Carlos buys twenty-five pounds of starter feed to feed his flock of new baby chickens. Each week the chicks eat two pounds of food.
Define units for the time since Carlos bought starter feed and the amount of starter feed left.
After one week, how many pounds of starter feed does Carlos have left?
The baby chicks eat starter feed only for the first six weeks of their lives. How many pounds of starter feed will Carlos have left when the chicks are ready to move on to other food?
Enter a variable for the time since Carlos bought starter feed and use this variable to write an expression for the amount of starter feed left.
Use the Worksheet to complete the problem. The column labels describe the quantity from the problem scenario that the column is about. The row labels describe the type of value that goes in the row: quantity descriptions, units of measure, algebraic expressions, or numeric values to answer a question.
Quantity Name
Time
Starter Feed Left
Unit
After one week, how many pounds of starter feed does Carlos have left?
Question 1
The baby chicks eat starter feed only for the first six weeks of their lives. How many pounds of starter feed will Carlos have left when the chicks are ready to move on to other food?
Question 2
Expression
Units:
- Time: weeks
- Starter Feed Left: pounds
After one week, Carlos has 23 pounds of starter feed left (25 pounds - 1 week x 2 pounds/week = 23 pounds).
When the chicks are ready to move on to other food after six weeks, Carlos will have 13 pounds of starter feed left (25 pounds - 6 weeks x 2 pounds/week = 13 pounds).
Let t be the time in weeks since Carlos bought starter feed, then the expression for the amount of starter feed left is:
25 - 2t (in pounds)
The Fullerton Fire Company sells pins as a fundraiser. They spent $thirteen to make the pins and they are sold for five dollars each. The net revenue made from the fundraiser is the profit from the pins sold minus the cost of making the pins.
Define a unit for the net revenue.
Jared, a fire fighter, sold the first two pins yesterday. What is the fire company's total revenue so far?
After 2 days, the fire company has sold three pins. How much total revenue has the fire company made?
Enter a variable for the number of pins sold and use this variable to write an expression for the net revenue.
Use the Worksheet to complete the problem. The column labels describe the quantity from the problem scenario that the column is about. The row labels describe the type of value that goes in the row: quantity descriptions, units of measure, algebraic expressions, or numeric values to answer a question.
Quantity Name
Pins Sold
Net Revenue
Unit
pins
Jared, a fire fighter, sold the first two pins yesterday. What is the fire company's total revenue so far?
Question 1
After 2 days, the fire company has sold three pins. How much total revenue has the fire company made?
Question 2
Expression
Units:
- Pins Sold: pins
- Net Revenue: dollars
The unit for net revenue is dollars.
Jared sold 2 pins, so the fire company's total revenue so far is $10 (2 pins x $5/pin = $10).
After 2 days, the fire company has sold 3 pins, so their total revenue is $15 (3 pins x $5/pin = $15).
Let n be the number of pins sold, then the expression for the net revenue is:
5n - 13 (in dollars)
You and your friends record your favorite Shakespearean sonnets. You take seventeen seconds to introduce yourselves on the recording. Then you take four seconds to read each line of the sonnet.
Define a unit for the length of the recording.
What is the length of the recording in seconds after reading six lines of the sonnet?
How many seconds does it take you and your friends to read nine lines?
Enter a variable for the number of lines read and use this variable to write an expression for the length of the recording.
Use the Worksheet to complete the problem. The column labels describe the quantity from the problem scenario that the column is about. The row labels describe the type of value that goes in the row: quantity descriptions, units of measure, algebraic expressions, or numeric values to answer a question.
Quantity Name
Lines Read
Length of Recording
Unit
lines
What is the length of the recording in seconds after reading six lines of the sonnet?
Question 1
How many seconds does it take you and your friends to read nine lines?
Question 2
Expression
Units:
- Length of Recording: seconds
- Lines Read: lines
The unit for the length of the recording is seconds.
After reading six lines of the sonnet, the length of the recording is 41 seconds (17 seconds introduction + 4 seconds/line x 6 lines = 41 seconds).
