Tasks MTH 4151

Section 2.9 task questions

Guideded task questions

Start

Instructions

1. Read the entire task question.

Task questions or word questions can be overwhelming!This presentation guides you through 4 task questions. For each question:

2. Select how much guidance you want.

3. Go through 1 or more steps to the final answer!

Task 1

Task 2

Task 3

Task 4

Click to choose a task question

Task Question #1

Jason has been recording the daily maximum temperature and the number of eggs produced by the hens in his backyard. He proudly showed you his graph and ask for your help to predict the number of eggs if tomorrow's temperature is 37 degrees celcius. Create an algebraic model and use it to help Jason.

just A hint

ready to enter my answer

some help

Build and use the equation to answer the question

The main question. if temperature is 37 find # of eggs

From the graph -> determine the equation of that straight line. Then use that equation to answer the question. If the temperature (x) is 37 degree Celsius, how many egg (y) will there be? Work on it. Then close this window to- get more guidance by clicking on the "SOME HELP" button. - enter your answer by clicking on the "READY TO ENTER MY ANSWER" button.

13 eggs

3 eggs

12 eggs

If temperature is 37 degrees celcius, predict the number of eggs

Task question #1

OH NO~~Not quite correct!

Task question #1

Return

Equation will come from the graph. So focus on the graph!The x-axis represents?

Number of eggs

Where? What?

Temperature

Task question #1

The x-axis represents temperature.

The x-axis represents temperature.

Focus on the graph!The y-axis represents?

Number of eggs

Where? What?

Temperature

Task question #1

The y-axis represents number of eggs.

The y-axis represents number of eggs

Task question #1

Determine the equation of the line you see on the graph.x = temperature, y = # of eggs

y = 0.25x+3

y = 4x-72

y = 0.25 x +13

https://youtu.be/p-YYXCDEcLQ

The equation isy = 0.25x + 3

sample solution

(20,8)

(40,13)

(you could use a different set of values but you should get the same equation)

With an equation

If you have a temperature value (x), you can use the equation to find the number of eggs (y).with a value for x 1. Replace 'x' with the value in the equation.2. Find the y-value

Now use the equation to answer the question.

13 eggs

3 eggs

12 eggs

If temperature is 37 degrees celcius, predict the number of eggs

Task question #1

x = 37 replace 'x' with '37' in the equation then find the y-value

12 eggs!

Using the equation37 degrees celciuswould give you12 eggs

Task Question #1

Jason have been recording the daily maximum temperature and the number of eggs produced by the hens in his backyard. He proudly showed you his graph and ask for your help to predict the number of eggs if tomorrow's temperature is 37 degrees celcius. Create an algebraic model and use it to help Jason.

Answer:With a temperature of 37 degrees celcius, the model predicts 12 eggs.

Algebraic model meansfind and use the equation for the answer.

Graph is important!Analyze it to see what it is showing you!

You can find the equation of a straight line using just 2 sets of coordinates (x,y)

Task Question #2

just A hint

ready to enter my answer

some help

Many people want to escape the cold winter in Quebec by going somewhere warm for the winter. Your friend is trying to convince you to take a vacation with him to Las Vegas! Below are the results of his analysis on the cost of the vacation. Create an algebraic model for the data. Then use it to determine if $2000 would be enough for you and your friend to vacation in Las Vegas for 14 days.

Build and use the equation to answer the question

Main question 1. Calculate the cost for you and your friend for 14 days. 2. Determine if it is within the $2000 budget.

Main question 1. Calculate the cost for you and your friend for 14 days. 2. Determine if it is within the $2000 budget.

From the table of values -> determine the equation representing the pattern between: the duration (x) and the cost per person (y) Then use that equation to answer the question. Is $2000 enough for you and your friend for 14 days. There are two ways you can use the equation to answer the question. 1. Use the equation to determine how many days you can stay if you have $2000 for two people. Then compare your result to the 14 days in the question. 2. Use the equation to determine how much it would cost to stay 14 days for two people. Then compare your result to the $2000 budget. Work on it. Then close this window to- get more guidance by clicking on the "SOME HELP" button. - enter your answer by clicking on the "READY TO ENTER MY ANSWER" button.

Now use the equation to calculate the cost of vacationing 14 days for 2 persons.

$2498

$196

$1249

Task question #2

x = 14 replace 'x' with '14' in the equation then find the y-value then look at the question AGAIN! (hint hint)

Return

Task question #2

OH NO~~Not quite correct!

x = 14 replace 'x' with '14' in the equation then find the y-value then look at the question AGAIN! (hint hint)

Equation will come from the table. So focus on the table!Which one is the independent variable (x)?

