Becoming Sherlock by Jason Kozel

Transformation 2013 Design Challenge Planning Form Guide Design Challenge Title: Becoming Sherlock Teacher(s): Bonnie McClung School: Transformation 2013 T-STEM Center Subject: Algebra 1 Abstract: During this design challenge, students will develop an educational game targeting solving one-step and multi-step equations, as well as problems involving proportions.

MEETING THE NEEDS OF STEM EDUCATION THROUGH DESIGN CHALLENGES

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Begin with the End in Mind The theme or â&#x20AC;&#x153;big ideasâ&#x20AC;? for this design challenge: Solving linear equations is an absolute requirement for success in Algebra I. This design challenge is intended to motivate the student to solve different types of linear equations and understand their relevance in the world. TEKS/SEs that students will learn in the design challenge: (A.1) Foundations for functions. The student understands that a function represents a dependence of one quantity on another and can be described in a variety of ways. The student is expected to: (C) describe functional relationships for given problem situations and write equations or inequalities to answer questions arising from the situations; (D) represent relationships among quantities using concrete models, tables, graphs, diagrams, verbal descriptions, equations, and inequalities. (A.3) Foundations for functions. The student understands how algebra can be used to express generalizations and recognizes and uses the power of symbols to represent situations. The student is expected to: (A) use symbols to represent unknowns and variables (A.4) Foundations for functions. The student understands the importance of the skills required to manipulate symbols in order to solve problems and uses the necessary algebraic skills required to simplify algebraic expressions and solve equations and inequalities in problem situations. The student is expected to: (A) find specific function values, simplify polynomial expressions, transform and solve equations, and factor as necessary in problem situations; (B) use the commutative, associative, and distributive properties to simplify algebraic expressions

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(A.5) Linear functions. The student understands that linear functions can be represented in different ways and translates among their various representations. The student is expected to: (C) use, translate, and make connections among algebraic, tabular, graphical, or verbal descriptions of linear functions. (A.6) Linear functions. The student understands the meaning of the slope and intercepts of the graphs of linear functions and zeros of linear functions and interprets and describes the effects of changes in parameters of linear functions in real-world and mathematical situations. The student is expected to: (G) relate direct variation to linear functions and solve problems involving proportional change. (A.7) Linear functions. The student formulates equations and inequalities based on linear functions, uses a variety of methods to solve them, and analyzes the solutions in terms of the situation. The student is expected to: (A) analyze situations involving linear functions and formulate linear equations or inequalities to solve problems; (B) investigate methods for solving linear equations and inequalities using concrete models, graphs, and the properties of equality, select a method, and solve the equations and inequalities; and (C) interpret and determine the reasonableness of solutions to linear equations and inequalities. Key performance indicators students will develop in this design challenge: Solve equations using models, tables, graphs, and algebraic properties and interpret and determine the reasonableness of solutions; manipulate algebraic expressions to simplify them using the distributive, associative, and commutative properties; analyze a problem and formulate an equation or inequality to represent the situation; investigate and select a method to solve the equation or inequality; identify and sketch the linear parent function; describe and predict the effects of changing “m” and “b” on the graph of the linear parent function; determine how to identify linear functions by making connections between various representations; define slope and intercepts of linear functions; determine slope (rate of change) and intercepts from various representations; describe how direct variations are related to linear functions; represent linear inequalities graphically on a coordinate plane.

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21st century skills that students will practice in this design challenge: www.21stcenturyskills.org     

Demonstrate originality and creativeness in work Developing, implementing and communicating new ideas to others Articulating thoughts and ideas clearly Demonstrating ability to work with others in a group to produce a product Assuming shared responsibility in group work

STEM career connections and real world applications of content learned in this design challenge:

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Students will use computer online activities to practice skills. Students will design and produce a product to be shared with the class.

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The Design Challenge Your company has been hired to design an educational game that students can play and demonstrate their mastery of solving linear equations and inequalities. The equations and inequalities should include one-step and multi-step solutions, as well as problems involving proportions. The game should include at least five word problems involving linear equations and three word problems involving linear inequalities. Please be sure to include a way for the players to know if they get their answers correct. You may also set time limits if you desire. This is a very large contract being awarded to your company so put your minds to work!!

