sets of numbers.
1. 123, 56, 92, 90            a. median_____ b. mean _____
2. 0.50, 0.75, 1, 1.25, 0.80  a. median_____ b. mean _____
3. 6, 9, 10, 15               a. median_____ b. mean _____
Show and explain how you got your answer.

The 10 most successful coached in the history of the National Football League are
listed, along with the numbers of games won through the end of the 1997-1998
season.
Coach                     Games
                          won
Don Shula                 347
George Halas              324
Tom Landry                270
Curly Lambeau             229
Chuck Noll                209
Chuck Knox                193
Dan Reeves                172
Paul Brown                170
Bud Grant                 168
Steve Owen                155
Find the following landmarks for this data set.
a. median ____, b. maximum ___, c. minimum ___ d. mean ___ e. mode ___
f range ___
Show and explain how you got your answer.

Weights (in pounds) of emperor penguins: 60, 49,66, 64, 61, 60, 59, 65, 64, 65,
60
a. Draw a line plot for the data given above.
b. Find the following landmarks for this line plot
maximum ___ minimum _____ mode(s) _____ range _____
Show and explain how you got your answer.

Alice’s quiz scores are 75, 75, 70, 80, and 75
Bianca’s quiz scor3es are 50, 70, 90 100, and 65
1. Find each girl’s mean (or average) score
2. Make a line plot for Alicia’s scores and a second line plot for Bianca’s scores



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3. Is Alicia’s median score the same, or nearly the same, as Bianca’s median
score?
4 Are the girl’s median scores the same, or nearly the same, as their mean scores?
5. In which ways are Alicia’s and Bianca’s scores similar? In which ways are
their scores different?
6. Who do you think might be the better student?
Show and explain how you got your answer.

Heights were measured to the nearest centimeter for 12 boys and 12 girls. All of
the boys and girls were 12 years old.
Boys’ heights: 157, 150, 131, 143, 147, 169, 148, 147, 145, 163, 139, 151
Girls’ heights: a146, 164, 138, 149, 145, 167, 150, 156, 143, 148, 149, 160
1. Make a line plot for the boys’ data. Then find the minimum, maximum,
median, and mean of the boys’ heights.
2. Make a line plot for the girls’ data. Then find the minimum, maximum,
median, and mean of the girls’ heights.
Show and explain how you got your answer.

The perimeter of a regular polygon is 30 feet. What is the length of each side of
the pentagon? Show and explain how you got your answer.

Every week Ms. Penczar gives a math quiz to her class of 15 students. The table
shows the class’s average scores for a six-week period.
Week Class
         Average
1        68
2        66
3        79
4        89
5        91
6        88
1. Draw a bar graph that shows the same information. Be sure to give the graph a
title, and to label each axis. Then use that bar graph you just drew to answer these
questions.
2. The highest average score occurred in Week ___
3. The lowest average score occurred in Week ___
4. How many time was there an improvement from one week to the next/
5. How many times was there a decline from one week to the next/
6. The greatest one-week improvement occurred between Week ___ and Week
___.
7. There was little improvement in the class average after Week ___


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8. Name a possible set of scores for Ms. Penczar’s 15 students that would result in
the class average given for Week 2.
Show and explain how you got your answer.

A parking lot charges $3.00 for the first hour or fraction of an hour and $2.00 for
each additional hour or fraction of an hour.
a. Complete the table below.
b. What is the cost of parking for 2 ½ hours? . Find the perimeter of a regular
hexagon whose sides are 9 centimeters long. Show and explain how you got your
answer.
Time           Over
30 min.        $3.00
1 hr.          $3.00
2 ½ hr
3 hr 59 min
5 hr
5 hr 15 min
Draw a step graph of the parking lot charges. What is the cost of parking for 1 hour
and 15 minutes? What is the cost of parking for 3 hours and 45 minutes? Show
and explain how you got your answer.

Which requires more paint: a rectangular ceiling 30 feet by 40 feet or a highway
median strip 3 inches wide and 1 mile long? Show and explain how you got your
answer.




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Suppose you have enough material for 22 feet of fence. You want to enclose the
largest possible rectangular region with this fence.
1. If you know the perimeter and length f a rectangle, how can you find its width?
2. The table below lists the length f some rectangles with a perimeter of 22 ft. Fill
in the missing widths and area. If it helps, draw the rectangle on your gird paper.
Let the side of each grid square represent 1 foot.
Length       1      2     3      4     5      6      7      8      9      10
(ft)
Width        10     9
(ft)
Perimeter 22        22    22     22 22        22     22     22     22     22
(ft)
Area         10     18
(square
ft)

3. If you have not already done so, draw each rectangle from the table above on
your grid paper.
4. 1. What are the length, and width of the rectangle(s) in the table with the largest
area?_____ b. What is that area? ____
5. Create a graph to plot the length and area of each rectangle identified in the
table above.
6. Find a rectangle whose perimeter is 22 feet and whose area is larger than the
area of the rectangle in Problem 4 above. What is the length? Width? Area?
Show and explain how you got your answer.

Three gallons of juice will provide _____one-cup servings. You are in charge of
buying food for a picnic. Seventy people are expected to attend. If you plan to
give each person 1 cup of juice, how many gallons of juice should you buy? Show
and explain how you got your answer.

If you drink 1 cup of milk each day, about how many gallons of milk do you drink
per month? About how many gallons of milk per year? Show and explain how you
got your answer.

How many cups are there in 2 cans of soft drink? About how many cans of soft
drink are there per gallon? Show and explain how you got your answer.

Mr. Corbeto’s class kept a record of the highest and lowest temperatures in each of
five months.
Monthly Highest and Lowest Temperatures (°F)


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             Sept          Oct         Nov           Dec          Jan
Highest      82            688         58            48           38
Lowest       48            34          25            12 -5
Range        34            34          33            36           43
Create a bar graph showing the highest and lowest temperature for each of the five
months. Choose a title and label each axis. Use this bar graph to answer these
questions.
a. What was the lowest temperature recorded during the five months?
b. What was the range between the highest and lowest temperatures for
September?
c. Which month had the greatest range between the highest and lowest
temperatures?
d. What was that range?
One of Mr. Corbeto’s students said, “This graph shows that most days in
September are in the 80s, while most nights are in the 40s.” Explain why you
agree or disagree with his statement.

Chuck’s Canoe Rental has the following rates: $10 for the first hour or fraction of
an hour; $5 for each additional hour or fraction of an hour; $30 for the entire day.
Jim and his friends rent a canoe at 3:15 p.m. They don’t want to pay more than 20
dollars. By what time do they need to have the canoe back? Show and explain how
you got your answer.

Mr. and Mrs. Bates had their canoe out for 5 hours. Mr. Robb had his canoe out
for 8 hours. Both paid the same amount of money. Why is this? Show and explain
how you got your answer.

Unit 2
In the 1988 Olympic Games, the United States women’s 500-meter medley relay
team won this swimming event with a time of 4 minutes, 28.3 seconds. In 1972,
the United States women’s team won again in 4 minutes, 20.75 seconds. How
much faster was the 1972 team than the 1968b team? Show and explain how you
got your answer.




