Unit 7: Expressions and Equations: Systems
Duration of Days: 20
Students will understand the core logic and properties of simultaneous linear equations.
Solutions as Intersections:
That solutions to a system of two linear equations correspond to points of intersection because those points satisfy both equations simultaneously.
Classification of Solutions:
How to recognize if a system has one solution, no solution (parallel lines), or infinitely many solutions (the same line).
Students will apply multiple strategies to solve and model linear systems:
Solve Algebraically:
Use substitution and elimination methods to find exact solutions.
Estimate by Graphing:
Graph pairs of equations to estimate solutions and identify the point of intersection.
Solve by Inspection:
Recognize simple cases by inspection (e.g., equations with the same slope but different intercepts have no solution).
Model Real-World Problems:
Translate mathematical and real-world scenarios into two linear equations with two variables.
Assessment of student mastery will include:
| Lesson # | Lesson Title | Duration of Days |
|---|---|---|
| 1 | System Investigation | 2 |
| 2 | Solving by Graphing | 3 |
| 3 | Solving by Substitution | 4 |
| 4 | Solving by Elimination | 4 |
| 5 | Solving by Examination/Inspection | 3 |
| 6 | Word Problems | 2 |
| 7 | Review and Assessment | 2 |