Unit Work Sample
Chapter 7: Quadratic
Equations and
Functions
Algebra II Honors
Tyesha Deas
EDSE 778B-Spring 2011
Mrs. B. Oliver
Table of Contents
Section I:
Unit Topic or Title
3
Section II:
Contextual Factors
4
Section III: Part A
Unit Objectives
5
Section III: Part B
Assessment Plan
6
Section III: Part C
Results of the Pre-Assessment
7
Section III: Part D
Instructional Plan
8
Section IV:
Analysis of Student Learning
119
Section V:
Reflection and Self-Assessment
125
Section I: Unit Topic or Title
Unit Title: Quadratic Equations and Functions
This lesson will be taught to an Algebra II Honors class during 2 nd Block on B days. The
class is composed of nine females and twelve males. Eighteen students are
sophomores and three students are juniors. Thirteen students are gifted academically.
In this unit students will explore the characteristics of quadratic equations and functions,
learn the different ways to solve quadratic equations/functions, and learn how to graph
quadratic equations. This unit is taught after the unit on Irrational and Complex
Numbers, and the unit following this unit will be Variation and Polynomial Equations.
Section II: Contextual Factors
The students in this course are considered academically gifted. Because this is an
honors class, the pace of this class is faster than the college prep course. The class
consists of mostly sophomores, and their last math course was Geometry Honors.
Also, two of the three juniors’ previous math class was Geometry Honors. One of the
three juniors is taking Algebra II Honors for the second time. With that in mind, I will
have to make sure that the student who is repeating this class for the second time is
making connections to what he learned before.
In the last unit, students scored very well on the unit test, so I think that these same
group of students, given that they study and try to understand the material will score
well on the final test. This unit in is the “meat” of Algebra II. I expect students to
struggle with this unit to some degree because it will be their first time ever seeing many
of the concepts that will be presented in this unit. However, I still hold high expectations
for this group of students, and I expect for them to work hard and perform well on
assessments.
One other thing that I need to keep in mind with this group of students is that, even
though they are honor students, their Algebra I foundation is very weak. They are
missing a lot of key concepts, such as graphing things on a coordinate plane, as well as
some simple solving for variables.
Some things that I need to think about are that there is a late start day one day during
unit, and there is also a day in which we have early dismissal for parent conferences.
Another factor that may affect student learning is that this unit is taught during the
production of Hairspray, as well as other dance performances. Many of my students will
be participating in these extracurricular activities, causing them more focused on other
things after school than working on math.
Section III: Part A-Unit Objectives
Correlated
Unit Objectives
Standards/Expectations
1.
2.
IA-3.3 Carry out a procedure to solve
quadratic
equations
The student will solve quadratic
algebraically
(including
equations.
factoring,
completing
the
square, and applying the
quadratic formula).
The
students
will
solve
quadratic word problems.
3. The Students will graph quadratic
equations.
4.
The student will
discriminant of a
equation.
find the
quadratic
5.
The student will write quadratic
equations from given roots.
IA-3.5 Analyze given information
(including quadratic models) to
solve contextual problems.
IA-1.3 Apply algebraic methods to
solve problems in real-world
contexts.
IA-1.6 Understand how algebraic
relationships can be
represented in concrete
models, pictorial models, and
diagrams.
IA-1.5 Demonstrate an
understanding of algebraic
relationships by using a
variety of representations
(including verbal, graphic,
numerical, and symbolic).
IA-3.4 Use
the
discriminant
to
determine the number and type
of solutions of a quadratic
equation.
IA-3.6 Carry out a procedure to write
an equation of a quadratic
function when given its roots.
Section III: Part B-Assessment Plan
Pre-Assessment – The pre-assessment will be a list of questions that the students can
answer based on things that will be taught during the lesson. Some students will be
able to answer most of the questions, will some student will not be able to answer any.
This will guide my teaching because the questions that will be asked will cover a
standard or an objective for the unit. The questions that the students “score” poorly on
will be stressed more throughout the unit. For each question correct, the student will
earn 1 point for a max of 14 points.
Post-Assessment – The post-assessment will be a unit test that will cover many of the
objectives covered in this unit. I want the test to be a fair assessment of what the
students have learned in the unit. The test will be scored according to the point value of
the question, for a max of 100 points.
Another post-assessment that will be given will be the exact pre-assessment questions.
I will give this as a way of seeing the growth of the student. This is also my way of
assessing the student knowledge on question they saw before the unit, now after the
unit, just in case they don’t score will on the unit test, I will still be able to see that the
students did learn some of the objectives and standards.
Other Assessments – Other assessments for this course will be in the form of quizzes
throughout the unit after a section has been taught. Quizzes are accord according to
point value of each question, with a max of 100 points.
Section III: Part C-Analysis of Pre-Assessment
The pre-assessment was a questionnaire with six questions. The questions were based
mostly off how to solve quadratic formulas, its roots, and the graph of parabolas. The
total point value of the questionnaire was 14 points, 1 point for each answer.
Number of students per score
Pre-Assessment Scores
5
4
3
2
1
0
0
0.5
1
1.5
2
3
4
5
6
Points Earned On Pre-Assessment
The above graph shows points scored on the pre-assessment, to the number of
students. Zero is the lowest number of points scored on the pre-assessement, while six
points was the highest number of points scored. I think that this shows that the students
really don’t know much about the concepts in this unit, so this is going to allow me to
teach the most of the students something new. Some of the answers were close
answers, or it looked like the some of the students had an idea of what was being asked
on the pre-assessment, but were unclear with their answers. Because of this, I hope
that in my teaching I am able to claifiy some of the unclear answers they gave, so that
the concepts are more concrete in their minds. The student who scored the highest, is
the daugther of a math teacher, but she also is repeating this course for the second
time.
Section III: Part D-Instructional Plan
Unit
Objectives
Type of ActivityWhole/Pairs/Small
Group/Individual
Assessment
Item
Materials/Resources
#2 & #4 from PreAssessment
Completing the
square and
Quadratic
Formula
Pairs and Whole
Discriminant
Whole, Pair, and Individual
#5 from PreAssessment
Textbook, Smartboard Notes
Word Problems
Whole, Pair, Individual
#11 and #12 on
Unit Test
Textbook, Smartboad Notes
Write equations
from given roots
Whole, Pair, Individual
Quiz
#10 from Unit Test
Textbook, Smartboard Notes
Quiz 8-#1-4
Text book, Smartboard
Notes
#1 & #2 from Unit
Test
The strategies used in this unit are whole group learning, pair learning, and individual
learning. I think this will benefit the students because it allows the students to see a
concept taught, and then it allows the students to either work in pairs or individually to
solve problems.
Section 7.1: Completing the Square – This section will be taught in conjunction with
Sections 7.2 and 7.3. There will be whole group learning, and then students will work
pairs or in individually to work on the concepts in of this section. Students will also have
independent work by way of homework. [Standard IA-3.3]
Section 7.2: Quadratic Formula – This section began after the last unit’s test,
however, this section was retaught when the unit actually began so that it was taught in
conjunction with Sections 7.1 and 7.2. The students worked at their desk to complete a
worksheet that explained how to use the quadratic formula and had ten quadratic
equations to be solved. After this section was taught, it was revisited so that the word
problems from this section could be taught. [Standard IA-3.3]
Section 7.3: The Discriminant – This section was taught during Sections 7.1 and
Section 7.2. This section was taught with more whole group learning and pair learning.
The students used previous homework problems to understand the discriminant of
quadratic equations. [Standard IA-3.4]
Section 7.4: Equations in Quadratic Form – This section was taught in a whole group
setting, and the students were given the opportunity to work on a few problems
independently and the problems were discussed after they were given a chance to work
on them. [Standard IA-3.3, 3.5]
Section 7.5: Graphing y – k = a(x – h)2 – This section taught with whole group
learning. Because the concepts of this lesson are more difficult than most of the
sections so far, this section was taught at a slower pace. The students were given
independent work for homework and the problems were discussed the next day.
[Standard IA-1.5]
Section 7.6: Quadratic Functions – Again, because this was the first time the students
have seen this concept, I went a little slower, making sure that they understood the
concept before moving on. Some of the concepts of this section used concepts form
the completing the square section, so I was able to revisit those concepts, and build on
them in this section. Students were given homework for independent practice.
[Standard IA-4.2]
Section 7.7: Writing Quadratic Equations and Functions – This section was going to
be taught in two parts, however, that didn’t go according to planned. I taught this
section to the class, and then had students work in pairs to figure out equations to given
roots. Afterwards, this I taught the word problems from this section, and allowed
students to work independently on them for homework. [Standard 3.6]
Algebra II Honors – Unit Guide
Chapter 7 – Quadratic Equations and Functions
(Algebra and Trigonometry Structure and Method-Book 2)
IA-1.3 Apply algebraic methods to solve problems in real-world contexts.
IA-1.5 Demonstrate an understanding of algebraic relationships by using a variety of representations (including
verbal, graphic, numerical, and symbolic).
IA-1.6 Understand how algebraic relationships can be represented in concrete models, pictorial models, and
diagrams.
IA-3.3 Carry out a procedure to solve quadratic equations algebraically (including factoring, completing the square,
and applying the quadratic formula).
IA-3.4 Use the discriminant to determine the number and type of solutions of a quadratic equation.
IA-3.5 Analyze given information (including quadratic models) to solve contextual problems.
IA-3.6 Carry out a procedure to write an equation of a quadratic function when given its roots.
IA-4.2 Carry out a procedure to determine specified points (including zeros, maximums, and minimums) of
polynomial functions.
IA-4.4 Analyze given information (including polynomial models) to solve contextual problems.
Class Dates
Section/Topic (Assessment)
February 23-A
February 24-B
February 25-A
February 28-B
Test – Chapter 6
March 1-A
March 2-B
Quiz 7-1, 7-2, 7-3
7-2 The Quadratic Formula
(Word Problems)
Quiz 7-2 (Word Problems)
7-4 Equations in Quadratic Form
Quiz 7-4
7-5 Quadratic Functions and
Their Graphs
Quiz 7-5
7-6 Quadratic Functions
Quiz 7-6
7-7 Writing Quadratic Equations
and Functions
Quiz 7-7
7-7 Writing Quadratic Equations
and Functions (Word Problems)
Quiz 7-7 (Word Problems)
Review
Test – Chapter 7
March 3-A
March 4-B
March 7-A
March 8-B
March 9-A
March 10-B
March 11-A
March 14-B
March 15-A
March 16-B
March 17-A
March 18-B
March 21-A
March 22-B
7-1, 7-2, 7-3 Completing the Square,
The Quadratic Formula, &
The Discriminant
Projected Assessment
7-2 HW: Written P. 313-
314 #1-17 odd 25, 27
7-1 HW: Written P. 309310 #1a, 3b, 5c 7, 9, 11,
13-23 odd,
7-3 HW: Oral P. 319
ALL, Written: P. 320
#13-23 odd (Modified
instructions)
TBA
7-4HW: Written P. 323-
324 #1-19 odd
7-5HW: Written P. 331332 #1-29 odd
7-6HW: Written P. 336
#1-29 odd
7-7HW: Written P. 342
#1-27 odd
TBA
Review Sheet
INSTRUCTOR: Tyesha Deas
TITLE OF LESSON: The Complex Number
GRADE LEVEL: 9-11th
(Section 6-8), Chapter 6 in Review, Intro to the
Algebra 2 Honors (2B, 3A)
Quadratic Formula (7-2)
STANDARDS
OBJECTIVES
GOALS
MATERIALS
PART OF LESSON
UNIT: Irrational and Complex
Numbers & Quadratic
Equations and Functions
South Carolina Mathematics Standards:
Standard IA-3.2: Carry out a procedure to perform operations with complex
numbers (including addition, subtraction, multiplication, and
division).
At the end of this lesson, students will be able to:
1. …add, subtract, multiply, and divide complex numbers.
2. …use the quadratic formula to solve the roots to quadratic equations.
1. Students should be competent with adding, subtracting, and multiplying
complex numbers. Students should also be competent with recognizing
the cycle of i.
2. Students should understand the basic concept of the quadratic formula
and how to properly plug in the coefficients of a quadratic equation to
find the roots.
1. Introducing the Quadratic Formula Worksheet (Mcgraw-Hill. (2005).
Glencoe algebra 2. New York: Glencoe/Mcgraw-Hill)
2. Quiz 6-8
3. Pre-assessment to Chapter 7 (3A)
4. Review Sheet for Test
DETAILS & SPECIFICS
Go over homework from previous night (Section 6-8)
Review concepts of Section 6-8 before quiz. Review the imaginary number i.
ANTICIPATORY SET Quiz on Section 6-8
Have students begin Pre-Assessment to Chapter 7 after the test.
Go over quiz
LEARNING
ACTIVITIES PART:
PRESENTATION OF
INFORMATION AND
MODELING
CHECKING FOR
UNDERSTANDING
Give students the Introducing the Quadratic Formula worksheet. Explain the
quadratic formula to find the roots of a quadratic equation.
Show:
(factorable) and
(not factorable)
Ask students if they are understanding what is being taught or what questions they
may have.
GUIDED PRACTICE
Have students complete problems 1-10 on the Introducing the Quadratic Formula
INDEPENDENT
PRACTICE
(Homework for the Quadratic Formula be given after the test—p. 313-312 #1-17
odd, 25, 27)
Ask students when the quadratic formula can be used, the type of solutions the
quadratic formula produces, and what letters are used to solve a quadratic
formula…maybe have students state the quadratic formula.