In the 1924 Olympics Games, Fred Tootell of the United States won the hammer
throw with a distance of 53.295 meter. In 1928, Patrick O’Callaghan of Ireland
won with a distance of 51.39 meters. Which man threw the greater distance? By
how much? Show and explain how you got your answer.


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One container holds 3.8 liters of liquid. Another container holds 500 milliliters of
liquid. How much do the two containers hold in all? Show and explain how you
got your answer.

The school supply store purchased 500 notebooks. They were shipped in boxes
that could hold 12 notebooks each. How many boxes were needed to ship the
entire order? Show and explain how you got your answer.

The fastest winning team for the New York Marathon (Juma Ikangaa of Tanzania,
1989) is 2 hours and 8.01 miles per hour. The second fastest time is 2 hours and
8.12 minutes (John Kagwe of Kenya, 1997). How much faster was Ikangaa’s time
than Ksawe’s? Show and explain how you got your answer.

Driver Buddy Baker (Oldsmobile, 1980) holds the record for the fastest winning
speed in the Daytona 500 at 177.602 miles per hour. Bill Elliott (Ford, 1987) has
the second fastest speed at 176.263 miles per hour. How much faster is Baker’s
speed than Elliott’s? Show and explain how you got your answer.

The highest scoring World Cup Soccer Final was in 1954. 26 games were played,
and 140 goals were score, for an average of 5.38 goals per game. In 1950, 22
games were played, and 88 goals were scored, for an average of 4 goals per game.
What is the difference between the 1954 and the 1950 average goals per game?
Show and explain how you got your answer.

In the 1908 Olympic Games, Erik Lemming of Sweden won the javelin throw with
a distance of 54.825 meters. He won again in 1912 with a distance of 60.64
meters. How much longer was his 1912 throw than his 1908 throw? Show and
explain how you got your answer.

Toni has a set of metal discs. Each disc has a thickness of 0.3 cm. If she puts 8 of
the discs in a stack, what will be the height of the stack? Show and explain how
you got your answer.

This June, 1.4 inches of rain fell in Carrollville. The average rainfall for the month
is 4 times as much. What is the average rainfall for June? Show and explain how
you got your answer.

Stamps cost $0.33 each. How much will 25 stamps cost? Show and explain how
you got your answer.



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Joe buys the Morning Star newspaper each day. The price of the paper is 35 cents
a day on Monday through Saturday. The Sunday edition costs $1.75. How much
does Joe spend in a week on the newspaper? Show and explain how you got your
answer.

Tina multiplied correctly but forgot to place the decimal point in the product
below. Place it correctly for her. 12.3 * 5.07 = 6 2 3 6 1 Show and explain how
you got your answer.

On average, Americans use about 27 gallons of water to shower. That’s about how
many half-gallons? About how many quarts? If a person took 1 shower a day,
about how many gallons would the person use in 1 year? 10 1,000 10,000
100,000      Show and explain how you got your answer.

Seventy-seven children signed up to play in the basketball tournament. Each team
has at least 5 players on it. If each child plays on only one team, what is the
greatest number of teams that can play in the tournament? Show and explain how
you got your answer.

Janine rides her bike at an average speed of 11.8 miles per hour. At that speed,
about how many miles can she ride in 6 ½ hours? Show and explain how you got
your answer.

Catherine types at an average rate of 1.25 pages per quarter hour. If she types for 2
¾ hours, about how many pages can she type? Show and explain how you got your
answer.

Find the area in square meters of a rectangle with length 1.4 m and width 2.9 m.
Show and explain how you got your answer.

The U.S. Postal Service claims that from December 1 to December 24, Americans
mail an average of 76 million holiday cards per day. About how many holiday cards
does the average American send during this period? Does this statistic seem
reasonable? Show and explain how you got your answer.

Marta’s mother is 5 times as old as Marta. Marta’s mother is 25. How old is
Marta? Show and explain how you got your answer.
In a few years Marta’s mother will be 3 times as old as Marta. How old will Marta
be then? Show and explain how you got your answer.
How old will Marta’s mother be? Show and explain how you got your answer.



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Sara is ¼ the age of her father. Sara’s father is 60. How many years older than
Sara is Sara’s father? Show and explain how you got your answer.
How many years ago was Sara 1/10 of her father’s age? Show and explain how
you got your answer.
How old was she then? Show and explain how you got your answer.

Four people are driving from Seattle to San Francisco, a distance of about 810
miles. They want to share the driving equally. About how far should each person
drive? Show and explain how you got your answer.

A professional hockey stick costs about $27. Jake’s team has $546 to use for
equipment. How many hockey sticks can the team buy? Show and explain how
you got your answer.

In 1650, it took 50 days to sail from London, England, to Boston, Massachusetts, a
distance of about 3,700 miles. On average, about how many miles were sailed
each day? Show and explain how you got your answer.

Tutunendo, Columbia, has the greatest annual rainfall in the world – about 464
inches per year. On average, about how many inches is that per month (to the
nearest whole number)? Show and explain how you got your answer.

It costs $42,000 to rent 1,000 square feet of office space in a New York skyscraper
for one year. What is the cost per month? Show and explain how you got your
answer.

A family of four spent about $3,040 on a 5-day Colorado ski vacation
(transportation not included). What was the approximate cost of the vacation per
person per day? Show and explain how you got your answer.

Seven people had lunch. The bill was $29. Divide $29 into 7 equal shares. How
much is one share, in dollars and cents? Show and explain how you got your
answer.

A board 125 centimeters long is cut into 12 pieces of equal length. What is the
length of each piece, to the nearest length of a centimeter? Show and explain how
you got your answer.

A 2-meter ribbon is cut into 6 pieces of equal size. What is the length of each
piece, to the nearest tenth of a centimeter? Show and explain how you got your
answer.


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Mr. Jacobson has a can of Mancala beans. He asks Bill to divide the beans into
sets of 48 beans each. There are 389 beans in the can. How many sets of 48 can
Bill make? Show and explain how you got your answer.

Sharon is organizing her CD collection. She has 68 CDs in all. Each CD rack
holds 25 CDs. How many racks does she need to hold her entire collection? Show
and explain how you got your answer.

Jesse is making cookies for the class bake sale. He plans to charge 25 cents per
cookie. He wants to make at least 342 cookies (one for each student in the school).
Each batch makes about 25 cookies. How many batches should he make? Show
and explain how you got your answer.

Mrs. Hanley’s sixth grade class is putting on a play for the rest of the school.
Rows of chairs will be set up in the gymnasium. If there are 21 chairs in each row,
how many rows are needed for the 297 people who are expected to come? Show
and explain how you got your answer.

Nestor’s favorite baseball team is the Chicago Cubs. He went to 18 games last
year. Nestor usually sits in the upper boxes, where tickets cost $15. This year,
he’s saved $238 for tickets. How many tickets will he be able to buy with this
amount of money? Show and explain how you got your answer.

Regina, Ruth, Stanley, and Sam sold lemonade. They charged $0.20 per glass.
They collected a total of $29.60. They paid $8.00 for supplies, and they split the
money that was left evenly. How much did each of them receive? Show and
explain how you got your answer.

