| Title: |
Unit 5: Walk the Line (Graphing) |
| Creator: |
Terry Jones: tljones@access.k12.wv.us |
| Contributing Authors: |
Melinda J. Akers: mjakers@access.k12.wv.us |
| Subject: |
Mathematics |
| Grade Level: |
Seventh Grade |
| Unit Calendar: |
Unit Calendar
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| Big Ideas: |
Transform information among multiple representations Graphing linear and nonlinear equations involving real world situations |
| Content Standards and Objectives |
| Objective ID |
Objectives |
| M.S.7.1 |
Through communication, representation, reasoning and proof, problem solving, and making connections within and beyond the field of mathematics, students will · demonstrate understanding of numbers, ways of representing numbers, and relationships among numbers and number systems, · demonstrate meanings of operations and how they relate to one another, and · compute fluently and make reasonable estimates. |
| M.O.7.1.1 |
compare, order, and differentiate among integers, decimals, fractions, and irrational numbers using multiple representations (e.g., symbols, manipulatives, graphing on a number line). |
| M.O.7.1.3 |
using simple computation and problem-solving situations, demonstrate fluency and justify solutions in performing operations with rational numbers including negative numbers for - adding
- subtracting
- multiplying
- dividing
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| M.O.7.1.5 |
analyze and solve grade-appropriate real-world problems with whole numbers, integers, decimals, fractions and percents including problems involving - discounts,
- interest,
- taxes,
- tips,
- percent increase or decrease, and justify solutions including using estimation and reasonableness.
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| M.S.7.2 |
Through communication, representation, reasoning and proof, problem solving, and making connections within and beyond the field of mathematics, students will - demonstrate understanding of patterns, relations and functions,
- represent and analyze mathematical situations and structures using algebraic symbols,
- use mathematical models to represent and understand quantitative relationships, and
- analyze change in various contents.
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| M.O.7.2.3 |
solve problems by creating an input/output function table(including, but not limited to, spreadsheets) to predict future values, given a real-world situation involving rational numbers. |
| M.O.7.2.5 |
solve one-step linear equations and inequalities using a variety of strategies containing rational numbers with integer solutions; graph solutions, and justify the selection of the strategy and the reasonableness of the solution. |
| M.O.7.2.6 |
plot lines within the Cartesian coordinate plane from a table of values to solve mathematical real-world problems. |
| M.O.7.2.7 |
determine the slope of a line from its graphical representation. |
| M.O.7.2.8 |
represent algebraically and solve real-world application problems and justify solutions. |
| M.S.7.3 |
Through communication, representation, reasoning and proof, problem solving, and making connections within and beyond the field of mathematics, students will: · analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships, · specify locations and describe spatial relationships using coordinate geometry and other representational systems, · apply transformations and use symmetry to analyze mathematical situations, and · solve problems using visualization, spatial reasoning, and geometric modeling. |
| M.O.7.3.3 |
apply rotations, reflections, translations to plane figures and determine the coordinates of its transformation and compare and contrast the new figure with the original. |
| * - Standard ID |
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| 21st Century Learning |
| Information and Communication Skills: |
- 21C.S.5-8.1 - The student will access, analyze, manage, integrate, evaluate, and create information in a variety of forms using appropriate technology skills and communicate that information in an appropriate oral, written, or multimedia format.
- 21C.O.5-8.1.LS1 - Student, when presented with a problem, identifies the information needed, uses text, people, online databases and search engines to filter relevant information efficiently, analyzes information for biases, synthesizes information gathered and creates an effective and efficient response to the problem.
- 21C.O.5-8.1.LS2 - Student interprets abstract visuals and creates products (e.g. digital storytelling) that reflect a growing understanding of visual language and require the effective use of tools (e.g. cropped photos, original charts and graphs, well-chosen images from databases, video clips).
- 21C.O.5-8.1.LS3 - Student presents thoughts, ideas, and conceptual understanding efficiently, accurately and in a compelling manner and enhances the oral or written presentation through the use of technology.
- 21C.O.5-8.1.TT1 - Student connects peripheral devices (e.g., scanners, digital cameras, video projectors, USB drives, printers, media storage devices) to computers and uses them efficiently and effectively. Student accesses server and/or network resources (e.g., file folders/software programs, bookmarked sites).
