Try first without a calculator. Please use a ruler when graphing.

Geometry Perimeter/Volume: Standards: 7.G Solve real-world/math w/ angles, area, SA Calculate the area and the perimeter or circumference for each shape below.

a.

b.

c.

The figure in part (a) of the above problem is the base for a prism standing 16 units high. What is the volume of that prism? Explain how you know.

Study Guide Chapters 7 & 9

Statistics & Probability Chance of something happening: Standards: 7.SP Investigate chance processes and develop Jaycee is an avid internet surfer and is often finding new things to download. One day his mother said “Jaycee, you need to be careful,” she began. “I just read an article saying the probability of downloading a virus from the internet is 12.5%” she said seriously. “No worries!” Jaycee quickly responded. “The article must have been wrong,” he casually replied. “Why would you say that?” his mother questioned. “Because,” Jaycee began, “That would mean every time I downloaded 100 items, I would have 12.5 viruses. You can’t have 0.5 of a virus! That just doesn’t make sense, so they clearly do not know what they are talking about!” Jaycee ended smugly. What do you think? Is Jaycee correct? Or, should he be worried as his mom suggested? In your explanation, make it clear that you understand what the probability means, as well as the percentage, and give suggestions to either Jaycee or his mom (or both!) Mrs. W had everyone in her class measure the length of room using foot long rulers. The students’ results are shown in the list below; all measurements are in feet. What are the mean and median values? Are there any outliers? Based on this list, can you make an educated guess of the length of the room? Do you have any advice for the students doing the measuring? Be clear and complete. 27, 25.5, 23.75, 28, 29, 28.5, 24.75, 27.75, 28, 19, 24, 25.5, 26.25, 26.75, 26, 27, 25, 28.25, 27, 26.75, 28, 36, 28, 25.75

Box & Whisker Plot / Stem & Leaf Plot: Standards: Review For her project, Carianne decided to survey her fellow classmates, asking “How many times have you flown on an airplane in your whole lifetime?” The results are shown in the stem-and-leaf plot.

a.   Represent this data as a box plot. Clearly label all parts.

b.   What percentage of the data is greater than the median? Why is that? Explain clearly.

c.   Christian just joined the class, and when Carianne asked him how many times he has flown on an airplane, she just about dropped her pencil. “Well,” Christian began, “My father has his own plane, so I’ve flown about 150 times.” What will this information do to the box plot? To the median? To the mean? Explain clearly how each will or will not change with this added data point.

A kindergarten class has just completed a counting competition. Below are the largest numbers students

were able to count up to:

120, 97, 111, 82, 47, 132, 94, 100, 91, 104, 126, 115, 100

Create a histogram and a box and whisker plot for the data.

How many times have you flown on an airplane?

Key 2|4 means 24

Kris read each day of her vacation. The following is a list of how many pages she read each day:

105, 39, 83, 54, 84, 75, 52, 96, 60

Find each of the following (you do not need to graph the data): a. Quartile 1 b. Quartile 3

c. Median d. Range

e. Interquartile Range (IQR)

Scale the number line below and make a box-and-whisker plot for the following data.

9, 22, 43, 2, 7, 14, 36, 12, 32, 45

a. Median: b. Lower quartile: c. Upper quartile: d. IQR: e. Range:

Manuel’s class created a bar graph for the data collected from the question “How many brothers and sisters do you have?”

a. How many students said they had 2 siblings?

b. How many more students said they had 1 sibling than said they had none?

c. How many students are represented in the bar graph?

d. What is the mean, median, and mode number of the siblings represented? Are any of those measures of central tendency impossible to find? Why?

Mean:

Median:

Mode:

0 0 1 2

3

4 or more

Number of siblings

Freq

uenc

y

5

Stem & Leaf Plot/Percentages: Standards: Review Three stem-and-leaf plots are shown each describing the ages of different groups of people.

a.   Describe the ages in Group A. If this is a classroom, what kind of classroom do you think this describes?

b.   Describe the ages in Group B. Why does it make sense that this data was collected in an office on “Take Your Child to Work Day”? If each parent brought only one child, how many office workers did not bring a child to work with them?

c. Describe the ages in Group C.

Use the graph at the right to answer the following questions.

a)   How many trees were surveyed to create this graph?

b)   How many trees were less than 70 feet tall? Explain.

c)   What seems to be the most common height for a black cherry tree?

Expressions & Equations 5-D Process: Standards: 7.EE.2 Real world/math problems using express The length of a rectangular field is seven meters less than four times its width. The perimeter is 136 meters. Calculate the length and the width of the field. The area of a right triangle is 36 square feet. The base is twice the height.

a. Draw and label the triangle.

b. Write an equation and solve it to find base and height.

The perimeter of a right triangle is 46 feet. The base is twice the height. The length of the hypotenuse (the diagonal side) is 6 inches more than the height.

Draw and label the triangle.

Write an equation and solve it to find all sides of the triangle.