A faucet drips at the rate of 2 fluid ounces per hour,. At this rate: How many
hours would it take to fill a 1-cup container? How many hours would it take to fill
a 1-quart container? How many 1-cup containers would be filled in 1 day? Show
and explain how you got your answer.

Reshi’s brother was 8 years old when Reshi was born. Reshi’s brother is not twice
as old as Reshi. How old is Reshi now? Show and explain how you got your
answer.

Unit 3
The circumference of a canister is about 30 inches. What is the diameter? About
___ What is the radius? About ____ Show and explain how you got your answer.


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The height of a rectangle is 15 inches. The area is 240 square inches. What is the
length of the base of the rectangle? Show and explain how you got your answer.

 “The height of a parallelogram is 4.5 centimeter. The length of the base of the
parallelogram is 19.6 centimeters. Show and explain how you got your answer.

The length of the base of a triangle is 16 cm. The height of the triangle is 19 cm.
What is the area of the triangle? Show and explain how you got your answer.

The area of the base of a cylinder is 4 square feet. The height of the cylinder is 6
feet. What is the volume of the cylinder? Show and explain how you got your
answer.

The volume of a rectangular prism is 108 cubic feet. The height of the prism is 12
feet. Show and explain how you got your answer.




Ever since the early years of the automobile, police have been trying to catch
speeding motorists. At first, officers were equipped with bicycles and stop-
watches. They hid behind trees or rocks and emerged to pursue offenders. An
Englishman, Lord Montague of Beaulieu, received a ticket for driving 12 miles per
hour.



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1. At a speed of 12 miles per hour, about how many miles could Lord Montague
travel in 1 minutes?
2. Tell how you solved this problem
3. Complete the table. Use the formula d = 0.2 * t
Show and explain how you got your answer.

Time (min)     Distance
t              (mi)
               0.2 = t
1              0.2
2              0.4
3
4
5
6
7
8
9
10


Michael is 5 years younger than Misha and 3 years older than Gary. Who si the
oldest? If Gary is 12 years old, how old is Michael? How old is the oldest of the
three? Show and explain how you got your answer.

Renee reads 30 pages per hour. At this rate, how many pages can she read in 3
hours? Would she be able to read a 220-page book in 7 hours? Show and explain
how you got your answer.

Wilson was paid $105 to cut 7 lawns. At this rate, how much was he paid per
lawn? Show and explain how you got your answer.

Gabriel blinks 80 times in 5 minutes. At this rate, how many times does he blink
in 2 minutes? In 4 minutes? Show and explain how you got your answer.
Michael can bake 9 batches of cookies in 3 hours. At this rate, how many batches
can he bake in 2 hours? Show and explain how you got your answer.

Elizabeth can run 5 miles in 2/3 of an hour. At this rate, how long does it take for
her to run 1 mile? Show and explain how you got your answer.




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If the length of the side of a square is 2 ½ inches, what is the perimeter of the
square? Show and explain how you got your answer.

If the length of the side of a square is 4 ¼ inches, what is the perimeter of the
square? Show and explain how you got your answer.

If the length of the side of a square is 1 ½ inches, what is the approximate area of
the square? Show and explain how you got your answer.

If the length of the side of a square is 3 ¼ inches, what is the approximate area of
the square? Show and explain how you got your answer.

In 5 years, Gina will be twice as old as Scottie. Scottie is 8 years old now. How
old will Gina be in 5 years? How old is Gina now? Show and explain how you got
your answer.




Ms. Villanova keeps a spreadsheet of her monthly expenses. Use her spreadsheet
to answer the questions below.
    A             B            C              D             E
1                 January      February       March         Total
2 Groceries       $125.25      $98.00         $138.80       $362.05
3 Phone Bill      $34.90       $58.50         $25.53
4 Car             $25.00       $115.95        $12.00
    Expenses
5 Rent            $750.00      $750.00        $750.00
1. What is shown in Cell B?
2. What is shown in Cell C4?
3. What cell contains the word Rent?
4. Which cell contains the amount $58.50?



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5. Ms Villanova used Column E to show the total for each row. Find the missing
totals and enter them on the spreadsheet.
6. Write a formula for calculating E3 that uses cell names.
7. Write a formula for calculating E5 that uses cell names.
8. Ms. Villanova found that she made a mistake in recording her March phone bill.
Instead of $25.23, she should have entered $35.35. After she corrects her
spreadsheet, what will the new total be in Cell E 3?
Show and explain how you got your answer.




Haylee and Chris want to earn money during summer vacation.
    Haylee is going to cut lawns. Her father will lend her $190 o buy a lawn
      mower. She figures that she can cut 10 lawns per week and make $12 per
      lawn, after paying for oil and gasoline.
    Chloe is going to work in an ice cream shop. The owner will provide a
      uniform free of charge and pay her $4.80 per hour. She will work 3 ½ hours
      per day, 5 days per week.
Complete this table to show how much profit each girl will have made after 1
week, 2 weeks, 3 weeks, and so on. (Assume they do not have to pay taxes.)
Time (weeks)                Profit (dollars)
                        Haylee       Chloe
Start                   -190         0
1                       -70          84


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2
3
4
5
6                    530
7
8                                 672
9
10
a. Who will have made more money by the end of 5 weeks?
b. How much money will that girl have made?
c. Who will make more money during the summer?
Show and explain how you got your answer.



Jenna and Thomas like to babysit. Jenna charges $3 per hour. Thomas charges
$6.00 for the first hour and $2 for each additional hour.
Complete the table to show how much each babysitter will have made after 1hour,
2 hours 3 hours, and so on,
Time (hours) Jenna’s Profit              Thomas’s Profit
1
2
3
4
5
6
2. Graph the babysitters’ profits. Label the lines “Jenna” and “Thomas”.
3. Did Jenna or Thomas think of a better way to charge customers? Explain your
answer.

The sixth grade class intends to rent the roller rink for a fund-raiser. Students plan
to charge the following prices for admission to the Roller Skating Party. Adults
(18 years or older) $4 Students $2 The roller rink charges a rental fee of $150.
What will be the profit if 30 adults and 50 children attend? What will be the profit
if 20 adults and 30 children attend? Show and explain how you got your answer.

Unit 4
The table below shows the results of a survey of people’s favorite Olympic sports.
Create a circle graph to represent this data.
Favorite          Percent of People

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Sport
Gymnastics     35%
Swimming       15%
Basketball     40%
Other          10%
Show and explain how you created the graph

Joe has a board 8 ¾ inches long. He cuts off 1 ¼ inches. How long is the
remaining piece? Show and explain how you got your answer.

Mr. Ventrelli is making bread. He adds 1 ¼ cups of white flour and 1 ¼ cups of
wheat flour. The recipe calls for the same number of cups of water as cups of
flour. How much water should he add? Show and explain how you got your
answer.

A board is 6 3/8 inches long. Verna wants to cut off enough so that it will be 5 1/8
inches long. How much should she cut off? Show and explain how you got your
answer.

