Lesson Title: Solving Quadratic Equations
Date: _____________ Teacher(s): ____________________
Course: Common Core Algebra 1, Unit 3
Start/end times: __________________
Lesson Objective(s): What mathematical skill(s) and understanding(s) will be developed?
A.REI.4 Solve quadratic equations in one variable.
b. Solve quadratic equations by inspection (e.g., for x2 = 49), taking square roots, completing the square, the
quadratic formula and factoring, as appropriate to the initial form of the equation. [Recognize when the quadratic
formula gives complex solutions and write them as a+/-bi for real numbers a and b.]
MP1:
MP2:
MP3:
MP4:
MP5:
MP6:
MP7:
MP8:
Make sense of problems and persevere in solving them.
Reason abstractly and quantitatively.
Construct viable arguments and critique the reasoning of others.
Model with mathematics.
Use appropriate tools strategically.
Attend to precision.
Look for and make use of structure.
Look for and express regularity in repeated reasoning.
Common Core Algebra I, Unit 3
Lesson Launch Notes: Exactly how will you use the
first five minutes of the lesson?
Have students pick an algebraic method (inspection,
taking a square root, factoring, completing the square,
or quadratic formula) for solving a quadratic formula,
and then write an equation that they would solve using
this method. Students should solve the equation using
the method they chose and justify why they chose that
method. Have a few students share their equations and
methods.
(Look for evidence of MP1, MP3, and MP6.)
Lesson Closure Notes: Exactly what summary activity,
questions, and discussion will close the lesson and provide
a foreshadowing of tomorrow? List the questions.
Think-Pair-Share on the following question:
When you see a quadratic equation, what do you look for
when deciding how to approach solving it?
Foreshadowing: Is there ever a scenario where none of
the methods will work? What do you think the graph of
this would look like?
(Look for evidence of MP4.)
Lesson Tasks, Problems, and Activities (attach resource sheets): What specific activities, investigations,
problems, questions, or tasks will students be working on during the lesson?
1. Students will begin by solving a quadratic equation (in one variable) by all the algebraic methods above
(inspection/square root, factoring, completing the square, or quadratic formula). It may not be possible to use
inspection/square root, and students should explain why that method is not appropriate. The student should then
pick the best method and explain why they believe it to be the best (efficiency, minimizes mistakes, easy of
computation, etc.). Assign, or allow students to choose, one of the following equations, which vary by
complexity.
2
a. x 100  0
2
b. x  180
2
c. x  x 12  0
2
d. 4 x 12x  9  0
2

e. x  8x  1
2

f. 4 x 19x  5  0
2

g. 3x  5x  1




HCPSS Secondary Mathematics Office (v2); adapted from: Leinwand, S. (2009). Accessible mathematics: 10 instructional shifts that raise student
achievement. Portsmouth, NH: Heinemann.
Lesson Title: Solving Quadratic Equations
Course: Common Core Algebra 1, Unit 3
Date: _____________ Teacher(s): ____________________
Start/end times: __________________
2. After solving using every method, have students create a visual presentation showing work for all 5 methods.
They should include a section explaining which method they prefer and why. Options can include, but aren’t
limited to:
a. Cube (template attached)
b. Foldable
c. Mobile (with the equation at the highest point and the solutions hanging below)
d. Power Point presentation
e. Tabbed book (template attached)
f. Poster
g. Student created videos
h. Student suggested medium, with teacher approval
3. In a gallery walk, or other format, allow students to display their visual presentations. Peer critique can help
establish when further clarification, recalculation, or other modifications are needed. Students should pay
particular attention to the justification that students use for their selected method. Allow students time to adjust
their product if necessary.
4. Informally, as a class or in small groups, have students discuss the pros and cons of the different methods. Have
students create a new product to help other students choose the best method given a quadratic equation in one
variable. Each product should provide justification for the best methods by referencing key features of the
equation and how the method is used. Options can include, but aren’t limited to:
a. A flowchart, starting with any possible quadratic equation. Encourage students who finish early to add a
section dedicated to what to do when there are no real solutions.
b. A pamphlet presenting the pros and cons of each method and giving examples of equations that would
be best solved by each method
c. A poster or glog
d. A Power Point presentation. Challenge students to make it interactive with buttons and other navigation
devices that allow students to jump through the different methods.
e. A song, poem, story, etc.
f. Student suggested medium, with teacher approval
5. Allow students to present this product to the class. Discuss both the justifications and the way they were
presented. Encourage students to be critical and question their peers’ products in constructive ways.
6. Label different sections of the room (can be limited to just the chalkboard) with the different methods. With
students working independently, in pairs, or in small groups, distribute a few equations, written on large slips of
paper, to each. After some private think time, have students sort their equations, without solving them, to the
appropriate areas of the room based on what would be the best solution method. During the activity, or
afterwards, students should make suggestions and corrections in each area. When a discrepancy arises, have
students present a case for both methods and come to a conclusion based on this discussion.
7. Distribute students around the room (students can choose or be assigned) with equal numbers of students in each
area. Have students then solve the problems with the given method.
(Look for evidence of MP1, MP2, MP3, MP4, MP5, MP6, MP7, and MP8.)
Evidence of Success: What exactly do I expect students to be able to do by the end of the lesson, and how will I
measure student mastery? That is, deliberate consideration of what performances will convince you (and any outside
observer) that your students have developed a deepened (and conceptual) understanding.
Students will solve quadratic equations using multiple methods, when applicable.
Students will choose an appropriate solution method based on the specific equation.
Notes and Nuances: Vocabulary, connections, common mistakes, typical misconceptions, etc.
Vocabulary – Reinforce terms like trinomial, factor, radical
Connections – Students can refer to previous work with the algebraic methods. In the past, students have also had to
HCPSS Secondary Mathematics Office (v2); adapted from: Leinwand, S. (2009). Accessible mathematics: 10 instructional shifts that raise student
achievement. Portsmouth, NH: Heinemann.
Lesson Title: Solving Quadratic Equations
Course: Common Core Algebra 1, Unit 3
Date: _____________ Teacher(s): ____________________
Start/end times: __________________
pick and justify solution methods, particularly with systems of equations. They may find similarities within the two
selection processes.
Common mistakes/ typical misconceptions –
 Forgetting to give both the positive and negative answer when taking a square root
 Not rearranging an equation that is not equal to zero or not in standard form
 Forgetting one or more of the necessary steps in completing the square
Resources: What materials or resources are essential
for students to successfully complete the lesson tasks or
activities?
Homework: Exactly what follow-up homework tasks,
problems, and/or exercises will be assigned upon the
completion of the lesson?
Calculators – only used for computation or to check
answers. Limit to scientific calculators, if possible.
Chart paper, poster paper, markers, colored pencils,
scissors, etc.
Student computers
Choose three methods for solving quadratics. Choose two
equations from your textbook to solve using the given
method. One of the equations may be a simple example,
but the other should be more challenging.
Lesson Reflections: What questions, connected to the lesson objectives and evidence of success, will you use to
reflect on the effectiveness of this lesson?
Can students justify a method for a given equation?
Do students pick the most efficient method or default to a favorite?
Howard County Public Schools Office of Secondary Mathematics Curricular Projects has licensed this product
under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License.
HCPSS Secondary Mathematics Office (v2); adapted from: Leinwand, S. (2009). Accessible mathematics: 10 instructional shifts that raise student
achievement. Portsmouth, NH: Heinemann.