**A. Unit Overview:**

**Content Area:**Math**Unit Title:**Variables and Patterns Introducing Algebra**Target Course/Grade Level:**Resource Room Math/Grade 8**Instructor’s Name:**Kim Fassett**School:**Lakeside Middle School**Date:**July 21, 2011**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.

**Primary interdisciplinary connections:**Science, History, Health/PE, Literacy

**21st century themes: **

- Health Literacy: http://www.vpul.upenn.edu/shs/health_proedu.php (evaluation)
- Global awareness: http://www.watsoninstitute.org/ (explanation)
- Financial, Economic, Business, and Entrepreneurial literacy: http://www.mymoney.gov/ (engagement)

**21st century skills:**

- Information Literacy: http://www.weather.com/weather/tenday/08332 (engagement)
- Media Literacy: http://espn.go.com/new-york/?ex_cid=2010_psrc_loca_york_aqui&partner=Google (exploration)
- Creativity and Innovation: http://allrecipes.com/Default.aspx (evaluation)

**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 : **

**Common Core Standards**:

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.

- 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?* - 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**

- Make sense of problems and persevere in solving them.
- Reason abstractly and quantitatively.
- Construct viable arguments and critique the reasoning of others.
- Model with mathematics.
- Use appropriate tools strategically.
- Attend to precision.
- Look for and make use of structure.
- Look for and express regularity in repeated reasoning.

** ****3. Unit Essential Questions:**** **

- How or when can one use variables and/or patterns to make decisions and solve real-world problems?
- What is the relationship between variables and patterns?
- How can we use the relationship between patterns and variables with data we have collected or with data we are provided?

**4. Unit Enduring Understandings:**** **

- What did you learn today about variables and patterns and how could you explain or show someone at home what you learned?
- How could you explain the relationship of variables and patterns to someone at home in the future if you needed to?
- How can you show someone at home relationship between variables and patterns with data you collect or with data that’s provided?

**C. Evidence of Learning: **

**Summative Assessments**

Tests/Projects

**Formative Assessments**- Informal observations
- Daily Homework and review
- Classwork/ review
- Daily warm-up (4 Square) and review
- Pre-Quiz and review (1Day)

** ****D. Equipment / Resources**

**Equipment / Technology needed throughout the Unit:**- Internet
- laptop
- SmartBoard/Ti84 Calculator software
- Ti84 Calculator
- SmartDocument Camera
- Stop watch (showing seconds)
- Paper cut outs of hexagons
- Copies of student lab sheets
- Graph paper
- Colored pencils
- pencil
- Blackline masters
**Teacher Resources**- Connected Math Teacher Planner pgs. 71-77
- Graphing calculator and linking cable
- Internet
- laptop
- SmartBoard/Ti84 Calculator software
- SmartDocument Camera
- Stop watch (showing seconds)
- Blackline Masters
- EZschool http://www.ezschool.com/EZSheets/
- Kuta http://www.kutasoftware.com/free.html

**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: **

- Begins with an activity to connect to
**Previous Knowledge**and to**Student Interest / Preferences.** - Includes
**High Quality Curriculum**– - Connected Math-
- Variables and Patterns
- -Investigation 4 Patterns and Rules
- Includes
**Flexible Grouping**via – (based on activity or student need or both) - Homogeneous

- Heterogeneous
- Cooperative learning groups
- Peer buddies
- Pairs
- Whole Class
- Independent work
- Provides
**Respectful Tasks**within a**Supportive Learning Environment**via**Multiple Means.**

**G. Universal Design for Learning Options**

**Multiple Means of Representation****Guideline 1: Provide options for perception**

** **http://aim.cast.org/experience/decisionmaking_tools/aim_explorer

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.

**Guideline 2: Provide options for language, mathematical expressions, and symbols**

http://www.edutopia.org/arts-opening-minds-integration-video

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!

**Guideline 3: Provide options for comprehension**

http://illuminations.nctm.org/ActivitySearch.aspx

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**

http://www.skype.com/intl/en-us/welcomeback/

"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:**

** **

ICoachMath

http://www.icoachmath.com/math_dictionary/mathdictionarymain.html

Mathisfun

http://www.mathsisfun.com/

CoolMath

http://www.coolmath-games.com/