Download - SB IGC – 201 -201 ALGEBRA I · EOC Project: Create Your Own City Map As a city planner, you have been asked to create a street-map and master plan for a new sub-division that is

Adapted from © Houston ISD Curriculum 2014– 2015

Page 1 of 3

SB 463 IGC – 2017-2018 ALGEBRA I Adapted from Houston ISD Curriculum

EOC Project: Create Your Own City Map

As a city planner, you have been asked to create a street-map and master plan for a new sub-division that is being developed. Your final product must be represented on a coordinate plane and include all of the guidelines and requirements listed below.

Project guidelines:

• All streets must be labeled with the name of the road. Buildings and landmarks must be labeled.

• Lines cannot be horizontal or vertical unless otherwise denoted.

• Each of the following community requirements must be represented by a different equation.

For instance, you may not use the same equation to satisfy two different requirements.

• The map should be easy to read and colorful – be creative!

Community Requirements:

1. Locate and plot the City Central Square at the origin.

2. Draw a street that models the parent linear function and place your house at point (3,3).

3. Create one street modeled by a line with a positive slope passing through the points (-8,0) and(0,6). Write the correct equation for the line in function notation. Indicate the Domain and Range inset notation for the street.

4. Create one street modeled by a line with a negative slope passing through the points (0,-2), and(-7,0). Write the correct equation for the line in standard notation. Create a billboard that shows thetable that corresponds to this linear equation (contains at least 4 points).

5. Create one street modeled by a line with a slope of 0 and has a y-intercept of -12 and a Domain of(- ∞,10]. Write the correct equation for the line. Indicate the range for the street.

6. Create one street modeled by a line with an undefined slope that intersects your house andhas a Range of [-1,6]. Write the correct equation for the line. Indicate the domain for thestreet.

7. Plot the location of the following public service buildings: Police station located at (-8,8), Fire stationlocated at (-10,2), and the Hospital located at (-2,11). Calculate the slope between the Police Stationand Hospital using only the slope formula.

8. Create a street that is parallel to the line from #4 that has a y-intercept of -6. Write the equation forthe new street in slope-intercept form.

9. Create a u-turn street in your city modeled by a quadratic equation with the following conditions: avertex at (3,6), a y-intercept of 10.5 and an “a” value of !

!. Write the function that models this u-turn in

vertex form and find the Line of Symmetry.

10. Create a park in your city by shading the region bounded by the equations from #2, #3, #4 and #8.Using the equations for those lines, correctly determine the inequalities that define the shaded region.

11. Create a hike and bike trail that models the following quadratic function: y = −2𝑥! -16x -23 with aDomain of [-7, -1]. Place restroom facilities and a water fountain at the roots of the trail’s function. Placea bench at the vertex of the trail’s function.

12. Plot points to represent ten different businesses with a negative correlation in Quadrant IV.

13. Use substitution to find the intersection of the lines from #2 and #4.


Page 2 of 3

14. Find the Exponential equation that passes through the following points: (-1, !!), (0,1), (1,2), (2,4), (3,5).

Indicate the Domain and Range in set notation for the street.

15. The population of your city in 1990 was 400,000 and is growing at a rateof 5% per year. Answer the questions on your city key using this information.


Page 3 of 3

Student Guided Practice/Supplemental Aid

Vocabulary (Define and give example/picture)

1. Domain:2. Range:3. Vertex:4. Origin:5. Correlations:6. Function Notation:7. Parallel Lines:8. Root:9. Slope:10. Y – Intercept:11. Intersection:12. X-Intercept:13. Zero:14. Coordinate:15. Axis of Symmetry:16. Exponential Function:

Examples

A. Write a linear equation that crosses the points (0,0) and (15,15) B. Create a table using the following equation y = -3x + 8 C. Find the equation that is parallel to y = 12x - 2 and crosses the point (6,2) D. Graph the following inequalities y ≥ 17x + 3 and y < -6x -2 E. Find the solution to the systems y = 4x – 2 and y = -.5x +8 F. Graph, find the roots, vertex and the line of symmetry of y = -.25x2 – x + 8

Please make sure that you show all your work and get these problems checked before you move on to the project


Page 4 of 3

City Key

Use the following template to record the required information for your city map.

