REI.B.3 & 4: Quadratic Formula, Completing the Square, and Factoring. Oh my!

wizard of oz

Just like Dorothy, the Tin Man, and the Scarecrow were scared of lions, and tigers, and bears in the Wizard of Oz, 10th grade students will most likely be scared of solving quadratic equations by completing the square, the quadratic formula, and factoring. However, through proper instruction, enough practice, and effective formative assessments, solving linear equations and inequalities and quadratic equations will be nothing to worry about.

x equals 2

This learning progression would be taught in a beginning 10th grade algebra classroom. The Common Core State Standards that will be addressed are HSA.REI.B.3, HSA.REI.B.4.A, and HSA.REI.B.4.B. Additionally, MP.4, MP.6, and MP.7 are the mathematical practice standards that align with this learning progression.

Since this is such a dense Common Core cluster, there will be four lessons that make up this learning progression. Students have previously learned what equations and expressions are and how they are different, how to categorize polynomials, steps to solving simple linear equations, and how to graph linear equations. The progression will begin by teaching the students how to solve more advanced linear equations and inequalities. This lesson may take a couple of days depending on how advanced the students are. The students will learn how to graph inequalities and how to attend to precision in writing their answers and labeling their graphs. For the second lesson, students will learn what completing the square means and how it is useful in finding roots of quadratic equations. Each time they complete the square, they will be required to draw a picture to show how they came up with the number that they are adding to both sides. An example of a problem on their worksheet, which is used as their formative assessment for this lesson, is provided below. Once students understand how to complete the square, they will move on to the third lesson and will learn what the quadratic formula is, how it is used, and how it can be derived from completing the square. Finally, the fourth lesson entails teaching students how to factor a quadratic equation when the leading coefficient is 1. By using frequent formative assessment techniques such as worksheets, class activities, and exit slips, the students and the teacher will both be able to track the students’ progress towards the learning targets.

completing the square

 

 

The equations will be written on the board and the students will copy them from the board onto their equation box. They will then complete the picture and solution. They will have 4 pages scaffolded like the worksheet shown on the left. Picture taken from http://mathequalslove.blogspot.com.au/2015/05/algebra-2-solving-quadratics-inb-pages.html

 

 

 

 

Learning Progression: Learning Progression

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