Tim is making papier-mache. The recipe calls for 1 ¾ cups of paste. Using only
½-cup, ¼-cup, and 1/3-cup measures, how can he measure the correct amount?
Show and explain how you got your answer.



Tim walked ½ mile from school to the park, Then he walked ¼ mile to the store to
get milk and orange juice. These items cost 2 ½ dollars. Then he walked home,
another ¾ of a mile. How far did Tim walk in all? Show and explain how you got
your answer.

Jonathan bought a peck of Jonathan apples, a peck of Golden Delicious apples a
half-bushel of Red Delicious apples, and 1 ½ bushels of McIntosh apples. How
many bushels of apples did he buy in all? Show and explain how you got your
answer.

Jonathan estimates that he can make about 12 quarts of applesauce per bushel of
apples. About how many quarts of applesauce can he make from the apples he
bought? Show and explain how you got your answer.




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South High beat North High in basketball, scoring 4/5 of the total points. Rachel
scores ¼ of South High’s points. What fraction of the total points did Rachel
score? Show and explain how you got your answer.

Josh was making raisin muffins for a party. He needed to triple the recipe, which
called for ¾ cups of raisins. How many cups of raisins did he need? Show and
explain how you got your answer.

At the Ashley Long Middle School, 7/8 of the sixth graders live within one mile of
the school. About 2/3 of those sixth graders walk to school. None who live a mile
or more away walk to school. About what fraction of the sixth graders walk to
school? Show and explain how you got your answer.

For Calista’s 12th birthday party, her mom will order pizza. ¾ of the girls like
vegetables on their pizza. However, 1/3 of those girls don’t like green peppers.
What fraction of all the girls will eat a green pepper and onion pizza? If 12 girls
are at the party (including Calista) how many girls will not eat a green pepper and
onion pizza? Show and explain how you got your answer.

Pavan, Jonathan, Nisha, and Gloria walked on the sixth grade nature hike. They
finished ½ the length of the trail in the first hour. Then they slowed down and
watched some interesting insects. In the second hour, they walked ½ of the
distance that was left. In the third hour, they were moving more slowly still and
walked only ½ of the remaining distance. If they continue slowing down at this
rate, what fraction of the trail will they actually walk in their fourth hour of hiking?
Show and explain how you got your answer.

This spreadsheet shows students’ times, in seconds, for two different runs.
                A               B               C              D
1               Student         Run 1           Run 2          Average
2               Jake            23              21
3               Steve           20              19
4               Allison         21.5            21
a. Calculate the average time for each student. Write these average times on the
spreadsheet.
b. Using cell names, write a formula for calculating Jake’s average time.
Show and explain how you got your answer.

Sonia bought 3 5/8 yards of fabric to make a dress. The pattern for the dress calls
for only 2 1/3 yards of fabric. How much fabric will be left to make something
else? Show and explain how you got your answer.


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Fill in the missing numbers
Fraction       Decimal    Percent
¾
               0.225
                          40%
1/3
                          65%
               0.9
Show and explain how you got your answer.

Use the Percent Circle on your Geometry Template to divide a circle and its
interior (the total ) into sectors whose sizes correspond to the percent form of the
data.
Art, Barb, and Cyrus ran for sixth-grade class president. The election results are
shown in the table below. Fill in the percent column. Then use your Percent
Circle to draw a circle graph of the data.
               Election Results
Name             Number of            Percent of Total
                 Votes                Vote
Art              8
Barb             10
Cyrus            22
Total            40                   100%
Create a title and label your circle graph.
Show and explain how you got your answer.
Doug, Bree, and Fred drove from Denver to Kansas City. The number of hours
each one drove is shown in the table below. Fill in the percent column. Then use
your Percent circle to draw a circle graph of the data.
               Driving Time
Name          Number of            Percent of Total
              Hours                Time

Doug         6
Bree         4.5
Fred         3
Total        12.5                 100 %
Create a title and label your circle graph.
Show and explain how you got your answer.




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A CD that regularly costs $15 is on sale for 20% off. What is the discount in
dollars? What is the sale price? Show and explain how you got your answer.

A boom box that costs $120 is on sale for 25% off. What is the discount in
dollars? What is the sale price? Show and explain how you got your answer.

A bank gives interest of 5% a year. What is the interest of 5% a year. What is the
interest on $100.00? What is the interest on $500.00? What is the interest on
$1,000,000.00? Show and explain how you got your answer.

The $2.50 price of a hot dog at a major league baseball park is shared as follows:
20% pays for the hot dog, bun, and fixings
20% pays the concession stand workers
10% is profit for the concession stand owner
10% pays for cleaning and other costs
40% goes to the team and stadium owners
How much do the hot dog, bun and fixings cost? How much do the team and
stadium owners get? How much does the concession stand owner get? Show and
explain how you got your answer.

Martin is building two picture frames. He used 4 ½ feet of lumber for one frame
and 2 ¾ feet for the other frame. How many feet of lumber did he use in all? Show
and explain how you got your answer.




A survey asked students ages 8 to 18 the following question: If you were stranded
on a desert island and could choose only one of the things listed below to have
with you, which would you choose?
Medium                     Number Percent of
                           of         Students
                           Students
Computer with internet 99
access
CDs, tapes, or radio       72
Television                 39
Video games                39
Books or magazines         27
Videos                     12
Nothing                    12


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Total                     300
Use the Percent Circle on the Geometry Template to draw a circle graph to display
this data. Show and explain how you got your answer.

The table below shows the results of a Bureau of the Census study of how people
get to work. Use the Percent Circle to draw a circle graph of the results.
Method of Transportation            Percent of
                                    People
Drive alone                         75.1%
Carpool                             13.2%
Walk or work at home                5.3%
Take public transportation or       6..4%
other
Show and explain how you got your answer.

Unit 5
A group of 193 sixth-graders are entered in a 3-on-3 basketball tournament. How
many complete teams of 3 players can be formed? What would you do about any
“leftover” students? Show and explain how you got your answer.




The table below shows a breakdown, by age group, of adults who listen to classical
music.
a. Calculate the degree measure of each sector to the nearest degree.
b. Use a protractor to make a circle graph. Do not use the Percent Circle. Write a
title for the graph.
Age             Percent of         Degree
                Listeners          Measure
18 – 24         11%
25 – 34         18%
35 – 44         24%
45 – 54         20%
55 – 64         11%
65+             16%
On average, about 8 million adults listen to classical music on the radio each day.



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a. Estimate how many adults between the ages of 35 and 44 listen to classical
music on the radio each day.
b. Estimate how many adults at least 45 years old listen to classical music on the
radio each day
Show and explain how you got your answer.

This table below shows the elective courses taken by a class of seventh graders.
Complete the table. Then, use a protractor to make a circle graph to display the
information. Do not use the Percent Circle. Write a title for the graph.
Course       Number       Fraction Decimal Percent Degree
             of           of           Equival of              Measure of
             students     students     ent        students Sector
Music        6
Art          9
Computer 10
Photograp 5
hy

Frank saved $93 for his birthday celebration. He wants to take some friends to a
baseball game. If tickets cost $8 apiece, how many tickets can he buy? Show and
explain how you got your answer.




