Linear Equations and their Graphs Aisha Khan

Have they not travelled in the land,

and have they hearts wherewith to

feel and ears wherewith to hear? For

indeed it is not the eyes that grow

blind, but it is the hearts, which are

within the bosoms, that grow blind.

Quran 22:46

Algebra I Spring 2014

Rationale: Changes in gas prices, tuition rates, and housing prices are something

that affects all of us at one point or another in our lives. Therefore, it is useful to be

able to predict how these figures have and will changes over time. This is done

through the use of algebra. In this unit, students learn about the graphs of lines,

something that is fundamental is all higher level math classes. In addition, this unit

teaches students the science of measuring and predicting change.

Summary: This unit begins with learning about the equations of lines, how to

construct them, and how to graph them. From there, students will be asked to

research college tuition prices from the past, graph this data, and come to a

conclusion about the cost of a college education five years from now. The unit will

end with the students presenting their findings in the form of a report and oral

presentation.

Essential Question(s):

How can I use linear equations in the real world?

How and when do I draw a line of best fit?

How can I use this information to solve a problem?

Common Core:

HSA.CED.A.2

o Create equations in two or more variables to represent relationships

between quantities; graph equations on coordinate axes with labels

and scales

HSA.REI.D.10

o Understand that the graph of an equation in two variables ins the set

of all its solutions plotted in the coordinate plane, often forming a

curve (which could be a line).

HSS-ID.B.6

o Represent data on two quantitative variables on a scatter plot, and

describe how the variables are related

Fit a function to the data; use functions fitted to data to solve

problems in the context of data. Use given functions or choose

a function suggested by the context. Emphasize linear,

quadratic and exponential models

Informally assess the fit of a function by plotting and analyzing

residuals.

Fit a linear function for a scatter plot that suggests a linear

association

HSS-ID.C.7

o Interpret the slope (rate of change) and the intercept (constant term) of

a linear model in the context of the data.

Literacy Strategies:

Exit Slip

Admit Slip

Mapping

Teacher-Student Correspondence

Reflective Writing

Multigenre project

Length of Unit: ~ 4 weeks

Materials and Resources:

- school: computers, internet access, and relevant software

- teacher: class time dedicated to the project

- student: time at home, a final report and presentation

Assessment:

- pre: class discussion about problem solving, lesson on coordinate grid if

necessary

- formative: in class writings, correspondence, quizzes to assess ability

- summative: final presentation and report

~ Day 1 Lesson Plan ~

Topic: Graphing and Writing Equations of Lines

Objective(s):

After administering the pretest, both students and teacher will be able to gauge the

level of expertise the students have with pre-algebra

Students will have a basic understanding of what algebra focuses on.

Materials needed:

SmartBoard, Whiteboard Paper, Pencil

Phase 1: Administer pretest; go over questions on white board with student

volunteers

Phase 2: Review material if necessary

Phase 3:

Guided Discussion:

Examples of insurance premiums vs Age/Gender

How can we use this information?

What steps did researchers have to take to collect the information and present it in

this form?

What are benefits of this kind of visual?

Phase 4: Recap

Assign practice problems if necessary

Exit Slip: Come up with your own example of algebra in real life

Presentation Model Lesson Plan

Topic: Graphing linear equations

Objective(s):

Given a set of linear equations, students will describe graph behavior

Given a set of linear equations, students will graph equations

Materials Needed:

SmartBoard

PowerPoint Presentation

Graph Paper

Worksheets (HW)

Phase 1: Introduction: Clarify aims and establish set.

Recall the 3 different forms of linear equations

Goal today is to predict graph behavior and to graph by hand

Phase 2: Present the advance organizer

Equation in slope intercept form, The graph of this equation

Most convenient for graphing

How do we get from here to here?

Phase 3: Present learning materials (outline of content):

Breaking down the parts of an equation in slope intercept form

Slope – rise/run

Y intercept

How those components manifest themselves on a graph

Starting point

Rate of change from one point to the next

Positive/negative slope and the direction of the graph

Steps for graphing an equation in slope intercept form

1. Place y intercept

2. Use slope graph next points

3. Check graph against original equation – do they match?

Phase 4: Application: (check for understanding and strengthen student thinking)

Ask students to demonstrate on the board

Worksheets to be completed during class

Homework for more practice

Source: Arends, R.I. (2008). Learning to Teach (7th

Ed). McGraw-Hill Higher

Education.

Direct Instruction Lesson Plan

Topic: Slope – Intercept form of the equation of the line

Objective(s):

Given a graph or a pair of points, students will write the slope – intercept form of

the equation of the corresponding line

Materials needed:

SmartBoard, Whiteboard, markers

Phase 1: Introduction: Clarify goals and establish set.

Have examples of lines and non – lines on the SmartBoard

Ask what makes a line a line

Review components of slope – intercept form

Phase 2: Demonstrate skill or process (use Task Analysis):

1. Find the slope

2. Fill in components of the equation

3. Plug in given point and solve for y – intercept

4. Write final equation

One example points equation, one graph equation

Phase 3: Provide guided practice:

Worksheet, going through one step at a time as a class for one of each type of

problem

Students finish remainder of worksheet individually and check their work with a

partner

Phase 4: Check for understanding and provide feedback:

Circulate as students work to make sure everyone works independently first

Have students put answers on the whiteboard when finished (ask for volunteers?)