To read nine lines, it takes you and your friends 53 seconds (17 seconds introduction + 4 seconds/line x 9 lines = 53 seconds).
Let n be the number of lines read, then the expression for the length of the recording is:
4n + 17 (in seconds)
Carrie rents a table at the local coffee shop for twenty-five dollars per week to use for tutoring. She charges students eight dollars per hour for her tutoring services.
Define units for the time that Carrie tutors and the amount Carrie earns.
If Carrie tutors a total of seven hours one week, how much money will she earn?
Next week is a busy week for Carrie. She is scheduled to tutor for eighteen hours. How much money will she earn?
Enter a variable for the time that Carrie tutors and use this variable to write an expression for the amount Carrie earns.
Use the Worksheet to complete the problem. The column labels describe the quantity from the problem scenario that the column is about. The row labels describe the type of value that goes in the row: quantity descriptions, units of measure, algebraic expressions, or numeric values to answer a question.
Quantity Name
Time Tutoring
Money Earned
Unit
If Carrie tutors a total of seven hours one week, how much money will she earn?
Question 1
Next week is a busy week for Carrie. She is scheduled to tutor for eighteen hours. How much money will she earn?
Question 2
Expression
Units:
- Time Tutoring: hours
- Money Earned: dollars
If Carrie tutors for a total of seven hours one week, she will earn $56 (7 hours x $8/hour = $56).
If she tutors for eighteen hours the next week, she will earn $169 (18 hours x $8/hour + $25/week = $169).
Let t be the time Carrie spends tutoring, then the expression for the amount Carrie earns is:
8t + 25 (in dollars)
While on the ocean, you see a dolphin that is twenty five meters behind you. It swims towards you at three meters per second. Represent distances behind your position as negative numbers. Represent distance in front of you as positive numbers.
Define units for the time that you see the dolphin swimming and the position of the dolphin compared to you.
After eight seconds, what is the dolphin's position relative to you?
After thirteen seconds, what is the dolphin's position relative to you?
Enter a variable for the time that you see the dolphin swimming and use this variable to write an expression for the position of the dolphin compared to you.
Use the Worksheet to complete the problem. The column labels describe the quantity from the problem scenario that the column is about. The row labels describe the type of value that goes in the row: quantity descriptions, units of measure, algebraic expressions, or numeric values to answer a question.
Quantity Name
Time
Position of Dolphin Compared to You
Unit
After eight seconds, what is the dolphin's position relative to you?
Question 1
After thirteen seconds, what is the dolphin's position relative to you?
Question 2
Expression
Units:
- Time: seconds
- Position of Dolphin Compared to You: meters
After eight seconds, the dolphin is two meters in front of you (25 meters - 8 seconds x 3 meters/second = 2 meters).
After thirteen seconds, the dolphin is 14 meters in front of you (25 meters - 13 seconds x 3 meters/second = 14 meters).
Let t be the time that you see the dolphin swimming, then the expression for the position of the dolphin compared to you is:
25 - 3t (in meters)
At the school carnival, the student council sold temporary tattoos of the school mascot. They purchased a batch of the tattoos for $ten, and sold each one for $four.
Define a unit for the amount of money made.
How much money did the student council make by selling five tattoos?
How much money did the student council make by selling nine tattoos?
Enter a variable for the number of tattoos sold and use this variable to write an expression for the amount of money made.
Use the Worksheet to complete the problem. The column labels describe the quantity from the problem scenario that the column is about. The row labels describe the type of value that goes in the row: quantity descriptions, units of measure, algebraic expressions, or numeric values to answer a question.
Quantity Name
Tattoos Sold
Money Made
Unit
tattoos
How much money did the student council make by selling five tattoos?
Question 1
How much money did the student council make by selling nine tattoos?
Question 2
Expression
Units:
- Money Made: dollars
- Tattoos Sold: tattoos
The unit for the amount of money made is dollars.
By selling five tattoos, the student council made $10 in profit (5 tattoos x $4/tattoo - $10 = $10).