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Map the Design Challenge Taught Taught Already before the during Learned project the project

Performance Indicators 1. Simplify expressions (combine like terms) 2. Understand the concept of equivalence

X X

3. Solve linear equations and inequalities at all levels

4. Write word problems that will be solved using linear equations and inequalities 5. Solve problems involving proportions

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Team-Building Activity It is important that teachers provide team-building activities for students to help build the 21st Century Skills that are necessary for success in the workforce. Team-building helps establish and develop a greater sense of cooperation and trust among team members, helps students adapt to new group requirements so that they can get along well in a new group, serves to bring out the strengths of the individuals, helps identify roles when working together, and leads to effective collaboration and communication among team members so that they function as an efficient, productive group. Our students are often not taught how to work in groups, yet we assume that they automatically know how. Use team-building activities with your students so that you can see the benefits which include improvement in planning skills, problem solving skills, decision making skills, time management skills, personal confidence, and motivation and morale. Cup Stack Team-Building Activity Objectives:  Participants work together in teams to accomplish a timed task.  Participants practice effective communication skills.  Participants reflect on one’s participation in a teamwork setting. Group Size: 3 to 4 participants (ideal is 4 participants) Materials: You will need a watch or clock with a second hand or a timer/stopwatch to time 1 minute 15 seconds. Each team will need 15 foam cups and a rubber band with 4 strings attached like rays of sun.

string

Setup:  Cut string into 2-foot lengths. Tie four strings to the rubber band evenly spaced around the circle. It should look like a sun with four rays coming out. Rubber band  Divide the cups into stacks of 15. Procedures:  Explain to the class that they will participate in a team-building activity that focuses on accomplishing a task and communication.  Distribute a set of materials to each team. Explain that the task is to build a pyramid using the cups with a 1 minute 15 second time limit. The pyramid will begin with 5 cups in a row at the base, 4 cups on the next row, 3 cups in the middle row, then 2 and finally 1 cup at the top. Group members may not touch the cups with their hands or any part of their body, even if the cups fall. Each person may only hold the end of one string attached to the rubber band (unless group size is 3 and then one participant may hold 2 strings). Group members must work together to stretch and relax the rubber band to grab each cup and place the cup in the right place.  When groups are ready, give them 30 seconds to practice and plan.  At the end of 30 seconds, have them disassemble their practice pyramid. When they are ready, start timing 1 minute 15 seconds. When time is up, stop the activity and check each team’s progress.  Debrief the activity with these questions: o Was anyone frustrated at all during the activity? If so, how was it handled?

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Why is teamwork so important for this activity? Did any team come up with a strategy for working together as a team? If so, what was the strategy? o Are you ever in a situation where you must use teamwork? Is it always easy for you? Why or why not? o What are some skills needed to be good at teamwork? o How did you contribute to your team? Did you give suggestions? Lead or follow? Encourage or cheer? o How would you do the activity differently if you were asked to do it again? ď ˛ Reset and repeat the activity. Give teams 30 seconds to strategize before starting the time. After the task, debrief with these questions: o Did your teamwork improve this time? How and why did it improve? o Why is good communication important to accomplishing this task? o How would you use this in your classroom, on your campus, or with other teams? o o

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5E Lesson Plan Design Challenge Title: Becoming Sherlock TEKS/TAKS objectives: A.1C,D; A.3A; A.4A,B; A.5C; A.6G; A.7A,B,C Engage Activity **Please note that students should have some experience with combining like terms prior to engaging in this activity.** Prior to beginning this PBL unit, make sure you have access to the computer lab so students can participate in the activities. Explain to the students how important it is to maintain equivalence when solving equations. Have the students access the following web site: http://illuminations.nctm.org/ActivityDetail.aspx?ID=10 They will go through the exploration involving algebraic equivalence. Explain to the students that we will be solving lots of linear equations in the next class period. These equations should involve relevant real-life applications as well as seeking mastery of this concept. (See Handout #1 below) Tell the students they will get an opportunity to show their understanding of linear equations through a design challenge and then present them with the design challenge that will be the culmination of their activities: Your company has been hired to design an educational game that students can play and demonstrate their mastery of solving linear equations and inequalities. The equations and inequalities should include one-step and multi-step solutions, as well as problems involving proportions. The game should include at least five word problems involving linear equations and three word problems involving linear inequalities. Please be sure to include a way for the players to know if they get their answers correct. You may also set time limits if you desire. This is a very large contract being awarded to your company so put your minds to work!! Engage Activity Products and Artifacts Students will write in their journals and answer the following questions.  What word do you “see” in equation?  List some other words that begin with “equa”  What is the opposite operation of addition? multiplication?  What happened to the scale when you added something to one side?  In your own words, pose a problem and explain to another student how you would go about solving that equation Debrief and allow students to share some of their reflections about the engage activity.

