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Stage 1 – Desired ResultsUnit Summary: (Write a 3-4 sentence summary of your unit) Students will assess their current standard of living. They will be asked to devise a plan for maintaining the standard of living if they were to move out at age 18. If attending college, they would receive a $2,000 per semester scholarship. If they find that they cannot maintain their standard of living (which many will) they will be asked to look at what they are willing to let go in order to find a standard of living that is realistic. Those who feel that they can justify the ability to maintain their current standard of living will be asked to consider other situations in which their standard of living my exceed their expected means.

Established Goals

What content standards and program goals will the unit address?

8.EE.B.5. Graph proportional relationships, interpreting the unit rate as the slope of the graph.

8.F.B.4. Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.

8.SP.A.2. Know that straight lines are widely used to model relationships between two quantitative variables.

8.MP.2. Reason abstractly and quantitatively.

8.MP.3. Construct viable arguments and critique the reasoning of others.

8.MP.4. Model with mathematics.

TransferLinear models may model change over time if time is one of the variables.

The cost of maintaining one’s standard of living is relatively linear, when utilities and food costs are looked at as an average expense per month rather than the fluctuations they may see dependent on holidays or special occasions, as function of cost per month over a period of x months.

At some point students will move out of their parents’ homes and will have to consider how much they will have to earn to maintain the standard of living they wish to have.

These implications apply to the idea of net worth as an adult or in the banking profession as assets vs. liability, where one would aim to have more assets than liabilities.

MeaningUnderstandingsStudents will understand that:

proportional relationships have a constant rate of change and that the unit rate is the vertical change when the horizontal change is one.

Proportional relationships can be graphed as a line.

The initial value is the output when the input is equal to zero

Essential QuestionsHow would your standard of living change if you decided to move out of your home after finishing high school?

What makes a function or equation linear?

How are linear equations useful?

When is it better to look at a table of values of a linear equation instead of a graph?

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8.MP.5. Use appropriate tools strategically.

8.MP.6. Attend to precision.

8.MP.7. Look for and make use of structure.

8.MP.8. Look for and express regularity in repeated reasoning

8.EE.B.6. Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b.

8.w.6 Use technology, including the Internet, to produce and publish writing and present the relationships between information and ideas efficiently as well as to interact and collaborate with others.

8.W.7 Conduct short research projects to answer a question (including a self‐generated question), drawing on several sources and generating additional related, focused questions that allow for multiple avenues of exploration.

8.W.8 Gather relevant information from multiple print and digital sources, using search terms effectively; assess the credibility and accuracy of each source; and quote or paraphrase the data and conclusions of others while avoiding plagiarism and following a standard format for citation.

8.L.6 Acquire and use accurately grade‐appropriate general academic and domain specific words and phrases; ‐gather vocabulary knowledge when considering a word or phrase important to comprehension or expression.

A linear relationship may also be represented by a table of values (input and output)

Straight lines are sometimes used to model relationships between two variables, in this case the number of months and the total cost of living.

Linear functions can be used to represent real data that may be of value.

How can you compare two linear functions?

How will your decision to attend college or not attend college affect your standard of living directly after high school? In the long run?

AcquisitionStudents will know …

Rate of change is the slope when the denominator is 1 (the vertical change if the horizontal change is 1)

The y-intercept is the value of the output when the input is 0 (the place where the line crosses the y-axis

The y-intercept represents the initial value

The slope of a linear function is constant

Students will be skilled atDetermining rate of change from a graph or a table of values

Graphing linear functions

Comparing linear functions

Making changes to the rate of change and or the initial value to change the graph

Supporting their findings by presenting data graphically, on a table and in written form.

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8.W.1 Write arguments to support claims with clear reasons and relevant evidence.

b. Support claim(s) with logical reasoning and relevant evidence, using accurate, credible

c. Use words, phrases, and clauses to create cohesion and clarify the relationships among ideas and concepts.

d. Use precise language and domain‐specific vocabulary to inform about or explain the topic

e. Establish and maintain a formal style.

f.Provide a concluding statement or section that follows from and supports the information or explanation presented.

