A.  Unit Overview:  

  1. Content Area: Math
  2. Unit Title:  Variables and Patterns Introducing Algebra
  3. Target Course/Grade Level: Resource Room Math/Grade 8
  4. Instructor’s Name: Kim Fassett
  5. School:   Lakeside Middle School
  6. Date:  July 21, 2011
  7. Unit Summary: Variables and Patters, the first unit in the Connected Mathematics algebra strand is a unit that develops students’ ability to explore a variety of situations in which change occurs. Students will be collecting, organizing and representing data in charts, graphs and formulas and will be able to use these concepts in everyday real-world situations.
  8. Primary interdisciplinary connections:  Science, History, Health/PE, Literacy

21st century themes: 

21st century skills:

Unit Rationale:

To discover order, analyze, construct, and predict how and why we use patterns and variables using data and their uses in everyday real-world and mathematical situations. Learning to observe, describe, and record changes is the first step in analyzing and searching for patterns in a real-world situation. We will be reviewing several concepts that students have had over the last few years organizing and using data, graphing patterns and basic algebra skills. However, the student levels are at a below average level so it is important to be sure that we build their confidence as well refresh their skills. Variables and patterns are terms used within the entire 8th grade interdisciplinary curriculum so this will allow students to continue to use their vocabulary skills knowledge. Another high-quality rationale for this review is to explore the use of a new more advanced calculator for the 8th grade group. 

B.  Learning Targets :  

7.EE.3. Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. For example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation.
7.EE.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.

    1. 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. For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width?
    2. Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem. For example: As a salesperson, you are paid $50 per week plus $3 per sale. This week you want your pay to be at least $100. Write an inequality for the number of sales you need to make, and describe the solutions.

    2.  Standards for Mathematical Practice

 3.  Unit Essential Questions:

4.  Unit Enduring Understandings:

C.  Evidence of Learning:


 D.  Equipment / Resources

E.  Lesson Plan Topics / Titles

Lesson 1:  Variables and Coordinate Graphs 
Lesson 2:  Graphing Change
Lesson 3:  Check Up
Lesson 4:  Analyzing Graphs and Tables
Lesson 5:  Patterns and Rules
Lesson 6:  Quiz
Lesson 7:  Using Graphing Calculators
Lesson 8:  Looking Back and Looking Ahead: Unit reflections

F.  Teacher Notes about Lesson Plans

 Each lesson:

G.  Universal Design for Learning Options

The AIM Explorer is designed to be used by a reader working collaboratively with an educator, tutor, parent, or assistive technology specialist as a guide. The guide may create a student account in order to re-assess reader preferences at a later time, or lead the reader on an exploration without creating an account. In both cases a reader summary profile will be created at the end of the exploration, but student preferences will only be saved if an account is created. Alternatively, a reader could initiate an exploration independently. The AIM Explorer allows users to explore their preferences for customizable features such as: magnification, text and background colors, and layout, TtS voice and speed, and more.

OMA is Tucson's remarkable school transformation program that is increasing student achievement through arts integration. The OMA Program, developed in the Tucson Unified School District (TUSD), uses the arts to teach academic standards in math, science, reading, writing and social studies and is designed around state and federal standards. In OMA schools, all ethnic backgrounds, regardless of socioeconomic status, showed improvement on mandated tests (AIMS, Terra Nova, and Stanford 9) in all tested areas. The quality of the OMA Program and the documented student achievement results have gained national recognition from the U.S. Department of Education, Harvard Project Zero, Arts Education Partnership, and others. Pay special attention to how the integration of the arts benefits English Language Learners. Linking to content that crosses language barriers, while taking steps to develop vocabulary and build communication skills are effective examples of promoting cross-linguistic understanding!

Illuminations was designed to support the NCTM standards for mathematics. This website offers interactive tools to facilitate exploration of math concepts.

2.  Multiple Means of Action and Expression

Guideline 4: Provide options for physical action

http://aim.cast.org/learn/accessiblemedia/allaboutaimThis site serves as a resource to state- and district-level educators, parents, publishers, conversion houses, accessible media producers, and others interested in learning more about and implementing AIM and NIMAS. AIM are specialized formats of curricular content that can be used by and students with print-disabilities. They include formats such as Braille, audio, large print, and electronic text. The audio and the electronic text formats are excellent examples of providing options in the mode of physical response for students who have difficulty turning pages or holding a book.

Guideline 5: Provide options for expression and communication

http://scratch.mit.edu/Scratch is designed to help young people (ages 8 and up) develop 21st century learning skills. As they create and share Scratch projects, young people learn important mathematical and computational ideas, while also learning to think creatively, reason systematically, and work collaboratively. Scratch provides students with an array of ways to demonstrate learning - through creating interactive stories, animations, games, art.  http://scratch.mit.edu/projects/Calliope23/423530

Guideline 6: Provide options for executive functions

http://www.studygs.net/timman.htm  This site provides study guides and strategies in areas of learning such as thinking, studying, planning and communication. The section on time management offers helpful tips on planning and prioritizing.

3.  Multiple Means of Engagement

Guideline 7: Provide options for recruiting interest

http://www.pbis.org/school/what_is_swpbs.aspxThe TA Center on Positive Behavioral Interventions and Supports has been established by the Office of Special Education Programs, US Department of Education to give schools capacity-building information and technical assistance for identifying, adapting, and sustaining effective school-wide disciplinary practices. PBIS's focus on environmental aspects that lead to problem behavior is reflective of the importance of varying threats and distractions. 

Guideline 8: Provide options for sustaining effort and persistence

"Skype allows you to make free calls over the internet to other people on Skype for as long as you like, to wherever you like." Skype is another powerful example of a tool that can be used to foster collaboration and communication among students across classrooms, districts, states, and countries! 

Guideline 9: Provide options for self-regulation

http://worksheetplace.com/index.php?function=DisplayCategory&showCategory=Y&links=2&id=279&link1=31&link2=279  Find templates for goal-setting worksheets to use with your students to support their organizational skills. These organizational worksheets are great examples of strategies that guide students' goal-setting.

H.  Online Resources :

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