6th RP.3

A shop owner wants to prevent shoplifting. He decides to install a security camera on the ceiling of his shop. Below is a picture of the shop floor plan with a square grid. The camera can rotate 360°. The shop owner places the camera at point P, in the corner of the shop.

  1. The plan shows where ten people are standing in the shop. They are labeled A, B, C, D, E, F, G, H, J, K. Which people cannot be seen by the camera at P?
  2. What percentage of the shop is hidden from the camera? Explain or show work.
  3. The shopkeeper has to hang the camera at the corners of the grid. Show the best place for the camera so that it can see as much of the shop as possible. Explain how you know that this is the best place to put the camera.

6.RP.3; 6.G.1-4 – Painting a Barn

Alexis needs to paint the four exterior walls of a large rectangular barn. The length of the barn is 80 feet, the width is 50 feet, and the height is 30 feet. The paint costs $28 per gallon, and each gallon covers 420 square feet. How much will it cost Alexis to paint the barn? Explain your work.

6th NS.5

Denver, Colorado is called “The Mile High City” because its elevation is 5280 feet above sea level. Someone tells you that the elevation of Death Valley, California is −282 feet.

  1. Is Death Valley located above or below sea level? Explain.
  2. How many feet higher is Denver than Death Valley?
  3. What would your elevation be if you were standing near the ocean?

6th EE.2

Some of the students at Kahlo Middle School like to ride their bikes to and from school. They always ride unless it rains.

Let d be the distance in miles from a student's home to the school. Write two different expressions that represent how far a student travels by bike in a four week period if there is one rainy day each week.

6th NS.1

It requires 1/4 of a credit to play a video game for one minute.

Emma has 7/8 credits. Can she play for more or less than one minute? Explain how you know.

How long can Emma play the video game with her 7/8 credits?

7th NS.1

A number line is shown below. The numbers 0 and 1 are marked on the line, as are two other numbers a and b.

7th NS.

Which of the following numbers is negative? Choose all that apply. Explain your reasoning.

a)a − 1

b)a − 2

c)−b

d)a + b

e)a − b

f)ab + 1

7.RP.1-3

Four different stores are having a sale. The signs below show the discounts available at each of the four stores.

1. Two for the price of one2. Buy one and get 25% off the second

3. Buy two and get 50% off the second one4. Three for the price of two

A. Which of these four different offers gives the biggest price reduction? Explain your reasoning clearly.

B. Which of these four different offers gives the smallest price reduction? Explain your reasoning clearly.

7.RP.3; 7.G.6 – Sand Under the Swing Set

The 7th graders at Sunview Middle School were helping to renovate a playground for the kindergartners at a nearby elementary school. City regulations require that the sand underneath the swings be at least 15 inches deep. The sand under both swing sets was only 12 inches deep when they started.

The rectangular area under the small swing set measures 9 feet by 12 feet and required 40 bags of sand to increase the depth by 3 inches. How many bags of sand will the students need to cover the rectangular area under the large swing set if it is 1.5 times as long and 1.5 times as wide as the area under the small swing set?

7.RP.2 - Art Class, Variation 1

The students in Ms. Baca’s art class were mixing yellow and blue paint. She told them that two mixtures will be the same shade of green if the blue and yellow paint are in the same ratio.

The table below shows the different mixtures of paint that the students made.

A / B / C / D / E
Yellow / 1 part / 2 parts / 3 parts / 4 parts / 6 parts
Blue / 2 part / 3 parts / 6 parts / 6 parts / 9 parts
  • How many different shades of paint did the students make?
  • Some of the shades of paint were bluer than others. Which mixture(s) were the bluest? Show work or explain how you know.
  • Carefully plot a point for each mixture on a coordinate plane like the one that is shown in the figure. (Graph paper might help.)
  • Draw a line connecting each point to (0,0). What do the mixtures that are the same shade of green have in common?

7.RP.2 Robot Races

Carli’s class built some solar-powered robots. They raced the robots in the parking lot of the school. The graphs below show the distance d, in meters, that each of three robots traveled after t seconds.

  1. Each graph has a point labeled. What does the point tell you about how far that robot has traveled?
  2. Carli said that the ratio between the number of seconds each robot travels and the number of meters it has traveled is constant. Is she correct? Explain.
  3. How fast is each robot traveling? How can you see this in the graph?

8th NS.1

For each pair of numbers, decide which is larger without using a calculator. Explain your choices.

8.NS.2 Irrational Numbers on the Number Line

Without using your calculator, label approximate locations for the following numbers on the number line.

8.SP.1; 8.SP.2 Birds’ Eggs

  1. A biologist measured a sample of one hundred Mallard duck eggs and found they had an average length of 57.8 millimeters and average width of 41.6 millimeters. Use an X to mark a point that represents this on the scatter diagram.
  2. What does the graph show about the relationship between the lengths of birds' eggs and their widths?
  3. Another sample of eggs from similar birds has an average length of 35 millimeters. If these bird eggs follow the trend in the scatter plot, about what width would you expect these eggs to have, on average?
  4. Describe the differences in shape of the two eggs corresponding to the data points marked C and D in the plot.
  5. Which of the eggs A, B, C, D, and E has the greatest ratio of length to width? Explain how you decided.

8th EE.5

Kell works at an after-school program at an elementary school. The table below shows how much money he earned every day last week.

