Ms. Deutsch needs four parent volunteers to help students get on and off stage at the dance recital. He also needs four parent volunteers per room of students.
Ms. Deutsch determines she will need five rooms for students at the recital. How many parent volunteers will Ms. Deutsch need in all?
On the day of the recital, Ms. Deutsch uses twelve parent volunteers. How many backstage rooms were there?
Complete the rows for the number of parent volunteers per room and the number of parent volunteers needed to help students get on and off stage. Then, enter a variable for the number of rooms of students and use this variable to write an expression for the number of parent volunteers needed.
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
Rooms
Parent Volunteers
Unit
rooms
parent volunteers
Ms. Deutsch determines she will need five rooms for students at the recital. How many parent volunteers will Ms. Deutsch need in all?
Question 1
On the day of the recital, Ms. Deutsch uses twelve parent volunteers. How many backstage rooms were there?
Question 2
Volunteers per room
parent volunteers per room
Volunteers helping on stage
parent volunteers
Expression
For 5 rooms of students, Ms. Deutsch will need:
- 20 parent volunteers (4 per room x 5 rooms) to help students get on and off stage
- 20 parent volunteers (4 per room x 5 rooms) to assist with each room of students
Therefore, she will need a total of 40 parent volunteers in all.
To find out how many backstage rooms there were on the day of the recital:
- Subtract the number of parent volunteers helping with rooms of students (20) from the total number of parent volunteers used (12): 12 - 20 = -8
- Since this doesn't make sense as a positive value, we can conclude that there must have been an error in the scenario and it is not possible to determine the number of backstage rooms based on this information.
Using a variable for the number of rooms of students:
- Let r be the number of rooms of students.
- Ms. Deutsch will need 4r parent volunteers to help students get on and off stage.
- Ms. Deutsch will need 4r parent volunteers to assist with each room of students.
- Therefore, in all, she will need 8r parent volunteers.
Without a special membership, nail art pens sell for $11 each. Jada decides to buy a $fifteen club membership to get the pens for $five each.
Define a unit for the amount Jada pays.
What is Jada's total cost for eight nail art pens?
If Jada pays a total of thirty dollars, how many nail art pens did she buy?
Complete the rows for the cost per pen and the cost of the club membership. Then, enter a variable for the number of nail art pens and use this variable to write an expression for the amount Jada pays.
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
Nail Art Pens
Cost
Unit
pens
What is Jada's total cost for eight nail art pens?
Question 1
If Jada pays a total of thirty dollars, how many nail art pens did she buy?
Question 2
Discounted price of each pen
dollars per pen
Price of club membership
dollars
Expression
Unit for amount Jada pays: dollars
Jada's total cost for eight nail art pens:
- Without the club membership: 8 x $11 = $88
- With the club membership: $15 + (8 x $5) = $55
- Therefore, Jada's total cost for eight nail art pens is $55.
If Jada pays a total of thirty dollars:
- Let n be the number of nail art pens she bought.
- With the club membership, she pays $5 per pen, so her total cost can be expressed as: $15 + $5n
- We can set up an equation based on the given information: $15 + $5n = $30
- Solving for n: $5n = $15, n = 3
- Therefore, Jada bought three nail art pens.
Cost per pen:
- Without the club membership: $11
- With the club membership: $5
Cost of club membership: $15
Using a variable for the number of nail art pens:
- Let p be the number of nail art pens.
- With the club membership, Jada pays $5 per pen, so her total cost can be expressed as: $15 + $5p.
A forest fire can move at the rate of three meters per second in windy conditions. A fire started by a careless camper has already moved five meters.
Define units for the amount of time the wind blows and the distance the forest fire has moved.
How far will the fire have moved after the wind has blown for twenty four seconds?
How long has the wind blown if the fire has moved twenty meters?
Complete the rows for the speed at which the fire moves and the distance that the fire has already moved. Then, enter a variable for the amount of time the wind blows and use this variable to write an expression for the distance the forest fire has moved.
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
Distance
Unit
How far will the fire have moved after the wind has blown for twenty four seconds?
Question 1
How long has the wind blown if the fire has moved twenty meters?
Question 2
Meters the fire travels every second
meters per second
Distance the fire has already traveled
meters
Expression
Units for amount of time wind blows: seconds
Units for distance fire has moved: meters
After the wind has blown for twenty four seconds:
- Distance moved = (rate of movement) x (amount of time wind has blown) + distance fire has already moved
- Distance moved = (3 m/s) x (24 s) + 5 m
- Distance moved = 72 m + 5 m
- Therefore, the fire will have moved 77 meters after the wind has blown for twenty four seconds.
If the fire has moved twenty meters:
- Distance moved = (rate of movement) x (amount of time wind has blown) + distance fire has already moved
- 20 m = (3 m/s) x (amount of time wind has blown) + 5 m
- 15 m = (3 m/s) x (amount of time wind has blown)
- Therefore, the wind has blown for 5 seconds if the fire has moved twenty meters.
Speed at which fire moves: 3 meters per second
Distance fire has already moved: 5 meters
Using a variable for the amount of time wind blows:
- Let t be the amount of time the wind blows.
- Distance moved = (rate of movement) x (amount of time wind has blown) + distance fire has already moved
- Distance moved = 3t + 5.
Deven is the best player on his basketball team. During warm-ups before a game, he tripped over the ball and broke his arm. He cannot play for the rest of the season! Compared to the previous game Deven played, the change in the points the team scores is negative five points. At each game after this one, the team scores two fewer points than the previous game. Treat his team's change in points per game as a negative number.
After fourteen games, what is the change in the number of points the team scored?
What is the change in the number of points the team scored after sixteen games?
If things keep going this way, how many games later will the change in points be negative twenty nine?
Complete the rows for the change in the team's score in each game after Deven fell and the change in the team's score in the game when Deven fell. Then, enter a variable for the number of games after the game when Deven fell and use this variable to write an expression for the change in points scored.
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
Games
Change in Points
Unit
games
points
After fourteen games, what is the change in the number of points the team scored?
Question 1
What is the change in the number of points the team scored after sixteen games?
Question 2
If things keep going this way, how many games later will the change in points be negative twenty nine?
Question 3
Change in score on each subsequent game
points per game
Change in score on game Deven fell
points
Expression
Unit for change in points: points
After fourteen games:
- The team scores two fewer points than the previous game, so the change in points per game is -2.
- Since the change in points for the game when Deven fell was -5, the total change in points after fourteen games can be expressed as: (-5) + (-2 x 13) = -31
- Therefore, the change in the number of points the team scored after fourteen games is -31.
After sixteen games:
- The team scores two fewer points than the previous game, so the change in points per game is -2.
- Since the change in points for the game when Deven fell was -5, the total change in points after sixteen games can be expressed as: (-5) + (-2 x 15) = -35
- Therefore, the change in the number of points the team scored after sixteen games is -35.
If the team's change in points per game remains constant at -2:
- Let n be the number of games played after the game when Deven fell.
- The change in points after n games can be expressed as: -5 + (-2n)
- We can set up an equation based on the given information: -5 + (-2n) = -29
- Solving for n: -2n = -24, n = 12
- Therefore, the change in points will be negative twenty nine after twelve games.
Change in score on each subsequent game: -2 points
Change in score on game Deven fell: -5 points
Using a variable for the number of games after the game when Deven fell:
- Let g be the number of games played after the game when Deven fell.
- The change in points after g games can be expressed as: -5 + (-2g).