• Creator(s):

# Standards and objectives

Learning Objectives:

• Understand what a quadratic funciton is
• Solve quadratic equations by factoring
• Solve quadratic equations by completeing the square
• Graph quadratic functions in standard form and vertex form
• Solve quadratic equations by graphing and analyzing the graph of various quadratic functions
• Determine when to use each method of solving a quadratic and what the pros and cons are of each method
• Apply understanding of qudaratics and explain how to use and apply each method of solving

Common Core State Standards:

• CCSS.MATH.CONTENT.HSA.APR.B.3
Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial.
• CCSS.MATH.CONTENT.HSA.CED.A.1
Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.
• CCSS.MATH.CONTENT.HSA.REI.B.4
Solve quadratic equations in one variable.
• CCSS.MATH.CONTENT.HSA.REI.B.4.A
Use the method of completing the square to transform any quadratic equation in xinto an equation of the form (x - p)2 = q that has the same solutions. Derive the quadratic formula from this form.
• CCSS.MATH.CONTENT.HSA.REI.B.4.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.
• CCSS.MATH.CONTENT.HSF.IF.C.7.A
Graph linear and quadratic functions and show intercepts, maxima, and minima.
• CCSS.MATH.CONTENT.HSF.IF.C.8.A
Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context.

# Introduction

## Student

In this unit we will be learning how to solve quadratic equations. Before we can do so, we need to make sure that your math skills are ready for the lesson and that you understand what a quadratic function is.

Please complete the two warm-up activities below:

1. Complete this warm-up activity on IXL to review how to factor trinomials.

Throughout this unit, you will learn four different ways to solve a quadratic equation. You will learn that you cannot always use any method you like to solve a quadratic equation, sometimes you have to use one method over another. As we go through each method, please take notes on this frayer model. This will be due at the end of the unit.

## Teacher

Student Objectives:

• Students will learn what a quadratic equation is
• Students will demonstrate prior knowledge of factoring trinomials which they will need later in the lesson

This lesson is designed for a student in Algebra 1 entering the quadratics unit. With the format of hte lesson, I would imagine this taking place in a flipped classroom to maximize the time with the teacher. Students should complete the notes at home, so they can participate in the activity during class with their peers and then demonstrate mastery to the teacher using the IXL program. The teacher should be a math teacher with experience teaching quadratics and prefereably one who knows the strngths and weaknesses of the individual students since this unit would ideally be covered later in the year.

Student's prior knowledge:

• Factoring trinomials
• Add, subtract, and multiply polynomials
• Solving equations
• Evaluating expressions

Students should complete the IXL activity to 100% to demonstrate mastery of prior knowledge in order to be successful in this unit.

Students will then read an article which explains what quadratic equations are. They should take notes in their notebook on this topic.

Once students have completed their IXL and their notes, the teacher should then hand out the Frayer Model to each student and have them fill in the first page on Quadratic equations. The rest of the squares will be filled in throughout the remaining lessons. This should be collected and turned in for credit at the end of the unit. The Frayer Model is a proven method of helping students understand vocabulary by explaining it and several different ways. Studnets should write down their own definiton and come up with their own examples and non-examples. They may need help finding a relevent non-example for their first word

Below is an example of what their Frayer Model could look like:

# 1. Solving quadratics by factoring

## Student

Lesson - In your math notebook, go through the following lessons on how to solve a quadratic equation by factoring and take notes.

Activity - Four in a row factoring game

• Choose a partner to work with
• Each group will be given 2 dice (two different colors) and a board game sheet. Determine what colored dice will be for the top of the board game, and which one will be for the side. Write it on the paper
• With your partner, one person will roll both dice and go to the indicated square on the board game
• Both players will factor the equation, when finished, raise your hand and wait for the teacher
• The teacher will come and check the first person's answer. If they get it correct, they can write their name in that square. If they get it wrong, then the teacher will check their partner's answer and see if it is correct. If the other partner gets the answer correct, then they may steal the square and write their name in it
• Now it is the next players turn to do the same thing
• This will continue until one player has four squares in a row

Assessment - You must obtain a smart score of 80 or higher. If you have worked for over 45 minutes and still cannot reach that score, then you will receive additional help from your teacher

Update - On Scholar you need to reply to the following prompt and comment on at least 2 other people's comments. Your answers should be in complete sentences and you must have at least 2 sen

Make a prediction on why there are 2 solutions to a quadratic equation and where you might see these appear on the graph.

## Teacher

Lesson - This is a flipped classroom, so these should be done at home the night prior to the lesson

• Students will go through this on their own
• Ensure that they are taking notes
• Students should complete their Frayer Model when finished

Activity - This is done in class (any student who didn't do the notes should work on that independently)

• Distribute only page 2 of this activity
• Page 3 has all answers for you to quickly check students answers before they sign their name in each square

Assessment - Once finished with the activity, students should complete this

• Students should complete the IXL to at least an 80, you may want to encourage students to go to 100 by offering extra credit
• If any student has worked for over 45 minutes and is still struggling, then set aside time to work on the skill with them. Here is extra practice to use with the student

Update - This should be done the last 10 minutes of class

• All students should make an update to Scholar and comment on at least 2 other classmates updates
• All answers should be complete sentences

# 2. Solving quadratics by completing the square

## Student

Lesson - In your math notebook, go through the following lessons on how to solve a quadratic equation by factoring and take notes.

Activity - Tic Tac Toe Game

• Get into groups of 2

• Decide who is going to be X’s and who is going to be O’s

• Each player should solve one problem on their list of questions by completing the square. Note: You don’t need to go in order of question number.

