Resources for Algebra. INSTITUTION North Carolina State Dept
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DOCUMENT RESUME ED 406 205 SE 059 920 AUTHOR Caison, Becky; And Others TITLE Resources for Algebra. INSTITUTION North Carolina State Dept. of Public Instruction, Raleigh. PUB DATE [97] NOTE 365p. AVAILABLE FROMNorth Carolina State Department of Public Instruction, 301 N. Wilmington Street, Raleigh, NC 27601-2825. PUB TYPE Guides Classroom Use Teaching Guides (For Teacher)(052) EDRS PRICE MFO1 /PC15 Plus Postage. DESCRIPTORS *Algebra; Elementary Secondary Education; Learning Activities; Mathematics; Problem Solving IDENTIFIERS *Mathematics Activities ABSTRACT This document presents ideas and activities for teaching algebra. The section on "Week by Week Essentials" provides seven resources in a weekly format. It includes writing ideas that provide an algebra prompt and requires students to organize their thoughts and present them in a coherent fashion, and connections to the real world that identify situations or problems where algebra is an important tool in their investigations and explanations. Also included are specific mathematics vocabulary; ideas from teachers about organization, management, assessment, curriculum, standards, projects, and grading; calculator tips that identify the calculator routines that are most likely to be used; problems that review a recently covered concept or skill; and problems for students to do outside of class that further extend concepts or skills students have used in the past. The "Activities" section contains detailed layouts for classroom exercises designed to last for an hour or more. Supporting materials are provided in the "Blackline Masters." (JRH) *********************************************************************** Reproductions supplied by EDRS are the best that can be made from the original document. *********************************************************************** Resources for Algebra PERMISSION TO REPRODUCE AND DISSEMINATE THIS MATERIAL AS E N GRAN ED BY TO THE EDUCATIONAL RESOURCES INFORMATION CENTER (ERIC) -4ip Alt; /U.S. DEPARTMENT OF EDUCATION Office of Educational Research and Improvement DUCATIONAL RESOURCES INFORMATION CENTER (ERIC) This document has been reproduced as ed from the person or organization 11111.11W originating it. Minor changes have been made to improve reproduction quality. Points of view or opinions stated in this document do not necessarily represent official OERI position or policy. am Public Schools of North Carolina State Board of Education . Jay Robinson, Chairman 1. AW Department of Public Instruction . Michael E. Ward, State Superintendent 2 State Board of Education 301 N. Wilmington Street Raleigh, North Carolina 27601-2825 Jay M. Robinson Kathy A. Taft Chairman Greenville Wilmington Prezell R. Robinson Margaret B. Harvey Vice Chairman Kinston Raleigh Evelyn B. Monroe Kenneth R. Harris Pinehurst Chairman Emeritus Charlotte Lowell Thomas Blowing Rock Barbara M. Tapscott Chairman Emeritus Robert R. Douglas Burlington Asheville Dennis A. Wicker Lieutenant Governor Jane P. Norwood Raleigh Charlotte Harlan E. Boyles Eddie Davis, III State Treasurer Durham Raleigh Table of Contents Introduction Goals and Objectives (G) I. Week by Week Essentials (W) Activities (A) Black line Masters (B) 4 Introduction Introduction Algebra is an universal theme that runs through all of mathematics and is important in nearly every aspect of the workplace.Algebraic thinking is a necessity for the intelligent consumer of goods and information. In 1989 algebraic ideas became a strand that runs through the K-8 curriculum (see B- 12 and B-13).In 1991 the North Carolina State Board of Education designated Algebra 1 as one of three units of mathematics required for high school graduation. With curriculum revisions approaching, the Department of Public Instruction began five years of staff development for Algebra teachers. Over one thousand teachers participated in at least thirty hours of workshops.The Resources for Algebra document is offered as a culmination to that staff development and an opportunity for teachers to re-examine the 1992 Algebra 1 Standard Course of Study. Resources for Algebra presents Algebra 1, wherever possible, as calculator-assisted and activity- or application-centered. Teachers should feel free to modify, reorder, and/or rewrite any or all of the ideas and activities. This is a document that teachers can build upon and remake to fit their classroom.It is a good model for a staff development activity within a school or school district.Using a similar format, teachers can create their own entries and share their resources in a similar document. Resources for Algebra Public Schools of North Carolina Problems and activities are correlated with the Algebra Standard Course of Study in the Goals and Objectives (G-1 - G-68) section. * * * * * * * * * * Week by Week Essentials (W-1 - W-80) provide seven resources in a weekly format. Although they are presented in chronological order, teachers should review the entire section before jumping in. The second page of each Week is in