Great standards – are there any ELA standards that also align with your unit?

UbD Unit Plan RubricStage 1 – Desired results 3 2 1 0 Feedback

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1. Identifies the relevant standards, mission, or program goals to be addressed in the unit

Key standards (content, skills, and/or practices) are referenced. Standards align to the big ideas and essential questions and connect with your internship experience

2.5

Great – see comment

2. Identifies the knowledge needed to achieve understanding and address the established goals

Includes all knowledge needed for students to achieve understanding. Knowledge is listed as the facts that will be learned in the unit.

2.5

One small comment

3. Identifies the skills needed to achieve understanding and address the established goals

Includes all skills and processes students should be able to perform at the end of the unit and which will be needed to for students to achieve understanding.

3 Great!

4. Identifies understandings that represent the big ideas and concepts that students should understand by the end of the unit.

The targeted understanding is stated clearly and specifically. It is framed as a generalization, which specifies the big idea that students should understand.

3 Great!

5. Is framed by a few open-ended, thought provoking, and focusing essential questions

The essential questions are important and thought provoking. They have more than one correct answer and require inquiry rather than recall. They have great potential for engaging students. They provide a unifying focus to guide teaching and learning

2.5

See comments above

6. Specifies the long-term transfer goals that cut across domains and involve genuine accomplishment

Includes crosscutting concepts/domains. Transfer goals are interdisciplinary, connect with past/future content/skills/practices and/or relate to life outside of school.

3 Good!

7. Aligns all the elements so that Stage 1 is focused and coherent

All elements align with each other, fit with the Big idea of the project and relate to your internship experience.

3 Yes – everything aligns nicely

Total 19.5/21 Great job! This is an excellent foundation for what looks to be a great unit. Please look over the few comments I have.

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Stage 2 - Assessments

Performance Task (in GRASPS format)Goal

Your goal is to create a financial model, or plan, for a standard of living you would desire to have or maintain if you were to move out of your home after high school graduation

The goal is to understand how linear functions and systems of equations can assist you in making decisions.

The problem or challenge is creat a model that is reasonable given the wages you might earn based on possible income of a high school graduate holding no other degrees or diplomas.

The obstacles I will have to overcome is a misconception of what “a lot” of money is. Students figuring what the limits of hours worked are and what wages they may be able to earn as recent high school graduates.

Role You have just graduated from high school You want to move out of your home and continue maintaining the same standard of living Your job is to create a plan in order to maintain the standard of living, or if the standard of living

proves to be too high, to create a viable standard of living.Audience

You must convince your parents that you can move out and be financially independent Your parents agree to give you $150 a month towards your expenses if you can prove to them

that you have a viable plan.Situation

The context you find yourself in is as a senior in high school at the end of the first semester of the school year.

The challenge involves finding sources to fund your living in a way that helps you maintain your standard of living, or adjusting your standard of living to meet the monetary funds you are capable of acquiring legally.

Product, Performance, and purpose You will create a visual presentation which exhibits income against expenses for each of the

different scenarios you test. You need to be able to defend your standard of living using real data about current rent rates and

possible income based on a high school education. Along with your visual presentation, you will need to write a letter to your parents explaining the

measures you have taken to ensure their credit will not be ruined by cosigning for your new home/apartment.

You will also submit a list or diagram of monthly expenses paid for the standard of living that you currently have compared to the standard of living you have planned for.

Standards and Criteria for Success Your visual presentation must be neat. Lines must be straight and have qualities that make them

easily distinguishable. Your writing must be free of mechanical and grammatical errors and include all of the parts of a

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properly written letter. Your final budget will be assessed based on evidence of potential living expenses and potential

earnings in the current market. It will be judged on neatness and clarity of the presentation, and the quality of the written letter’s ability to explain the method by which you reached the budget you have proposed.