• Once each person has finished, you both put your appropriate mark in the box that has your correct answer. Note: Not all answers will be shown in the boxes provided

• If there are 2 of the same answer, then you may choose which box to make your mark

• Once a player has gotten 3 boxes in a row with their mark, they win!

Assessment - You must obtain a smart score of 80 or higher on IXL. If you have worked for over 45 minutes and still cannot reach that score, then you will receive additional help from your teacher

Update - On Scholar you need to reply to the following prompt and comment on at least 2 other people's comments. Your answers should be in complete sentences and you must have at least 2 sentences.

Why would you have to solve quadratics by completing the square instead of factoring?  Is there a situation when you could do either method?

## Teacher

Lesson - This is a flipped classroom, so these should be done at home the night prior to the lesson

• Students will go through this on their own
• Ensure that they are taking notes
• Students should complete their Frayer Model when finished

Activity - This is done in class (any student who didn't do the notes should work on that independently during this time)

• Make sure that students choose a different partner than they did in lesson 1
• Distribute only page 2 of this activity
• Ensure that students are obtaining the correct answers

Assessment - Once finished with the activity, students should complete this

• Students should complete the IXL to at least an 80, you may want to encourage students to go to 100 by offering extra credit
• If any student has worked for over 45 minutes and is still struggling, then set aside time to work on the skill with them. Here is extra practice to use with the student

Update - This should be done the last 10 minutes of class

• All students should make an update to Scholar and comment on at least 2 other classmates updates
• All answers should be complete sentences

# 3. Solving quadratics by graphing

## Student

Lesson - In your math notebook, go through the following lessons on how to solve a quadratic equation by factoring and take notes.

Activity - Graphing real world quadratics

• For this activity, you will work independently
• You must answer all questions listed on the first page of the activity as well as sketch your quadratic on graph paper

Assessment - You must obtain a smart score of 80 or higher. If you have worked for over 45 minutes and still cannot reach that score, then you will receive additional help from your teacher

Update - On Scholar you need to reply to the following prompt and comment on at least 2 other people's comments. Your answers should be in complete sentences and you must have at least 2 sen

Give a real life example of a quadratic that you can see in the world around you.  Explain what the x and y axis would be measure in and what the x and y intercepts mean in that example and what the minimum or maximum value represents.

## Teacher

Lesson - This is a flipped classroom, so these should be done at home the night prior to the lesson

• Students will go through this on their own
• Ensure that they are taking notes
• Students should complete their Frayer Model when finished

Activity - This is done in class (any student who didn't do the notes should work on that independently during this time)

• Distribute activity

Assessment - Once finished with the activity, students should complete this

• Students should complete the IXL to at least an 80, you may want to encourage students to go to 100 by offering extra credit
• If any student has worked for over 45 minutes and is still struggling, then set aside time to work on the skill with them. Here is extra practice to use with the student

Update - This should be done the last 10 minutes of class

• All students should make an update to Scholar and comment on at least 2 other classmates updates
• All answers should be complete sentences

## Student

Lesson - In your math notebook, go through the following lessons on how to solve a quadratic equation by factoring and take notes.

Media embedded July 21, 2016

• Get into groups of 2 or 3
• The teacher will hand out one task card to each group and a recording worksheet for all of your work and answers
• Once the timer begins, you will have one minute to solve the problem on your task card as a group
• All group members must record their work and final answers on their worksheet
• When the timer goes off, you will pass your card to the group on your right and you will receive another card from the group on your left
• Once you have finished all task cards, the teacher will reveal the answers and go over any questions you may have

Assessment - You must obtain a smart score of 80 or higher on IXL. If you have worked for over 45 minutes and still cannot reach that score, then you will receive additional help from your teacher

Update - On Scholar you need to reply to the following prompt and comment on at least 2 other people's comments. Your answers should be in complete sentences and you must have at least 2 sentences.

Explain why would you need to use the quadratic formula to solve a quadratic equation and not one of the other methods we have learned?

## Teacher

Lesson - This is a flipped classroom, so these should be done at home the night prior to the lesson

• Students will go through this on their own
• Ensure that they are taking notes
• Students should complete their Frayer Model when finished

Activity - This is done in class (any student who didn't do the notes hsould work on that independently during this time)

• Before the lesson, print and cut out all of the task cards on this document and make copies of the recording sheet
• Ensure that groups are with different partners than lesson 1 and 2
• Distribute the worksheet and one task card to each gorup
• Set a timer for one minute and repeat that timer until all groups have finished all of the task cards

Assessment - Once finished with the activity, students should complete this

• Students should complete the IXL to at least an 80, you may want to encourage students to go to 100 by offering extra credit
• If any student has worked for over 45 minutes and is still struggling, then set aside time to work on the skill with them. Here is extra practice to use with the student

Update - This should be done the last 10 minu

• All students should make an update to Scholar and comment on at least 2 other classmates updates
• All answers should be complete sentences

# Project/Assessment

## Student

Your final task is to work in a group to solve some quadratic equation using the four methods we learned in the lessons above. Your group will then present your work in either a poster, slideshow, pamphlet, or another approved form of presentatoin. You should be working in a group of four and each person is responsible for demonstrating a different method of solving quadratics. You will be graded by your peers based on the rubric provided on the document.

Once you have finished, please fill out this short survey to describe how well you understand the material covered in this unit.

## Teacher

• Teacher should assign groups of 4 with varied ability levels in each group so they can help each other
• They must first complete the problems on teh worksheet provided
• Once they have finished the worksheet, then they will work on their presentation. This may include, but is not limited to, a poster, a pamphelt, a presentaiton, or any other form that you see fit
• Once all groups have finished, the teacher should set up a gallery walk of every groups' work and students can offer feedback to each group