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Engage Activity Materials/Equipment Computer with internet access, journal/paper, pencil Engage Activity Resources http://illuminations.nctm.org/ActivityDetail.aspx?ID=10 Handout #1 Explore Activity Have students work in groups of 3 or 4. You may decide how to establish groups or have them choose a card from a stack numbered 1, 2, 3, and 4 (depending upon the number of students in your class). Like numbers will form the groups. An advantage to your deciding the groups is to make sure disadvantaged students do not all get in the same group. Once groups are assigned, have the students complete the team-building activity together to build cohesive groups and improve communication among team members. For a detailed description of this activity and materials see: http://regentsprep.org/Regents/math/teachres/Ttiles.htm You may make your own equations or follow the site above and make problems from the activity for the students. This way, you have a good resource for reference. http://regentsprep.org/Regents/math/solveq/TRSolvEq.htm Teacher should act as facilitator during this process and make sure students are “balancing their equations” properly. Follow this activity with a handout of equations to solve. (See Handout #2 below) Teacher may want to pause for two class days and work on solving equations before continuing with the PBL. Students should understand that zero is a perfectly acceptable answer and sometimes there is no solution to a problem. Students will also need a firm foundation of solving linear inequalities. Have them work on solving linear inequalities through the use of the following website: http://mathdemos.gcsu.edu/mathdemos/ineq/ineq.html. Provide the students with the following accompanying worksheet: http://mathdemos.gcsu.edu/mathdemos/ineq/Vinequlab.pdf to use during the exploration of the applet. Explore Activity Products and Artifacts Students will solve the equations in the activity

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Students will write in their journals and answer the following questions:  When solving equations, which operation do you perform first to begin your balancing?  Which operation do you perform last?  How does this relate to PEMDAS (order of operations)?  What happens when you subtract a number that is larger than the number on the other side of the equation?  What are some of the main differences between solving linear equations and linear inequalities? Explore Activity Materials/Equipment Card stock of different colors, sandwich bags, paper and pencil for scratch work, computer with internet access, handout problems Explore Activity Resources Handout #2 http://regentsprep.org/Regents/math/teachres/Ttiles.htm http://regentsprep.org/Regents/math/solveq/TRSolvEq.htm http://mathdemos.gcsu.edu/mathdemos/ineq/ineq.html http://mathdemos.gcsu.edu/mathdemos/ineq/Vinequlab.pdf Explain Activity Have the students share their completed equations with the rest of the class and compare solutions. See how many of them checked their solutions in the original problem. Debrief if necessary and correct any misconceptions or algebra errors that are being made. Remind the students again of the importance of being able to solve linear equations of all types. Since their challenge will be to design a game using linear equations and inequalities, direct them to a computer lab utilizing the following site: http://www.shodor.org/interactivate/activities/ and Reference Algebra Four (about half way down the page). Students should work through various levels, keeping a journal of their activities and results. Let them work in pairs so they can compete against one another. If you have the capability of using this activity with the entire class, you could have them compete against each other in their groups and gradually speed up the time to solve the equations. When students have completed this activity to your satisfaction, they will return to their groups and begin working on the design challenge. Take time to brainstorm with them about ideas for games and make a wall hanging for their reference as they begin to plan. Guide them in this process and ask questions about types of games they have played in the past (Bingo, board games, etc.). Be sure to have poster board, tag board, colored pencils, objects for player movements, dice, card stock, etc. available for their use. Ask if there are any questions and clarify any misunderstandings.

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Explain Activity Products and Artifacts Journal Entries:  Record your thoughts about the activity  What level of difficulty did you reach?  What type of problem gave you the most trouble? Results of brainstorming Explain Activity Materials/Equipment Computer with internet access, paper, journal, large chart paper, colored pencils, dice, objects for players (buttons, colored tag board squares, etc.) Explain Activity Resources http://www.shodor.org/interactivate/activities/

Elaborate Activity

Present each student with a copy of the design challenge. Have them outline for you a plan of action. This plan can be in the form of an outline or flow chart. Students must present this to you before they begin their final product. Tell them they have to have a minimum of twenty problems in their game and at least five linear equation word problems and at least three linear inequalities word problems. The problems should include all the types of equations and inequalities studied in this unit. As each group shares their plan, give them the necessary materials and tell them they may want to do a rough sketch on large chart paper first. The creativity of children is amazing. Just act as facilitator, making sure they are staying on task, and let them go!! Praise them as you see them making progress and make suggestions as necessary but this is their product and they need to claim ownership. You will need to check their equations to make sure they are correct. Elaborate Activity Products and Artifacts Outline or flow chart Rough sketch Finished Product

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Elaborate Activity Materials/Equipment Poster board, tag board, card stock, colored pencils, dice, objects for players, large chart paper Elaborate Activity Resources None Evaluate Activity