You must meet the following criteria All visual presentations must be exhibited on a grid. The letter is to be written to the person(s) currently providing you with you living situation

either typed in 12 pt. New Times font and double spaced and printed on copy paper, or hand written on standard college ruled filler paperThe lists of changed expenses must be comprehensive and include the estimated monthly cost for each category such as groceries, or eating out.

Other Evidence: (quizzes, tests, prompts, work samples, labs, etc.)

Students will work on this project at the conclusion of the linear equations and systems of equations unit. Prior to the unit, students will take a pre-assessment with an understanding that the same assessment will serve as a post assessment. They will correct only the misconceptions from the first attempt as the post assessment.

Students will be observed daily and I will provide verbal feedback and ask probing questions to help them move forward if they become “stuck”.

A daily reflection of progress will be turned in as a participation grade. “Today I _________. Tomorrow I need to_______________, I have a question about ________________________.” This will help me to following day so that I may begin with addressing any common questions as a class, and addressing other students individually.

During the research portion, students will turn in a duplicate of their findings to verify they are heading in the correct direction.

A vocabulary quiz will be given at approximately the mid-point so that students can ensure to use correct academic language in their letters and/or presentations.

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Student Self-Assessment and Reflection-Self-assessment: Students will provide a daily reflection of their learning in the “Today I ________________” statement as shown in the above section.

Peer assessment: Rubrics will be provided in order for students to reflect on their progress and the progress of their peers. Every other day, students will work with other student(s) to assess the work against the rubric.

Self-reflection: At the end of the unit students will reflect on their rubric based scores and return the rubric for their portfolio. An additional 3 points will be assigned to the self-reflection

Stage 3 – Learning Plan

Use the WHERETO format from UbD. Delete this line from your final project.

How much will a ride cost you? Students will analyze taxi fare for a given distance, but will not be given the time of day. Students will discuss with each other their findings and any issues they encountered in finding the solution. Students will also discuss the observations made during the task. (Three acts way, Act 1: Given little to no other information, students discuss what they need to solve the problem-one guess to low, one guess too high, Act 2: Given the necessary information, Act 3: solution (W,H,E1,R,E2,O)

Review of graphing given a table of input/outputs. Students will use the data from the taxi activity to graph points on a graph coordinate plane and will make observations about

Pre-AssessmentsWhat pre-assessments will you use to check student’s prior knowledge,skill levels, and potential misconceptions? BT formative assessment and the Taxi cab activities will serve as pre-assessments

Progress Monitoring• How will you monitor students’ progress toward acquisition, meaning, and transfer, during lesson events?During lessons and activities students will have the opportunity to ask questions or confirm thinking/progress.

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those points (W,E1,O) A second taxi cab company will be presented and students

will be asked which costs more/less. Students will use their own strategies to figure this out. They will also address the question of if/when the cost between the two companies is equal. Groups will share and compare strategies and recored the comparisons in a diagram or graphic organizer The different strategies will be compared and contrasted. They will discuss which strategy or visualization best helped them understand the scenario. This includes discussing how graphing can help compare data. (W,HE1,R,E,O)

. End of unit task will be presented along with scoring rubrics

in order for students to have the end goal in mind throughout learning (W,H,E2)

We will relate student observations to key terms and use create a KWL chart based on the essential questions(E1,R.O).

Group/Class discussion regarding what the students need to know in order to maintain the current standard of living. (W,H,E1,R,E2,T,O)

Research in computer lab/using mobile lab to find cost of living, pay for high school graduates and prices of services not provided by parents(E1,E2,T,0)

Students will analyze income (assets) and expenses (liabilities) to determine if the standard of living is maintainable and begin to look for areas to cut costs (liabilities) or areas in which they could afford some luxuries(E1,R,T).

