# Appleby Algebra 1

Appleby Algebra 1

Unit :3 / Dates**Math Florida Standard(s):**/

**MAFS. 912.AREI.4.10**Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line). Recognize that the graphical representation of an equation in two variables is a curve, which may be a straight line. Explain why each point on a curve is a solution to its equation. (DOK 1)

**MAFS.912 F-IF.2.4**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 given a verbal description of the relationship. Define and recognize the key features in tables and graphs of linear and exponential functions:

**MAFS. 912.F-IF.2.6**Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. Recognize slope as an average rate of change. (DOK 2) MAFS.912.F-LE.1.1 Distinguish between situations that can be modeled with linear functions and with exponential functions. Prove that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals. Equal intervals, and that exponential functions grow by equal factors over equal intervals. (DOK 3)

**MAFS.912.A-CED.1.2**: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. (DOK 2

**) MAFS. 912.F-IF.3.9:**Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum. (DOK 2)

**MAFS.912.A-CED.1.3**Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context (DOK 3)

**MAFS.912.A-REI.4.11**: Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions. (DOK 2) MAFS.912.S-ID.3.7: Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data (DOK 2). MAFS.912.A-REI.4.12: Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes. (DOK 2)

Learning Goal: / The student is expected to distinguish between situations that can be modeled with linear functions and with exponential functions, graph functions expressed symbolically and show key features of the graph and calculate and interpret the average rate of change of a function. They must also be able to identify the effect on the graph of replacing f(x) by f(x) + k, k f(x) (kx), and f(x + k) for specific values of k and compare properties of two functions

each represented in a different way. The student is also expected to represent constraints by equations or inequalities, and be able, to explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); graph the solutions to a linear inequality in two variables as a half-plane and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes.

Assessments / Pre Assessment Circle Map on equations

Formative Assessments Cornell Notes

Collaborative Assignments

Homework

Exit Slips

Summative Assessment Review Quiz

Equations Quiz 2

Equations Unit Test

**Essential Question(s):**/ How can you use a linear function to solve real-world problems?

What is a linear function?

How can you identify and use intercepts in linear relationships?

How can you relate rate of change and slope in linear relationships?

How can you use different forms of linear equations to solve real-world problems?

How can you represent a linear function in a way that reveals its slope and y-intercept?

How can you represent a linear function in a way that reveals its slope and a point on its graph?

How can you write a linear equation in standard form given properties of the line including its slope and points on the line?

What are the ways in which you can transform the graph of a linear function?

How can you compare linear functions that are represented in different ways?

How can you use linear equations and inequalities to solve real-world problems?

How can you model linear relationships given limited information?

How can you use functions to solve one-variable equations?

How do you write and graph linear inequalities in two variables?

Vocabulary / linear function standard form x-intercept y-intercept

rate of change slope slope-intercept form point-slope form

transformation parent function Parameter half-plane

linear inequality in two variables solution of an inequality in two variables

**Progress Monitoring/ Feedback Loop**/ If student has a low pre assessment or formative assessment, the teacher will monitor and possibly suggest before or after school tutoring to insure he is learning the unit adequately.

If the student has a 70 or below on a quiz he can study more and retake it within a 7 day period for full credit. If the student has below a 70, the instructor will provide real time remediation

Tuesday 10/18 / Unit 3 Linear Functions / DOK 2

Daily Agenda

Daily Objective /

- We will begin to investigate the chapter by unpacking the standards.

BELL RINGER /

- What do you know about graphing?

I DO: /

- Assess and Monitor the class

WE DO: /

- Bell ringer
- Review Unit 2 test
- Unpack the standards

YOU DO:

Homework /

- Write a reflection , a paragraph or two about your growth on equations and inequalities

EXIT TICKET:

(5 minutes) /

- What is this unit about?

Wednesday 10/19 /

**Unit 3 Linear Functions**/ DOK 2

Daily Agenda

Daily Objective /

- Students will learn to determine if a function is linear or not when given a table, an equation, or a graph using Cornell Notes, guided practice, and independent practice

BELL RINGER /

- What makes a line linear???