Fraction Busting: Standards: 7.NS Apply/extend fraction operations; 7.EE.2 Real world/math problems using express Solve each rational equation.

Extra Challenge

6.2c + 8 = 12.34 –1 = 4.4n – 6.94

Build each equation, simplify as much as possible, and solve for x or y. Be sure to record each step of your solution process. If you cannot solve for the given variable, explain why not.

x – 3 = –1 –3 + 4x – (1 + 3x) = 1 – 2x + 4 2y – 6 – y = y – 1

56x − 3

4= 1112

518

x = 15

12.4 + 8u = 8.8 56+ v = 4

9

47w = 28 3

10x − 1

5= 1

9x + 2

= 23x

Solve and graph

1 +2 x < 13

Write an inequality to represent each of the following graphs.

Writing Expressions: Standards: 7.RP Analyze proportional relationships and u; 7.EE.2 Real world/math problems using express Use the distance formula to solve the following problem.

Mimi is piloting her airplane traveling at an altitude 24,000 feet. She has been directed by air traffic control to climb to 30,000 feet. The airplane climbs at 1200 feet per minute. How many minutes will it take for the airplane to reach 30,000 feet?

23x +1= x − 4 0.5x − 0.5 = 0.75x +1− x

Combining Like Terms: Standards: Create equivalent expressions 7.EE.1 Simplify. 25 + 5b + 6b2 – 8b – (–5) + 13b2 2(x + 5) + 3x2 – 7x2 – 6x – 9 9x + 6 – 4x – 2x + 1 – 15 2(6x + 5) + 2x2 – 7x – 11

Ratios & Proportions Scale factor with percentages: Standards: 7.RP Analyze proportional relationships Solve for the missing side lengths in the similar shapes below.

Using a decimal to find percent discount: Standards: 7.RP Analyze proportional relationships Edie has a unicorn farm. She currently feed her unicorns a total of 18 kilograms of marshmallows per day. She wants to start training her unicorns to compete in a rainbow-jumping race. This requires the unicorns to consume 12% more each day. How many total kilograms of marshmallows Edie will need to feed her unicorns each day during training? Calculate the total amount in two different ways.

A pet store has 125 crickets and sells 52% of them in one day. How many crickets do they have left? A store buys a sweater at a wholesale price of $15 and increases the price by 30% to sell. What is the new price of the sweater? Calculate the sales price of a music player that Calculate the total cost of a $4.50 birthday

typically sells for $120 that is marked 25% off. card with a 5.5% sales tax.

Solve:

a. 24 is what percent of 60? b. 20% of what number is 24? c. 19% of 60 is what number?

Solving Proportions: Standards: 7.RP Analyze proportional relationships

Solve each proportion.

Write a proportion to represent the following problem and solve.

Mika counted 24 red M&M’s in a package of 80 M&M’s. How many red M&M’s should Mika

expect to find in a package of 200 M&M’s?

One batch of cookies requires two eggs and two and a half cups of flour. How many cups of flour are needed to make three and a half batches of cookies? Write and solve a proportion.

1628 =

x21

87 =

52y

52= 13x

x100

= 78

Unit Rate: Standards: 7.RP Analyze proportional relationships Percent Increase and Decrease

Find the percent change.

Marty earned $12 per hour but then received A day old cake originally priced at $40 has

a raise. He now makes $14 per hour. been marked down to sell for $25.

What is the percent change? Indicate if the change is a percent increase or decrease.

a.   The price of gasoline rose from $1.25 to $3.75.

b.   If the price reverses from $3.75 to $1.25, what is the percent change?

It cost Mrs. Ferreira $4.40 to get into a movie in 1983. Today it costs $11.00 to go to a movie in some

theaters. What is the percent increase in price?

Challenge Questions— For those looking to stretch their thinking… 1.) Thanks to an erratic pitch, Sumi’s living room window needs new glass. The glass shops prices depend on the area of each pane of glass (their price sheet is shown below.)

Area Price Area Price

0 to 399 sq. cm $25 1000 to 1999 sq. cm $139

400 to 599 sq. cm $49 2000 to 2499 sq. cm $219

600 to 799 sq. cm $69 2500 to 2999 sq. cm $299

800 to 999 sq. cm $99 3000 sq. cm and up $0.10 per sq. cm

a. At right is the design for Sumi’s window with the actual measurements. What will be the total cost to replace each pane of glass? Note: the four panes of glass making up the outer circular region are equal in area. b. In Sumi’s county, the tax rate is 6.5%. How much will the bill be with tax included?

2.) Thurgood’s neighborhood swimming pool is a basic rectangular shape, 20 feet by 15 feet. Like most pools, it has a shallow end and slopes down to a deep end. A cross-section of his pool with the measurements is shown below. What is the volume of this swimming pool? Show your work.

a. The county is planning on draining the pool for repairs, but they are worried the cost of refilling it will be too high. A gallon of water costs just $0.15, and one cubic foot of water is about 7.5 gallons. What will it cost to refill the pool?