Students will finalize their “standard of living” and write up the justification explaining adjustments that were made and why(W,E2,T,O)

After finishing the project students will reflect on the process and the value it held for them. Their focus should be on the usefulness and authenticity of the task. They will compare the final product of this task to the initial taxi cab task.(R,E2,T,O)

I will have a signaling method available for each table so that when signaled students do not feel singled out to the rest of the class. I will approach the table to answer any questions. They will turn in daily tickets out of “Today I__________” which can be filled in with what was learned or completed, “Tomorrow I will __________” Filling in the plan for the next day“I have a question about___________”

• What are potential rough spots andstudent misunderstandings? Students tend to forget that the input/output represent points on a graph. Students may be hesitant based on not being happy with current living standards. This will be presented as the opportunity to plan for the future they would like to have. Another potential rough spot is students who may lack motivation because they plan to live at home.

• How will students get the feedback they needStudents may receive immediate feedback by asking questions or ask I walk around the classroom monitoring progress.

If they do not ask questions their feedback will be provided the next day in response to their daily ticket out.

The most common questions or concerns as assessed by the daily ticket out will be addressed as a whole class at the beginning of the class period.

If I find that many have the same questions during the class, then I may choose to address those questions or concerns during the class period rather than waiting until the next day.

Students will also receive feedback from each other as they work independently but gain ideas and insights from each other. The students, having access to the rubric at all times, will conduct informal assessments of peer work approximately twice a week.

Self Check:

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- Are all three types of goals (acquisition, meaning, and transfer) addressed in the learning plan? Yes, all three goals are met. Students need to acquire knowledge about pay rates and cost of living, this provides meaning at the same time for assets and liabilities or income vs. expenses. Finally, students will transfer information from the first activity to complete the final project.

- Does the learning plan reflect principles of learning and best practices? Yes, students self and peer assess, they have a rubric and are allowed to explore their own experiences and college options.

- Is there tight alignment with Stages 1 and 2? Yes, I aligned the activities to the essential questions and goals.

- Is the plan likely to be engaging and effective for all students? Many students can’t wait to move out based on an idealistic view of independent life. It is likely to engage most students in the light that most, if not all, students will eventually move out of their parents’/guardians’ homes.

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APPENDICESRequired:

1) Include a 2-3 paragraph explanation of how this unit relates to your internship experience.

My internship involved data analysis for a credit union. I learned about how the credit union can loan money based on the deposits made by members. They typically will not lend out more than what borrowers have deposited. I used data about individual members and groups of members based on account activity or balance to crease visual representations (graphs) of potential loss upon the closing of said accounts. While these functions were not linear, they did show linear trends.

During my internship, I learned about assets and liabilities. In other words, I learned about income and expenses. Students need to be prepared to live in a financially driven world. However, many students have an unrealistic expectation of maintaining their current standard of living after moving away from home and becoming independent adults. Students will most likely learn that the assets they will have access to as young, independent adults falls far below their unexpected liabilities and will need to make cuts to unnecessary items, or luxuries.

In completing this activity, my hope is that students will acquire a more realistic view of potential income and expenses having earned only a high school diploma. They will also be exposed to more careers, and a variety of colleges and universities and the cost of attending these institutions. The motivating factor of this project is that most of us eventually move out of our parents’ homes. Perhaps with a realistic plan in place, students will be more prepared.

2) Resources & Technology Integration: Key materials, internet resources, and technologies that will enhance learning have been identified. Students will need access to computers and the internet. Low tech supplies will be graphing paper and rulers. Students may opt to check their work against programs such as Desmos or graphing calculators, it is not required. Another option for research is to ask high school friends/family or recent high school graduates about their employment status and pay.

Optional: Include any other information such as sample work products, tests, rubrics, etc.

UbD Stage 2 RubricStage 2 – Assessments 3 2 1 0 Feedback

1. Specifies valid assessment evidence of all desired results: Stage 2 aligns with Stage 1

The task clearly provides a valid measure of the targeted understanding. Students are required to demonstrate the desired understanding to successfully complete the task.

2 Again – hoping to see more connection with stage 1 understandings/transfer

2. Includes Authentic performance tasks based on one or more facets of understanding.

The task is highly authentic, involving a direct or simulated application of the targeted understanding. The task is complex and involves the types of challenges or constraints that adults face in the world beyond the classroom. Students develop actual products or performances for an identified audience/client.