- 21C.O.5-8.1.TT3 - Student recognizes different file format extensions (e.g., .doc, .xls, .ppt, .rft, .pdf, .jpeg, .gif, .mpg, .wav, .mp3) and can import the different formats into documents, presentations, spreadsheets and databases.
- 21C.O.5-8.1.TT6 - Student uses advanced features and utilities of spreadsheet software, (e.g. functions, formulas, filters, sorts, creates graphs and charts), to perform calculations and to organize, analyze and report data.
- 21C.O.5-8.1.TT7 - Student uses advanced features and utilities of presentation software (e.g., design templates, design layouts (fonts/ colors/ backgrounds) animation and graphics, inserting pictures, objects, movies, sound, charts, hyperlinks, and graphs) to create an original product.
- 21C.O.5-8.1.TT9 - Student uses telecommunications tools (e.g., email, web pages, blogs, discussion groups, list-servs, etc.) to learn academic content and to gather, share and publish information to various audiences.
- 21C.O.5-8.1.TT10 - Student uses Internet browsers, various search engines, book marking features, and advanced search techniques to gather information; student evaluates the information for validity, bias, appropriateness, content and usefulness.
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| Thinking and Reasoning Skills: |
- 21C.S.5-8.2 - The student will demonstrate the ability to explore and develop new ideas, to intentionally apply sound reasoning processes and to frame, analyze and solve complex problems using appropriate technology tools.
- 21C.O.5-8.2.LS1 - Student engages in a critical thinking process that supports synthesis and conducts evaluations by applying comprehensive criteria.
- 21C.O.5-8.2.LS3 - Student engages in a problem solving process that divides complex problems into simple parts in order to devise solutions.
- 21C.O.5-8.2.LS4 - Student creates thoughtful ideas and solutions and takes risks as he/she works toward goal despite mistakes. Student begins to consistently think of all the possibilities and diverges to become more expansive with his/her thoughts/ideas that lead to the creation of original products.
- 21C.O.5-8.2.TT2 - Student collaborates with peers, experts, and others using telecommunications and collaborative tools to investigate curriculum-related problems, issues, and information, and to develop solutions or products for audiences inside and outside the classroom.
- 21C.O.5-8.2.TT3 - Student uses multiple technology tools for gathering information in order to solve problems, make informed decisions, and present and justify the solutions.
- 21C.O.5-8.2.TT4 - Student formulates a plan and uses technology tools and multiple media sources to compare and analyze information in order to solve real-world problems.
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| Personal and Workplace Skills: |
- 21C.S.5-8.3 - The student will exhibit leadership, ethical behavior, respect for others; accept responsibility for personal actions considering the impact on others; take the initiative to plan and execute tasks; and interact productively as a member of a group.
- 21C.O.5-8.3.LS1 - Student manages emotions and behaviors, engages in collaborative work assignments requiring compromise, and demonstrates flexibility by assuming different roles and responsibilities within various team structures.
- 21C.O.5-8.3.LS2 - Student is flexible in approach to solving problems and completing tasks, considers alternative methods, solutions and perspectives, abandons strategies that do not work, and reallocates time and resources as priorities change.
- 21C.O.5-8.3.LS3 - Student sets challenging goals and strategically plans to reach those goals, monitors performance and adjusts effort and strategies, seeks assistance when needed, and demonstrates focused commitment to reaching the established goals.
- 21C.O.5-8.3.LS4 - Student demonstrates ethical behavior and works responsibly and collaboratively with others, in academic and social contexts, to accomplish both individual and team goals related to improved academic, extracurricular and co-curricular performances.
- 21C.O.5-8.3.LS5 - Student exhibits interpersonal and problem-solving skills when in the role of leader. He/she helps others stay focused on the goal, monitors progress of the group, and successfully moves the group toward the goal.
- 21C.O.5-8.3.LS6 - Student maintains focus on larger project goal, frames appropriate questions, reflects on possible courses of action and their likely consequences, develops and initiates a plan of action with appropriate smaller objectives and benchmarks, and submits the completed project when due.
- 21C.O.5-8.3.TT1 - Student protects software, hardware and network resources from viruses, vandalism, and unauthorized use and uses proper techniques to access, use and shut down technology equipment.
- 21C.O.5-8.3.TT4 - Student complies with county acceptable use policy. Student discusses legal and ethical behaviors related to acceptable use of information and communication technology (e.g., privacy, security, copyright, file-sharing, plagiarism) and predicts the possible effects of unethical use of technology (e.g., consumer fraud, intrusion, spamming, virus setting, hacking) on the individual and society, as well as identify methods for addressing these risks.
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| Essential Questions: |
Why do we use graphing in our world? How can inequalities help you describe relationships? How can plotting points on a coordinate plane help us determine specific locations in real life? How can transformations be applied to real-world situations? How can translations of data be used in the real world? How can writing an equation of a line help you solve real world problems? What are the similarities and differences between the images and pre-images generated by transformations? What is the relationship between the coordinates of the vertices of a figure and the coordinates of the vertices of the figure‘s image generated by transformations? When can translations of data be used in the real world? Why do we need to be able to plot points and graph figures and equations? |
| Student Will KNOW: |
How to graph inequalities and shade correctly How to graph inequalities on a number line How to graph linear and non linear equations How to plot ordered pairs on a coordinate plane Math symbol >, <, ≥, ≤, =, | |, °, ÷, ×, +,and – Relevant vocabulary words as introduced in each lesson The different transformations The formula for finding the slope of the line The method for writing equations The use of function tables What the x-axis and y-axis represent Where the x-axis and y-axis are located |
| Student Will UNDERSTAND: |
Switching from one representation to another can reveal new information about a relationship Understand relationships among multiple representations Graphs can be used to represent data Data can be represented in many different formats Transformations on a grid can be used to solve real world problems |
| Student Will Be Able To DO (Skill): |
Apply reflections given coordinate points Apply reflections of geometric figures Apply rotations given coordinate points Apply rotations of geometric figures Apply transformations given coordinate points Apply transformations of geometric figures Choose an appropriate math symbol; >, <, ≥, ≤, =, | |, °, ÷, ×, +,and – Plot inequalities on a number line Plot points on a coordinate plane Plot points on a number line Recognize the relationships among multiple representations Use a graphing calculator Use input/output function tables Write equations of a line given a point and slope Write equations of a line given two points of the line |
| Research-Based Instructional Strategies: |
Calculators Collaboration Cooperative groups – random and organized Different summarizing strategies Differentiated Instruction including tiered lessons and activities to address different learning styles Journal Notebook Peer and self evaluation Technology representations Think pair share Vocabulary development Word wall |
| Materials/Resources/Websites: |
http://funbasedlearning.com/algebra/graphing/points/default.htm http://education.ti.com/educationportal/sites/US/homePage/index.html Chart paper Colored pencils Computer Coordinate graphs Coordinate grid transparency Examples of rotations Excel program (or printed copy of the workbook) Fantastic Function game board Fantastic Function player markers Graph paper Graphing calculator Index cards Internet access Notebook paper Number cubes Overhead calculator Overhead transparency Pattern blocks Patty paper Pencil Poster board / display board Poster Paper PowerPoint Projector pens Protractor Rulers Straight edge Student journals Vocabulary notebooks |
| Multiple Assessments/Rubrics: |
Formative Self-Assessment Peer evaluation Project rubrics FATP Real-World Problems Student Presentations Summative GRASPS |
| Files Uploaded |
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| Date Created: |
November 17, 2007 |
| Date Modified: |
April 27, 2008 |
Unit Plan Outline (Lesson Plans) |
Unit 5 Lesson 01: Graphing on a Number Line
Unit 5 Lesson 02: Graphing Points in 4 Quadrants
Unit 5 Lesson 03: Function Tables
Unit 5 Lesson 04: Finding Slope of a Line
Unit 5 Lesson 05: Writing Equations
Unit 5 Lesson 06: Graphing Linear Equations
Unit 5 Lesson 07: Graphing Linear Equations with Calculator
Unit 5 Lesson 08: Graphing Inequalities and Shading
Unit 5 Lesson 09: Graphing Nonlinear Equations
Unit 5 Lesson 10: Translations
Unit 5 Lesson 11: Reflections
Unit 5 Lesson 12: Rotations
Unit 5 Lesson 13: Race Track (Culminating Activity)
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