Unit 6
You draw one card at random from a regular deck of 52 playing cards (no jokers).
What is the chance of drawing a (n) 4?, a card with a prime number?, a face card
(jack, queen, king)?, an even-numbered black card? Show and explain how you got
your answer.

The distance from New York to San Francisco is about 2,930 miles. A bus made
this trip in 6 days. On average, about how many miles did the bus travel each day?
Show and explain how you got your answer.

How much does a box containing 5 horseshoes weigh, if each horseshoe weighs
about 2 ½ pounds? Show and explain how you got your answer.

One and a half dozen golf tees are laid in a straight line, end to end. If each tee is 2
1/8 inches long, how long is the line of tees? Show and explain how you got your
answer.


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A standard-size brick is 8 inches long and 2 ¼ inches high and has a depth of 3 ¾
inches. What is the volume of a standard-size brick? Show and explain how you
got your answer.

You roll 2 six-sided dice. Give the probability of rolling a 2?, a 12?, a 0?, an even
number? Show and explain how you got your answer.

The distance from Chicago to Los Angeles is about 2,060 miles. A family drove
the distance in 4 days. On average, about how many miles did the family travel
each day? Show and explain how you got your answer.

I am a 3-dimensional shape. I have 5 faces. Two faces are triangles. The other
faces are rectangles. What am I called? Show and explain how you got your
answer.

Diana wants to make a 15’-by-20’ section of her yard into a garden. She will plant
flowers in 2/3 of the garden and vegetables in the rest of the garden. How many
square feet of vegetable garden will she have? Show and explain how you got your
answer.

Leo is in charge of buying hot dogs for family math night. Out of 300 people, he
expects about 3/5 of them to attend. Hot dogs come 8 to a package, and Leo
figures he will need to buy 22 packages so that each person can get 1 hot dog.
Show and explain how you got your answer.

Luis figures that one person can eat about 3/8 of a large pizza. How many people
can he serve with 6 large pizzas? Show and explain how you got your answer.

Amelia makes rock candy and sells it in ½ pound packages. How many packages
can she make from 15 pounds of rock candy? Show and explain how you got your
answer.

Ian worked 20 minutes cutting the grass and was only 1/3 finished. How long will
the whole job take? Show and explain how you got your answer.

Rosario bought 5 large packages of flour tortillas. She wanted to divide each in
half and then freeze all of them. How many packages will she freeze? Show and
explain how you got your answer.




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Twelve golf balls in a package are orange. If the orange golf balls make up 2/3 of
the package, how many balls are in the package? Show and explain how you got
your answer.

Alan bought a model car for $8.98, a pair of shoes for $14.49, and a new jacket for
$24.95. How much more did he spend on the jacket than on the model car? Show
and explain how you got your answer.

Square corners, 6 centimeters on a side, are removed from a 36-centimeter-by-42-
centimeter piece of paper. The paper is then folded to form an open box. What is
the surface area of the inside of the box? Show and explain how you got your
answer.

Complete this sentence with an algebraic expression. If each bag of potatoes
weighs at least p pounds, then 6 bags weigh at least _______________ pounds.
Show and explain how you got your answer.

Complete this sentence with an algebraic expression. Jack is 6 inches taller than
Michael. If Jack is h inches tall, then Michael is ______________ inches tall.
Show and explain how you got your answer.

At a garage sale, Alisha sold her CDs for $29.00. her stuffed dog for $7.65, and her
old tricycle for $12.80. How much more did she sell her CDs for than her old
tricycle? Show and explain how you got your answer.

Use parentheses and as many numbers and operations as you can to write an
expression equal to the target number. You may use each number just once in an
expression. Numbers: 3, 9, 11, 12, 19 Target number: 36. Show and explain how
you got your answer.

Tell what additional information you need to solve the following problem: Melissa
took 3 friends to lunch. She had $20 to spend on lunch. All 4 people ordered
spaghetti. How much change did Melissa receive from her $20? Show and explain
how you got your answer.

Tell what additional information you need to solve the following problem: Sam
has 2 baseball cards that are worth $7 each. The rest of his cards are worth $1
each. How much is his collection worth in all? Show and explain how you got
your answer.

Unit 7


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The area (A) of a circle is given by the formula A =   r squared, where r is the
radius of the circle. Use the formula to calculate the area of a circle with a radius
of 2 cm. Show and explain how you got your answer.

The highest point on Earth is the top of Mt. Everest, which is 8, 848 meters above
sea level. The lowest point on land is the Dead Sea, which is 399 meters below sea
level. The lowest point on Earth’s surface is thought to be in the Pacific Ocean at
11.34 meters below sea level. How much higher is the top of Mt. Everest than the
Dead Sea? How many more meters below sea level is the lowest point on Earth
than the Dead Sea? Show and explain how you got your answer.

A gym teacher is dividing her class into two teams to play soccer. Do you think
she should choose the teams “at random”? Show and explain how you got your
answer.

Suppose that there is a list of jobs that need to be done for your class (such as
collecting books, taking messages, etc.). How might you use random numbers to
assign the jobs “at random”, without using any pattern or showing favoritism?
Show and explain how you got your answer.

The formula C = (F-32)  5/9 can be used to convert temperatures from Fahrenheit
to Celsius. Calculate the temperature in degrees Celsius for 68 F, and for 131 F.
Show and explain how you got your answer.
Ron hates to decide what to wear. He made spinners to help him pick his clothes
each day. The statements below describe his spinners. Draw spinners to match the
statements. Label or color each section with the correct color.
Pants: He is twice as likely to wear his blue pants as his tan pants. He will wear
his black pants about 1/14 of the time. About 60% of the time, he will wear his
blue pants.
Shirts: He will wear his yellow shirt the least often. He will wear his red shirt
about half as often as his white shirt. About 37 ½% of the time, he will wear his
blue shirt. He will wear his white shirt about 1 out of every 3 times.
Show and explain how you got your answers.

Marlene played a game with a friend. The rules were, “Take turns rolling a die.
The first player to roll a 6 wins.” Marlene figured she would win if she let her
friend roll first. Why did Marlene think she would win if her friend rolled first?
Show and explain how you got your answer.




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Ron hates to decide what to wear. He made spinners to help him pick his clothes
each day. The statement below describes his spinners. Draw spinners to match the
statements. Label or color each section with the correct color.
Pants                                  Shirts
He is twice as likely to wear his blue He will wear his yellow shirt the east
pants a his tan pants. Her will wear   often. He will wear his red shirt
his black pants about Explain how      about half as often as his white shirt.
you got your answer.]¼ of the time. About 37 ½% of the time, he will
About 50 % of the time, he will wear wear his blue shirt. He will wear his
his blue pants.                        white shirt about 1 out of every 3
                                       times.
Show and explain how you got your answer.

The highest point in North America is the top of Mt. McKinley, Alaska, with an
elevation of 20,320 feet. The highest point in the lower 48 states of the United
States is the top of Mt. Whitney, California, with an elevation of 14, 494. The
lowest point in the United States is in Death Valley, California, at 2882 feet below
sea level. How higher is the top of Mt. McKinley than Mt. Whitney? How many
feet below Mt. McKinley is Death Valley? Show and explain how you got your
answer.