3 Great!

3. Provides sufficient opportunities for students to reveal their achievement

2 Again - What about the math – where is the criteria for correct math

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The proposed assessments provide sufficient evidence to permit confident inferences about each student’s overall understanding. Appropriate diversity is evident in the assessment methods; students have many opportunities to reveal the depth and breadth of their understanding.

calculations and graphing? - this should match up with stage 1 understandings/transfer

4. Includes evaluative criteria to align each task to desired results and to provide suitable feedback on performances

Provides built-in and detailed feedback on performances. (Ex. rubric).

3

5. Other Evidence: (quizzes, tests, prompts, work samples, labs, etc.)

Includes 6 or more “other” assessments. The assessments are both varied in format and specific in what concept/topic they are assessing. Assessments are directly related to the objectives, goals, and standards in stage 1. Assessments provide opportunities for students with varying learning styles and strengths to excel. (Ex. Quiz on slope, lab on mineral structure, etc.)

3

6. Student Self-Assessment and Reflection

Teach students to self-reflect/assess. Self-assessments provide students with opportunities to consider the understanding, the quality of their work and the value and meaning of the unit/lesson.(Ex. Journal entries, final thoughts/ticket out/take home message at the end of each lesson, Daily jottings, end of unit reflection.)

2.5

Total 15.5 This looks good – just hoping to see some slight modifications based on my comments

UbD Stage 3 RubricStage 3 – Learning Plan 3 2 1 0 Feedback

1. Includes Learning events and instruction needed to help learnersa) Acquire targeted knowledge and skillsb) Make meaning of important ideasc) Transfer their learning to new situations

The unit/lesson moves beyond facts to fully explore key ideas through illuminating experiences. Lessons and activities equip students to effectively prepare for final performance tasks to demonstrate the targeted understanding.

a3

b3

c3

2. Effectively incorporates the WHERETO elements so that the unit is likely to be engaging and effective for all learners.

3

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Explicitly includes each part of the WHERETO in the UbD plan and the plan is likely to be engaging and effective for all students.3. To what extent will students be hooked – engaged in digging into the big ideas (through inquiry, research, problem solving, and experimentation)?

The unit has a powerful hook stimulated by thought-provoking experiences early on. Students will likely pay more attention than usual and take a greater interest than usual in the complex ideas. Connects to the performance task.

3

3. Pre-Assessment

Identifies pre-assessments that will be used to check student’s prior knowledge, skill levels, and potential misconceptions.

3

4. Progress Monitoring

Outlines/includes how you will monitor students’ progress toward acquisition, meaning, and transfer, during lesson events.

3

5. Misunderstandings

Identifies potential rough spots and student misunderstandings to demonstrate that you have thought through the unit ahead of time.

3

6. Feedback

Provides an explanation of how the students will get feedback

2.5

Good addition!

7. Appendices: (Not required until the final due date)

Required:1) Include a 2-3 paragraph explanation of how this unit relates to your internship experience.

2) Resources & Technology Integration: Key materials, internet resources, and technologies that will enhance learning have been identified.

Optional: Include any other information such as sample work products, tests, rubrics, etc.

8.5

4 – Appendix 1 - Great explanation of the projects connection to the workplace. I only hoped you would talk a little more about some of the skills/practices that you are bringing back to the classroom.

4.5 – Appendix 2 – Good resources – see comments

Total (out of 37) 35/37Final Project Total (55) 50.5/55 Great work on this

project! Again, just make sure you are giving the students time to struggle a little and develop deep understanding! I really like the relevance of this project! Good luck teaching it this year

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ExpensesItem Description Monthly Cost

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Total Monthly Expenses (continue on another page if necessary)

Potential EmploymentCompany Name/Job Description Hourly wage or Salary

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Home/Apartment RentalHome/Apartment (Name, BR/Bath) Monthly Rate

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College/University TuitionCollege/University Name Tuition Rate-$2000

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