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Model Mathematics Curriculum
Unit Implementation Plan
UNIT COVER SHEET
Name:
Ann Propheter
Grade Level:
Unit Title: Chapter 4: Pearson Algebra 2.
Algebra II
Quadratic Functions and Equations
Dates of Instruction: 10/6, 10/13, 10/17, 10/19, 10/21, 10/25, 10/27, 10/31
Unit Timeframe: 8 days
Day 1:
10/6
Lesson: Parabola and quadratic expressions
Task: U and Quadratic Functions/Assessment: Functions Scoot
and Boogie
Day 2:
10/13
Lesson: Transformation of quadratic
functions/Task: How'd "U" do That/assessment: Movin' On Up
(function edition)
Day 3:
10/17
Lesson: Quadratic functions can be used to model real life
situations./task: Quadratic Gallery Walk, Box problem.
Day 4:
10/19
Lesson: Factor to change from standard form to factored form.
Task: Factored form of a quadratic/Assessment: Factored
form Fever
Day 5:
10/21
Lesson: Geometric method for completing the square
Task: gas law and practice problems
Day 6:
10/25
Lesson: Solve quadratic equations with complex
solutions/task: using the imaginary unit i, Gallery Walk - solving
quadratic equations
Day 7:
10/27
Lesson: Derive the quadratic formula by completing the square
Task: Are your quads in a U/Assessment: Quadratics Puzzle
Activity
Day 8:
10/31
Lesson: Solving Quadratic Systems/Task: The Basketball
problem, Review
Standards Alignment
Content Standards:
A.SSE.3¨ Choose and produce an equivalent form of an expression to reveal and
explain properties of the quantity represented by the expression.
A.REI.1: Explain each step in solving a simple equations as following from the
equality of numbers asserted at the previous step, starting from the assumption that
the original equation has a solution.
A.REI.4: Solve quadratic equations in one variable.
A.REI.7: Solve simple systems consisting of a linear equation and a quadratic
equation in two variables algebraically and graphically.
F.BF.3: Identify the effect on the graph of replacing f(x) by f(x) + k, kf(x), f(kx), and f(x
+ k) for specific values of k
F.IF.4: For a function that models a relationship between two quantities, interpret key
features of graphs and tables in terms of the quantities, and sketch graphs showing
key features.
F.IF.5: Relate the domain of a function to its graph and to the quantitative relationship
it describes
F.IF.7: Graph functions expressed symbolically and show key features of the graph.
F.IF.8: Write a function defined by an expression in different but equivalent forms to
reveal and explain different properties of the function
F.IF.9: Compare properties of two functions each represented in a different way .
N.CN.7: Solve quadratic equations with real coefficients that have complex solutions.
Targeted Mathematical Practices:
1. Make sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively
3. Construct viable arguments and critique the reasoning of others.
4. Model with mathematics
5. Use appropriate tools strategically
Skip 6. Attend to precision
7. Look for and make use of structure
8. Look for and express regularity in repeated reasoning
Model Mathematics Curriculum
Unit Implementation Plan
UNIT4:
Quadratic Functions
DAY: 6
DAILY LESSON PLAN
Objectives
Pre-assess prior knowledge. (Using the Imaginary Unit, i)
Solve quadratic equations using the properties of square roots.  I can solve a
quadratic equation by square roots.  I can solve quadratic equations with complex
solutions.
Content
Standards
A.SSE.3: Choose and produce an equivalent form of an expression to reveal and
explain properties of the quatity represented by the expression.
a. Factor a quadratic expression to reveal the zeros of the function it defines.
b. Complete the square in a quadratic expression to reveal the maximum value
of the function it defines.
A.REI.1: Explain each step in solving a simple equation as following from the
equality of numbers asserted at the previous step starting from the assumption
that the original equation has a solution. Construct a viable argument to justify a
solution method.
A.REI.4: Solve quadratic equations in one variable.
a. Use the method of completing the square to transform any quadratic equation
in z into an equation of the form (x - p)^2 = q that has the same solutions. Derive
the quadratiec formula from this form.
b. Solve quadratic equations by inspection 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.