I DO: /

- Assess & Monitor Class

WE DO: /

- Review Bell ringer
- Cornell Notes
- Guided Practice

YOU DO:

Homework / Linear vs non linear

Determine if data is linear.

Create a: 1) foldable 2) thinking map 3) written paragraph (pick one)

**Rubric for Homework**

**Points Possible:**/ Details: / Points Awarded:

15 / Tell how to determine if data is linear in an equation

15 / Give example of linear equation.

Give example of non-linear equation.

15 / Tell how to determine if data is linear in a table.

15 / Give an example of a linear table.

15 / Give an example of a non-linear table

10 / Give an example of a linear graph

10 / Give example of non-linear graph

5 / Proper Paper Heading

EXIT TICKET:

(5 minutes) /

- What makes a graphed line nonlinear?

Thursday 10/20 /

**Unit 3 Linear Functions**/ DOK 2

Daily Agenda

Daily Objective / Students will be introduced to rate of change (slope) and learn how to calculate it using 2 points or a graph using Cornell Notes and Algebra Nation

BELL RINGER

( 5 Minutes) / Am I linear?

I DO: /

- Assess & Monitor class

WE DO: /

- Go over Bell Ringer
- Turn in homework
- Cornell Notes- Intro to Slope
- Algebra Nation- Section 4 Topic 2

YOU DO:

Homework /

- Pick one: Worksheet= Be sure to show your steps

EXIT TICKET:

(5 minutes) /

- What is slope ( Rate of Change)?

Friday 10/21 /

**Unit 3 Linear Functions**/ DOK 3

Daily Agenda

Daily Objective /

- Students will learn how to graph a line using intercepts using Cornell Notes and guided Practice

BELL RINGER

( 5 Minutes) /

- Find the rate of change

I DO: /

- Assess & Monitor

WE DO: /

- Go over bell ringer
- Turn in homework
- Cornell Notes
- Guided practice Page 215 (2-20 even) Think Pair Share

You DO:

Homework /

- Finish Guided Practice if you have not done so

. EXIT TICKET:

(5 minutes) /

- What is standard form used for?

Monday 10/24 /

**Unit 3 Linear Function**/ DOK 2

Daily Agenda

Daily Objective / Students will review concepts taught in this unit in preparation for the quiz using scribe and squire

Bellringer- / Intercepts, standard form, rate of change.

I DO: /

- Assess and monitor the class

WE DO: /

- Go over bell ringer
- Go over Fridays guided practice
- Set up scribe and squire review sheet odds and 227-231 odds in text.

YOU DO:

Homework /

- Student’s must complete the review before taking the quiz
- Review sheet (2,4,6 ,28,34,36,38)
- Page 227-231(2,6,8,10,16, 22,24)

EXIT TICKET:

(5 minutes) /

- What do I need to study for tomorrow’s test.

Tuesday 10/25 /

**Unit 3 Linear Functions**/ DOK 2

Daily Agenda

Daily Objective / Students will show mastery on concepts by taking a pencil and paper quiz. Then they will unpack the standards for the next module within the unit.

BELL RINGER / Check your homework

I DO: /

- Assess & Monitor

WE DO: /

- Any questions on homework?
- Go over formulas

YOU DO:

Homework /

- Take the quiz
- Unpack the standard in the next module

EXIT TICKET:

(5 minutes) /

- Reflect on the quiz? How did you do??

Wednesday 10/26 / Unit 3 Linear Functions / DOK 2

Daily Agenda

Daily Objective / Students will review the standards and learn the purpose of slope intercept form and how it helps you graph and analyze equations using Cornell Notes, guided practice and independent practice.

BELL RINGER / How do you graph a line?

