Unit Overview:  

• Content Area: Mathematics (Algebra)
• Unit Title:  Writing Rules and Equations
• Target Course/Grade Level: 7th grade resource room math
• Instructor’s Name: Becky Konschak
• School:   Lakeside Middle School
• Date:  7/21/11

 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.

Learning Targets:  

• Common Core Standards :
• Expressions and Equations 7.EE

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.

• Standards for Mathematical Practice

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:

• What are the variables involved in this relationship?
• How can you use the relationship between variables to write a rule?
• How can you use a rule to write an equation?

Unit Enduring Understandings:

• Increases and decreases in rates, distance, profits, revenue, and expenses can be seen in tables and on graphs.
• There are patterns of increases or decreases in real world problems that can be written as a rule.
• Algebraic equations can be used to solve real world problems such as finding rates, distance, profits, revenue, and expenses.

Evidence of Learning:

• Summative Assessments Weekly quizzes and end of unit test
• Formative Assessments - Daily, students will be expected to begin with a warm-up, participate in activities and/or discussion, do class work and homework, create visual/kinesthetic representations, and complete exit tickets.  Individuals will be encouraged to solve the problem by using paper and pencil, by using a graphing calculator, or by using some combination of these two methods.

 Equipment / Resources

• Equipment / Technology needed throughout the Unit: SMART Board and projector, computers, document camera, notebooks/journals, graphing calculators, whiteboard.  The following websites will be used in the warm-ups, lessons, and learning centers:
• www.helpprogram.net (computer center activity – allows students to go through lessons at their own pace and supplements instruction),
• http://www.onlinemathlearning.com/one-step-equations-3.html,
• http://pbskids.org/cyberchase/games/functions/functions.html (SMART Board game - students must figure out what the rule is that is used to “create the clones”),
• http://www.bbc.co.uk/education/mathsfile/shockwave/games/planethop.html (SMART Board game - plot points & determine the equation created by the line),
• http://www.onlinemathlearning.com/algebra-help.html (for help with algebra topics, definitions, worksheets, videos),
• http://www.onlinemathlearning.com/graphing-lines.html (videos of graphing lines by plotting points). 

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. 

• Teacher Resources: Connected Mathematics 2: Variables and Patterns Teacher’s Guide

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

 Each lesson:

• Begins with an activity to connect to Previous Knowledge and to Student Interest / Preferences.
• Includes High Quality Curriculum - Connected Mathematics 2: Variables and Patterns, also see D 1 (above) for additional resources that are used during lessons.
• Includes Flexible Grouping via – During class each day students will think/pair/share, participate in differentiated small groups, do activities at differentiated learning centers, and complete independent work.
• Provides Respectful Tasks within a Supportive Learning Environment via Multiple Means.  (see next page)

 Universal Design for Learning Options

Multiple Means of Representation

• Guideline 1: Provide options for perceptionFor the many students that cannot read well,   http://www.newbedford.k12.ma.us/edtech_toolkit/students/cast/classroom/getting_started.htm.
• Guideline 2: Provide options for language, mathematical expressions, and symbolsTo help the students learn the vocabulary and concepts of writing equations, they will use the http://www.ronblond.com/MathGlossary/  math glossary to take notes/write definitions about the terms.
•  Guideline 3: Provide options for comprehensionhttp://quizlet.com/create_set/ is an activity that will be available for those students that would like to make flashcards.

Multiple Means of Action and Expression

• Guideline 4: Provide options for physical actionhttp://www.dessci.com/en/products/mathplayer/ will allow me to create web pages for the students.
• Guideline 5: Provide options for expression and communicationSince many of my students struggle with getting things written or typed, http://www.spellchecker.net/spellcheck/ will help the pupils feel more confident about their work.
• Guideline 6: Provide options for executive functionsA project option may include using http://cst.cast.org/cst/guest/PAGE,tutorial?vid=internet to help students.

Multiple Means of Engagement

• Guideline 7: Provide options for recruiting interestThis (http://www.spdbayarea.org/SPD_tips_for_teachers.htm) will be used to help me find tips to integrate different students according to their needs.
• Guideline 8: Provide options for sustaining effort and persistenceTo help the class maintain attention to their task, we will use http://www.udlcenter.org/sites/udlcenter.org/files/Noise_Thermometer.jpg.
• Guideline 9: Provide options for self-regulationThe students will need to set some goals for themselves.  http://www.teachersatrisk.com/2009/02/08/helping-my-students-set-goals-the-smart-way/ will help the class complete that task.

Online Resources:

The following websites were used in preparing additional strategies, accommodations, and modifications in the above lessons:

• http://funbasedlearning.com/algebra/graphing/points3/ - for students struggling with plotting points on a 4-quadrant grid.
• http://www.sheppardsoftware.com/mathgames/numberballs/numberballsAS2.htm - for students struggling with sequencing integers.
• http://www.sheppardsoftware.com/mathgames/Numberballs_algebra_I/numberballsAlgebraI.htm - for sequencing simple equations in the form ax=y.
• http://www.shodor.org/interactivate/activities/VerticalLineTest/ - students are asked to decide of the points on the graph form a function so that an equation can be written.
• http://www.crickweb.co.uk/ks1numeracy.html#fmach – function machine calculates outputs.
• http://www.classzone.com/cz/books/msmath_2_na/resources/applications/animations/chapter_7/html/g7_7_7.html - enter values into the function machine and then determine the equation that created the output.  (Good practice – creates an x y table of the values for the students to see.)
• http://www.classzone.com/cz/books/msmath_3_na/resources/applications/animations/chapter_11/html/g7_7_8.html - using the given equation, find the y-values and then plot the points from the table to make the graph of the equation.  (Good practice – gives you feedback to help you correct mistakes.)
• http://teams.lacoe.edu/documentation/classrooms/amy/algebra/5-6/activities/functionmachine/functionmachine5_6.html - function machine (other things also available on this site for algebra)

• http://www.bbc.co.uk/schools/ks2bitesize/maths/number/mental_maths/play.shtml - difficult (for more advanced students to help them practice their mental math).