![](https://res.cloudinary.com/mathmedic-prod/image/authenticated/s--4xg9s96J--/v1627566517/Website_Hero_Images_2400_02_1ae83b1e89.jpg)
Factoring Quadratics (Lesson 6.3 Day 1)
Unit 1: Sequences and Linear Functions
Day 1: Recursive Sequences
Day 2: Applications of Arithmetic Sequences
Day 3: Sum of an Arithmetic Sequence
Day 4: Applications of Geometric Sequences
Day 5: Sequences Review
Day 6: Quiz 1.1 to 1.4
Day 7: Linear Relationships
Day 8: Point-Slope Form of a Line
Day 9: Standard Form of a Linear Equation
Day 10: Quiz 1.5 to 1.7
Day 11: Unit 1 Review
Day 12: Unit 1 Test
Unit 2: Linear Systems
Day 1: Linear Systems
Day 2: Number of Solutions
Day 3: Elimination
Day 4: Larger Systems of Equations
Day 5: Quiz 2.1 to 2.4
Day 6: Systems of Inequalities
Day 7: Optimization Using Systems of Inequalities
Day 8: Quiz 2.5 to 2.6
Day 9: Unit 2 Review
Day 10: Unit 2 Test
Unit 3: Function Families and Transformations
Day 1: Interpreting Graphs
Day 2: What is a function?
Day 3: Translating Functions
Day 4: Quiz 3.1 to 3.3
Day 5: Quadratic Functions and Translations
Day 6: Square Root Functions and Reflections
Day 7: Absolute Value Functions and Dilations
Day 8: Equations of Circles
Day 9: Quiz 3.4 to 3.7
Day 10: Unit 3 Review
Day 11: Unit 3 Test
Unit 4: Working with Functions
Day 1: Using Multiple Strategies to Solve Equations
Day 2: Solving Equations
Day 3: Solving Nonlinear Systems
Day 4: Quiz 4.1 to 4.3
Day 5: Combining Functions
Day 6: Composition of Functions
Day 7: Inverse Relationships
Day 8: Graphs of Inverses
Day 9: Quiz 4.4 to 4.7
Day 10: Unit 4 Review
Day 11: Unit 4 Test
Unit 5: Exponential Functions and Logarithms
Day 1: Writing Exponential Functions
Day 2: Graphs of Exponential Functions
Day 3: Applications of Exponential Functions
Day 4: Quiz 5.1 to 5.3
Day 5: Building Exponential Models
Day 6: Logarithms
Day 7: Graphs of Logarithmic Functions
Day 8: Quiz 5.4 to 5.6
Day 9: Unit 5 Review
Day 10: Unit 5 Test
Unit 6: Quadratics
Day 1: Forms of Quadratic Equations
Day 2: Writing Equations for Quadratic Functions
Day 3: Factoring Quadratics
Day 4: Factoring Quadratics. Part 2.
Day 5: Solving Using the Zero Product Property
Day 6: Quiz 6.1 to 6.4
Day 7: Completing the Square
Day 8: Completing the Square for Circles
Day 9: Quadratic Formula
Day 10: Complex Numbers
Day 11: The Discriminant and Types of Solutions
Day 12: Quiz 6.5 to 6.9
Day 13: Unit 6 Review
Day 14: Unit 6 Test
Unit 7: Higher Degree Functions
Day 1: What is a Polynomial?
Day 2: Forms of Polynomial Equations
Day 3: Polynomial Function Behavior
Day 4: Repeating Zeros
Day 5: Quiz 7.1 to 7.4
Day 6: Multiplying and Dividing Polynomials
Day 7: Factoring Polynomials
Day 8: Solving Polynomials
Day 9: Quiz 7.5 to 7.7
Day 10: Unit 7 Review
Day 11: Unit 7 Test
Unit 8: Rational Functions
Day 1: Intro to Rational Functions
Day 2: Graphs of Rational Functions
Day 3: Key Features of Graphs of Rational Functions
Day 4: Quiz 8.1 to 8.3
Day 5: Adding and Subtracting Rational Functions
Day 6: Multiplying and Dividing Rational Functions
Day 7: Solving Rational Functions
Day 8: Quiz 8.4 to 8.6
Day 9: Unit 8 Review
Day 10: Unit 8 Test
Unit 9: Trigonometry
Day 1: Right Triangle Trigonometry
Day 2: Solving for Missing Sides Using Trig Ratios
Day 3: Inverse Trig Functions for Missing Angles
Day 4: Quiz 9.1 to 9.3
Day 5: Special Right Triangles
Day 6: Angles on the Coordinate Plane
Day 7: The Unit Circle
Day 8: Quiz 9.4 to 9.6
Day 9: Radians
Day 10: Radians and the Unit Circle
Day 11: Arc Length and Area of a Sector
Day 12: Quiz 9.7 to 9.9
Day 13: Unit 9 Review
Day 14: Unit 9 Test
Learning Targets
Multiply polynomial factors using distribution or rectangle diagrams.
Factor quadratic equations in the form of ax2+bx+c when a=1.
Tasks/Activity | Time |
---|---|
Activity | 15 minutes |
Debrief Activity with Margin Notes | 10 minutes |
QuickNotes | 5 minutes |
Check Your Understanding | 10 minutes |
Activity: What's Missing?
Lesson Handouts
Media Locked
Media Locked
Media Locked
Answer Key
Media Locked
Homework
Media Locked
![](https://cdn.mathmedic.com/image/authenticated/s--nvEJVQIj--/v1627673648/DSC_0678_edit_58c5b086f1.jpg)
Experience First
Today is a big day. We're going to take on FACTORING! And we're going to do it without telling the students HOW to factor before they start factoring. It's a tall order. To accomplish this, we've created a sequence of problems that have slight variations from one to the next in order to help students notice how the factors must change in order to get a certain product. The level of difficulty will increase slightly between each problem so that students can get from the simplest problem to the most challenging without any jumps that are too large. Depending on your students' skill level with multiplying binomials, you may want to start with a warm-up to make sure everyone is on the same page. (There is a warm-up linked above.) This activity on first glance may look like a Drill and Kill lesson, but it's not. We promise. We've made 15 equations, each with different pieces missing. Each question was intentionally written to help students notice how changing the value of b or c affects the factors or how where you put a negative makes a difference. Students should work in their groups to find all of the missing pieces to the equations. As you are checking in on them, do your best to not give them direction on how to proceed. Instead we want to direct them to look for patterns in the structure. Guiding Questions: Ask each group to put answers on the board. Since there are so many questions, each group should be able to contribute.
Formalize Later
During the debrief of the activity, we really just want to hear what the students have to say about their work. You don't need to discuss every problem. As you are monitoring the groups while they are working, pay attention to which problems they have the hardest time with. You can highlight those during the debrief. You will definitely want to discuss examples m and o to discuss looking for common factors that can be taken out. There are some special cases (difference of squares and perfect square trinomials) that you can identify if you want, but you don't have to. We don't want our students to memorize the "trick" for factoring perfect square trinomials, but we usually point out what they are. Besides that, there are really not a lot of margin notes because our goal here was not to teach tricks for factoring but instead to help students develop an understanding of how the factors and the product are related. After going through the QuickNotes, give students time to work on the Check Your Understanding problems. If you have the time, go over the answers. Students may need some help with questions #3-5.