Financial Planning: Modeling Investments with Sequences & Equations
Created byHolly McCarty
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Financial Planning: Modeling Investments with Sequences & Equations

Grade 10Math1 days
In this project, students will learn to apply arithmetic sequences and linear equations to create a comprehensive financial plan. They will model investments, project financial growth, and design a complete financial plan, considering long-term financial goals and investment strategies. The project uses a rubric to assess students' understanding of linear equation forms, investment modeling, growth projection, and overall financial planning skills. Students will reflect on how creating a financial plan changed their perspective on long-term financial planning and the role of math in financial literacy.
Financial PlanArithmetic SequencesLinear EquationsInvestment ModelingFinancial GrowthLong-Term Planning
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Inquiry Framework

Question Framework

Driving Question

The overarching question that guides the entire project.How can we use arithmetic sequences and linear equations to create a comprehensive financial plan that promotes long-term financial growth and stability?

Essential Questions

Supporting questions that break down major concepts.
  • How can arithmetic sequences model investments?
  • How do linear equations relate to financial growth?
  • What are the key components of a financial plan?

Standards & Learning Goals

Learning Goals

By the end of this project, students will be able to:
  • Students will be able to create a comprehensive financial plan.
  • Students will be able to model investments using arithmetic sequences.
  • Students will be able to use linear equations to represent financial growth.
  • Students will be able to write the equation of a line in point-slope form.
  • Students will be able to write the equation of a line in slope-intercept form.
  • Students will be able to identify and apply arithmetic sequences.

Entry Events

Events that will be used to introduce the project to students

Financial Fairytale

Students receive a mysterious letter detailing an inheritance with unusual conditions tied to smart financial planning. They must decipher the conditions (arithmetic sequences, linear growth) to unlock the inheritance and 'live happily ever after,' connecting math to real-world wealth management.
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Portfolio Activities

Portfolio Activities

These activities progressively build towards your learning goals, with each submission contributing to the student's final portfolio.
Activity 1

Linear Lineup

Learn to write linear equations.

Steps

Here is some basic scaffolding to help students complete the activity.
1. Define slope-intercept form.
2. Define point-slope form.
3. Convert between forms.

Final Product

What students will submit as the final product of the activityWorksheet with solved equations.

Alignment

How this activity aligns with the learning objectives & standardsWrites equations in different forms.
Activity 2

Investment Modeler

Model investment scenarios with sequences.

Steps

Here is some basic scaffolding to help students complete the activity.
1. Set up initial investment.
2. Define yearly deposit.
3. Calculate yearly balances.

Final Product

What students will submit as the final product of the activityInvestment growth model.

Alignment

How this activity aligns with the learning objectives & standardsModels investments with sequences.
Activity 3

Growth Projector

Project investment growth with linear equations.

Steps

Here is some basic scaffolding to help students complete the activity.
1. Define initial value.
2. Define growth rate.
3. Project future value.

Final Product

What students will submit as the final product of the activityFinancial growth projection.

Alignment

How this activity aligns with the learning objectives & standardsRepresents financial growth with equations.
Activity 4

Financial Blueprint

Design a complete financial plan.

Steps

Here is some basic scaffolding to help students complete the activity.
1. Define financial goals.
2. Create investment strategy.
3. Project financial growth.

Final Product

What students will submit as the final product of the activityComplete financial plan.

Alignment

How this activity aligns with the learning objectives & standardsCreates a comprehensive financial plan.
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Rubric & Reflection

Portfolio Rubric

Grading criteria for assessing the overall project portfolio

Financial Planning Portfolio Rubric

Category 1

Linear Lineup: Equation Mastery

Assesses the student's proficiency in writing and converting linear equations between slope-intercept and point-slope forms.
Criterion 1

Form Definition & Conversion

Accuracy and completeness in defining and converting between slope-intercept and point-slope forms.

Exemplary
4 Points

Provides precise definitions of slope-intercept and point-slope forms, and flawlessly converts between them, demonstrating a deep understanding of their relationships.

Proficient
3 Points

Accurately defines slope-intercept and point-slope forms and converts between them with minimal errors.

Developing
2 Points

Defines slope-intercept and point-slope forms with some inaccuracies and struggles with conversions, requiring some assistance.

Beginning
1 Points

Demonstrates difficulty in defining slope-intercept and point-slope forms and is unable to convert between them effectively.

Category 2

Investment Modeler: Sequence Application

Evaluates the student's ability to model investment scenarios using arithmetic sequences.
Criterion 1

Sequence Modeling

Effectiveness in setting up initial investments, defining yearly deposits, and calculating yearly balances using arithmetic sequences.

Exemplary
4 Points

Creates a sophisticated investment model using arithmetic sequences, accurately representing initial investments, yearly deposits, and balance calculations with clear and insightful justifications.

Proficient
3 Points

Develops a clear investment model using arithmetic sequences, accurately calculating yearly balances based on initial investments and yearly deposits.

Developing
2 Points

Constructs an investment model using arithmetic sequences with some errors in calculations or unclear representation of initial investments and yearly deposits.

Beginning
1 Points

Attempts to model an investment scenario with arithmetic sequences but demonstrates significant errors in calculations and struggles to represent key investment components.

Category 3

Growth Projector: Linear Projection

Assesses the student's ability to project investment growth using linear equations.
Criterion 1

Growth Projection Accuracy

Precision and justification in defining initial values, growth rates, and projecting future values using linear equations.

Exemplary
4 Points

Projects future investment growth with exceptional accuracy and provides comprehensive justifications for the defined initial value, growth rate, and projected values, demonstrating a deep understanding of linear relationships.

Proficient
3 Points

Projects investment growth accurately using linear equations, clearly defining initial values and growth rates to determine future values.

Developing
2 Points

Projects investment growth using linear equations with some inaccuracies or inconsistencies in defining initial values, growth rates, or projected values.

Beginning
1 Points

Struggles to project investment growth using linear equations and demonstrates significant errors in defining initial values, growth rates, and projecting future values.

Category 4

Financial Blueprint: Comprehensive Plan

Evaluates the student's ability to design a comprehensive financial plan, integrating investment strategies and growth projections.
Criterion 1

Plan Coherence & Strategy

Clarity, feasibility, and integration of financial goals, investment strategies, and growth projections in the financial plan.

Exemplary
4 Points

Creates a highly coherent and feasible financial plan with clearly defined financial goals, a sophisticated investment strategy, and accurate growth projections, demonstrating exceptional foresight and financial acumen.

Proficient
3 Points

Develops a comprehensive financial plan with well-defined financial goals, a reasonable investment strategy, and realistic growth projections.

Developing
2 Points

Designs a financial plan with some financial goals, an investment strategy, and growth projections, but may lack coherence or feasibility in certain areas.

Beginning
1 Points

Presents a rudimentary financial plan with unclear financial goals, a poorly defined investment strategy, and unrealistic growth projections.

Reflection Prompts

End-of-project reflection questions to get students to think about their learning
Question 1

How did creating a financial plan change your perspective on the importance of long-term financial planning?

Text
Required
Question 2

To what extent do you agree with the statement: 'Arithmetic sequences and linear equations are essential tools for financial planning'?

Scale
Required
Question 3

Which activity (Linear Lineup, Investment Modeler, Growth Projector, Financial Blueprint) was most challenging and why?

Multiple choice
Required
Options
Linear Lineup
Investment Modeler
Growth Projector
Financial Blueprint