Cost per person in dollars

Where? What?

Duration in # of days

Task question #2

The independant variable (x)is the duration in days

The independant variable (x)is usually the first row/colum of the table

Focus on the table!What is the dependent variable (y)?

Cost per person in dollars

Where? What?

Duration in days

Task question #2

The dependent variable(y)is the cost per person in $

The dependant variable (y)is usually the second row/colum of the table

With an equation

x = duration of the vacation in daysy = cost of the vacation per person

If you use an equation to model the relationship between 'x' and 'y' in the table.We can use the equation and substitute the duration of the vacation in days (x) to find the cost of the vacation per person (y)

Task question #2

Represent the pattern (how values change) in the table as an equation.Possible strategy -> graph the tableAlternative strategy -> calculate how the y-variable (cost per person) goes up each time.

y = 115x + 81

y = 196

y = 81x + 115

xy

If you have a table of values but not sure what to do with it.... draw it on a cartesian plane!

https://youtu.be/p-YYXCDEcLQ

The equation isy = 81x+115

sample solution

(you could use a different set of values but you should get the same equation)

Now use the equation to calculate the cost of vacationing 14 days for 2 persons.

$2498

$196

$1249

Task question #2

x = 14 replace 'x' with '14' in the equation then find the y-value then look at the question AGAIN! (hint hint)

Vacationing 14 days for 2 persons would cost$2498

Using the equation14 days would cost $1249 for one person.And $2498 for 2 persons!

Task Question #2

Answer:No, vactioning 14 days for 2 persons would cost $2498. And it is over the $2000 budget!

Table is important!First row/column is usually x.Second row/column is usually y.

Always check to see if you answer the question. Don't stop with just the calculation.

If you are stuck... If there is no graph for the table.. Graph the table.

Task Question #3

just A hint

ready to enter my answer

some help

Album sales from the late Leonard Cohen were growing steadily each year after 2006. The record comapny representing Cohen has this table of values showing the record sales. Determine, algebrically, how many MORE records were sold in 2019, compared to 2018.

Build and use the equation to answer the question

The main question. How many MORE records were sold in 2019, compared to 2018. Determine the # of record sales in 2018. Determine the # of record sales in 2019. Calculate the difference between these two values.

From the table of values -> determine the equation representing the pattern between: the year (x) and the records sales in hundreds (y) Then use that equation to answer the question - how many more records were sold in 2019, compared to 2018. You can either interpret the equation to find out how many more records were sold every year.OR Calculate the records sold in 2018. Calculate the records sold in 2019. Find the difference between these two years. Work on it. Then close this window to- get more guidance by clicking on the "SOME HELP" button. - enter your answer by clicking on the "READY TO ENTER MY ANSWER" button.

Use the equation to answer the question:How many more records were sold in 2019, compared to 2018.

1.85 more record sales

185 more record sales

3855 more record sales

Task question #3

To find out how many MORE record sales in 2019, compared to 2018. 1. You will need to calculate the # of record sales in 2019 (by replacing "x" as 2019 in the equation and find the corresponding y-value) 2. You will also need to calculate the # of record sales in 2018 (by replacing "x" as 2018 in the equation and find the corresponding y-value) 3. Then subtract the two y-values to find out how many MORE records were sold.

Return

Use the equation to answer the question:How many more records were sold in 2019, compared to 2018.

Task question #3

OH NO~~Not quite correct!

To find out how many MORE record sales in 2019, compared to 2018. 1. You will need to calculate the # of record sales in 2019 (by replacing "x" as 2019 in the equation and find the corresponding y-value) 2. You will also need to calculate the # of record sales in 2018 (by replacing "x" as 2018 in the equation and find the corresponding y-value) 3. Then subtract the two y-values to find out how many MORE records were sold.

We should focus first on.... THE TABLE!The independent variable (x) is ....?

Record sales

Where? What?

Year

Task question #3

The independent variable(x) is year

The independant variable (x)is usually the first row/colum of the table

Record sales

Where? What?

Year

Task question #3

The dependent variable (y) is ....?

The dependent variable (y)is number of record sales

so 14.5 is not 14 records sales but 1450 record sales

The dependant variable (y)is usually the second row/colum of the table

so 14.5 is not 14 records sales but 1450 record sales

With an equation

x = yeary = record sales (hundreds)

Use an equation to model the relationship between 'x' and 'y' in the table.Then if you have a new x-value, you can use the equation to find the corresponding y-value. In this case, substitute 'x' with 2019 to find the number of record sales (hundreds) in that year.