Tell which measure is needed: perimeter, circumference, area, or volume.
a. Jean is going to tile her kitchen floor. She needs to know how many square foot
tiles to buy. Show and explain how you got your answer.
b. Tyrone needs to add 1 drop of anti-chlorine solution to his aquarium for every 2
liters of water. He wants to know how many drops to add. Show and explain how
you got your answer.
c. Mrs. Vui plans to build a circular fence around her garden. She wants to know
how much fencing to buy. Show and explain how you got your answer.

Claire has 7 more crayons than3 times the number of crayons Royce has. If Royce
has 12 crayons, how many does Claire have? Write an algebraic expression and
solve the problem. Show and explain how you got your answer.

Alinda has seen 4 fewer than1/2 the number of movies that her sister has seen. If
her sister has seen M movies, how many has Alinda seen? If her sister has seen 20
movies, how many has Alinda seen? Write an algebraic expression and solve the
problem. Show and explain how you got your answer.




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Imagine that you are taking a multiple-choice test. Four possible answers are
given for each question. You are to circle the correct answer. Suppose there are 20
questions for which you don’t know the correct answer. You decide to guess for
each of these questions. What is the probability (chance) of answering a question
correctly? How many of the 20 questions would you expect to answer correctly by
guessing? Show and explain how you got your answer.

Tell which measure is needed: perimeter, circumference, area, or volume.
a. Warren plans to install wood molding where his living room walls meet the
ceiling. He needs to know how much wood to buy. Explain how you got your
answer.
b. Tina runs on a circular track. She knows the diameter of the track. She wants to
find the distance around. Explain how you got your answer.
c. Fertilizer is to added to Flo’s garden at the rate of 1 cup for every 2- square feet.
Flo wants to know how much fertilizer to add. Explain how you got your answer.


Sandy is planning her outfit for the school dance. She has narrowed her choices to
a red, white, or blue dress and to a pair of red or white shoes. Make a tree diagram
to show all possible combinations of dresses and shoes. Show and explain how you
got your answer.

Ten of the students in Mrs. Moore’s class play the piano. Two of the10 also play
the guitar. In all, 15 students play the piano, the guitar, or both the piano and
guitar. Use this information to complete a Venn diagram labeled piano and guitar. Show and
explain how you got your answer.

Unit 8
A computer printer prints 6 pages in 2 minutes. How many pages will it print in 5
minutes? Show and explain how you got your answer.

Jessica trains at an indoor track during the winter. She can run 24 laps in 8
minutes. At this rate, how many laps can Jessica run in 12 minutes? Show and
explain how you got your answer.

Ms. Marquez is reading stories her students wrote. She has read 5 stories in 40
minutes.
a. At this rate, how long would it take her to read 1 story?
b. How long will it take her to read all 30 of her students’ stories?
Show and explain how you got your answer.

Sam scores 75 points in the first 5 basketball games.

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a. On average, how many points did he score per game?
b. At this rate, how many points might he score in a 15-game season?
Show and explain how you got your answer.

Last year, 55 students sold $1,210 worth of candy for their band’s fund-raiser.
a. On average, how many dollars’ worth of candy did each student sell?
b. This year, 67 students will be selling candy. If they sell at the same rate as last
year, how much money can they expect to raise?
Show and explain how you got your answer.

Art worked at the checkout counter from 5?30 P.M. to 11P.M. He earned $33.
a. How much did he earn per hour?
b. Art works 27 ½ hours per week. How much will he earn in 1 week?
Show and explain how you got your answer.
Molly filled a measuring cup with milk to the 3//4 cup mark. Now she wants to
add ½ cup of buttermilk to the cup. To what mark should she pour the buttermilk?
Show and explain how you got your answer.

Janine watches about 12 hours of television per week. Complete the table. Then
use your protractor to make a circle graph of the information. Create a title.
Type of show        Number of           Percent of          Degrees
                    Hours               Hours
Comedy              4
Educational         1
News                2
Sports              3
Cartoon             2
Total
Show and explain how you got your answer.

Melissa planted 10 flowers in 30 minutes. At this rate, how long would it take her
to plant 50 flowers? Show and explain how you got your answer.

Rudy was filling his fish tank. He was adding 1 quart every 4 minutes. How many
quarts did he add in 28 minutes? Show and explain how you got your answer.

Fred rode 240 kilometers on a bike trip. He converted this distance to miles (16
kilometers = 10 miles). How many miles did he ride? Show and explain how you
got your answer.




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Louis drinks 1 gallon of water a day. How many days will it take him to drink 28
pints of water? Show and explain how you got your answer.


Robin rode her bike at an average speed of 8 miles per hour. At this rate, how far
would she travel in 3 hours? Show and explain how you got your answer.

A high-speed copier makes 90 copies per minute. How long will it take to make
270 copies? Show and explain how you got your answer.

Talia rode her bike at an average speed of 10 miles per hour. At this rate, how
long would it take Talia to ride 15 miles? Show and explain how you got your
answer.

Angela earns $6 per hour baby-sitting. How long must she work to earn $72?
Show and explain how you got your answer.

There are 9 calories per gram of fat. How many grams of fat are there in 63
calories? Show and explain how you got your answer.

If carpet costs $22.95 per square yard, how much will 12 square yards of carpet
cost? Show and explain how you got your answer.

There are 80 calories in 1 serving of soup. How many serving of soup contain 120
calories? Show and explain how you got your answer.

A car goes 480 miles on a 12-gallon tank of gas. How many miles is this per
gallon? Show and explain how you got your answer.

Aaron read the first 48 pages of a mystery novel in 3 hours. At this rate, how long
will it take him to read 80 pages? Show and explain how you got your answer.

A TV station runs 42 minutes of commercials in seven half-hour programs. How
many minutes of commercials does it run per hour? Show and explain how you got
your answer.

Belle bought 8 yards of ribbon for $6. How many yards could she buy for $9?
Show and explain how you got your answer.




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Before going to France, Maurice exchanged $25 for 125 French francs. At that
exchange rate, how many French francs could he get for $80? Show and explain
how you got your answer.

One gloomy day, 4 inches of rain fell in 6 hours. At this rate, how many inches of
rain had fallen after 4 hours? Show and explain how you got your answer.

Ben’s apartment building has 9 flights of stairs. To climb to the top floor, he must
up 144 steps. How many steps must he comb to get to the fifth floor? Show and
explain how you got your answer.

At sea level, sound travels 0.52 mile in 3 seconds. What is the speed of sound in
miles per hour? Show and explain how you got your answer.

Cherie made a deal with her mother. If Cherie could mow the lawn in 1 hour or
less, she would get paid double. In 45 minutes, she mowed 7/10 of the lawn. If
she continues to mow at the same rate, will she finish mowing the lawn in time to
be paid double? Show and explain how you got your answer.

Peabody’s Bookstore had a sale. Complete the table Then use your protractor to
make a circle graph of the information. Include a title for the graph.
Book Category       Number          Percent of         Degrees
                    Sold            Total
Fiction             280
Sports              283
Children’s          125
Travel              212
Computer            100
Total
Show and explain how you got your answer.

