The Architectural Consultant Task

Instructions for Teacher:

There are 2 tasks. The task with the asterisk * is scaffolded for ELLs and Special Education students.

Place students in groups of 2-3 at your discretion, though it is recommended to put ELLs and Special

Education students together, so they can work on the same modified task.

For problems where they are asked to graph, provide them with STAAR EOC Algebra 1 graph paper.

Try not to give the task as a packet to the students. When making copies, it is recommended to copy

each part separately. (Part I together, then Part II, then Part III, the extension)

This task might take struggling learners anywhere from 1-2 class blocked periods and is meant to be an

application of Algebra 1 concepts with a focus on linear functions (and some Math Models topics that

they have covered in CRM 1 such as using different representations to analyze data, such as bar graphs).

For suggested answers, you might want to look at the scaffolds given on The Architectural Consultant

Task*.

Name: ____________________________________ Date: ______________ Period: _____________

The Architectural Consultant Task (Part I)

You have been chosen to work as an architectural consultant to help

design the new elementary and middle schools for Austin ISD. As is

typical with any consulting firm, jobs are billed at an hourly rate to the

client. During the last two months, you have worked on three projects

(Unnamed School 1, Unnamed School 2, and Unnamed School 3). Part

of your responsibility as a consultant is name each of the schools. Your

billable rate is $175.00 per hour.

Answer the following questions in groups of 2-3. For each question,

you must explain your reasoning in complete sentences. You may

make use of the different multiple representations that you have

learned to help you with each question.

PART I:

1. How much would you make on project #1 (Unnamed School 1) if you worked 35 hours? Unnamed School #2 for

27 hours? Unnamed School #3 for 48 hours? Create a table and bar graph (using the STAAR graph paper) that

display the data for each project. Make sure to choose an appropriate scale for the graph.

2. You want to buy a new car that is worth $38,000 and want to pay it in cash. Have you made enough money

from the three projects? Write a sentence describing how you found this answer.

3. On which project did you make the most money? How much more?

4. What were your average earnings per project? How did you find this amount?

Use the STAAR Algebra 1 graph paper to create and use a bar graph to answer the following questions. Answer in

complete sentences. Remember to start by re-phrasing the question.

5. What information, in the context of the situation, can be seen immediately by looking at the graph? (Hint: Look

at the axes of your graph.)

6. Can you use the graph to find out how much you made if you worked a total of 15 hours? Why or why not?

7. What information do bar graphs in general illustrate well?

8. What information from the situation does your particular bar graph not display?

The Architectural Consultant Task (Part II)

1. Complete this table. Use the same hourly rate of $175.00 as above.

Time Worked (hours) Earnings (dollars)

1

2

3

4

5

6

10

15

20

2. Display the data in problem #9 in a scatterplot. Label each axis clearly. Describe the relationship between Time

Worked (hours) and Earnings (dollars) in a complete sentence.

3. How much would you earn if you worked:

a. 4 hours?

b. 12 hours?

c. 17 ½ hours?

d. 20 hours 15 minutes?

e. 8 hours 20 minutes?

4. Use your calculator to find the algebraic expression for finding your total earnings (T) if you worked for H hours.

Interpret the slope and y-intercept in the context of the situation.

The Architectural Consultant Task (Part III)

Extension:

Instead of charging your current hourly rate of $175.00, your firm is considering

charging $15 less per hour, along with a one-time $75 consultant fee. Is that a smart

business decision? Why or why not? Is there a point in the graph where it does not

matter which option you choose? What is that point? What does it mean?

Find the algebraic rule for the new situation and interpret the slope and y-intercept in complete sentences.

Name: ____________________________________ Date: ______________ Period: _____________

The Architectural Consultant Task * (Part I)

You have been chosen to work as an architectural consultant to help

design the new elementary and middle schools for Austin ISD. As is

typical with any consulting firm, jobs are billed at an hourly rate to the

client. During the last two months, you have worked on three projects

(Unnamed School 1, Unnamed School 2, and Unnamed School 3). Part

of your responsibility as a consultant is name each of the schools. Your

billable rate is $175.00 per hour.

Answer the following questions in groups of 2-3. For each, you must

explain your reasoning in complete sentences.

1. How much would you make on project #1 (Unnamed School 1) if you worked 35 hours?

I can expect to make __________ on project ______ if I worked ________ hours because

___________________________________________________________________________________________.

2. How much did you make on project #2 (Unnamed School 2) if you worked 27 hours?

I can expect to make __________ on project ______ if I worked ________ hours because

___________________________________________________________________________________________.

3. How much would you make on project #3 (Unnamed School 3) if you worked 48 hours?

I can expect to make __________ on project ______ if I worked ________ hours because

___________________________________________________________________________________________.

4. You want to buy a new car that is worth $38,000 and want to pay it in cash. Have you made enough money

from the three projects? Write a sentence describing how you found this answer.