Upon completion of their games and after you have checked all of the problems and solutions in each game, set up stations around the classroom with one game at each station and give the students an opportunity to play all of the games. Tell the students that they will not have a chance to complete each of the games, but that they need to really get an idea of how each game is played. Provide the students with a remarks sheet at each station so that students can provide each team with feedback regarding what went well, what didn’t go as planned, and suggestions on how to improve it. Preface this part with a discussion regarding what constructive feedback looks like and doesn’t look like. Make sure that students provide positive, constructive feedback for each game. Pre-read the feedback and edit it for content if necessary, then provide the feedback to each group. Have the students reflect in their journals regarding how their groups worked together, their own participation in their group, and the feedback that they received from the other groups regarding their game. Use the attached rubric to evaluate each group’s game. Evaluate Activity Products and Artifacts Play games, constructive feedback, journal reflections Evaluate Activity Materials/Equipment Games, feedback sheets, journals, pencils Evaluate Activity Resources None

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Handout #1 Solve each equation. Show ALL steps and check your answer. 1. -8 + x = 3

2. y + 7 = 7

3. 12 – p = 5

5. 7x = 42

6. 4p = 2 6 9

9. 2x – 15 = - 17

1 q = 12 13

4. x + 7/4 = 2/3

8. 13 = - 3 n

10. -5x + 12 = 2x – 3

11. Anna bought 6 cans of dog food that each cost the same amount. She spent $5.40. Write an expression to determine the cost of one can of dog food. Solve the equation to find how many cans she bought.

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Handout #2 Solve each equation and show ALL steps. Check your answers. 1.

c = 5.5 10

3 7

6x + 5 – 10x = 18

7 = 3 – ( x + 2)

7. 17 = 3 ( r – 5 ) + 8

8. 5x – 7 = - 7x + 17

y 14

3. 14 = 10 – 2x

32 = 5 – 2y

9. 3(2x + 1 ) + 3 = 5( x + 1)

10. A car rental company is charging $50 for rental and $.75 per mile for gasoline. Write an equation to express the cost of driving the car x miles. How much would you have to pay if you traveled 100 miles?

11. The ratio of faculty to students at your high school is 1:22. There are 1210 students in the high school. How many faculty members are there?

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12. When you are traveling, you have to exchange your U.S. money for foreign money. It changes very often. On this particular day, the exchange rate was 65 U.S. dollars for 50 euro. How many U.S. dollars were 150 euros worth this day?

13. Jamie earns $25,000 per year plus a 3.2% commission on his sales. Find Jamieâ&#x20AC;&#x2122;s total salary for the year when his sales are valued at $325,000.

14. You are running for student council and you need 75 signatures for your petition. So far, you have 15 signatures. How many more do you need?

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Plan the Assessment Engage Artifact(s)/Product(s): Journal Entry

Explore Artifact(s)/Product(s): Solutions to equations/inequalities, Journal entry

Explain Artifact(s)/Product(s): Journal entry

Elaborate Artifact(s)/Product(s): Outline or flow chart, Rough sketch, Finished Product

Evaluate Artifact(s)/Product(s): Play games, Constructive feedback, Journal entry

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Rubric Student shows complete Student shows partial understanding of all understanding of all types of linear equations linear equations

Student shows little understanding of linear equations

Solutions

Student solves all Student solves most problems accurately problems accurately and clearly shows steps and shows steps

Student makes several key mistakes and does not include steps

Clarity of Instruction

Instructions are clearly Instructions are stated Instructions are not stated but questions could arise stated

Neatness

Product is neat and demonstrates pride in ownership

Product is somewhat neat with a few detractors

Outline/flowchart

Indicates clear understanding of project directions and provides a clear flowchart/outline

Student demonstrates Student is somewhat understanding of clear but needs guidance project but needs on the flow chart/outline a few suggestions on the flowchart/outline

On-task behavior

Student was on-task all of the time and focused on the job

Student was mostly on-task and focused on the job

Variety of Problems

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Variety of problems Solutions Clarity of instructions Neatness Outline/flowchart On-task behavior

Product does not clearly demonstrate pride in ownership

Student was somewhat on-task but had to be redirected several times

40 points 20 points 10 points 10 points 10 points 10 points

Students lose points under variety if they did not include all of the types of equations and inequalities outlined in the design challenge (5 points for each type not included). Students lose points under solutions by not including them or creating a game that is difficult to find the solutions. Students lose points under clarity if the instructions are somewhat clear or no instructions are given On-task behavior is part of the observations during the act of facilitating the design challenge.

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Story Board  Week 1 Activities

Week 2 Activities

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Day 1 Engage (30 minutes) Explore (60 minutes) Day 6 Elaborate (90 minutes)

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Day 2 Explore cont. (90 minutes)

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Day 3 Explain (90 minutes)

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Day 7 Evaluate (90 minutes)

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Day 8 Evaluate (90 minutes)

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Day 4 Elaborate (90 minutes)

Day 9

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Day 5 Elaborate (90 minutes)

Day 10

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