Unit 8, Lesson 14
Rewriting Quadratic Expressions
Extra Support Materials for Algebra 1
14.1
Warm-up
Standards Alignment
Building On
Addressing
Building Toward
HSA-REI.B.4.a
Use the method of completing the square to transform any quadratic equation in into an equation of the form that has the same solutions. Derive the quadratic formula from this form.
Instructional Routines
NoneMaterials
NoneActivity Narrative
In this Warm-up, students write quadratic expressions in standard form of the type when given values for and . In the associated Algebra 1 lesson, students will use quadratic expressions in this form to factor into perfect squares. As students write expressions in standard form they look for and make use of structure (MP7).
Launch
Ask students to give the general form of a quadratic expression in standard form. If students struggle to provide the general form, ask for an example of a quadratic expression in standard form. Display the general form of a quadratic expression in standard form for all to see: .
Activity Synthesis
The purpose of the discussion is for students to get familiar with using many variables and unknowns to create an expression when some of the values are known. Select students to share their solutions. Here are some questions for discussion:
- “Do you notice anything special about the expression in standard form for the first question? How would you factor it?” (It is a perfect square since it can be factored as .)
- “Do you have a good method for separating letters that represent numbers you know from letters that will stay in the final solution?” (I like to write out the general form I should work with, then immediately replace any letters with values I know. Like if I know , then I would start with and then write . This helps me separate which letters have known values (like ) and which do not (like ).)
14.2
Activity
Instructional Routines
MLR7: Compare and ConnectMaterials
NoneActivity Narrative
In this activity, students rewrite quadratic expressions in factored form into standard form. This activity expands on previous work by requiring students to expand the expressions for which the coefficient of the quadratic term is non-zero. Students look for and make use of structure (MP7) when they use the distributive property or table to rewrite expressions.
Monitor for students who use these different strategies to organize their work when using the distributive property:
- Priya’s method of using a diagram
- Tyler’s method of using expressions
This activity uses the Compare and Connect math language routine to advance representing and conversing as students use mathematically precise language in discussion.
Launch
Arrange students in groups of 2. Select work from students with different strategies, such as those described in the Activity Narrative, to share later.
Activity
14.3
Activity
Instructional Routines
NoneMaterials
NoneActivity Narrative
In this activity, students solve for values of and using some given information. In the associated Algebra 1 lesson, students use similar equations to help complete the square for quadratic expressions with a non-zero leading coefficient. As students analyze their approaches to using the given information, they reason abstractly and quantitatively (MP2).