Working-out Simultaneous Linear Equations
For the identified standard address each of the following prompts.
Analyze and solve pairs of simultaneous linear equations.
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. (8.EE.8)
Working-out Simultaneous Linear Equations
Student-Friendly Format
How might you display the standard for your students?
The student will: demonstrate an understanding of how to solve linear equations in two variables algebraically and estimate their solutions by graphing the equations and solve simple cases by inspection.
Appropriate Parts
Knowledge and Skill Objectives
How you might explain the standard, and its parts, to a colleague?
Remember to identify each objective as either a knowledge objective or a skill objective, and to present the objectives in the appropriate teaching sequence if the sequence is of consequence. You must justify your sequence decision.
Analyze graph systems of linear equations whose solutions do not have integer coordinates. (Knowledge)
Use elimination and substitution to solve systems of linear equations. (Skill)
Demonstrate understanding that a system can have a unique solution, no solution, or infinitely. (Skill)
Solve problems in real-world contexts, including converting temperatures from Celsius to Fahrenheit. (Skill)
Working-out Simultaneous Linear Equations
Sequence Justification
This sequence begins with simple concept knowledge of analyzing graphs of linear equations whose solutions do not have integer coordinates. They will begin looking at these graphs to analyze what these graphs look like for a linear system. After understanding these estimations, they will begin solving systems of linear equations using substitution and elimination. They will use their estimations of the solution from a graph to verify their algebraic solution is correct. Once they demonstrate an understanding that a system can have a unique solution, no solution, or infinitely many solutions they will begin solving problems in real-world context by doing things like converting temperature from Celsius to Fahrenheit.
Prerequisite Knowledge and Skills
How might you explain prerequisite objectives to a colleague?
Remember to identify each prerequisite objective as either a knowledge objective or a skill objective.
Explain the concepts to solving multistep equations. (Knowledge)
Demonstrate how to solve multistep equations. (Skill)
Analyzing the shape of the graph of a linear equation. (Knowledge)
Use the method of elimination to solve a system of equations (Skill)
Predict that the graph of a linear equation is a line and select points on and off the line to verify their claim. (Skill)
Use APA referencing style.