Introduction to Functions 9th Grade Algebra Unit by Rachel ...

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Introduction to Functions

9th Grade Algebra Unit

by Rachel McGuire

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Table of Contents

Context Analysis ................................................................................................................................. 3

Content Analysis ................................................................................................................................. 5

Content Outline ................................................................................................................................... 7

Concept Map .......................................................................................................................................... 9

Common Core State Standards ................................................................................................ 10

Pre-Test¡­¡­¡­¡­¡­¡­¡­¡­¡­. ........................................................................................................................ 13

Pre Assessment ................................................................................................................................. 17

Lesson Plans.¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­¡­23

Lesson Plan 3.1 Relations and Functions, Domain and Range ....................................... 23

Lesson Plan 3.2 Linear vs Nonlinear Functions .................................................................... 34

Lesson Plan 3.3 Function Notation ............................................................................................ 39

Lesson Plan 3.4 Graphing Standard Form .............................................................................. 47

Lesson Plan 3.5 Graphing Slope-Intercept Form ................................................................. 55

Lesson Plan 3.6 Transformations ............................................................................................... 67

Unit Overview ..................................................................................................................................... 84

Post Test¡­¡­¡­¡­¡­¡­¡­¡­¡­ .................................................................................................................. 85

Post Assessment............................................................................................................................... 90

Reflection and Self Evaluation ................................................................................................. 96

Teaching Materials .......................................................................................................................... 98

Resources ............................................................................................................................................. 98

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Context Analysis

Community Factors

Milan High School is located in Milan, Michigan and part of the Milan Area

Schools district. The building houses ninth through twelfth grade students.

Milan is a small community with a population of about 14,253 people and is

located about 15 miles south of the Ypsilanti/Ann Arbor area. Most of the

area consists of farms and many students work on their parents land. Only

14.6% of adult men over 25 and 18.5% of women went on to college after

high school. Of those percentages, only about half of them graduated with a

bachelor¡¯s degree. The median household income is about $82,000 and the

average family size is 3. A majority of students come from two parent

households and 92% of the student body (out of about 600 students) is

Caucasian.

Classroom Factors

In my classroom we have 36 individual student desks. Most of the classes

are relatively full, with only 1 or 2 desks left empty. In my class I like to

promote cooperative learning. Most days the desks are arranged into groups

of 4 in order to do so. Unfortunately we have very limited technology

available to us. We are limited to a classroom set of TI-84 calculators. Every

day in class the agenda is written on a side whiteboard and materials for the

day are on the front board typically accompanied by a ¡°do-now¡± startup

problem. The students know to come in, pick up any handouts, a calculator,

and their binder that they are allowed to keep in the classroom.

Student Characteristics

A majority of my algebra classes are freshman students. Many of them are

still getting used to high school and can tend to be lacking in maturity levels.

This being the case, I have to keep the class as structured as possible and I

can¡¯t put too much responsibility on the students. I also have a high number

of students on IEP plans and another portion of students are retaking the

class. For many students, algebra is a new concept and students do not have

very much prior knowledge relevant to the class material. A lot of these

characteristics will play a significant role when it comes to planning my unit.

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Implications for Instruction

Due to the high level of IEPs and students retaking algebra, my unit will

need to move at a slower pace. Most of this material is brand new and I will

have to demonstrate a lot of the concepts. Unfortunately this will limit the

opportunities for inductive and cooperative lessons. Also due to the

characteristics of the class, I believe cooperative group work may be difficult

for some students. Many students tend to have issues focusing and staying

on task when they are permitted to work in a group. I will need to make

sure I give very clear directions and explain what my expectations are for

the class periods when we are working in groups.

Rationale

Students:

Have you ever wondered how much it would cost you for every minute you

talk on the phone? How about how long it will take to fill up that pool you¡¯ve

been thinking about all summer? In this unit we will discover how we can

model real life problems with linear relationships. We will also learn how to

graph these functions in order to visualize the relationship. Several of the

problems we encounter on a daily basis can be modeled using a linear

function and we don¡¯t even realize we are doing it.

Teachers:

This unit covers all of the material pertaining to the introduction of linear

functions including domain and range, function notation, graphing, and

transformations. The unit directly reflects several of the High School

Functions Common Core State Standards and aligns with the school district¡¯s

benchmarks. The material is presented in a variety of ways including group

work, hands-on activities, and individual work to monitor personal progress

and to prepare students for the summative assessment.

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Content Analysis

Common Core State Standards

HSF-IF.A.1 Understand that a function from one set (called the domain) to another

set (called the range) assigns to each element of the domain exactly one element

of the range. If f is a function and x is an element of its domain, then f(x) denotes

the output of f corresponding to the input x. The graph of f is the graph of the

equation y = f(x).

HSF-IF.A.2 Use function notation, evaluate functions for inputs in their domains,

and interpret statements that use function notation in terms of a context.

HSF-IF.C.7a Graph linear and quadratic functions and show intercepts, maxima,

and minima.

HSA-CED.A.2 Create equations in two or more variables to represent relationships

between quantities; graph equations on coordinate axes with labels and scales.

HSF-IF-LE.A.1b Recognize situations in which one quantity changes at a constant

rate per unit interval relative to another.

HSF-IF-LE.A.2 Construct linear and exponential functions, including arithmetic and

geometric sequences, given a graph, a description of a relationship, or two inputoutput pairs (include reading these from a table).

HSF-BF.1a Write a function that describes a relationship between two quantities.

HSF-BF.B.3 Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x),

f(kx), and f(x + k) for specific values of k (both positive and negative); find the

value of k given the graphs. Experiment with cases and illustrate an explanation of

the effects on the graph using technology. Include recognizing even and odd

functions from their graphs and algebraic expressions for them.

Generalizations

?

We can model real world situations with linear functions.

Focus Question: Can you think of any problems that have a linear

relationship?

?

A linear function has two variables and has a constant rate of change.

Focus Question: How can I determine if two objects will have a linear

relationship?

?

Function Notation can be used as another way to write a function to easily

represent the input and output.

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