A can of worms for fishing costs $2.80. There are 20 worms in a can.
a. What is the cost per worm?
b. At this rate, how much would 26 worms cost?
Show and explain how you got your answer.

An 11-ounce bag of chips costs $1.99.
a. What is the cost per ounce rounded to the nearest cent?
b. What is the cost per pound, rounded to the nearest cent?
Show and explain how you got your answer.



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Just 1 gram of venom from a king cobra snake can kill 150 people. At this rate,
about how many people would 1 kilogram kill? Show and explain how you got
your answer.

A good milking cow produces nearly 6,000 quarts of milk each year. At this rate,
about how many gallons of milk will a cow produce in 5 months? Show and
explain how you got your answer.

A dog-walking service costs $117 for 6 months. What is the cost for 2 months?
For 3 years? Show and explain how you got your answer.

A 1-pound bag of candy, containing 502 pieces, costs 16.8 cents per ounce. What
is the cost of 1 piece of candy? 1.86 cents      2.99 cents     0.33 cents ½
cent? Show and explain how you got your answer.

Mr. Rainier’s car uses about 1.6 fluid ounces of gas per minute when the engine is
idling. One night he parked his car but forgot to turn off the motor, He had just
filled his tank. His tank holds 12 gallons. About how many hours will it take
before his car runs out of gas? Show and explain how you got your answer.

Ms Riley drove her car at 60 miles per hours for 4 hours. How far did she travel?
Show and explain how you got your answer.

A bamboo plant grow 8 inches per day. How tall will it be after 7 days? Show and
explain how you got your answer.

A rocket is traveling at 40,000 miles per hours. How far will it travel in 168
hours? Show and explain how you got your answer.

Chelsea can ride her bicycle at 9 miles per hour. At this rate, how long will it take
her to ride 30 miles? Show and explain how you got your answer.

Australia is moving about 3 inches per year with respect to the southern Pacific
Ocean. How many feet will it move in 50 years? Show and explain how you got
your answer.

Alan is walking to a friend’s house. He has gone 6/10 of the distance in 48
minutes. If he continues at the same speed, about how long will the entire walk
take? Show and explain how you got your answer.




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A candle burned 3/8 of the way down in 36 minutes. If it continues to burn at the
same rate, about how many more minutes will the candle burn before it is used up?
Show and explain how you got your answer.

There are 2 facedown cards for every face-up card. If 6 of the cards are face-up,
how many cards are facedown? Show and explain how you got your answer.

You have 12 cards. One out of every 4 cards is face-up. The rest are facedown.
How many cards are face-up? Show and explain how you got your answer.

There are 4 facedown cards for every 3 face-up cards. If 8 of the cards are
facedown, how many cards are face-up? Show and explain how you got your
answer.

Three out of every 5 cards are face-up. If 12 cards are face-up, how many cards
are there in all? Show and explain how you got your answer.

There are 2 face-up cards for every 5 facedown. If there are 21 cards in all, how
many cards are face-up? Show and explain how you got your answer.

You have 5 face-up cards and no facedown cards. You add some facedown cards
so that 1 in every 3 cards is face-up. How many cards are there now? Show and
explain how you got your answer.

You have 5 face-up cards and 12 facedown cards. You add some face-up cards so
that 2 out of very 5 cards are face-up. How many cards are there now? Show and
explain how you got your answer.

You have 8 face-up cards and 12 facedown cards. You add some face-up cards so
that 2/3 of the cards are face-up. How many cards are face-up? How many are
facedown? Show and explain how you got your answer.

A spinner lands on blue 4 times for every 6 times it lands on green. How many
times does it land on green if it lands on blue 12 times? Show and explain how you
got your answer.

It rained 2 out of 5 days in the month of April. On how many days did it rain that
month? Show and explain how you got your answer.




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Of the 42 animals in the Children’s Zoo, 3 out of 7 are mammals. How many
mammals are there in the Children/s Zoo? Show and explain how you got your
answer.

Last week Charles spent 2 hours doing homework for every 3 hours he watched
TV. If he spent 6 hours doing homework, how many hours did he spend watching
TV? Show and explain how you got your answer.

Five out of 8 students at Lane Junior High School play a musical instrument. 140
students play an instrument. How many students attend Lane School? Show and
explain how you got your answer.

A choir has 50 members. Twenty members are sopranos. How many sopranos are
there for every 5 members of the choir? Show and explain how you got your
answer.

Mr. Dexter sells subscriptions to a magazine for $18 each. For each subscription
he sells, he earns $8. One month, he sold $900 in subscriptions. How much did he
earn? Show and explain how you got your answer.

At Kozminski School, the ratio of weeks of school to weeks of vacation is 9 to 4.
How many weeks of vacation do students at the school get in one year? Show and
explain how you got your answer.

The class library has 3 fiction books for every 4 nonfiction books. If the library
has a total of 63 books, how many fiction books does it have? Show and explain
how you got your answer.

 There are 48 students in the sixth grade at Robert’s school. Three out of 8 sixth
graders read two books last month. One out of 3 students read just one book. The
rest of the students read no books at all. How many books in all did the six graders
read last month? Show and explain how you got your answer.

You have 45 coins. Five out of every 9 are HEADS UP and the rest are TAILS
UP. How many coins are HEADS UP? Show and explain how you got your
answer.

You have 36 coins. The ratio of HEADS-UP coins to TAILS-UP coins is 3 to 1.
How many coins are HEADS-UP? Show and explain how you got your answer.




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You have 16 coins that are HEADS UP and 16 coins that are TAILS UP. After
you add some coins that are TAILS UP, the ratio of HEADS UP to TAILS UP
coins is 1 to 1.5. How many coins are TAILS UP? How many coins in all? Show
and explain how you got your answer.



At Richards Middle School, there are 448 students and 32 teachers. The San
Miguel Middle School has 234 students and 18 teachers. Which school has a
better ratio of students to teachers, that is, fewer students per teacher? Show and
explain how you got your answer.

In a recent game, the Mansfield School basketball team took 15 three-point shots
and made 6 shots. What percent of its shots did the team make? Show and explain
how you got your answer.

The team also took 20 two-point shots and made 45% of them. How many two-
point shots did the players make? Show and explain how you got your answer.

The team made 80% of its free throws (one-point shots). If players made 16 fee
throws, how many free throws did they attempt? Show and explain how you got
your answer.

How many shots did the team take in all? How many points did the team score in
all? Show and explain how you got your answer.

The 12 girls in Ms. Arnold’s class make up 40% of the class. How many students
are in Ms. Arnold’s class? Show and explain how you got your answer.

A sow had a litter with 3 female piglets and 5 male piglets. What percent of piglets
are female? Show and explain how you got your answer.

Matt bought his favorite movie on video for 40% off of he regular price. He paid
only $18. What was the regular price? Show and explain how you got your answer.

In Illinois in 2000, people paid 3% of their income for state tax. What was the tax
on an income of $65,000? Show and explain how you got your answer.