CLOSURE
INSTRUCTOR: Tyesha Deas
GRADE LEVEL: 9-11th
Algebra 2 Honors (2B, 3A)
STANDARDS
OBJECTIVES
GOALS
MATERIALS
TITLE OF LESSON: Section 7-1:
Completing the Square, Section 7-2: The
Quadratic Formula, Section 7-3: The
Discriminant
UNIT: Quadratic Equations and
Functions
South Carolina Mathematics Standards:
Standard IA-3.3 Carry out a procedure to solve quadratic equations
algebraically (including factoring, completing the square,
and applying the quadratic formula).
Standard IA-3.4 Use the discriminant to determine the number and type of
solutions of a quadratic equation.
At the end of this lesson, students will be able to:
1. …solve quadratic equations by completing the square.
2. …solve quadratic equation by using the quadratic formula.
3. …determine the nature of roots of a quadratic equation by using its
discriminant.
1. Understanding the Quadratic Formula
2. Students should understand the basic concept of the quadratic formula
and how to properly plug in the coefficients of a quadratic equation to
find the roots.
1. Introducing the Quadratic Formula Worksheet (Brown, R. G., Dolciani,
M. P., Sorgenfrey, R. H., Kane, R. B. (2009). Algebra and trigonometry:
structure and method-book 2. Evanston, IL: McDougal Littell.)
2. Pacing Guide for Chapter 7 (Green Sheet)
3. Section 7-2 Homework
PART OF LESSON
DETAILS & SPECIFICS
Go over the objectives of the class.
Give students the Pacing Guide for Chapter 7 (Green Sheet)
ANTICIPATORY SET
Go over Homework form section 7-2. Briefly review the information from last class
(go over homework, 7-2 p. 313-314 #1-17 odd, 25, 27)
Move to section 7-3. Explain the discriminant of a quadratic. Work in review of the
LEARNING
previous sections homework. Work Example 1a, b, c from page 317, Example 2a, b,
ACTIVITIES PART:
c, d page 318, example 3 a, b, c)
PRESENTATION OF
Begin with section 7-1. Explain what completing the square means. Show examples
INFORMATION AND
(Example 1 from book page 307-308, example 2, and example 3). Work
MODELING
problems 2, 4, 20, 22, 24.
Ask students if they are understanding what is being taught or what questions they
CHECKING FOR
may have.
UNDERSTANDING
GUIDED PRACTICE
INDEPENDENT
PRACTICE
CLOSURE
Have students work on p. 310 # 14, 16, 18, p. 319 #1-3
7-1 HW: Written P. 309-310 #1a, 3b, 5c 7, 9, 11, 13-23 odd, 7-3 HW: Oral P. 319
ALL, Written: P. 320 #13-23 odd (Modified instructions)
Ask student the main steps to completing the square and the 3 ways to determine the
nature of the roots of quadratic equations through its discriminant.
INSTRUCTOR: Tyesha Deas
GRADE LEVEL: 9-11th TITLE OF LESSON: The Quadratic Formula
Algebra 2 Honors (2B, 3A)
(Section 7-2) Word Problems
STANDARDS
OBJECTIVES
GOALS
MATERIALS
UNIT: Quadratic Equations
and Functions
South Carolina Mathematics Standards:
Standard IA-1.3 Apply algebraic methods to solve problems in real-world
contexts.
Standard IA-1.6 Understand how algebraic relationships can be represented
in concrete models, pictorial models, and diagrams.
Standard IA-3.3 Carry out a procedure to solve quadratic equations
algebraically (including factoring, completing the square,
and applying the quadratic formula).
Standard IA-3.5 Analyze given information (including quadratic models) to
solve contextual problems.
At the end of this lesson, students will be able to:
1. …analyze information from word problems to set up quadratic equations
to solve.
2. …use the quadratic formula, complete the square, or factor to solve the
equations set up from the word problems.
1. Have students to understand the important information from the word
problems so that they can efficiently set up quadratic equations to solve
each problem.
1. Textbook – Brown, R. G., Dolciani, M. P., Sorgenfrey, R. H., Kane, R. B.
(2009). Algebra and trigonometry: structure and method-book 2.
Evanston, IL: McDougal Littell
2. Quiz on Sections 7.1, 7.2, 7.3
3. Homework from previous night. (Sections 7-1 and 7-3)
PART OF LESSON
DETAILS & SPECIFICS
Go over homework from previous night (Section 7.2)
ANTICIPATORY SET Review concepts from 7.1, 7.2, 7.3
Quiz on Section 7.1-7.3
LEARNING
Review with student the quadratic formula, completing the square, as well as
ACTIVITIES PART:
factoring. Explain that those concepts will be used to analyze and answer quadratic
PRESENTATION OF
word problems.
INFORMATION AND
Work even problems on page 314-315.
MODELING
Ask students if they are understanding what is being taught or what questions they
CHECKING FOR
may have.
UNDERSTANDING
GUIDED PRACTICE
INDEPENDENT
PRACTICE
CLOSURE
Have students try some of the word problems on their own. (even only)
Homework – page 314-315 1-13 odd
Ask students for the quadratic formula and the main steps to completing the square.
INSTRUCTOR: Tyesha Deas
GRADE LEVEL: 9-11th
TITLE OF LESSON: Equations in Quadratic
Algebra 2 Honors (2B, 3A)
Form (Section 7-4)
STANDARDS
OBJECTIVES
GOALS
MATERIALS
PART OF LESSON
ANTICIPATORY SET
UNIT: Quadratic Equations
and Functions
South Carolina Mathematics Standards:
Standard IA-3.3 Carry out a procedure to solve quadratic equations
algebraically (including factoring, completing the square,
and applying the quadratic formula).
Standard IA-3.5 Analyze given information (including quadratic models) to
solve contextual problems.
At the end of this lesson, students will be able to:
1. …recognize and solve equations in quadratic form.
1. To have students understand what part of an equation is quadratic
2. To be able to simplify equations that appear to be in quadratic form, so
that it’s easier to solve the problem by factoring, completing the square,
or using the quadratic formula.
1. Textbook – Brown, R. G., Dolciani, M. P., Sorgenfrey, R. H., Kane, R. B.
(2009). Algebra and trigonometry: structure and method-book 2.
Evanston, IL: McDougal Littell
2. Quiz answers to 7.1-7.3
3. Homework from previous night (Section 7-2)
DETAILS & SPECIFICS
Hand back and go over Quiz from 7.1-7.3
Go over homework from previous night (Section 7.2) word problems.
Give students examples of quadratic equations and ask the students what part of the
equation is quadratic. Exs.
,
,
LEARNING
( )
ACTIVITIES PART: Show how to work examples 1 -4 from the book (page 322-323), explaining that a
PRESENTATION OF substitution needs to be used in order to have to easily factor the problems. Then
INFORMATION AND solve for the variable by using the solutions from the new quadratic formula to solve
MODELING
for the variable that was used in the substitution.