I DO: /

- Assess & Monitor

WE DO: /

- Review unpacking the standards
- Cornell Notes: Slope Intercept form
- Guided Practice page 244-248 (2-24 even)
- Review guided practice

YOU DO:

Homework /

- Page 244 -248 (1-23 odds)

EXIT TICKET:

(5 minutes) /

- How does slope intercept form differ from standard form and which is better

Thursday 27 / Unit 3 Linear Functions / DOK 2

Daily Agenda

Daily Objective / Students will learn how to graph a line with point slope form using Cornell Notes, Guided Practice and independent practice

BELL RINGER / Graph a line 2 standard, two slope intercept

I DO: /

- Assess & Monitor the class

WE DO: /

- Review homework
- Cornell notes: Point slope form
- Guided Practice Page255-259( 2-20 evens)

YOU DO:

Homework /

- Page 255-259 odds (1-21)

EXIT TICKET:

(5 minutes) /

- When can I tell which form to use?

Friday 10/28 / Unit 3 Linear Functions / DOK 2

Daily Agenda

Daily Objective / Go to Mrs. Little’s room. Collaborative day

BELL RINGER

I DO: /

WE DO: /

YOU DO:

Homework /

EXIT TICKET:

(5 minutes) /

Monday Oct. 31 / Unit 3 Linear Functions / DOK 2

Daily Agenda

Daily Objective / Students will review concepts taught in this module to prepare for the quiz

BELL RINGER / slope intercept form, standard form, point slope form

I DO: /

- Assess and monitor

WE DO: /

- Think Pair Share review evens

YOU DO:

Homework /

- Finish guided practice if you need to

EXIT TICKET:

(5 minutes) /

- How can you tell the line shifts using vertex form?

Tuesday Nov 1 / Unit 3 Linear Functions / DOK 2

Daily Agenda

Daily Objective / Students will review concepts taught in this module to prepare for the quiz

BELL RINGER / slope intercept form, standard form, point slope form

I DO: /

- Assess and monitor

WE DO: /

- Think Pair Share review evens

YOU DO:

Homework /

- Review odds

EXIT TICKET:

(5 minutes) /

- What do you need to study for the quiz tomorrow?

Wednesday 11/3 / Unit 3 Linear Functions / DOK 2

Daily Agenda

Daily Objective / Students will take show mastery on the different forms of graphing using a pencil and paper quiz

BELL RINGER / Check homework

I DO: /

- Assess and Monitor

WE DO: /

- Go over homework

YOU DO:

Homework /

- Quiz 2
- Unpack the standards for the rest of the unit.

EXIT TICKET:

(5 minutes) /

- Reflect on how you are doing in this unit.

Thursday 11/4 / Unit 3 Linear Functions / DOK 2

Daily Agenda

Daily Objective

BELL RINGER

I DO: /

WE DO: /

YOU DO:

Homework /

EXIT TICKET:

(5 minutes) /

Friday 11/5 / Unit 3 Linear Functions / DOK 2

Daily Agenda

Daily Objective

BELL RINGER

I DO: /

WE DO: /

YOU DO:

Homework /

EXIT TICKET:

(5 minutes) /

Monday 11/8 / Unit 3 Linear Functions / DOK 2

Daily Agenda

Daily Objective

BELL RINGER

I DO: /

WE DO: /

YOU DO:

Homework /

EXIT TICKET:

(5 minutes) /

Tuesday 11/9 / Unit 3 Linear Functions / DOK 2

Daily Agenda

Daily Objective

BELL RINGER

I DO: /

WE DO: /

YOU DO:

Homework /

EXIT TICKET:

(5 minutes) /

Note: Learning Scales and Accommodations are below.

Scale / Learning Goals Scale:Equations and Inequalities

4.0 / Recognize when a modeling context involves constraints.

Create equations and inequalities in 1 variable & use them to solve real-world problems.

3.5 / In addition to 3.0 skills, I can do some of the 4.0 skills.

3.0

(GOAL)

With no help, I can do all these skills. / Solve multi-step linear equations and inequalities in one variable, including equations with coefficients represented by letters.

Explain and justify each step in solving linear equations and inequalities using properties of equality.

