ALEX Learning Activity

Graphville Shopping Excursion

A Learning Activity is a strategy a teacher chooses to actively engage students in learning a concept or skill using a digital tool/resource.

  This learning activity provided by:  
Author: DeLaura Downs
System:Jefferson County
School:Jefferson County Board Of Education
  General Activity Information  
Activity ID: 2311
Title:
Graphville Shopping Excursion
Digital Tool/Resource:
Graphville Shopping Excursion Rubric, Activity, and Questions
Web Address – URL:
Overview:

Students will create a map of a shopping excursion by solving systems of linear equations through graphing, substitution, or elimination. Students will then be able to determine the distance traveled through the mall using Pythagorean Theorem. Students will utilize previous grade level standards as a spiral review such as plotting coordinate pairs and using those pairs to find the distance between two points.

This activity is a result of the ALEX Resource Development Summit.
  Associated Standards and Objectives  
Content Standard(s):
Mathematics
MA2015 (2016)
Grade: 8
13 ) Interpret the equation y = mx + b as defining a linear function whose graph is a straight line; give examples of functions that are not linear. [8-F3]

Example: The function A = s2 giving the area of a square as a function of its side length is not linear because its graph contains the points (1,1), (2,4), and (3,9), which are not on a straight line.

Alabama Alternate Achievement Standards
AAS Standard:
M.AAS.8.13- Given a set of graphs, identify which graph is linear.
Mathematics
MA2019 (2019)
Grade: 6
11. Find the position of pairs of integers and other rational numbers on the coordinate plane.

a. Identify quadrant locations of ordered pairs on the coordinate plane based on the signs of the x and y coordinates.

b. Identify (a,b) and (a,-b) as reflections across the x-axis.

c. Identify (a,b) and (-a,b) as reflections across the y-axis.

d. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane, including finding distances between points with the same first or second coordinate.
Alabama Alternate Achievement Standards
AAS Standard:
M.AAS.6.11 Graph or identify ordered pairs in the first quadrant of the coordinate plane between 0 and 5, limited to whole numbers.
Mathematics
MA2019 (2019)
Grade: 7
Accelerated
6. Interpret y = mx + b as defining a linear equation whose graph is a line with m as the slope and b as the y-intercept.

a. Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in a coordinate plane.

b. Given two distinct points in a coordinate plane, find the slope of the line containing the two points and explain why it will be the same for any two distinct points on the line.

c. Graph linear relationships, interpreting the slope as the rate of change of the graph and the y-intercept as the initial value.

d. Given that the slopes for two different sets of points are equal, demonstrate that the linear equations that include those two sets of points may have different y-intercepts. [Grade 8, 9]
Mathematics
MA2019 (2019)
Grade: 8
9. Interpret y = mx + b as defining a linear equation whose graph is a line with m as the slope and b as the y-intercept.

a. Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in a coordinate plane.

b. Given two distinct points in a coordinate plane, find the slope of the line containing the two points and explain why it will be the same for any two distinct points on the line.

c. Graph linear relationships, interpreting the slope as the rate of change of the graph and the y-intercept as the initial value.

d. Given that the slopes for two different sets of points are equal, demonstrate that the linear equations that include those two sets of points may have different y-intercepts.
Mathematics
MA2019 (2019)
Grade: 8
12. Solve systems of two linear equations in two variables by graphing and substitution.

a. Explain that the solution(s) of systems of two linear equations in two variables corresponds to points of intersection on their graphs because points of intersection satisfy both equations simultaneously.

b. Interpret and justify the results of systems of two linear equations in two variables (one solution, no solution, or infinitely many solutions) when applied to real-world and mathematical problems.
Alabama Alternate Achievement Standards
AAS Standard:
M.AAS.8.12 Solve two-step linear equations where coefficients are less than 10 and answers are integers.
Mathematics
MA2019 (2019)
Grade: 8
27. Apply the Pythagorean Theorem to find the distance between two points in a coordinate plane.
Alabama Alternate Achievement Standards
AAS Standard:
M.AAS.8.27 Use the pythagorean theorem to find the hypotenuse when given the measures of two legs in a real-world context. Limit to Pythagorean triples.
Learning Objectives:

I can solve systems of linear equations by graphing, elimination, or substitution.

I can plot points on the coordinate plane.

I can graph a linear equation in y=mx+b form.

I can apply the Pythagorean Theorem to find the distance between two points.
  Strategies, Preparations and Variations  
Phase:
During/Explore/Explain
Activity:

Students will be given a copy of the story and will create a map using the information from the story. The students will solve systems of linear equations by graphing, elimination, or substitution to create the map. This is a great project that can be used in class over the course of several days in order to allow students the opportunity to grapple with real-world mathematics. The directions for completing the activity are detailed in the Google Doc. Teachers can provide a copy of the activity to each student via Google Classroom or by providing a hard copy to each student. Students will be allowed to work in small groups, but will each create their own maps. 
Assessment Strategies:

Attached rubric is part of learning activity and activity can be used as a summative assessment or a learning activity.

This can be done in the classroom or can be assigned as an independent project to be done at home.
Advanced Preparation:

Each student will need their own copy of Graphville Shopping Excursion.

Graph paper will be needed for a rough draft and final copies of the product.

Colored pencils, markers, etc. are optional and up to student/teacher discretion.
Variation Tips (optional):

The story could be altered to give students ordered pairs to graph rather than solving the systems of equations.

The story could be altered so all equations are given in slope-intercept form rather than the standard form.
Notes or Recommendations (optional):

This could very easily be used as a summative assessment rather than a learning activity. I allow students to work together on this activity, either in pairs or small groups.
  Keywords and Search Tags  
Keywords and Search Tags: coordinate pairs, graphing, graphing systems of equations, linear systems, simultaneous pairs of equations, system of equations