CHECKING FOR
UNDERSTANDING
GUIDED PRACTICE
INDEPENDENT
PRACTICE
CLOSURE
Work 2a, c, 4a, c, 6b
Ask students if they are understanding what is being taught or what questions they
may have.
Have students complete in class Oral Exercises 1-3, 11, but complete the whole
problem. Have students go to the board to work out problems so that students are
able to see the way their peers are thinking about the equations.
Homework – Page 323-324 #1-19 odd
Have students complete number 5 from page 324 as an exit slip.
INSTRUCTOR: Tyesha Deas
GRADE LEVEL: 9-11th
Algebra 2 Honors (2B, 3A)
TITLE OF LESSON:
Graphing y – k = a(x – h)2 (Section 7-5)
UNIT: Quadratic Equations and
Functions
South Carolina Mathematics Standards:
Standard IA-1.5: Demonstrate an understanding of algebraic relationships by
using a variety of representations (including verbal, graphic,
numerical, and symbolic).
STANDARDS
Standard IA-3.3 Carry out a procedure to solve quadratic equations
algebraically (including factoring, completing the square,
and applying the quadratic formula).
At the end of this lesson, students will be able to:
1. …graph parabolas that are in the form of y – k = a(x – h)2
OBJECTIVES
2. …find the vertex of a parabola as well as the axes of symmetry.
1. Students should understand how the a, h, and k effects the parent graph of
y = x2.
2. Students should know that the vertex is the coordinate (h, k) from the
GOALS
quadratic in graphing form.
3. Student should understand that the axis of symmetry is an x = h, the h
coming from the vertex.
1. Textbook – (Mcgraw-Hill. (2005). Glencoe algebra 2. New
York: Glencoe/Mcgraw-Hill)
MATERIALS
2. Quiz on Section 7.2 Word Problems and Section 7.4
3. Previous Night’s homework (Section 7-4)
PART OF LESSON
DETAILS & SPECIFICS
Go over homework from previous night (Section 7.4)
Answer any questions from the previous section.
Have students complete the quiz on section 7.2 and 7.4.
Ask students what the graph of quadratic equations look like and its name. Students
should say a parabola. Ask the students what they know about parabolas and if
they’ve graphed them before. Tell students that today’s lesson is to have students
ANTICIPATORY SET
graph quadratic functions.
Ask student if they know the parent function/equation for a quadratic formula, and
what the parabola looks like.
Show students the parent function y = x2and its graph. Explain that this is the bases
for all quadratics, and that the lesson today we will see how we move the parabola
depending on a, h, and k.
Show students the quadratic graphing form equation for quadratics. y – k = a(x – h)2
Ask students what they think the a does the graph. Show examples like y = -x2,
2
, and y = 2x2. Ask them to tell the difference between the graph, and how it
changes from the parent function. ( |a| > 1 – narrow, 0 < a <1 – wide, a > 0 – opens
up, a < 0 – opens down)
LEARNING
ACTIVITIES PART:
PRESENTATION OF
INFORMATION AND
MODELING
Ask students what they think the h does to the graph. Show examples like y = (x –
3)2, and y = (x + 5)2. Students should realize that the h moves the parent function
horizontally, and when h > 0 it moves to the right, when h < 0 it moves to the left.
Ask students if the know what the k does to the parent function. Show examples like
y – 3 = x2, y + 6 = x2. Students should see that the k affects the y – intercept of the
graph, and moves the graph vertically along the y-axis. k < 0 moves down, k >0
moves up.
Tie all the concepts together by using the graphing form, y – k = a(x – h)2. Tell
students that the vertex is (h, k), and that the axis of symmetry is x=h, the same h that
comes from the vertex. Example y – 2= 2(x – 4)2. Students should recognize that
(4, 2) is the vertex, the graph will be narrow since a = 2, and the graphs opens
upward. Students should also recognize that the graph moves up 2 units and moves
to the right 4 units.
Work on oral exercises (page 330 1-8) as a whole group and ask students to tell what
the a, h, and k are, the vertex, and the axis of symmetry. After students have
mastered this skill have students, ask students how to find the x and y intercepts.
Plug in zero for x when finding the y intercept, and plug in zero for y when finding x
intercepts.
Go back to the orals, and have students match the graphs with the questions based off
what they know about the vertices and the x- and y intercepts.
CHECKING FOR
UNDERSTANDING
GUIDED PRACTICE
INDEPENDENT
PRACTICE
CLOSURE
Show students how to write an equation to a parabola based off the information given
from the parabola, like the vertex and a point that is on the parabola. Show example
3 from the book, page 330.
Ask students if they are understanding what is being taught or what questions they
may have.
Have students work on the numbers 2, 8, 20 from the book.
Homework – Page 331 – 332 # 1 – 29 odd
Ask students how a, h, and k affect the parent function. Ask students what the axis of
symmetry is, as well as how to find the x and y intercepts.
INSTRUCTOR: Tyesha Deas
GRADE LEVEL: 9-11th
Algebra 2 Honors (2B, 3A)
STANDARDS
OBJECTIVES
GOALS
MATERIALS
TITLE OF LESSON:
Quadratic Functions (Section 7-6)
UNIT: Quadratic Equations and
Functions
South Carolina Mathematics Standards:
Standard IA-4.2: Carry out a procedure to determine specified points
(including zeros, maximums, and minimums) of polynomial
functions.
At the end of this lesson, students will be able to:
1. …analyze a quadratic function to tell if it’s a parabola.
2. …graph quadratic functions by changing the functions in to equations by
completing the square.
3. …find the vertex of an equation/function without completing the square.
4. …find the minimum and maximum value of a parabola.
1. Students should be able to tell whether or not the graph of a function is a
parabola.
2. Students should know how to find the vertex of a function by using the
equations given for h, k. This is done without completing the square.
3. Student should understand that the axis of symmetry is an x = h, the h
coming from the vertex.
4. Find the max and min of a parabola.
1. Textbook – (Mcgraw-Hill. (2005). Glencoe algebra 2. New York:
Glencoe/Mcgraw-Hill)
2. Answers to quiz 7.2 and 7.4
3. Chapter 7 Study Guide
4. Previous Night’s homework (Section 7-5)
PART OF LESSON
DETAILS & SPECIFICS
Hand back and go over quiz 7.2, 7.4
Go over homework from previous night (Section 7.5)
Answer any questions from the previous section.
ANTICIPATORY SET Give students Chapter 7 Study guide for their test.
Asks students what makes an equation a parabola. Students should say that the
squared term in the equation or function makes that equation or function have a
parabolic graph.
Begin by asking the students if they can graph f(x) = 2(x – 3)2 + 1. The student
mostly like will say that they can graph it, but ask them if they notice something
different about this equation/function that is different from other ones they’ve seen
before. They should say that instead of it having y = or 0 = , that it’s an f(x) =
equation. Ask students what f(x) can be changed to. F(x) = y.