2.5 / In addition to all 2.0 skills, I can do some of the 3.0 skills.

2.0

With no help, I can do all these skills. / Solve linear equations in one variable using inverse operations and properties of equality.

Solve inequalities in one variable using inverse operations and properties of equality.

Recognize and recall specific vocabulary.

1.5 / On my own, I can do some of the 2.0 and 3.0 skills.

1.0 / With help, I can do some of the 2.0 and 3.0 skills.

0.5 / With help, I can do some of the 2.0 skills.

0.0 / Even with help, I have no success.

WICR Strategies used during each unit.

Writing

Writing activities that help

students understand the

content / Inquiry

Questioning strategies

that help students

understand the content / Collaboration

Working together with a

partner or in a group of

students to understand, to

problem solve, or to

complete a task/project / Reading

Any strategies in reading

that help students

understand

Writing-to-Learn

• summaries

Process writing

• using a rubric as evaluation

On-demand/Timed writing

• writing that is completed in class within a set amount of time

• grade is evaluated using a rubric

Cornell Notes

• taking notes on the most important information

• summarizing

• using the notes to study

Reflective writing

• students write about what they have learned and what they still need / Higher level questioning

in classes

• Costa’s Level 1: Students

find the answers right there

in the text.

• Costa’s Level 2: Students

must figure out the answer

from information in the

text.

• Costa’s Level 3: Students

apply what they have

learned or use what they

have learned to evaluate or

create. / Think Pair Share

Sharing ideas with a

partner or in a group

Carousel/Gallery Walk

Problem solving in groups

Projects in groups / Before reading activities

• vocabulary activities

• accessing prior knowledge

• making predictions

During reading activities

• marking the text

• Cornell notes

• graphic organizers

After reading strategies

• summarizing

• group projects

Accommodations used daily on an individual basis in accordance with IEP and 504 plans and ELL Students

- Read directions for the student
- Check for understanding
- Allow to leave class for assistance
- Extra time for exams
- Daily agenda

- Allow student time to step out to de-escalate
- Testing in small groups
- Use of a planner/binder for organization
- English Language Dictionary

- Extended time on assignments =1 day
- Preferential seating
- Written direction given
- Break directions into chunks

- Read Aloud to Students
- Visual manipulatives
- Cooperative Learning,
- Vocabulary, Description, Introduction,

Student Friendly Mathematical Practice Statements

MAFS.K12.MP.1.1 Make sense of problems and persevere in solving them.

• Make a plan!

• Try different approaches when your problem is hard.

• Solve your problem in more than one way.

• Check whether your solution makes sense.

MAFS.K12.MP.2.1 Reason abstractly and quantitatively.

• Explain the meanings of the numbers, words, pictures, symbols, and objects you and others use

MAFS.K12.MP.3.1 Construct viable arguments and critique the reasoning of others.

• Explain both what to do and why it works.

• Work to make sense of others’ mathematical thinking.

MAFS.K.12.MP.4.1 Model with mathematics.

• Apply math to real-world situations.

• Use models such as graphs, drawings, tables, symbols, numbers, and diagrams to solve problems.

MAFS.K12.MP.5.1 Use appropriate tools strategically.

• Choose appropriate tools for your problem.

• Use mathematical tools correctly and efficiently.

• Estimate and use what you know to check the answers you find using tools.

MAFS.K12.MP.6.1 Attend to precision.

• Communicate your mathematical thinking clearly and precisely.

• Use the level of precision you need for your problem.

• Be accurate when you count, measure, and calculate.

MAFS.K12.MP.7.1 Look for and make use of structure.

• Find, extend, analyze, and create patterns.

• Use patterns and structures to solve problems.

MAFS.K12.MP.8.1 Look for and express regularity in repeated reasoning.

• Use patterns and structures to create and explain rules and shortcuts.

• Use properties, rules, and shortcuts to solve problems.

• Reflect on your thinking before, during, and after you solve a problem.