MA.07

STANDARDS

8.EE.B.5 Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed.

8.EE.C.8 Analyze and solve pairs of simultaneous linear equations.

1. Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously.
2. Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection. For example, 3x + 2y = 5 and 3x + 2y = 6 have no solution because 3x + 2y cannot simultaneously be 5 and 6.
3. Solve real-world and mathematical problems leading to two linear equations in two variables. For 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.

Standards for Mathematical Practice: 

SMP 1 Students will make sense of problems and persevere in solving them by researching prices, writing equations and solving a system of equations to make a decision.

SMP 2 Students will reason abstractly and quantitatively to determine which wholesale provider has a better deal for water bottles.

SMP 3 Students will construct a viable argument to propose which wholesale provider their business partner should use and critique the reasoning of others when working with a partner.

SMP 4 Students will model with mathematics by creating equations and a graph to represent the costs of water bottles and memberships for each store.

SMP 7 Students will look for and make use of structure by reading the graph they create to interpret the results.

Standards courtesy of Common Core State Standards © Copyright 2010. National Governors Association Center for Best Practices and Council of Chief
State School Officers. All rights reserved. 

REQUIRED KNOWLEDGE AND EXTENSIONS

PRIOR KNOWLEDGE

In math six and seven, students have worked extensively with the ratios and rates. Earlier in math 8 module 4, students engaged with constant rates and applied them in linear equations.

PLACEMENT

BEFORE

This Cornerstone will fall after lesson 29 in module 4. Prior to this Cornerstone, students have engaged in six lessons in module 4 focused on systems of equations. Students have:

• Compared the graphs that comprise a system of linear equations in the context of constant rates. (Lesson 24)
• Identified and verified the solution of a system of equations by finding the point of intersection. (Lesson 25)
• Determined when a system of linear equations has no solution. (Lesson 26)
• Determined when a system of linear equations has infinitely many solutions and solved systems using substitution. (Lesson 27)
• Solved systems of linear equations using elimination. (Lesson 28)
• Wrote and solved systems of linear equations from word problems. (Lesson 29)

DURING

During the Cornerstone, students will apply their understanding of writing linear equations and solving systems of equations. Students will write and solve a system of linear equations to compare the membership costs and water bottles prices at wholesale stores. They will solve the system to make a decision of where to buy water from.

AFTER

After the Cornerstone, students will use systems of equations to convert between Celsius and Fahrenheit (Lesson 30). To make space for the Cornerstone, finding Pythagorean triples (Optional Lesson 31) will be skipped. To finish module 4, students will complete only questions 1, 2, 3, 4 and 6 in the end-of-module assessment.

In module 5 and 6 students will continue to explore linear functions to represent real world situations. Teachers are encouraged to refer back to this cornerstone to draw on student prior experience when engaging with linear functions.

PLANNING

PLANNING

The suggestions for multiple means of engagement, representation, and expression are meant to make the lessons accessible to all learners. All suggestions are embedded into the natural flow of the lessons and are italicized for emphasis. Some of the suggestions come directly from the Eureka Math lessons and are noted as such. Teachers may add alternative ways to make the lessons more accessible based on student need.

INSTRUCTIONAL APPROACH

This Cornerstone utilizes the 5E Instructional Model.

BACKGROUND INFORMATION

The key concepts of this Cornerstone is to ensure that students have the ability to help keep their families safe.  Students should understand how to identify and community helpers and responsible adults in case of an emergency.  Students will practice locomotor and non-locomotor as well as move in various pathway and direction avoiding obstacles. This Cornerstone will promote in-depth discussions that will encourage students to be more aware of their surroundings and begin brainstorming about evacuation routes and ways to stay safe. These discussions may lead to lesson extensions and collaboration with other teachers within your organization.