LEARNING
ACTIVITIES PART:
Explain to student that they must change f(x) to y first before thinking about graphing
PRESENTATION OF
the function. This now changes the function to an equation. Then have student write
INFORMATION AND
the equation in quadratic graphing form by moving the 1 to the other side and
MODELING
changing it to y – 1= 2(x – 3)2. Students should recognize this form from the last
lesson, being able to identify the vertex (3, 1), the axis of symmetry (x=1), and they
look of the graph.
Ask students if they can graph, f(x) = 3x2 – 6x +1. They can, if they change the
function to an equation. Now it is y = 3x2 – 6x +1. Ask students if the equation is in
the quadratic graphing form. It isn’t, so what do they think we need to do to the
equation to make it look like y – k = a(x – h)2. Ask student what y – k = a(x – h)2
reminds them of. (Completing the square). Therefore students need to change the
standard form of the quadratic equation into the quadratic graphing form to graph the
function. This would be a great time to review completing the square. However, this
time instead of 0 = the equation, it is now y = the equation. The new equation will
be y – 2 = 3(x – 1)2. From this from, students should recognize the vertex and the
axis of symmetry. Student should also know how to find the x- and y- intercepts.
After doing this, tell students that there is a much easier way to find the vertex of a
function without having to complete the square if they remember the formulas for h
and k.
Tell student that if they know h, they don’t need to remember the formula for k, since
h, is x, and by find y, students know the plug x back into the equation. This is used
with h(x) and k(y).
Have students find the vertex of g(x) = 6 + 6x – 3x2 by using the formula for h and k.
Show the students how to use the formula for both h and k, and then show them that
once they find h, they can plug in that value for x, to find the k value.
Discuss domain and range of parabolas with the students. (Example 3 from page
334). Tell students that the domain of every parabola is all real numbers, and the
range of parabolas is from how low or how high the parabola goes along the y axis.
Use Example 3.
CHECKING FOR
UNDERSTANDING
GUIDED PRACTICE
INDEPENDENT
PRACTICE
CLOSURE
Ask students what they think the max or min of a parabola is based off sketched
drawings of parabolas that is open upward, and one that is open downward. (upward
min and downward max). As students what they think makes a parabola have a max
or min. Students should remember that a flips the graph upward or downward. So if
a > 0 then the function or equation has a minimum value. If a < 0 then the function
has a maximum value. Students should also recognize that the max or min value
comes from the k value from the vertex.
Ask students if they are understanding what is being taught or what questions they
may have.
Have student work the orals (page 335 #1-6) to tell if the function as a max or min
and at what value.
Homework – Page 336 # 1 – 29 odd
Asks students what the first thing they should do in graphing functions.
Also ask students the process of changing a function in standard form to quadratic
graphing form.
Ask students the formulas for h, k…
Ask students how to determine the min or max value of a parabola.
INSTRUCTOR: Tyesha Deas
GRADE LEVEL: 9-11th
Algebra 2 Honors (2B, 3A)
STANDARDS
OBJECTIVES
GOALS
MATERIALS
PART OF LESSON
ANTICIPATORY SET
TITLE OF LESSON:
Writing Quadratic Equations and Functions
(Section 7-7)
UNIT: Quadratic Equations and
Functions
South Carolina Mathematics Standards:
Standard IA-1.6: Understand how algebraic relationships can be represented
in concrete models, pictorial models, and diagrams.
Standard IA-3.6: Carry out a procedure to write an equation of a quadratic
function when given its roots.
At the end of this lesson, students will be able to:
1. …write quadratic equations from the given roots.
1. Students should be able to tell write a quadratic equation from given
roots.
2. Students should understand the relationship between the coefficients of a
quadratic equation and the roots.
1. Textbook – (Mcgraw-Hill. (2005). Glencoe algebra 2. New York:
Glencoe/Mcgraw-Hill)
2. Quiz on Section 7.5 – 7.6
3. Note sheet (Nature of Roots in Relation to the graph)
4. Previous Night’s homework (Section 7-6)
DETAILS & SPECIFICS
Go over homework from previous night (Section 7.6)
Answer any questions from the previous section.
Give students Quiz on section 7.5 – 7.6
Give student the Nature of Roots in Relation to the graph, explaining that the
discriminant also can tell what type of graph the parabola will be. If two real roots,
the parabola crosses the x axis. If there is one double root then it crosses the x axis at
the max or min point (the vertex). If the roots are imaginary, then the parabola does
not cross the x axis.
Begin by asking students the process of thinking for factoring a quadratic equation.
Student should say that they think about factors of the last term, and how those
factors sum together to get the middle term. If they don’t ―get‖ this, then give a
sample problem and ask students how they would factor this problem. Eventually
they will come up with the ―process‖ of factoring.
LEARNING
ACTIVITIES PART:
PRESENTATION OF
INFORMATION AND
Tell students that instead of factoring quadratic equations, they would be learning
MODELING
how to create the equations based off the roots.
Show students that r1 and r2 are the roots given to a quadratic equation. Explain that
an equation can begin by writing, (x - r1)(x - r2) = 0. By multiplying the two
binomials together, the equation becomes,
. A is only used when the sum or
product is a fractional number and not an integer. A is used to make the equation
have integral coefficients.
Ex: roots are -3 and 1. The sum of these roots is -2; the product of the roots is -3. So
the equation to be x2 – 2x – 3 = 0. After showing this example, allow students to
work on #11-14 from page 342 from Oral Exercises, and then allow them to share
with a partner their answers. Then call on students to tell what answer they had, and
allow students to work their answers on the board.
__________________________________________________________________
Begin word problems from this section if time allows. Explain to students that once
they’ve set up the quadratic equations, that the main goal is to find the min and max.
Student should remember that the min and max comes from the vertex (h, k).
Students will have to find h, to solve for k, and k will be the min or max of the
problem. Work the even problems from the book, page 343 -344.
CHECKING FOR
UNDERSTANDING
GUIDED PRACTICE
INDEPENDENT
PRACTICE
CLOSURE
Ask students if they are understanding what is being taught or what questions they
may have.
Have students work on 14, 16, 18 from page 342 and number 6 from page 343.
Homework – Page 342 # 1 – 27 odd, page 343 # 1-11 odd
Ask students what the ―formula‖ is for writing the equation of a parabola given the
roots of the equation.
Also ask students the main idea behind finding the min or max of an equation.
INSTRUCTOR: Tyesha Deas
GRADE LEVEL: 9-11th
Algebra 2 Honors (2B, 3A)
STANDARDS
OBJECTIVES
GOALS
MATERIALS
TITLE OF LESSON:
Writing Quadratic Equations and Functions
(Section 7-7) Word Problems
UNIT: Quadratic Equations and
Functions
South Carolina Mathematics Standards:
Standard IA-1.6: Understand how algebraic relationships can be represented
in concrete models, pictorial models, and diagrams.
Standard IA-3.6: Carry out a procedure to write an equation of a quadratic
function when given its roots.