Task question #3

y = 1.85x + 3696.6

y = 1.85x +3725.6

y = 1.85x - 3696.6

The table shows you how record sales (y) changed over the year (x).Visualize the relationship by graphing the table of values (or analyze the pattern)Then represent the relationship with an equation.

xy

If you have a table of values but not sure what to do with it.... draw it on a cartesian plane!

https://youtu.be/p-YYXCDEcLQ

The equation isy = 1.85x - 3696.6

ps.When x is year,the b-value (y-intercept) could be really very big negative (or positive) value.(ex. -3696.6)

sample solution

(you could use a different set of values but you should get the same equation)

Use the equation to answer the question:How many more records were sold in 2019, compared to 2018.

1.85 more record sales

185 more record sales

3855 more record sales

Task question #3

To find out how many MORE record sales in 2019, compared to 2018. 1. You will need to calculate the # of record sales in 2019 (by replacing "x" as 2019 in the equation and find the corresponding y-value) 2. You will also need to calculate the # of record sales in 2018 (by replacing "x" as 2018 in the equation and find the corresponding y-value) 3. Then subtract the two y-values to find out how many MORE records were sold.

1.85 hundreds of recordsor185 records!

185 more records were sold!

sample solution(There are more than one way to get this answer)

Task Question #3

Answer:185 more records were sold.

Read the question carefully!

Table is important!So is the unit between the brackets.

Always check to see if you answer the question. Don't stop with just the calculation.

Task Question #4

just A hint

ready to enter my answer

some help

Charles started eating healthy & exercising regularly for almost 2 years! He is very proud of what he has achieved! This table chronicles Charles' weight throughout the years. If the trend continues, determine Charles' weight in July 2014

Meaning we can use the equation to extrapolate what would happen after October 2013

The main question. The weight in July 2014

You know you need to find the equation representing time (x) and weight (y). But you cannot enter "June" in your calculator. Nor can you simply enter "6" for both June 2012 and 2013. So you need to do something about that... perhaps change time to number of months after June 2012.

1. Determine the equation representing Charles' weight (y) as a function of number of months after June 2012 (x)2. Then use the equation to determine Charle's weight (y) in July 2014 (x)

89 kg

I am completely lost... Put me back to the question please

79 kg

Task question #4

1. Draw the graph if needed 2. Use the two sets of coordinates on the line to determine the equation of the line. 3. Use the equation to determine Charles' weight in July 2014. July 2014 is _________ months after June 2012.

Return

Task question #4

OH NO~~Not quite correct!

Equation will come from the pattern in the table. So focus on the table.What are the independent (x) and dependent (y) variables?

Weight - Time in onth/year

Time in month/year - Weight

Month - year

Task question #4

The independent variable is time in month/yearThe dependent varaible is weight.

x y

x y

The independent variable is time in month/yearThe dependent varaible is weight.

But how can we enter "June 2012" into a calculator? "6" ? How about June 2013? "6" too?

Need to modify the month-year

I don't know

Enter any June as '6', August as '8', etc.

Task question #4

Yes, modification is needed.Ex. number of months after June 2012

Cannot simply enter "6" for both June 2012 & 2013. We need to have a different number for different month-year!

We can modify the month-year,as number of months after June 2012

Modified month-year

So you have an unique value for each month-year.This is your new independent variable (x)*have another idea? Check it with your teacher.

0

2

4

6

8

10

12

14

16

June 2012 --> 0 (beginning)

August 2012 --> 2 months after June 2012

October 2012 --> 4 months after June 2012

December 2012 --> 6 months after June 2012

February 2013 -> 8 months after June 2012

April 2013 --> 10 months after June 2012

June 2013 --> 12 months after June 2012

August 2013 -> 14 months after June 2012

October 2013 --> 16 months after June 2012

1. Determine the equation representing Charles' weight (y) as a function of number of months after June 2012 (x)2. Then use the equation to determine Charle's weight (y) in July 2014 (x)

89 kg

I am completely lost...

79 kg

Task question #4

1. Draw the graph if needed 2. Use the two sets of coordinates on the line to determine the equation of the line. 3. Use the equation to determine Charles' weight in July 2014. July 2014 is _________ months after June 2012.

79kg!

sample solution

Sample solution

Task Question #4

Answer:Charles would weight 79.06 kg in July 2014.

Be prepare to modify a table of values a little bit.

When in doubt, GRRAPH IT!*you'll get some partial mark.

Even if you are not sure how to answer the question, get the equation! *you'll get some partial mark!

CONGRATS!

Try again