MondayWednesday Friday

Time worked1.5 hours 2.5 hours 4 hours

Money earned$12.60. $21.00 $33.60

Mariko has a job mowing lawns that pays $7 per hour.

a. Who would make more money for working 10 hours? Explain or show work.

b. Draw a graph that represents y, the amount of money Kell would make for working x hours, assuming he made the same hourly rate he was making last week.

c. Using the same coordinate axes, draw a graph that represents y, the amount of money Mariko would make for working x hours.

d. How can you see who makes more per hour just by looking at the graphs? Explain.

8th EE.3

An ant has a mass of approximately 4×10−3 grams and an elephant has a mass of approximately 8 metric tons.

How many ants does it take to have the same mass as an elephant?

An ant is 10−1 cm long. If you put all these ants from your answer to part (a) in a line (front to back), how long would the line be? Find two cities in the United States that are a similar distance apart to illustrate this length.

Note: 1 kg = 1000 grams, 1 metric ton = 1000 kg, 1m = 100 cm, 1km = 1000 m

8th EE.8

Consider the equation 5x−2y=3. If possible, find a second linear equation to create a system of equations that has:

  1. Exactly 1 solution.
  2. Exactly 2 solutions.
  3. No solutions.
  4. Infinitely many solutions.
  5. Bonus Question: In each case, how many such equations can you find?

N-Q.1; N-Q.3

As Felicia gets on the freeway to drive to her cousin's house, she notice that she is a little low on gas. There is a gas station at the exit she normally takes, and she wonders if she will have to get gas before then. She normally sets her cruise control at the speed limit of 70mph and the freeway portion of the drive takes about an hour and 15 minutes. Her car gets about 30 miles per gallon on the freeway, and gas costs $3.50 per gallon.

  1. Describe an estimate that Felicia might do in her head while driving to decide how many gallons of gas she needs to make it to the gas station at the other end.
  2. Assuming she makes it, how much does Felicia spend per mile on the freeway?

N-Q.3

Quincy is a tour guide at a museum of science and history. During a tour of the museum, he tells some visitors about a fossilized dinosaur bone that is on display in the museum. He says, “Twenty years ago, a group of paleontologists donated this dinosaur bone to our museum. At the time, they told us that they had estimated the age of the bone to be approximately 90million years. So now, the bone is about 90million and 20years old.” Evaluate the validity of Quincy's statement.

N-RN.1

A.SSE.3-4

Judy is working at a retail store over summer break. A customer buys a $50 shirt that is on sale for 20% off. Judy computes the discount, then adds sales tax of 10%, and tells the customer how much he owes. The customer insists that Judy first add the sales tax and then apply the discount. He is convinced that this way he will save more money because the discount amount will be larger.

  1. Is the customer right?
  2. Does your answer to part (a) depend on the numbers used or would it work for any percentage discount and any sales tax percentage? Find a convincing argument using algebraic expressions and/or diagrams for this more general scenario.

A.SSE.1

Fred decides to cover the kitchen floor with tiles of different colors. He starts with a row of four tiles of the same color. He surrounds these four tiles with a border of tiles of a different color (Border1). The design continues as shown below:

Dina writes, t=4(b−1)+10where tis the number of tiles in each border and bis the border number.

  1. Explain why Dina's equation is correct.
  2. Emma wants to start with five tiles in a row. She reasons, “Dina started with four tiles and her equation was t=4(b−1)+10. So if I start with five tiles, the equation will be t=5(b−1)+10. Is Emma’s statement correct? Explain your reasoning.
  3. If Emma starts with a row of ntiles, what should the formula be?

A-APR.4

Alice was having a conversation with her friend Trina, who had a discovery to share:

“Pick any two integers. Look at the sum of their squares, the difference of their squares, and twice the product of the two integers you chose. Those three numbers are the sides of a right triangle.”

Trina had tried this several times and found that it worked for every pair of integers she tried. However, she admitted that she wasn't sure whether this "trick" always works, or if there might be cases in which the trick doesn't work.

  1. Investigate Trina's conjecture for several pairs of integers. Does her trick appear to work in all cases, or only in some cases?
  2. If Trina's conjecture is true, then give a precise statement of the conjecture, using variables to represent the two chosen integers, and prove it. If the conjecture is not true, modify it so that it is a true statement, and prove the new statement.
  3. Use Trina's trick to find an example of a right triangle in which all of the sides have integer length, all three sides are longer than 100 units, and the three side lengths do not have any common factors.

A-CED.3

The coffee variety Arabica yields about 750 kg of coffee beans per hectare, while Robusta yields about 1200 kg per hectare (reference). Suppose that a plantation has ahectares of Arabica and rhectares of Robusta.

  1. Write an equation relating aand rif the plantation yields 1,000,000 kg of coffee.
  2. On August 14, 2003, the world market price of coffee was$1.42 per kg of Arabica and $0.73 per kg of Robusta. Write an equation relating aand rif the plantation produces coffee worth $1,000,000.

A-APR.2

A-REI.6

Nola was selling tickets at the high school dance. At the end of the evening, she picked up the cash box and noticed a dollar lying on the floor next to it. She said,

I wonder whether the dollar belongs inside the cash box or not.

The price of tickets for the dance was 1 ticket for $5 (for individuals) or 2 tickets for $8 (for couples). She looked inside the cash box and found $200 and ticket stubs for the 47 students in attendance. Does the dollar belong inside the cash box or not?