By selling nine tattoos, the student council made $26 in profit (9 tattoos x $4/tattoo - $10 = $26).
Let n be the number of tattoos sold, then the expression for the amount of money made is:
4n - 10 (in dollars)
Gabriel hoped to make his fortune telling fortunes. He borrowed $twenty from his little sister to buy a glowing crystal ball, and set it in the window with high hopes. However, the crystal ball required new batteries often, increasing his debt by three dollars a day, and Gabriel couldn't find a single person who wanted his or her fortune told. Unfortunately.
Define units for the amount of time that Gabriel had the crystal ball and Gabriel's financial state.
Show Gabriel's financial state two days after he got the glowing crystal ball.
Show Gabriel's financial state eighteen days after he bought the glowing crystal ball, when he removed the batteries and stuffed it under his bed.
Enter a variable for the amount of time that Gabriel had the crystal ball and use this variable to write an expression for Gabriel's financial state.
Use the Worksheet to complete the problem. The column labels describe the quantity from the problem scenario that the column is about. The row labels describe the type of value that goes in the row: quantity descriptions, units of measure, algebraic expressions, or numeric values to answer a question.
Quantity Name
Time Gabriel Had Crystal Ball
Gabriel's Financial State
Unit
Show Gabriel's financial state two days after he got the glowing crystal ball.
Question 1
Show Gabriel's financial state eighteen days after he bought the glowing crystal ball, when he removed the batteries and stuffed it under his bed.
Question 2
Expression
Units:
- Time Gabriel Had Crystal Ball: days
- Gabriel's Financial State: dollars
Two days after getting the crystal ball, Gabriel's debt has increased to $26 (the initial $20 borrowed from his sister, plus $3/day x 2 days for the batteries).
Eighteen days after buying the crystal ball, Gabriel's debt has increased to $74 (the initial $20 borrowed from his sister, plus $3/day x 18 days for the batteries). When he removes the batteries, his debt remains at $74.
Let t be the amount of time that Gabriel had the crystal ball, then the expression for Gabriel's financial state is:
20 + 3t (in dollars)
Guy is part of a team of marine biologists studying the southern resident orcas of the Pacific Northwest. He and a colleague record the number of chinook salmon eaten by each orca from two pods, J Pod and L Pod on a single day in May. Guy summarizes the data from J Pod and his colleague summarizes the data from L Pod. The graphical summaries they each chose are shown.
For each plot, complete the tasks for the characteristics to be determined. Press on the headings to open the tasks.
Number of Salmon Eaten by Orcas in J Pod
0
2
4
6
8
10
Mean = three point eight six three six three six three six salmon
Number of observations = twenty two orcas
Range
Mode
The following sentence or sentences contain missing information in the form of one or more blanks. For each blank, there will exist a corresponding input field. Use the input fields to complete the sentence or sentences.
The modal number of salmon eaten by orcas in J Pod represented on the dot plot be determined.
The following sentence or sentences contain missing information in the form of one or more blanks. For each blank, there will exist a corresponding input field. Use the input fields to complete the sentence or sentences.
The modal number of salmon eaten by orcas in J Pod can be determined by .
The following sentence or sentences contain missing information in the form of one or more blanks. For each blank, there will exist a corresponding input field. Use the input fields to complete the sentence or sentences.
The modal number of salmon eaten by orcas in J Pod represented on the dot plot is
salmon.
Number of Salmon Eaten by Orcas in L Pod
Range
Minimum Value
Median
The following sentence or sentences contain missing information in the form of one or more blanks. For each blank, there will exist a corresponding input field. Use the input fields to complete the sentence or sentences.
The range of the number of salmon eaten by orcas in L Pod can be determined by subtracting the from the maximum value.
The following sentence or sentences contain missing information in the form of one or more blanks. For each blank, there will exist a corresponding input field. Use the input fields to complete the sentence or sentences.
The minimum number of salmon eaten by orcas in L Pod is .
The following sentence or sentences contain missing information in the form of one or more blanks. For each blank, there will exist a corresponding input field. Use the input fields to complete the sentence or sentences.
The median number of salmon eaten by orcas in L Pod is salmon.
Molly and George are competing in a ballroom dancing competition. The winning couple is the one that can dance the longest without stopping. All the couples have already danced for twenty minutes. Each new song they dance to lasts for five minutes.
Define a unit for the time the couples dance.
Molly and George have counted seven new songs. How long have they been dancing?
After eighteen new songs, the first couple leaves the competition. How long has the couple been dancing?
Enter a variable for the number of new songs and use this variable to write an expression for the time the couples dance.
Use the Worksheet to complete the problem. The column labels describe the quantity from the problem scenario that the column is about. The row labels describe the type of value that goes in the row: quantity descriptions, units of measure, algebraic expressions, or numeric values to answer a question.
Quantity Name
New Songs
Time Dancing
Unit
songs
Molly and George have counted seven new songs. How long have they been dancing?
Question 1
After eighteen new songs, the first couple leaves the competition. How long has the couple been dancing?
Question 2
Expression
Units:
- Time Dancing: minutes
- New Songs: songs
The unit for the time the couples dance is minutes.
Molly and George have been dancing for 55 minutes (20 minutes + 7 new songs x 5 minutes/new song = 55 minutes).
After 18 new songs, the first couple leaves the competition. They have been dancing for 95 minutes (20 minutes + 18 new songs x 5 minutes/new song = 95 minutes).
Let n be the number of new songs danced, then the expression for the time the couples dance is:
20 + 5n (in minutes)
The Tour de France is a 2,235 mile long distance bicycle race that goes through all of France. So far, Latrell has ridden five miles of one mostly uphill stage of the Tour de France. He rides fourteen miles per hour during this stage.
Define units for the additional time Latrell rides and the distance Latrell rides.
How far will Latrell have ridden after an additional one hundred twenty minutes?
Latrell grabs a new water bottle from volunteers after six hours. How far has he traveled?
Enter a variable for the additional time Latrell rides and use this variable to write an expression for the distance Latrell rides.
Use the Worksheet to complete the problem. The column labels describe the quantity from the problem scenario that the column is about. The row labels describe the type of value that goes in the row: quantity descriptions, units of measure, algebraic expressions, or numeric values to answer a question.
Quantity Name
Additional Time Latrell Rides
Distance Latrell Rides
Unit
How far will Latrell have ridden after an additional one hundred twenty minutes?
Question 1
Latrell grabs a new water bottle from volunteers after six hours. How far has he traveled?
Question 2
Expression
Units:
- Additional Time Latrell Rides: minutes
- Distance Latrell Rides: miles
After an additional 120 minutes, Latrell will have ridden 23 miles (5 miles + 14 miles/hour x 2 hours = 23 miles).
After six hours (or 360 minutes), Latrell will have ridden 83 miles (5 miles + 14 miles/hour x 6 hours = 83 miles).
Let t be the additional time Latrell rides, then the expression for the distance Latrell rides is:
5 + 14t/60 (in miles)
An ecologist presents her findings at a town hall meeting. She estimates that there are fifteen hawk nesting sites on the town's nature preserve. She estimates the number of nesting sites will decrease by three nesting sites each year.
Define a unit for the amount of time.
Based upon her prediction, how many nesting sites will be on the preserve next year?
How many nesting sites will be on the preserve in three years based upon her prediction?
Enter a variable for the amount of time and use this variable to write an expression for the number of nesting sites remaining.
Use the Worksheet to complete the problem. The column labels describe the quantity from the problem scenario that the column is about. The row labels describe the type of value that goes in the row: quantity descriptions, units of measure, algebraic expressions, or numeric values to answer a question.
Quantity Name
Time
Remaining Nesting Sites
Unit
nesting sites
Based upon her prediction, how many nesting sites will be on the preserve next year?
Question 1
How many nesting sites will be on the preserve in three years based upon her prediction?
Question 2
Expression