Standard IA-3.5: Analyze given information (including quadratic models) to
solve contextual problems.
Standard IA-1.3: Apply algebraic methods to solve problems in real-world
contexts.
At the end of this lesson, students will be able to:
1. …write quadratic equations from given information in a word problem
2. …find the min or max of the quadratic equation that was written from
the word problems by finding h and k.
1. Student should be able to write the quadratic equation from a given
word problem to find the min and the max. Students should make
connections to the beginning of section 7.7.
1. Textbook – (Mcgraw-Hill. (2005). Glencoe algebra 2. New York:
Glencoe/Mcgraw-Hill)
2. Quiz on Section 7.5 – 7.6 (answers)
3. Previous Night’s homework (Section 7-7)
PART OF LESSON
DETAILS & SPECIFICS
Hand back and go over Section 7.5 - 7.6 quiz
Go over homework from previous night (Section 7.7) (Save word problems to do in
ANTICIPATORY SET
the lesson)
Answer any questions from the previous section.
Ask students about the word problems for homework. Because this is a difficult
LEARNING
ACTIVITIES PART: section with the word problems, problems should be solved in class. Work problems
PRESENTATION OF from homework 1-11 odd, and included any problems from the evens that were not
INFORMATION AND discussed from the previous lesson.
MODELING
Ask students if they are understanding what is being taught or what questions they
CHECKING FOR
may have.
UNDERSTANDING
GUIDED PRACTICE
INDEPENDENT
PRACTICE
CLOSURE
Have students rework question 7.
Study Guide for the test
Have students complete question 8, related to question 7, and have them turn in as an
exit slip.
INSTRUCTOR: Tyesha Deas
GRADE LEVEL: 9-11th
Algebra 2 Honors (2B, 3A)
STANDARDS
OBJECTIVES
GOALS
MATERIALS
PART OF LESSON
TITLE OF LESSON:
Chapter 7 Review
UNIT: Quadratic Equations and
Functions
South Carolina Mathematics Standards:
Standard IA-1.3 Apply algebraic methods to solve problems in real-world
contexts.
Standard IA-1.5 Demonstrate an understanding of algebraic relationships by
using a variety of representations (including verbal, graphic,
numerical, and symbolic).
Standard IA-1.6 Understand how algebraic relationships can be represented
in concrete models, pictorial models, and diagrams.
Standard IA-3.3 Carry out a procedure to solve quadratic equations
algebraically (including factoring, completing the square,
and applying the quadratic formula).
Standard IA-3.4 Use the discriminant to determine the number and type of
solutions of a quadratic equation.
Standard IA-3.5 Analyze given information (including quadratic models) to
solve contextual problems.
Standard IA-3.6 Carry out a procedure to write an equation of a quadratic
function when given its roots.
Standard IA-4.2 Carry out a procedure to determine specified points
(including zeros, maximums, and minimums) of polynomial
functions.
Standard IA-4.4 Analyze given information (including polynomial models)
to solve contextual problems.
At the end of this lesson, students will be able to:
1. …have a better understanding of the material in chapter 7 in order to be
prepared for the test.
1. Students should ask questions from the review sheet to that they are
prepared for the chapter 7 test.
1. Textbook – (Mcgraw-Hill. (2005). Glencoe algebra 2. New York:
Glencoe/Mcgraw-Hill)
2. Chapter 7 review sheet (answers)
DETAILS & SPECIFICS
ANTICIPATORY SET Ask student if they have any questions from the review sheet.
LEARNING
ACTIVITIES PART:
PRESENTATION OF
INFORMATION AND
MODELING
Allow students to work in pairs for about 30 minutes to work on the review sheet.
This allows students to learn from each other as they understand the concepts of the
chapter. Afterwards, ask students if they have any questions about the study guide.
Have students who know how to work the problems go to the board and help their
peers learn the material. Add to the discussion when needed.
Explain the set up of the test and what is expected of them from the test.
CHECKING FOR
UNDERSTANDING
Ask students if they are understanding what is being taught or what questions they
may have.
GUIDED PRACTICE
INDEPENDENT
PRACTICE
CLOSURE
-Homework- Study! Study! Study!
Close the class by encouraging the students to study for the chapter 7 test.
INSTRUCTOR: Tyesha Deas
GRADE LEVEL: 9-11th
Algebra 2 Honors (2B, 3A)
STANDARDS
OBJECTIVES
GOALS
MATERIALS
PART OF LESSON
TITLE OF LESSON:
Chapter 7 Test
UNIT: Quadratic Equations and
Functions
South Carolina Mathematics Standards:
Standard IA-1.3 Apply algebraic methods to solve problems in real-world
contexts.
Standard IA-1.5 Demonstrate an understanding of algebraic relationships by
using a variety of representations (including verbal, graphic,
numerical, and symbolic).
Standard IA-1.6 Understand how algebraic relationships can be represented
in concrete models, pictorial models, and diagrams.
Standard IA-3.3 Carry out a procedure to solve quadratic equations
algebraically (including factoring, completing the square,
and applying the quadratic formula).
Standard IA-3.4 Use the discriminant to determine the number and type of
solutions of a quadratic equation.
Standard IA-3.5 Analyze given information (including quadratic models) to
solve contextual problems.
Standard IA-3.6 Carry out a procedure to write an equation of a quadratic
function when given its roots.
Standard IA-4.2 Carry out a procedure to determine specified points
(including zeros, maximums, and minimums) of polynomial
functions.
Standard IA-4.4 Analyze given information (including polynomial models)
to solve contextual problems.
At the end of this lesson, students will be able to:
1. …complete chapter 7 test
1. Students should complete chapter 7 test after having had two weeks of
instruction and plenty of study.
1. Textbook – (Mcgraw-Hill. (2005). Glencoe algebra 2. New York:
Glencoe/Mcgraw-Hill)
2. Chapter 7 Test
3. Post-Assessment
DETAILS & SPECIFICS
ANTICIPATORY SET Ask students if they have any last minute questions about the test and address it.
Give student the Chapter 7 test.
LEARNING
ACTIVITIES PART: Have students complete post-assessment after the test.
PRESENTATION OF
INFORMATION AND If time allows for it, have students will need to begin working on chapter 8 with
section 8.1. Students should read the section and copy the definitions.
MODELING
CHECKING FOR
UNDERSTANDING
Ask students if they are understanding what is being taught or what questions they
may have.
GUIDED PRACTICE
INDEPENDENT
PRACTICE
CLOSURE
Classwork – Page 354 Oral Exercise All
Tell class that you hope they did well on the test, and that we’ll be beginning chapter
8 on Variation and Polynomial Equations the next class period.--
Section IV: Analysis of Student Learning
The post-assessment is in two parts. The post-assessment was going to be the chapter
7 test, however, while students were taking the tests, students keep complaining about
how hard the test was, and constantly asked questions during the test. I knew that we
had a great review, and that student were asking great questions, and were giving great
feedback during class. However, when the test came, the students acted like they’d
never seen any of the information, and thus, I decided to give the students the same
pre-assessment, as another part to the post-assessment to see if the students had any
growth from the beginning of the unit to the end of the unit. Again, the post-assessment
used had a total of 14 points, one point for each correct answer.