N.CN.7: Solve quadratic equations with real coefficients that have complex solutions
Mathematical
Practices
Look for and make use of structure. Look for and make use of repeated reasoning.
Critique the reasoning of others.
Materials
Using the imaginary unit i
Square root scoot
Preparation
Lesson
Activities
Gallery walk: Solving quadratic equations.
Students have reviewed quadratic functions and square root functions from
chapter 2. Set up the gallery walk.
Students should be split into 5 groups. Assign each group to a station. Have them
complete Exercise #1. Then, ask them to scoot to the next station. While at the next
station, students should check the work of the previous group and make
corrections as needed. Then, they will complete Exercise #2. Students should be
directed to scoot to next station. Repeat process until all stations have been
completed.
Square root scoot
Assessments
Pre assess students familiarity with complex numbers
Using the imaginary unit i
In what ways will you intentionally emphasize the development of student
mathematical practices through this lesson? Students will look for and express
regularity in repeated reasoning. During the gallery walk, they will construct viable
arguments and critique the reasoning of others.
Model Mathematics Curriculum
Unit Implementation Plan
UNIT4:
Quadratic functions DAY: 7
DAILY LESSON PLAN
Objectives
 I can solve a quadratic equation by completing the square.
 I can derive the quadratic formula by completing the square.
I can solve quadratic equations using the quadratic formula
Content
Standards
A.REI.4: Solve quadratic equations in one variable.
a. Use the method of completing the square to transform any quadratic equation in
x into an equation of the form (x - p)^2 = q that has the same solutions. Derive the
quadratic formula from this form..
b. Solve quadratic equations by inspection, 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 number a and b.
N.CN.7 Solve quadratic equations with real coefficients that have complex
solutions.
Mathematical
Practices
Look for and make use of structure.
Materials
Look for and express regularity in repeated reasoning.
work sheets
Preparation
Sample problems and discussion
Lesson
Activities
Students will work in pairs to derive the quadratic formula; then check their work
with the other members in their group.
Finding vertex from intercepts
Assessments
Using the quadratic formula
In what ways will you intentionally emphasize the development of student
mathematical practices through this lesson? The students can observe the
relationship between the quadratic formula and completing the square of the quadratic
equations. They must look for and make use of structure
Model Mathematics Curriculum
Unit Implementation Plan
UNIT4:
Quadratic functions 5
DAILY LESSON PLAN
I can
Objectives
Discovering a geometric method for completing the square.
Finding visual patterns of quadratic sequences
Complete the square on a quadratic function to rewrite that function in vertex
form.
Content
Standards
A.REI.1: Explain each step in solving a simple equation as following from the
equality of numbers asserted at the previous step, starting from the assumption
that the original equation has a solution. Construct a viable argument to justify a
solution method.
A.SSE.3.b: Choose and produce an equivalent form of an expression to reveal
and explain properties of the quantity represented by the expression.
Complete the square in a quadratic expression to reveal the maximum value of
the function it defines.
F.IF.8: Write a function defined by an expression in different but equivalent
forms to reveal and explain different properties of the function
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.
Mathematical
Practices
Look for and make use of structure. Students will continue to look for and make
use of structure as they factor and complete the square.
Reason abstractly and quantitatively.
Look for and express regularity and in repeated reasoning.
Materials
Completing the square geometrically using algebraic manipulatives.
A sample problem and an application
Vertex This!
Preparation
Discussion, development samples of the use of the Quad. Eq.
Copies of work sheets and quadratic equation puzzle. Reviewing complex
solutions
Lesson
Activities
Visualizing completing the square using algebra tiles from Illustrative Mathematics.
Quadratic Sequence 1 and 2. Visual patterns using Algebra tiles are shown.
Vertex This from live binders
Assessments
Activities to be used as assessment tools
Sample problem Completing the square(Solve the equation x^2 + x +1 = 0) and the
Ideal gas law (A certain number of Xenon gas molecules are placed in a container at
room temperature...) from Illustrative Mathematics
In what ways will you intentionally emphasize the development of student
mathematical practices through this lesson?