5. One way to keep track of how much money you have made on each project is to use a table. Fill in this table

showing the hours worked, and your earnings for each project.

Project Time Worked (hours) Earnings (dollars)

Unnamed School 1

Unnamed School 2

Unnamed School 3

6. Explain how you found the total earnings for each project to fill in the third column of the table.

7. On which project did you make:

a. The most money? I made the most money from project _____________ because

____________________________________________________________________________________.

b. The least money? I made the least money from project _____________ because

____________________________________________________________________________________.

8. How much more did you make on the third project than on the first project?

I made __________________ more money on project ___________ than on project _________.

9. What are your total earnings for all three projects?

I made ______________ in earnings for all three projects.

10. What were your average earnings per project? How did you find this amount?

On average, I made __________________ in earnings per project. I found this amount by

___________________________________________________________________________________________.

11. Use the information from your table to construct a bar graph on a blank grid. Clearly label the graph so that

anyone looking at it will understand the information it displays.

Title: ________________________________________________

Bar graphs display categorical data. We have three different categories displayed on the table. They are

______________________________, ____________________________, and ___________________________. The

categories go on the x-axis. The earnings will go on the y-axis. They are ________________________,

___________________, and __________________.

What scale will you use for the y-axis? Explain your reasoning.

____

____

___

___

___

___

____

____

(

)

____________________________ ( )

Use your bar graph to answer the following questions. Answer in complete sentences. Remember to start by re-

phrasing the question.

12. What information, in the context of the situation, can be seen immediately by looking at the graph? (Hint:

Look at the axes of your graph.)

The bar graph clearly displays ___________________________________ on the horizontal, or ______-axis. The

graph also displays ______________________________________ on the vertical, or _______-axis. Each bar

represents _____________________________________________________________________________.

13. Can you use the graph to find out how much you made if you worked a total of 15 hours? Why or why not?

I _________ use the graph to find out how much money I made if I worked a total of 15 hours, because

__________________________________________________________________________________________.

14. What information do bar graphs in general illustrate well?

In general, bar graphs illustrate _________________________________________________________________

___________________________________________________________________________________________.

15. What information from the situation does your particular bar graph not display?

Our group’s bar graph does not show ____________________________________________________________

___________________________________________________________________________________________

from the situation.

The Architectural Consultant Task * (Part II)

1. Complete this table. Use the same hourly rate of $175.00 as above.

Time Worked (hours) Earnings (dollars)

1

2

3

4

5

6

10

15

20

What is the independent variable? What is the dependent variable?

The independent variable is ____________________________ because _______________________________.

The independent variable is graphed on the _______-axis. The dependent variable is

______________________________ because _________________________________. The

_______________________ variable is graphed on the y-axis.

1. Display the data in problem in #16 in a scatterplot. Label each axis clearly. Describe the relationship between

Time Worked and Earnings in a complete sentence.

___

___

___

___

___

____

___

____

__ (

)

____________________________ ( )

Use the graph to determine the answer for the following questions. Answer in complete sentences.

2. How much would you earn if you worked:

a. 4 hours? I would earn _______________ if I worked ____________ hours because

__________________________________________________________________________________.

b. 12 hours? I would earn _______________ if I worked ____________ hours because

__________________________________________________________________________________.

c. 17.5 hours? I would earn _______________ if I worked ____________ hours because

__________________________________________________________________________________.

d. 20 hours 15 minutes? I would earn _______________ if I worked ____________ hours because

__________________________________________________________________________________.

3. Use your calculator to find the algebraic expression for finding your total earnings (T) if you worked for H

hours. Use the bank below to fill in the blanks.

a) The slope is ________________________. For every _______________________ worked, earnings

___________________ by _____________________ dollars.

b) The y-intercept is ___________________. At _____________ hours, earnings amount to ___________.

WORD BANK

0 increases positive hour(s)

125.50 decreases negative earning(s)

The Architectural Consultant Task * (Part III)

Extension:

Instead of charging your current hourly rate of $175.00, your firm is considering charging

$15 less per hour, along with a one-time $75 consultant fee. Is that a smart business

decision? Why or why not? You may use the table and graph below to show your work.

Time

Worked

(hours)

Earnings (dollars)

Without the

Consultant Fee

Earnings (dollars)

With the

Consultant Fee

1

2

3

4

5

6

10

15

20

1. Is there a point in the graph where it does not matter which option you choose? What is that point? What does it mean?

2. Find the algebraic rule for the new situation and interpret the slope and y-intercept.

Algebraic rule: _________________________________

Slope: ________________________________ Meaning: ____________________________________________

Y-Intercept: ____________________________Meaning: ____________________________________________

3. Which option is the better business decision? When is it the better decision? Write in complete sentences.