Number of Students per score
Post-Assessment Scores for Entire Class
5
4
3
2
1
0
0 0.5 1 1.5 2
3
4
5
Pre-Assessment
6
7
8
9
10 11 12 13 14
Post-Assessment
The graph depicted above shows the Pre- and Post-Assessment scores for the entire
class. The purple bars are the pre-assessment, and the red bars are the post
assessment. From the graph, one can conclude that after the unit was taught, students
scored high on the post assessment. The pre-assessment’s lowest score was 0 points,
while the lowest score on the post-assessment was 6 points. The highest score on the
pre-assessment was a 6 while the highest score on the post-assessment was the max
points, 14. The mean of the pre-assessment was about 2.1 while the mean of the post
assessment was 10.8. I think this shows that the students learned a lot from this unit.
As I taught the lessons, I would remind students about the questions that were on the
pre-assessment and then told them that what was being covered at the moment to help
them make the connections from the questions asked before the teaching and why it
was asked. The conclusion I can draw from this is that the students improved their preassessment scores as post-assessment scores after the unit was taught.
Number of Students per score
Post-Assessment Scores by Gender
5
4
3
2
1
0
6
7
8
9
10
Girls
Boys
11
12
13
14
This graph shows a comparison between boys and girls in the class. There were 9 girls
who completed the post assessment. There were 10 boys who completed the post
assessment. From the girls’ data, it appears that they scored slightly higher on the
post-assessment than the boys. The girls’ mean score was 11.6, while the boys mean
score was 10.1. The median score for the girls was 12, while the median score for the
boys 10.5. I think that there were a few factors that contributed to the girls having high
scores. The girls in the class seem to be more conscientious about their math work. All
the girls sit in the front of the room (by choice), while all the boys sit in the back (by
choice). When teaching, the girls are answering more questions when the questions
are asked without picking someone. The boys on the other hand, are more talkative,
and play around in class more than the girls. While teaching, I constantly have to calm
the boys down, not that I don’t with the girls, but more often than not, I’m asking a male
student to pay attention. There are a few exceptions. One of the male students is very
conscientious about his work, and makes some of the highest grades in the class. The
other boys in the class are conscience of their math work; however, they seem to take
math class a fun time sometimes. When students were asked to work in groups, or
pairs, the girls were more diligent with making sure they got their work done, and would
ask me if they were coming up with correct answers. Girls were also more willing to
volunteer to go to the board, than boys. The boys were often reluctant about being
asked any questions in class in which they had to answer aloud, because they were
unsure of their answers then the girls. Many studies have shown that around the age of
these students, girls are more likely to score poorly in their math classes and not
participate as actively as their male counterparts. However, in this class it seems to be
the opposite effect. I do think that the boys learned from the unit, however, I think that
they could have performed better on the post-assessment. Many of the students said
that they wished they could have had the post-assessment as their unit test because it
was easier than test. With the students making a comment like that, I think that they did
learn something from the unit, and felt better about answering the questions than they
had the first time.
Post-Assessment Scores for Two Individual Students
Student's Score on Post
Assessment
14
12
10
8
6
4
2
0
"Elizabeth"-Repeater
"Matthew" - 1st Time
The data above compares two students: one, “Elizabeth”, who has taken Algebra II
Honors for the second time, and another, “Matthew”, who is taking Algebra II Honors for
the first time. “Elizabeth” is repeating Algebra II Honors after taking Algebra II MEGSSS
last year with a final score of 70. According to the data, Elizabeth and Matthew scored
the same score of a 14 on the post assessment. Elizabeth has shown improvement
from her pre-assessment score to her post-assessment score. Elizabeth scored a 4 on
the pre-assessment, even after having seen the material before. Her post-assessment
score was a 14. This shows that she has learned the concepts that were on the preassessment as I was teaching them. Matthew also showed great improvement from his
pre-assessment score to his post-assessment score. His pre-assessment score was a
0, while his post-assessment score was a 14. This shows that Matthew also learned
the concepts of the pre-assessment so that he could correctly answer the same
questions on the post-assessment. I think this shows that Elizabeth is at the same level
up to the same level as one of the honor students, since she scored just as well as the
honors student, and maybe they are at about the same level of learning.
Distribution of Grades On Unit Test
0%
9%
5%
10%
76%
100-93 (A)
92-85 (B)
84-77 ( C)
76-70 (D)
60 & Below (F)
The data above shows the distribution of grades for the unit test. According to the data,
the students did not do well on the test. No student made an A. Two students made a
B (both 86), one student made a C (81.5), two students made scored a D (75 & 70.5)
and the rest, 16 students, scored 60 and below (68 to 18). It looks like the students
didn’t learn much during this unit. Only 24% of the students passed the test and 76% of
students failed the test. I was extremely disappointed in their test grades. The average
score was a 55, while the median was a 55 as well. The highest score was an 86 and
the lowest score was an 18. I do think the students learned a lot during the unit. I think
the students began to become overwhelmed while taking the test. I also think that the
comments by the students during the test caused other students to become unfocused.
A few students commented that the test was too hard and this gave others the
opportunity to say the same thing and complain. It also didn’t help that my other
Algebra II Honors class told some of the students that the test was hard, so therefore,
many of them came in thinking that they could not do the test, or that the test was too
hard. During the review of the test, I knew that the students knew the material, so I’m
not sure why students did not do better on the test than they did. One of the students
that scored the highest, usually scores the highest on all test anyway. The other
student who scored the 86 was a student who frequently came in after school to get
help.
Number of Students in each grade catergory
Distribution of Grades On Unit Test by Gender
10
9
8
7
6
5
4
3
2
1
0
100-93 (A)
92-85 (B)
84-77 ( C)
Boys
76-70 (D)
60 & Below
(F)
Girls
The data above depicts the tests scores made between the boys and the girls. The
boys’ averages test score was 48.1, while the girls’ average test score was a 64.
However, I think this slightly screwed because there are more boys than there are girls,
even though by the graph, it looks like the boys did better than the girls. Since there
were more boys, it also would mean that there is a greater chance of boys not doing
well on the test than there is girls. I also think that the average is hurting the boys’
score because the lowest score in the class, and 18 was made by a boy. Two boys
made the highest scores, of an 86. The girls’ lowest score was a 52, while their highest
score was an 81.5. I’m not sure if there is a correlation between why the boys might
have done worse than the girls. The only thing I can think of is that boys, with the
exception of the one who scored one of the highest scores in the class, isn’t as serious
in class as the girls, even though they have their moments as well. I think that out of
this class more girls came in after school to receive help when they needed it, with the
exception of the other boy that scored the highest score. When it all said and done, I
just think that the overall grades were poor regardless of what gender scored better
than the other.
