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
Answer:
Quantity Name | Games | Change in Points |
------------------------|-------|-----------------|
Unit | games | points |
After fourteen games, | 14 | -27 |
What is the change in | 16 | -31 |
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? | | |
Change in score on each | | |
subsequent game | | -2 |
points per game | | |
Change in score on game | | -5 |
Deven fell | | |
Expression | n-1 | -5-2(n-1) |
change by negative five.
Define units for the amount of fat removed and the number of calories.
How many calories would the food contain if ten grams of fat were removed?
How many calories would the food contain if one gram of fat were removed?
How much fat would have to be removed to reduce the number of calories to twenty eight?
Complete the rows for the reduction in calories per gram of fat removed and the calories in the food before fat is removed. Then, enter a variable for the amount of fat removed and use this variable to write an expression for the number of calories.
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
Fat Removed
Calories Remaining
Unit
How many calories would the food contain if ten grams of fat were removed?
Question 1
How many calories would the food contain if one gram of fat were removed?
Question 2
How much fat would have to be removed to reduce the number of calories to twenty eight?
Question 3
Change in calories for each gram of fat removed
calories per gram
Initial calories the food has
calories
Expression
Answer:
Quantity Name | Fat Removed | Calories Remaining |
------------------------------------|-------------|--------------------|
Unit | grams | calories |
How many calories would the food | 10 | -90 |
contain if ten grams of fat were | | |
removed? | | |
How many calories would the food | 1 | -9 |
contain if one gram of fat were | | |
removed? | | |
How much fat would have to be | 22.5 | 28 |
removed to reduce the number of | | |
calories to twenty eight? | | |
Change in calories for each gram of | | -4.5 |
fat removed | | |
Initial calories the food has | | 540 |
Expression | f | 540 - 4.5*f |
Samantha owes her brother fifty dollars. Each week she pays off two dollars of the debt to her brother. Represent the amount owed as a positive number.
Define units for the time Samantha has been repaying her brother and the amount Samantha owes.
How much does Samantha owe her brother after nineteen weeks?
How much does Samantha owe her brother after eleven weeks?
After how many weeks did Samantha owe her brother forty-four dollars?
Complete the rows for the amount Samantha pays her brother each week and the amount Samantha initially owes her brother. Then, enter a variable for the time Samantha has been repaying her brother and use this variable to write an expression for the amount Samantha owes.
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 Repaying
Amount Owed
Unit
How much does Samantha owe her brother after nineteen weeks?
Question 1
How much does Samantha owe her brother after eleven weeks?
Question 2
After how many weeks did Samantha owe her brother forty-four dollars?
Question 3
Change in amount owed each week
dollars per week
Initial amount owed
dollars
Expression
Answer:
Quantity Name | Time Repaying | Amount Owed |
------------------------|---------------|-------------|
Unit | weeks | dollars |
How much does Samantha | 12 | 26 |
owe her brother after | | |
nineteen weeks? | | |
How much does Samantha | 28 | 14 |
owe her brother after | | |
eleven weeks? | | |
After how many weeks did | 3 | 44 |
Samantha owe her brother | | |
forty-four dollars? | | |
Change in amount owed | | -2 |
each week | | |
Initial amount owed | | 50 |
Expression | w | 50 - 2*w |
You want to determine the savings for using a battery that can be recharged. The battery costs sixteen dollars. You save four dollars each time you recharge the battery. Represent the cost of the rechargeable battery as a negative number and savings as a positive number.
Define a unit for the net savings of the rechargeable battery.
What is your net savings if you recharge the battery ten times?
If your net savings is twelve dollars, how many times did you recharge the battery?
Complete the rows for the amount you save each time you recharge the battery and the cost of a rechargeable battery. Then, enter a variable for the number of rechargings and use this variable to write an expression for the net savings of the rechargeable battery.
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
Rechargings
Net Savings
Unit
rechargings
What is your net savings if you recharge the battery ten times?
Question 1
If your net savings is twelve dollars, how many times did you recharge the battery?
Question 2
Savings for each recharge
dollars per recharging
Cost of the rechargeable battery
dollars
Expression
Answer:
Quantity Name | Rechargings | Net Savings |
----------------------------------|-------------|-------------|
Unit | rechargings | dollars |
What is your net savings if you | 10 | 24 |
recharge the battery ten times? | | |
If your net savings is twelve | 8 | 12 |
dollars, how many times did you | | |
recharge the battery? | | |
Savings for each recharge | | 4 |
dollars per recharging | | |
Cost of the rechargeable battery | -16 | |
dollars | | |
Expression | r | 4*r - 16 |
The music club takes polls each year about the popularity of musicians. Jazzy Joe's popularity peaked when he scored forty points in the poll. Since then, his score has dropped four points every year.
Define a unit for the years that have passed.
How many points does Jazzy Joe have after two years?
If Jazzy Joe's rating score is twenty-eight points, how many years have passed?
Jazzy Joe wont't be allowed to play if his score hits zero. If things keep going this way, how many years later will this happen?
Complete the rows for the yearly decrease in Jazzy Joe's popularity score and Jazzy Joe's peak popularity score. Then, enter a variable for the years that have passed and use this variable to write an expression for Jazzy Joe's popularity score.
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
Popularity Score
Unit
points
How many points does Jazzy Joe have after two years?
Question 1
If Jazzy Joe's rating score is twenty-eight points, how many years have passed?
Question 2
Jazzy Joe wont't be allowed to play if his score hits zero. If things keep going this way, how many years later will this happen?
Question 3
Change in score each year
points per year
Peak popularity score
points
Expression
Answer:
Quantity Name | Time | Popularity Score |
-------------------------------|------|-----------------|
Unit | years| points |
How many points does | 32 | 32 |
Jazzy Joe have after two years?| | |
If Jazzy Joe's rating | 3 | 28 |
score is twenty-eight points, | | |
how many years have passed? | | |
Jazzy Joe wont't be allowed | 10 | 0 |
to play if his score hits zero.| | |
If things keep going this | | |
way, how many years later will | | |
this happen? | | |
Change in score each year | | -4 |
points per year | | |
Peak popularity score | | 40 |
points | | |
Expression | t | 40 - 4*t |
start in a race with a friend. Each second from the start of the race, your friend gains two yards on you.
Define units for the time you have been running and the distance you are ahead of your friend.
How far are you ahead of your friend after one second?
How far are you ahead of your friend after six seconds?
How many seconds does it take for your friend to catch up to you?
Complete the rows for the distance that your friend gains on you each second and the distance of your head start. Then, enter a variable for the time you have been running and use this variable to write an expression for the distance you are ahead of your friend.
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 Running
Distance Ahead
Unit
How far are you ahead of your friend after one second?
Question 1
How far are you ahead of your friend after six seconds?
Question 2
How many seconds does it take for your friend to catch up to you?
Question 3
Change in your lead each second
yards per second
The initial lead you have
yards
Expression