In the 200 presidential election, California had 54 electoral votes out of a total of
538. What percent of the electoral votes did California have? Show and explain
how you got your answer.


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Female college graduates earn only about 70% as much as male college graduates.
If the average female graduate earns about $40,000 a year, how much does the
average male graduate earn? Show and explain how you got your answer.

In 1999, about 75% of airline flights arrived on time. About how many of the 8.3
million flights arrived on time? Show and explain how you got your answer.

In 1997, about 9% of eighth grade students smoked daily. About how many of the
3,500,000 eighth graders smoked? Show and explain how you got your answer.

About 1 out of every 5 pounds of the body weight of an average adult is fat. What
percent of body weight is fat?
Muscles make up about 40% of the body weight of an average adult. About how
many pounds do the muscles of a 160-pound adult weight?
About 18% of the total bodyweight of an adult is bone. The rest is mostly water
and other fluids. If an adult weighs 150 pounds, about how many pounds are
bone? Show and explain how you got your answer.

If reduced-fat hot dogs have 8 fewer grams of fat than regular hot dogs, how much
fat do the regular hot dogs have? Show and explain how you got your answer.

 “PUBLILC TRANSPORTATION AUTHORITY AIMS TO INCREASE
RIDERSHIP BY 25%” If the public transportation system is currently collecting
about $28,000 per day, what will it collect per day if it reaches its goal? Show and
explain how you got your answer.

 “ATTENDANCE AT MUSIC HALL DOWN 12% OVER PREVIOUS YEAR
FOR 10-CONCERT SERIES” If there are 420 fewer people attending the concert
5 series, what was the total attendance for the previous year? Show and explain
how you got your answer.

Reginald read 168 pages of his book. He has 42 pages left. What percent of the
book has he read? Show and explain how you got your answer.

Last year, Maria’s insect collection had 250 insects in it. She added 60 more to her
collection this summer. By what percent did she increase her collection? Show
and explain how you got your answer.



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Jackie had a batting average of .250 for the season. If she went to bat 52 times
during the season, how many hits did she get? Show and explain how you got your
answer.

Ms. Camponella’s sixth graders were having a surprise birthday party for her. The
table below shows how many students signed up to bring each kind of treat.
a. Complete the table
b. Use your protractor to make a circle graph that displays the information Title
your graph
Treat       Number Signed       Degree Measure of
            Up                  Sector
Chips       8
Cookies 5
Drinks      3
Fruit       9
Show and explain how you got your answer.

Ms. Ruiz is driving at an average speed of 60 miles per hour. At this speed, how
far can she drive in 4.5 hours? Show and explain how you got your answer.

Jill walks at an average speed of 5 miles per hour. At this speed, how far can she
walk in 2.5 hours? Show and explain how you got your answer.

The distance from San Francisco to Los Angeles is about 420 miles. About how
many hours will it take to drive from San Francisco to Los Angeles at an average
speed of 55 miles per hour? Show and explain how you got your answer.

A dictionary measures 24 centimeters by 20 centimeters. The ratio of its length to
its width is about ___ to 1. Show and explain how you got your answer.

A sheet of legal-sized paper measures 14 inches by 8 ½ inches. The ratio of its
length to its width is about __________to 1. Is this the same ratio as for a sheet of
paper that measures 11 inches by 8 ½ inches? Show and explain how you got your
answer.

Jeffrey got 28 out of 30 problems correct on his math test. Lucille got 47 out of 50
problems correct on her math test. Who did better on the test? Show and explain
how you got your answer.

A ruler is 30 centimeters long and 2.5 centimeters wide. The ratio of its length to
its width is about __________to 1. Show and explain how you got your answer.


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Unit 9
Mr. Wilson’s 28 sixth graders had to read at least one nonfiction book – either a
biography or a science book. At the end of the grading period, Mr. Wilson tallied
the number of students who had read each kind of book. Nineteen had read at least
one biography, and 16 had read at least one science book. Draw a Venn diagram
to represent the number of students who read each kind of book. How many
students read at least one biography and one science book? Show and explain how
you got your answer.

Ricky and 5 of his friends are buying lunch. Each person gets a hamburger and a
soda. How much money will they spend in all? Write a number model to show
how you solved the problem. Show and explain how you got your answer.

Maureen signed her new book at a local bookstore. In the morning she signed 36
books, and in the afternoon she signed $51 books. It took her 5 minutes to sign
each. How much time did she spend signing books? Show and explain how you
got your answer.

Ms. Hays bought fabric for the school musical chorus. She bought 4 yards each of
one kind for 30 costumes and 4 yards each of another kind for 6 soloists. How
many yards did she buy in all? Show and explain how you got your answer.

Mr. Katz gave a party because all of the students got 100% on their math test. He
had budgeted $1.1.5 per student. It turned out that he saved $0.25 per student. If
there are 30 students, how much did he spend? Show and explain how you got
your answer.

Frederick and Lucille conducted a survey to find out how many of their classmates
had brothers and sisters. They surveyed 31 students and learned that 18 had at
least one sister and 20 had at least one brother. Draw a Venn diagram to represent
the results of Frederick and Lucille’s survey. How many students had at least one
brother and one sister? Show and explain how you got your answer.

Larry was reading a biography of Abraham Lincoln. He read 30 pages in 40
minutes. How many pages did he read in 60 minutes? Show and explain how you
got your answer.

A carton of milk costs $0.60. John bought 3 cartons of milk one day and 4 cartons
the next day. How much did he spend in all? Show and explain how you got your
answer.


1d683a63-5e7e-46aa-9938-7991f90d33d4.doc Page 36 of 37
During a typical week, Karen runs 16 miles, and Jacob runs 14 miles. About how
many miles in all do Karen and Jacob run in 8 weeks? Show and explain how you
got your answer.

Mark bought 6 CDs that cost $12 each. He returned 2 of them. How much did he
spend in all? Show and explain how you got your answer.

Max collects stamps. He had 9 envelopes, each containing 25 stamps. He sold 3
envelopes to another collector. How many stamps did he have left? Show and
explain how you got your answer.

Jean is sending party invitation to her friends. She has 8 boxes with 12 invitations
in each box. She has already mailed 5 boxes of invitations. How many invitations
are left? Show and explain how you got your answer.

Seven out of nine cards are face-up. If 16 cards are facedown, how many cards are
there altogether? Show and explain how you got your answer.

The ratio of facedown to face-up cards is 5:4. If there are 72 cards altogether, how
many cards are face-up? Show and explain how you got your answer.

When Marlene removed her dinner from the freezer, the temperature of the dinner
was -10C. She heated the dinner in the oven, and then put it on the table. It
cooled to room temperature, 23C, while she was talking on the phone. How many
degrees warmer was the dinner at room temperature than it was when removed
from the freezer? Show and explain how you got your answer.


Unit 10
Nancy can read 45 pages an hour. At that rate, about how long will it take her to
finish a 380-page book? Show and explain how you got your answer.

Grant collects marbles. His favorite store sells marbles for 69 cents per marble.
How many marbles can he buy if the has $15.00? Show and explain how you got
your answer.




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