Score on Unit Test
Unit Test Score of Two Individuals
78
77
76
75
74
73
72
71
70
69
68
67
66
65
64
"Matthew" - 1st Time
"Elizabeth" - Repeater
The data above shows the test score of two individual students, one student “Elizabeth”,
who is a repeater, and one student, “Matthew”, who is taking this course for the first
time. This data shows that Matthew scored better on the test than Elizabeth. I think this
has to do with the fact that Elizabeth did not complete three homework assignments
while Matthew completed all his homework assignments. Even though Elizabeth as has
seen the material before, she probably still need to do her homework to make sure that
she understood the concepts of the unit. However, at the same time, Matthew only
scored seven points higher than Elizabeth, but those seven points made Matthew have
passing grade. I also do not think that neither Matthew nor Elizabeth put forth their best
effort. I’m not entirely sure if there is any correlation between the two scores. Maybe
having seen this same information in another course did not make it easier for Elizabeth
to pass this test, even though it would stand to reason that she should have scored
higher than she did.
Grades
Grades for this unit were determined by quiz grades, homework grades, and the unit
test. Homework was given after every lesson, and if a student failed to do his or her
homework, ten percent was taken from their homework score. Test were 60% of
students’ grades, quizzes 20%, and homework 20%. Homework was assessed on
whether or not the students attempted to complete the assignment. Test and quizzes
were graded on accuracy. Quizzes were out of 100 points.
Section V: Reflection and Self-Assessment
Based off the results in the previous section, it looks like my students did not meet all of
the goals I set forth for them to learn. Seventy-six percent of the class failed the unit
test, even though the 15 out of the 19 (about 78%) students who took the postassessment passed (same from pre-assessment), while the whole class failed the preassessment. I do think that my students learned something from the unit, clearly shown
from the post-assessment results, but I think this only because the post-assessment
questions had limited about of actual computational math. Most of the questions
required that the students answered a question based of what they thought, while the
unit test asked students to answer math question computationally. However, there were
a few questions from the pre-assessment that were worded slightly differently on the
unit test that most of the students answered correctly. Overall, the results from this unit
are very disappointing.
If I reflect on their performance and base it off my own performance, I’d have to say that
it looks like I did not teach this unit very well. However, my coaching teacher as well as
others who observed me during this unit commented on how well I explained
information and that they thought my teaching of the unit was great. But because of the
how unsuccessful the students were, I equate that to me not having taught the unit well.
I feel that I have let the students down. There are many things I would like to and would
have done differently if I were given the opportunity to teach this unit again.
Because I am in someone else’s classroom, and am following their rules and guidelines,
I was unable to do some of the things I wanted to do. I think that this unit was more
teacher lead that necessary. I would have liked to have had more student-led learning
because I think students are able to better understand and retain information when they
discover for themselves what they are learning. The section on graphing quadratics, I
would have liked to have incorporated technology, such as the graphing calculator, or
Geometer’s Sketchpad. However, my coaching teacher thought it was unnecessary,
and a waste of time. Many of my students were in class while I was teaching that
section trying to figure out how to graph it on the calculator to see if they could make
connections with it. After all, the students are allowed to use their calculators on
assessments in class. I thought this would have been a great tool for them to use. I do
want the students to understand how to calculator and graph equations with paper and
pencil, but I also think that it’s important for them to learn the how to use the calculator
proficiently to find their answers. Maybe as part of the assessment, I could have had
the student to calculate and graph one equation with paper and pencil, and then allow
the students to also graph one by using their calculator. That way the students would
be using the knowledge of how to use a graphing calculator, and at the same time, I can
assess whether or not the students really understand the concepts.
Another thing I would have done differently with this unit was changing the pace. I think
the unit was taught to quickly, but this is the way my coaching teacher wanted it. This is
the first time that these students have ever seen quadratics, and they need to
understand how to solve quadratics by completing the square or using the quadratic
formula. Completing the square is not an easy concept to learn, and I think that I should
have broken the first section with completing the square, the quadratic formula and the
discriminant into two different sections, allowing one whole class period for completing
the square and one whole class period of the quadratic formula and the discriminant.
There were also two sections of word problems in this unit, and these students do not
have a strong background with word problems. I think that spending a day each for the
sections that had word problems would have been better than learning the concepts of
the section along with the word problems. That would allow the students to be able to
decipher and analyze each word problem and connect it to the main idea of the section.
I also probably would have done more assessing. Even though I asked a lot of
questions and had students demonstrate what they knew on the board, I think I should
have done more. I think quizzes are good, but I should have done more assessing if I
were allowed to. I also included a lesson plan on a review period, however, was not
allowed to use it, because again, it reviewing before a test is a waste of class time. I
think that that would have helped me gauge better where the students were in their
knowledge of the unit before the test. During the test, many of the students commented
that the test was too hard. I don’t think it was too hard, my coaching teacher didn’t think
it was too difficult, and the math department head did not think it was too hard. In fact,
both my coaching teacher and the department head said that it was not an “honors”
test, and was not a test that would challenge the students to a high level.
Question 5 of the test was the only question that I put on the test that was “easy” points
because I knew that the students would know how a, h, and k affected the position of a
quadratic equation. All other questions were asked in class, as well as on the review
sheet, just with different numbers. Two questions on the test were questions that the
students had seen on a previous quiz, or on the review sheet. As for the review sheet,
that was an optional assignment for the students. My coaching teacher believes it is up
to the student to want to do the work, and therefore should do the work. If they have
any questions, they needed to come before school or after school to get help, but the
review sheet was not discussed in class as a whole group. That is one thing I would
have changed. I probably would have allowed about 30 to 45 minutes in class for
students to ask questions about the review sheet so that they were not just waiting on
the answers of the review sheet that was posted online. That way I would be able to go
over some of the concepts that were unclear that to the students. Even if only one
student needed help with a concept, it probably means that there is another student in
the class that has the same question.
I also think that the students’ extracurricular activities also affected the students’
performance during this unit. Many students were a part of the Hairspray production,
and my of the students I think did not have the time to study like the normally would.
Some of the students I think just did not put for the effort needed to perform well. It was
also during advisement time, and some students were missing key instructional time
while they were in guidance signing up for classes for the next school year. The student
that scored the lowest, an 18, actually had advisement in the middle of the test. I told
him that his test was just as important and to try to get as much work done on it as
possible, but he was too excited about going to advisement, that he never came back to
finish is test. I did allow the class another twenty minutes on the test during the next
class period since so many students had not finished the test the first time.
I enjoyed teaching this unit, however, I’m disappointed that the students did not do as
well on the unit test that I would have liked or what I had hoped for. Next time I teach
this unit, I’ll keep in mind the changes I’d like to make to this unit, and hopefully, the
next group of students produces better results.