Students will look for and make sense of structure as they work with algebraic tiles.
We will use a quadratic function to model the Ideal gas Law, so students will be
required to reason abstractly and quantitatively.
Model Mathematics Curriculum
Unit Implementation Plan
UNIT4:
Quadratic Equation DAY: 8
DAILY LESSON PLAN
Objectives
 I can solve a system of equations involving a linear and quadratic equation
Review: Solve quadratic equations by method of choicethat results in real
and complex solutions.
ContentStandards
A.REI.7 Solve a simple system consisting of a linear equation and a quadratic
equation in two variables algebraically and graphically. For example, find the
points of intersection between the line y = –3x and the circle x 2 +y 2 = 3.
N.CN.7: Solve quadratic equations with real coefficients that have complex
solutions.
A.REI.4: Solve quadratic equations in one variable.
a. Use the method of competing the square to transform any quadratic
equation in x into an equation of the form (x - p)^2 = q that has the same
solutions. Derive the quadratic formula from this form.
b. Solve quadratic equations by inspection 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 a a + bi for real numbers a and b.
Mathematical
Practices
MP2: Reason abstractly and quantitatively.
MP4: Model with mathematics
MP7: Look for and make use of structure.
MP8: Look for and express regularity in repeated reasoning.
Materials
Copies of the basketball problem and graphing grids.
Preparation
Students have used several methods to solve quadratic equations. They have
solved linear systems of equations.
Lesson Activities
Assessment Title: Basketball.
The Bulls get a Turnover…and the crowd goes wild!!!
(hhhhaaaaaaaaaaaaaaaaa!) Brooks steals the ball from the other team and
dribbles across the circle to score the winning shot. Brooks’s location for the
turnover and the winning shot are indicated above.
Are your quads in a U
Assessments
Solving quadratics Puzzle Activity
In what ways will you intentionally emphasize the development of student
mathematical practices through this lesson?
Students demonstrate this practice when they can translate back and forth between the representation of
a quadratic and its applied meaning (for instance, completing the square on a quadratic describing
projectile motion to find its vertex and then interpreting the result as the maximum height the projectile
obtained, and then setting the quadratic equal to zero and solving to find the time at which the projectile
reached the ground. Students must make use of structure and express regularity in repeated reasoning.
Model Mathematics Curriculum
Unit Implementation Plan
UNIT4:
_Quadratic Equations_
DAY: __4_______
DAILY LESSON PLAN
Objectives
Solve quadratic equations using factoring to make connections to solutions and xintercepts.
Review techniques of manipulating quadratics to identify key features of a
parabola.
Content
Standards
A.SSE.2: Use the structure of an expression to identify ways to rewrite it.
Mathematical
Practices
A.SSE.3: Choose and produce an equivalent form of an expression to reveal and
explain properties of the quantity represented by the expression.
a. Factor a quadratic expression to reveal the zeros of the function it defines
b. Complete the square in a quadratic expression to reveal the maximum value of
the function it defines.
F.IF.8: Write a function defined by an expression in different but equivalent forms
to reveal and explain different properties of the function.
a. Use the process of factoring and completing the square in a quadratic funtion to
show zeros, extreme values, and symmetry of the graph, and interpret these in
terms of a context.
MP2: Reason abstractly and quantitatively.
MP3: Model with mathematics
MP7: Look for and make use of structure.
MP8: Look for and express regularity in repeated reasoning.
Materials
Copies of worksheets.
Preparation
We will review the factoring rules.
Use the Quadratics Representations as a review of quadratic manipulations
Lesson
Activities
Where Do I stand with Quadratics, live binders
Finding forms of Quadratics Summary, live binders
Assessments
In what ways will you intentionally emphasize the development of student
mathematical practices through this lesson?
Students will continue to look for and make use of structure as they factor, complete the square, and use
the quadratic formula to solve quadratics or highlight different quantities of interest.
Students will examine different forms of the same quadratic function and repeat use of appropriate
methods to move between those forms to reveal new information about the function