1 Write the coordinates for City Central Square:

2 Write the name of the street in which your house is located on:

Write the linear parent equation where your house is on:

3 Write the name of the street that has a positive slope and goes through points (-8,0) and (0,6):

Write the equation for the line in function notation:

Identify the domain, in set notation, of the street:

Identify the range in set notation of the street:

Is your street parallel to this new street? (Explain)


Page 5 of 3

4 Write the name of the street that models a line with a negative slope and crosses the points (-7,0) and (0,-2):

Write the equation of the line in standard notation (show your work):

Create a billboard that shows the table that corresponds to this linear equation. Show your work by using substitution.

Explain the difference between a positive and negative slope lines (Write in complete sentences)

Which street is steeper between question 3 and question 4?

x y

5 Write the name of the street that has a slope of zero which has the

y- intercept of -12 and domain is (-∞, 10]:

Write the equation of that line:

State the range of this street in inequalities format:


Page 6 of 3

6 Write the name of the street that has an undefined slope that intersects with your house:

Write the function of that street:

What is the domain when the range is [-1,6]?

What is the difference between the domain an range on this street?

7 Find the slope between the hospital and police station (Use the slope formula only)

8 Create a street that is parallel to the street on question #4 and has the y-intercept at -6. What is the name of that street:

What is the equation of that parallel street?

Explain why these two streets are parallel by using complete sentences:


Page 7 of 3

9 What is the name of the U-turn street:

What is the equation of this street? (in vertex form)

What is the equation of the line of symmetry:

Explain the transformation from the parent quadratic function and this street:


Page 8 of 3

10 What is the name of the park:

Write the four inequalities that you used to make the park:

11 What is the name of the quadratic trail represented by y = -2x2 - 16x + 23?

What is the location of the bench? (use the axis of symmetry)

What is the location of the restrooms and water fountains? (use the quadratic formula):


Page 9 of 3

12 List all the coordinates that represent the businesses: Business 1: Business 2: Business 3: Business 4: Business 5: Business 6: Business 7: Business 8: Business 9: Business 10:

Explain why the coordinates have a negative correlation:

13 Where do the streets intersect? use substitution method to prove it)


Page 10 of 3

14 What is the exponential equation of the street? (show your work)

What is the domain of this street ? (use set notation)

What is the range of this street ? (use set notation)

15 What will the current population be?

Using your calculator, determine in what year will the population reach one million:

EOC Project: Create Your Own City Map - Rubric

Alignment Project Requirements Scoring*

Guided Notes / Supplemental Aids 4 3 2 1

• Checkpoint 1 4 3 2 1

Community Requirement 1 4 3 2 1

A.3(C) Community Requirement 2 4 3 2 1

A.2(A) Community Requirement 3 4 3 2 1

A.2(C) Community Requirement 4 4 3 2 1

A.2(A) Community Requirement 5 4 3 2 1



A.3(B), A.3(A) Community Requirement 7 4 3 2 1

A.2(B) Community Requirement 8 4 3 2 1 A.6(B), A.7(C), A.8(A) Community Requirement 9 4 3 2 1 A.2(H), A.3(H), A.C(D) Community Requirement 10 4 3 2 1

• Checkpoint 3 4 3 2 1 A.7(A), A.6(A), A.6(B) Community Requirement 11 4 3 2 1


A.3(F), A.5(C) Community Requirement 13 4 3 2 1 A.9(E), A.9(C), A.9(A), A.9(D)

Community Requirement 14 4 3 2 1 A.9(E), A.9(C), A.9(A), A.9(D)



City Map Key

• Follows guidelines 4 3 2 1

• Demonstrates accurate mathematical understanding 4 3 2 1 Professional Representation

• Demonstrates sufficient progress on project development 4 3 2 1

• Demonstrates high standards for quality and neatness 4 3 2 1

• Produces creative and innovative map 4 3 2 1

• Correlates work to the map 4 3 2 1

OVERALL SCORE ___________ (>69 is the passing standard)

*4 3 2 1

• Shows complete understanding of the required mathematical knowledge.

• The solution completely address all mathematical components presented in the task.

• Shows nearly complete understanding of required mathematical knowledge.

• The solution addresses almost all mathematical components presented in the task. There may be minor errors.

• Shows some understanding of required mathematical knowledge.

• The solution addresses some, but not all mathematical components presented in the task.

• Shows limited or no understanding of the problem, perhaps only re-copying the given data.

• The solution addresses none of the mathematical components required to solve the task.