# 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.

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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: https://docs.google.com/document/d/10Z9frtv8ECDVjdIqAsyMVOrSK0BOfxHYmsLiVMHnlqA/edit?usp=sharing 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: 6 11 ) Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. [6-NS8] NAEP Framework NAEP Statement:: 8A2d: Solve problems involving coordinate pairs on the rectangular coordinate system. NAEP Statement:: 8NPO1d: Write or rename rational numbers. NAEP Statement:: 8NPO1e: Recognize, translate or apply multiple representations of rational numbers (fractions, decimals, and percents) in meaningful contexts. NAEP Statement:: 8NPO1h: Order or compare rational numbers (fractions, decimals, percents, or integers) using various models and representations (e.g., number line). Alabama Alternate Achievement Standards AAS Standard: M.AAS.6.11 - Graph or identify points in all four quadrants of the coordinate plane, given a coordinate plane on graph paper between -10 and 10. Mathematics MA2015 (2016) Grade: 8 8 ) Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b. [8-EE6] NAEP Framework NAEP Statement:: 8A4d: Interpret relationships between symbolic linear expressions and graphs of lines by identifying and computing slope and intercepts (e.g., know in y = ax + b, that a is the rate of change and b is the vertical intercept of the graph). NAEP Statement:: 8A5a: Make, validate, and justify conclusions and generalizations about linear relationships. Alabama Alternate Achievement Standards AAS Standard: M.AAS.8.8- Identify the slope of a line using the rise and run from the associated triangle on the coordinate plane to determine the slopes of the line. Mathematics MA2015 (2016) Grade: 8 10 ) Analyze and solve pairs of simultaneous linear equations. [8-EE8] a. Understand that solutions to a system of two linear equations in two variables correspond to points of intersections of their graphs because points of intersection satisfy both equations simultaneously. [8-EE8a] b. Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection. [8-EE8b] Example: 3x + 2y = 5 and 3x + 2y = 6 have no solution because 3x + 2y cannot simultaneously be 5 and 6. c. Solve real-world and mathematical problems leading to two linear equations in two variables. [8-EE8c] Example: Given coordinates for two pairs of points, determine whether the line through the first pair of points intersects the line through the second pair. NAEP Framework NAEP Statement:: 8A4a: Solve linear equations or inequalities (e.g., ax + b = c or ax + b = cx + d or ax + b > c). NAEP Statement:: 8A4c: Analyze situations or solve problems using linear equations and inequalities with rational coefficients symbolically or graphically (e.g., ax + b = c or ax + b = cx + d). Alabama Alternate Achievement Standards AAS Standard: M.AAS.8.10 - Identify the labeled point of intersection on graphs of two linear equations as a solution for both equations. 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. NAEP Framework NAEP Statement:: 8A1f: Interpret the meaning of slope or intercepts in linear functions. NAEP Statement:: 8A2b: Analyze or interpret linear relationships expressed in symbols, graphs, tables, diagrams, or written descriptions. Alabama Alternate Achievement Standards AAS Standard: M.AAS.8.13- Given a set of graphs, identify which graph is linear. Mathematics MA2015 (2016) Grade: 8 23 ) Apply the Pythagorean Theorem to find the distance between two points in a coordinate system. [8-G8] NAEP Framework NAEP Statement:: 8G1a: Draw or describe a path of shortest length between points to solve problems in context. NAEP Statement:: 8G3d: Use the Pythagorean theorem to solve problems.
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