Phase 5: Provide extended practice and transfer:

Homework: take the given table and write the equation of the line, predict the

output value for an input value not given beforehand.

Find the equation of the graph shown.

Problem-Based Instruction Model Lesson Plan

Problem: How much will you have to pay for a college education?

Content Objective(s):

Given a set of data, students will be able to draw a line of best fit with correct

slope.

Process Objective(s):

Students will use university websites to gather information on tuition rates and

offered majors.

Students will write a report of which university they would most likely attend and

why.

Students will use Microsoft Excel to graph lines to put in final paper.

Materials needed:

Computers, Graph Paper, SmartBoard

Phase 1: Introduction: Orient students to the problem:

Students will compare tuition rates ($/credit hour) at five different universities, two

chosen by the teacher, and three selected by the students. Universities must be

chosen based on location, and availability of preferred major.

Students will graph tuition rates over the last fifteen years and use this information

to predict how much they would pay if they chose to go to those universities (5

years away).

Finally, students will write a final summary, including graphs, of their findings and

choose which university they would ultimately choose and why. They will then

present these findings to the class using PowerPoint or other program

Phase 2: Organize students for study:

Show them how to find the tuition rates using an example of a university that they

will not be using.

Have students graph tuition rates on whiteboard, draw the line of best fit, and

predict the rate in 5 years.

Phase 3: Assist independent and group investigation:

Ask students to decide on a major they would like to investigate.

Give some links to popular universities and tips on how to navigate them.

Phase 4: Develop and present artifacts and exhibits:

If more than one student is investigating the same major, or if they are similar,

presentations will be given as a group.

Phase 5: Analyze and evaluate the problem-solving process:

In Class: students will write a short reflection on the process as a whole.

Discussion: what did you learn about your learning style, about presentations,

about college, etc?

Discussion Model Lesson Plan

Topic: Graphing and Writing Equations of Lines

Objective(s):

Given a series of points, students will write a linear equation with both slope and y

intercept correctly placed in the equation.

Given a series of points and the above mentioned equation, students will write the

equations of parallel and perpendicular lines and graph all three lines on the same

plane.

Materials needed:

SmartBoard, White Board

Phase 1: Clarify aims and establish set:

Review of all chapter material in preparation for exam

Understanding rates of change is essential moving forward.

Phase 2: Focus the discussion:

Rules: one voice at a time, keep discussion on topic

Q: How do we mathematically represent the idea of change?

Phase 3: Hold the discussion:

Guided Dicussion

Given real world situations:

For each set of information: is the slope positive or negative? What does this

indicate?

For cards stats vs oswalt: list possible x and y variables. Graph a few. Find line of

best fit, predict stats for next AB.

How will the graphs differ from each player to the next?

Given some points from the above tables, graph avg vs opponent, hr vs avg, etc.

what would lines parallel to these represent?

Phase 4: End the discussion:

Reiterate process for graphing lines, lines of best fit, parallel and perpendicular

lines.

Phase 5: Debrief the discussion:

Exit slip: Practice Questions

You’re Invited!

What? A Conference of Experts Discussing the Rising Tuition Costs in

this Country

When? October 21st - October 25th, 2013

Who? The Panel of Experts in Ms. Khan’s Class

What to Bring: You, Your Expertise, and Your Research

Presentations begin at 9 am sharp!!

See Rubric (over)

Linear Equations – Final Presentation Rubric

Requirement 0-10 11-20 21-30 Score

Oral Presentation

-Presentation is difficult to understand, without use of terms -Visual Aids are irrelevant and/or difficult to understand

-Most of presentation is delivered clearly, with some terms -Visual aids are easily understood and mostly relevant

-Clearly delivered, using specific terminology -Visual aids are relevant and easily understood

/30

Written Report

-Report is poorly written, including less than half of necessary subsections -Less than half of subsections are not clearly identified with headings

-Report is acceptably written, including all or most subsections -Most subsections are identified with headings

-Report is well-written, and includes all necessary subsections -All subsections are identified with subheadings

/30

Appropriate Use of Algebraic

Concepts

-Concepts were used incorrectly and appropriate conclusions were drawn

-Concepts were used correctly; conclusions were not drawn appropriately

-Concepts were used correctly and appropriate conclusions were drawn

/30

Total

/90

Calendar

Monday Tuesday Wednesday Thursday Friday

Week

One

Pretest and

Intro

Lecture/Revie

w:

Coordinate

Grids and

Graphing

Lesson:

Breaking

Down an

Equation

Lesson:

Standard/

Slope-

Intercept/

Point-

Slope

Form

Quiz 1

Week

Two

Lesson:

Graphing

Graphing

cont.

Intro to

Project: Parts,

Expectations

Lab Day

Quiz 2

(short),

Lab Time

Week

Three

Check In with

Students:

Individual

Conferences

Project Work Project Work Project

Work

Review:

All

material

thus far

Week

Four

Presentations

Presentations

Presentations

Presentati

ons

Party!

Jeopardy

?