Formative Assessment: Systems of Equations and Inequalities

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Objective

SWBAT demonstrate knowledge of systems of equations and inequalities.

Big Idea

A quick assessment will give you and your students feedback about the second half of the unit.

Lesson Author

Tim Marley

Troy, MI

Grade Level

Eleventh grade

Twelfth grade

Subjects

Math

Precalculus and Calculus

Systems of Equations and Inequalities

Algebra

Standards

HSA-APR.D.7

(+) Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide rational expressions.

HSA-CED.A.3

Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. For example, represent inequalities describing nutritional and cost constraints on combinations of different foods.

HSA-REI.C.6

Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.

HSA-REI.C.9

(+) Find the inverse of a matrix if it exists and use it to solve systems of linear equations (using technology for matrices of dimension 3 × 3 or greater).

MP1

Make sense of problems and persevere in solving them.

MP4

Model with mathematics.

MP5

Use appropriate tools strategically.

Quiz

30 minutes

We will start class by taking a short quiz that covers the topics in the second half of the unit - mainly systems of equations and inequalities. This is a formative assessment over solving systems with matrices, linear programming, and partial fraction decomposition so you can see how students do with these topics. If there are certain areas where they still need a little fine tuning- I will address it tomorrow during the review day. I provide a little bit more information about the quiz in the video below.

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Exam Review

20 minutes

After students finish the quiz, I give them this review for the upcoming unit exam. Like the exam, I tried to make a mix of skill based problems (solving a system using matrices) and more conceptual problems (writing a system of inequalities for a linear programming problem).

Question #5 is truly a culmination of all of the work we have done in this unit. Students are presented with four systems and are asked to solve each using any method they wish. Some systems will be best suited to matrices. Others will be much easier to graph and find intersection points. For one it may be easiest just to use substitution and solve algebraically. I really like a question like this because it tells me if students can use tools strategically (MP5) and choose the best method for solving. A student who has a deep understanding of the mathematics is usually very proficient in choosing an appropriate tool.

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