larger type so that it can easily be copied for use as a transparency. Writing Ideas provides an algebra prompt. Writing in the context of algebra requires students to organize their thoughts and to present them in a coherent fashion. It allows students the opportunity to reflect, persuade, and/or report mathematics for themselves as well as for others. Connections to the World identifies situations or problems where algebra is an important tool in their investigation and explanation. The WORDS are ... is intended to highlight and encourage clear, specific mathematics vocabulary in the classroom and among colleagues.Teacher to Teacher are ideas fromcolleagues about organization, management, assessment, curriculum, standards, projects, and grading. Calculator Tips tries to identify the calculator routines most likely to be used in an Algebra 1 classroom. Since these were written from a TI-81/82 perspective, teachers that use other models or brands should construct similar routines for their calculators. * * * * * * * * * * * * * Warm Ups are problems that review a recently covered concept or skill and can be solved by most students in ten minutes or less.(See W-73 - W-80 for answers.) Challenges are problems for students to do outside of class and extend concepts or skills students have used or are experienced with. Resources for Algebra Public Schools of North Carolina 7 The Activities (A-1 - A-48) are detailed layouts (concepts and competencies, goal, materials, description, and procedure) for classroom exercises which usually extend for a hour or more. Although they are identified in the Goals and Objectives by objective, the Activities, like many other entries, address several objectives. Many of the supporting materials for the Activities, Goals and Objectives, and Week by Week Essentials are provided in the Black line Masters (B-1 - B-143). Resources for Algebra has been in progress for the last two years. We greatly appreciate the time spent writing, editing, and revising ideas and activities by the principle writers, Becky Caison, Ann Crawford, and Jan Wessell. Many others contributed also, including Pat Baker, Eddie Banks, Kay Bennett, Betty Davis, Cyndy Davis, Susan Foster, Jennifer Gravely, Barbara Hardison, Kathy Hodge, Marcia Isley, Liz Kimbro, Julie Kolb, Sandra Leary, Lynne Lewis, Ginny Maxwell, Sarah Melton, Kathy Moore, Judy Mungle, Helen Owen, Debra Parker, Debbie Pergerson, Elfreda Robinson, P.A. Trogdon, Elsie Whisenant, and the NCDPI staff.Mathematics teachers in Richmond and Union counties provided valuable feedback. 8 Resources for Algebra Public Schools of North Carolina After you have had a chance to review and use these materials, please take a moment to let us know if Resources for Algebra has been useful to you. Your evaluation is important for the Eisenhower project that supported the development of these materials. Please respond to: Bill Scott Mathematics and Science Section Department of Public Instruction 301 N. Wilmington Street Raleigh, NC 27601-2825 Indicate the extent to which you agree with statements 1-5. Strongly Strongly Disagree Agree 1. The materials will be helpful in 1 2 3 4 5 teaching the goals and objectives for Algebra I in the Standard Course of Study. 2. I plan to use these materials with my 1 2 3 4 5 students in (course) 3. The materials are appropriate for 1 2 3 4 5 Algebra I. 4. The materials are interesting and 1 2 3 4 5 engaging. 5. The format of the materials encourages 1 2 3 4 5 their use. (over) Resources for Algebra Public Schools of North Carolina 9 6. How do you plan to use these materials in your classroom? 7. Additional comments: 10 Resources for Algebra Public Schools of North Carolina Goals and 1 Objectives (G 1 The learner will use the language of 1 algebra. 1.1 Evaluate algebraic expressions. A. Use your graphing calculator to store values for variables using the STO function. Evaluate expressions with the calculator. B. Give the students a set of expressions on the board (the overhead). Roll a die to determine the value to substitute for each expression. C. Calculator Tips (W-1, 41) D. Warm Ups (W-4, 10, 12, 40, 68, 72) L2 Use formulas to solve problems. A. Ask the students to talk to their parents and others to find out what kinds of formulas they use in life. In groups during class compile a list of the formulas used. Match the formula to who uses it. Have each group design a poster to illustrate the formula. Solve for different variables in the formula. B. Hand out formulas on index cards. Ask the students to write a problem for the formula he/she receives. Switch cards and repeat the process. C. The formula to convert Celsius (°C) to Fahrenheit (°F) is F = (915)C + 32. Derive the formula to convert Fahrenheit to Celsius. Have the students graph the formula on the calculator and create a table to convert between the two temperature scales. Resources for Algebra G-1 Public Schools of North Carolina 12 D. Sports offer a particularly rich context for using formulas. Let students investigate formulas in sports where they are most interested and create problems based on those formulas. Here is an example.