Unit Summary: In the context of an Ocean Bike Tour, students study tables, graphs, and equations to find the patterns or relationships. These investigations involve exploring distance tables and graphs, admission prices for individuals and groups, points received at Wild World Amusements, etc. Pupils will analyze tables, graphs, statements, and equations involved in the activities during the bike tour. The class will also write equations and solve word problems on this journey. The resource room classes generally have students with specific learning disabilities, other health impairments, emotional disturbances, autism, communication impairments, or multiple disabilities.
Primary interdisciplinary connection: Children’s Literature, Science, Social Studies
21st century themes: Financial, Economic, Business
21st century skills: Life and Career Skills, Critical Thinking and Problem Solving, Communication and Collaboration
Unit Rationale: Students do not realize all that is involved in traveling or starting a business and how to track mileage, revenue, expenses, and profits. These real world problems will help students see how to use algebra in life. They will learn how to plan a trip, or record financial transactions for daily home use as well as establishing a business to earn money.
Solving real-life and mathematical problems using numerical and algebraic expressions and equations.
4. Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.
a. Solve word problems leading to equations of the form px + q = r and
p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach.
1. Make sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively.
4. Model with mathematics.
5. Use appropriate tools strategically.
6. Attend to precision.
7. Look for and make use of structure.
8. Look for and express regularity in repeated reasoning.
Unit Essential Questions:
Unit Enduring Understandings:
Evidence of Learning:
Equipment / Resources
Students will be encouraged to use www.phschool.com (Web Code: ane-1317, ana-1354, ane-1412, anj-1051) for homework support and/or in class.
Lesson Plan Topics / Titles:
Lesson 1: Writing Equations 3.1 – one operation (one step equations about distance traveled at different speeds) and use those tables, graphs and equations to answer questions
Lesson 2: Writing More Equations 3.2 – two operations (two step equations) and how the pattern of change in a relationship is reflected in the equation, table, and graph of the relationship
Lesson 3: Paying Bills and Counting Profits 3.3 – equations for revenue, expenses, and profit
Lesson 4: Application/Connection/Extension problems – traveling: speed/distance, purchases with installments/tax/discounts, trip expenses, equations/formulas in geometry
Lesson 5: Making and Using Calculator Tables 4.1 - write rules and equations for the revenue, expenses, and profits for a bike tour
Lesson 6: Making and Using Calculator Graphs 4.2 - use the calculator tables to find interesting patterns, and to solve problems about values of both the independent and dependent variables - adjust window settings and the axes scales, and to trace a graph to find coordinates of specific points
Lesson 7: Extending the Tour 4.3 – comparing relationships - compare price quotes for two bike rental companies -
Lesson 8: More Application/Connection/Extension problems – (same type as in lesson 4)
Teacher Notes about Lesson Plans
Universal Design for Learning Options
Multiple Means of Representation
Multiple Means of Action and Expression
Multiple Means of Engagement
The following websites were used in preparing additional strategies, accommodations, and modifications in the above lessons: