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Understanding by Design 6-page Template, page 1 Unit Title: Medical Biotechnology Grade level: _7 Subject/Topic Areas: Math/Linear Functions – Unit 4 (continued linear from Unit 3B) Key Words: linear equation, ax + b = c and ax + b = cx + d, solution, real numbers, expression, first degree, variable Designed by: Diane Rogers Time Frame: 6 weeks School District: Kalamazoo Public Schools School: Milwood Magnet School Brief Summary of Unit (including curricular context): This guide will explore how to generate and solve linear equations from a given context as well as how to identify and interpret key elements of linear functions such as intercepts, starting point, slope, rate of change, etc. The guide will also focus on simplifying expressions and symbolic manipulation of expressions and equations of the first degree. Unit design status: □ Complete template pages – Stages 1, 2, and 3 (Review use) □ Completed blueprint for each performance task □ Completed rubrics □ Directions to students and teachers □ Materials and resources listed □ Suggested accommodations □ Suggested Extensions Status: initial draft (date _______ ) □ Revised draft (date __________) □ Peer reviewed □ Content reviewed □ Field tested □ Validated □ Anchored Notes: 6-Page Template, Page 2 Stage 1 – Identify Desired Results Established Goals: A.FO.07.12 Add, subtract, and multiply simple algebraic expressions of the first degree, e.g., (92x + 8y) – 5x + y, or x(x+2) and justify using properties of real numbers. A.PA.07.06 Calculate the slope from the graph of a linear function as the ratio of “rise/run” for a pair of points on the graph, and express the answer as a fraction and a decimal; understand that linear functions have slope that is a constant rate of change. A.PA.07.07 Represent linear functions in the form y = x + b, y = mx, and y = mx + b, and graph, interpreting slope and y-intercept. A.FO.07.13 From applied situations, generate and solve linear equations of the form ax + b = c and ax + b = cx + d, and interpret solutions. A.PA.07.03 Given a directly proportional or other linear situation, graph and interpret the slope and intercept(s) in terms of the original situation; evaluate y = mx + b for specific x values, e.g., weight vs. volume of water, base cost plus cost per unit. A.PA.07.04 For directly proportional or linear situations, solve applied problems using graphs and equations, e.g., the heights and volume of a container with uniform cross-section; height of water in a tank being filled at a constant rate; degrees Celsius and degrees Fahrenheit; distance and time under constant speed. What understandings are desired? Students will understand that… Equations are models that help us interpret data and/or a situation. Multiple representations of linear functions provide rich information to interpret a situation and make predictions for the future. What essential questions will be considered? How do we use data to communicate? What information can be found in a linear equation? What information is found in each representation? When is one representation more useful? What key knowledge and skills will students acquire as a result of this unit? Students will know… Students will be able to do… How one variable effects another Generate an equation from a given The components of equations in situation various forms such as y = x + b, y = Analyze the equation for the mx, y = mx + b, y = ax+ b, ax + b = c relationship between the variables and ax + b = cx + d Calculate a result given the value of How to symbolically manipulate simple one variable in an equation linear expressions and equations 6-Page Template, Page 3 Stage 2 – Determine Acceptable Evidence What evidence will show that students understand? Students will be given three equations from the Math-a-thon pledge plans. They will analyze which plan would yield the most profit for the fundraiser. Students will use their symbolic manipulation skills as well as their knowledge about the components of a linear equation to find a solution for the problem. The three plans will include two that are equal but look symbolically different. * Complete a Performance Task Blueprint for each task (see next page) Other Evidence (quizzes, tests, prompts, observations, dialogues, work samples): Math binder – homework assignments, vocabulary notes, partner quiz, class work notes on Investigation 3 Student Self-Assessment and Reflection: Math reflection –p. 69 in Moving Straight Ahead Think, pairs, share Summary discussions – whole group Exit pass Warm ups 6-Page Template, Page 4 Performance Task Blueprint Supplement to Stage 2 performance task What understanding and goals will be assessed through this task? Identify components of an equation – Compare 3 plans and evaluate which plan slope as a rate of change, intercepts, raises more money, evidence shown for variable relationships reasoning – table of values, graph, and/or What criteria are implied in the standards and understandings regardless of the task specifics? What qualities must student work demonstrate to signify that standards were met? Accurate table, graph, or equation used to Clarify the relationships between the explain answer, Appropriate symbolic given variables; thorough explanations manipulation used to prove answer Through what authentic performance task will students demonstrate understanding? St. Jude Children’s Research Hospital called Milwood Magnet School with a problem that we need your help to solve. The hospital officials were very impressed with your previous work on the pledge plans, but they wanted to know which plan was the best for raising money. St. Jude’s has given us three plans that we need analyzed. You are asked to compare and contrast the three plans and decide which plan will raise the most money for the hospital. Included in your solution must be an explanation of your mathematical reason. What student products and performances will provide evidence of desired understandings? Students will submit a written explanation that includes their mathematical reasoning for the best plan. By what criteria will student products and performances be evaluated? The table, graph or equation must be The analysis of the plans must compare labeled correctly and use appropriate and contrast the values of the number of intervals and scale. Symbolic problems completed and the money manipulation must accurately show that raised. two plans are equal. 6-Page Template, Page 5 Stage 3 – Plan Learning Experiences and Instruction Consider the WHERETO elements: W – Where are they going? Why are they learning this? What is required? Students must know how to interpret equations given a real world context. Students will use symbolic manipulation (for both expressions and equations) in every mathematics course to solve applied problems. At the 7th grade level problems are only of the first degree and are at most 3 step. Students need to understand the distributive property as a tool for solving these problems H – How will you Hook the students? (through inquiry, research, problem-solving, and experimentation) The context for balancing equations involves money. Each pouch contains the same number of coins and each side of the equation needs to remain balanced. As students solve the problem, they are looking for how many coins equal each pouch. E – How will you provide opportunities will for student to Explore and Experience the Big Ideas and concept? How will you equip them for required performances? Students will work through Investigation 3 in Moving Straight Ahead that explores the concepts necessary for this unit. Various Application, Connection, and Extension problems will be assigned as class work and homework that provide students will time to practice skills and solidify their understandings. R – Provide opportunities for student to Rethink, Rehearse, Revise and Refine their work based on feedback. Students collaborate throughout the investigation and have opportunities to display work and refine based on information gathered in class discussion. E – How will students Evaluate their work and set future goals? During the performance task, students will receive feedback based on the analysis of which plan is a better “deal” for the walker/cause and the donor. Students will also evaluate their own understanding of the mathematical concepts by answering the Math Reflection questions. T – How is the lesson Tailored to address student interests and learning styles? the investigations, the problems include real world situations such as cell phone plans, plans for hiring a DJ, etc. Each investigation is organized so that students can access some part of the lesson tasks. Students will be exposed to other students’ thinking during the summary portion of each lesson. O – How is it Organized to maximize engagement and effectiveness. Students are required to produce products such as tables, graphs and equations for various contextual problems. These items will be displayed and students will be asked to explain characteristics of the model as well as asked to make inferences and/or interpret the models to solve applied problems. This unit is very active and requires teams of people to collaborate in order to accomplish a task much like the work place of the 21st Century. 6-Page Template, Page 6 Stage 3 – Plan Learning Experiences and Instruction Monday Tuesday Wednesday Thursday Friday 1 2 3 4 5 Review y=mx+b Inv. 4.1 Inv. 4.1 Inv. 4.2 Inv. 4.2 **See notes below for this week. 6 7 8 9 10 Review for Quiz on 4.1 Quiz on 4.1 and 4.2 Inv. 4.3 Inv. 4.3 Inv. 4.4 and 4.2 11 12 13 14 15 Supplemental Lesson Supplemental Lesson Inv. 3.1 Inv. 3.2 Project Research Day Find slope using Find solutions from a See lesson plan coordinates. table, graph, and y y1 equation. Slope 2 x 2 x1 16 17 18 19 20 Supplemental Lesson Supplemental Lesson Supplemental Lesson Project work day Inv. 3.3 See lesson plan Solving One-Step Solving Two-Step Solving Two-Step Equations Equations Equations 21 22 23 24 25 Project Due Inv. 3.4 Inv. 3.5 Review Investigation 3 Project work day Check-Up Review 26 27 28 29 30 Review Assessment Assessment Re - Teach Re - Teach Content Area: Math Grade: 7th Lesson/Activity: Birth Defects Research Lesson Duration: 1 class period (58 minutes) Resources/Materials: lap tops or computer lab, Objective: (Students-friendly language-reference the GLCE the objective is related to) Students will research information on birth defects including the rates, characteristics, history, causes, and prevention in the U.S, China, and India. A.PA.07.07 Represent linear functions in the form y = x + b, y = mx, and y = mx + b, and graph, interpreting slope and y-intercept. A.FO.07.13 From applied situations, generate and solve linear equations of the form ax + b = c and ax + b = cx + d, and interpret solutions. Action Steps to Deliver the Lesson: Birth Defects Research To begin this lesson, discuss birth defects and propose thoughts and ideas about the rates of birth defects in different countries. Why would one country have a higher birth defect rate over another? Instruct students that they will be researching different birth defects and their rates in different countries. Allow 5-10 minutes. Students should research the rates of certain birth defects (Spina Bifida, cleft lip or Palate, Heart Defects, Excessive digits or missing limbs, etc.) in the U.S, India, and China. Their research should include a description of the characteristics of the birth defect (such as how it affects the body, how it progresses, and the life expectancy). In addition, students should research and gather information about the history, causes, prevention and treatments of birth defects in China, India and the United States. Students should record their information in their notebooks. Allow 40-45 minutes. With 5 minutes to go, bring the class back together and ask for students to share their findings. Which country had the highest birth defect rate? The lowest? Why do they think this is? Content Area: Math Grade: 7th Lesson/Activity: Lesson Duration: 1 class period (58 minutes) Resources/Materials: Birth defect research, access to a computer Objective: (Students-friendly language-reference the GLCE the objective is related to) A.PA.07.03 Given a directly proportional or other linear situation, graph and interpret the slope and intercept(s) in terms of the original situation; evaluate y = mx + b for specific x values, e.g., weight vs. volume of water, base cost plus cost per unit. A.PA.07.04 For directly proportional or linear situations, solve applied problems using graphs and equations, e.g., the heights and volume of a container with uniform cross-section; height of water in a tank being filled at a constant rate; degrees Celsius and degrees Fahrenheit; distance and time under constant speed. Action Steps to Deliver the Lesson: Rates of Birth Defects To begin this lesson, have the class decide on a birth defect from a country to use in order to create a table, graph, and equation as a whole class. Also, briefly summarize student ideas regarding how the trend may affect the countries population in the future. (Are there enough cases annually to significantly affect an entire country?) Allow 15-20 minutes. Then, instruct students to use their birth defect rates and information to make a table, graph, and/or an equation. Students can select one birth defect for all three countries to compare. Their analysis should include a table, graph, and/or equation for each country, in addition to a brief paragraph regarding the trends and the comparisons between the U.S., India, and China. OR Students may select to compare ALL the birth defects in ONE country. Their analysis should include tables, graphs, and/or equations for the rates of ALL birth defects in a particular country. They should include a brief summary of observable trends and a prediction regarding how these trends will affect future populations. Allow 25-30 minutes. With 5-10 minutes left of class, bring the class back together and ask for student volunteers to share some of their findings.