What are Perfect Squares?
Lesson 11
Unit 7
Quadratic Equations
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.
HSA-SSE.A.2: Use the structure of an expression to identify ways to rewrite it. For example, see 𝘹⁴ – 𝘺⁴ as (𝘹²)² – (𝘺²)², thus recognizing it as a difference of squares that can be factored as (𝘹² – 𝘺²)(𝘹² + 𝘺²).
Expressions and Equations
Warm Up
Unit 7 ● Lesson 11
x
3x
7x
5x
½x
X + 1
2X - 9
Warm-up
Page 254
Page 234
Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.
Unit 7 ● Lesson 11
Let’s see how perfect squares make some equations easier to solve.
We can recognize quadratic equations that have a perfect-square expression and solve the equations so that we can solve equations we could not solve previously.
Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.
Where were we? Where are we? Where are we going?
Unit 6 ● Lesson 11
Agenda Review
You are successful today when...,
● You can rearrange a quadratic equation to be written as ‘expression in factored form = 0’ and find the solutions.
● You can recognize quadratic equations that have a perfect-square expression and solve the equations.
Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.
Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.
11.2 Activity: Perfect Squares in Different Forms
You can recognize quadratic equations that have a perfect-square expression and solve the equations.
10 mins Total
3 mins individual - 2 mins group - 4 mins class share
pg 234
If these expressions are written in factored form, each one is the square of a linear expression:
(x + 3)², (x - 8)², and (x + ⅙)².
Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.
11.2 Activity: Perfect Squares in Different Forms
You can recognize quadratic equations that have a perfect-square expression and solve the equations.
5 mins Total
2 mins individual - 1 mins group - 2 mins class share
pg 235
Class
Seat 1
Seat 2
Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.
11.3 Activity: Two Methods
You can recognize quadratic equations that have a perfect-square expression and solve the equations.
10 mins Total
4 mins individual - 2 mins group - 4 mins class share
pg 235
Stand up
Hand up
Pair up
Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.
What are Perfect Squares?
You can recognize quadratic equations that have a perfect-square expression and solve the equations.
No
Yes
No
Yes
Rewriting the left side gives (x-8)(x-2) = 9, but now we are stuck. We can’t use the zero product property because the expression does not equal 0.
Lesson Synthesis
Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.
A Perfect Square
You can recognize quadratic equations that have a perfect-square expression and solve the equations.
(x + 10)² = 81
√(x + 10)² = √81
x + 10 = ±9
x + 10 = 9
x + 10 = -9
It is equivalent to (x+10)², so it is a factor squared.
8
Cool-down
Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.
Unit 6 ● Lesson 10
● I can rearrange a quadratic equation to be written as ‘expression in factored form = 0’ and find the solutions.
● I can recognize quadratic equations that have a perfect-square expression and solve the equations.
Learning
Targets
Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.
Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.