MixItUp.pdf

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UVA-SCPS Office of Mathematics Outreach with support from VADOE Mathematics and Science Partnership Grant Program NCLB Title II Part B Revised 8/14/12

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Mathematics Senior Level Capstone Course

Unit Overview

Title of Unit: Mix It Up Unit Designers:

Hunter Hagerty Loudoun

Mikhail Balachov Arlington

Unit Editor:

Su Chuang, Loudoun County Public Schools

Context:

Summary of the issue, challenge, investigation, or problem.

Ethanol is a fuel additive used to decrease dependency on foreign petroleum gasoline. Certain vehicles are capable of using different concentrations of ethanol in the fuel. Students will be asked to create a solution of a specific concentration of ethanol, when given two solutions of varying concentrations of ethanol. Students will also research and explore the implications and consequences of increased use of ethanol gasoline.

Number of Class

Hours: 4

Unit

Design: _x__Task Based ___Project Based Other Subject

Areas/Disciplines Addressed:

Science (Chemistry, Physics), Writing

Driving Question: How can you create different concentrations of solutions when the solutions available to you are of different concentrations? How can you create different concentrations of ethanol gasoline for your vehicle if you only had a source of 5% ethanol gasoline and a source of 20% ethanol gasoline?

Mathematics Content Addressed:

Linear Systems of Equations

Problem solving with Percents and Ratios

MPE Addressed:

Problem solving, decision making, & integration;

Understanding & Applying Functions; Procedure and Calculation Assumption of Prior

Knowledge:

Creating Systems of Equations Solving Systems of Equations

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2 College and Career

Readiness/21st Century Skills to be taught (T) during this unit or expectation (E) for student use during this unit and assessed (A): BIE Page 35-37

Collaboration

Students working in pairs

T & A Research

Prior Knowledge Skills

E

Communication (Oral and/or Written) Presentation and Poster

T & A Technology

Graphing Calculator

E

Critical Thinking/Decision Making Other: (Describe)

Major Products and/or Performances:

Group

Written report with solved problems

Or presentation to class (choose one of these options)

Presentation Audience: x Class

School Individual

Mathematical Journal Entry

Expert Community Other: Teacher

Launch: Event or experience used to engage the students interest and inquiry:

Coke v. Sprite

http://blog.mrmeyer.com/?p=9553 – 1 minute

This video presents students with a mixture problem with the soda solutions. If you took a fixed amount of Sprite and mixed it with the Coke or if the same amount of the Coke/Sprite mixture is taken and mixed into the Sprite, which has a greater amount of the original soda?

USA Today Article

http://content.usatoday.com/communities/driveon/post/2011/06/e15-e10-ethanol-alcohol-pollution-engine-damage-labels-gas-station-pump-epa/1

This article presents some of the concerns and controversies with the increased use of ethanol alcohol as a gasoline additive.

Evaluation: Formative Assessments (During the Unit)

Interview Practice Presentations

Mathematicians Journal x Notes

Preliminary

Plans/Outlines/Prototypes

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3

Rough Drafts x Concept maps

Field Tests Other:

Summative Assessment (End of Project)

Written Products, with a rubric x Peer Evaluation, with a rubric

Oral Presentation with a rubric x Self Evaluation, with a rubric

x Other Product(s) or

Performance(s), with a rubric

Other:

Resources Needed: On-site people, facilities: Teacher

Equipment/Technology: Graphing Calculator, Internet to show video, Research Materials: Optional Activity: lemonade concentrate, water, several cups Community Resources: None

Reflection Methods: Individual, Group, and/or Whole Class

Mathematicians Journal x Small/Focus Groups Whole Class Discussions x Fishbowl Discussions

Survey Other:

Material Adapted From: (Provide credit for any materials or activities adapted from other sources.) Dan Meyer’s Blog, dy/dan: http://blog.mrmeyer.com

Exeter’s Math Department www.exeter/academics/72_6539.aspx

USA Today article on 15% ethanol gas http://content.usatoday.com/communities/driveon/post/2011/06/e15-e10-ethanol-alcohol-pollution-engine-damage-labels-gas-station-pump-epa/1

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4 Virginia’s Senior Level Capstone Course

Instructional Plan Unit Title: Mix It Up

Driving Question: How can you create different concentrations of solutions when the solutions available to you are of different concentrations? How can you create different concentrations of ethanol gasoline for your vehicle if you only had a source of 5% ethanol gasoline and a source of 20% ethanol gasoline?

Task: Ethanol is a fuel additive used to decrease dependency on foreign petroleum gasoline. Certain vehicles are capable of using different concentrations of ethanol in the fuel. Students are asked to create a solution of a specific concentration of ethanol, when given two solutions of varying concentrations of ethanol. Students also research and explore the implications and consequences of increased use of ethanol gasoline. ENGAGE Teacher provides an experience to engage students. Number of hours : Video-1 min. Discussion-10 min. Introduce the problem Suggested Video: Coke v. Sprite

This video presents students with a mixture problem with the soda solutions.

http://blog.mrmeyer.com/?p=9553

If you took a fixed amount of Sprite and mixed it with the Coke, or if the same amount of the Coke/Sprite mixture is taken and mixed into the Sprite, which has a greater amount of the original soda?

Directions for Instructor:

 After showing the video clip, facilitate a whole class discussion about the Coke v. Sprite problem. What information is

provided? What questions are raised?

 Have students think, individually, of strategies to approach this problem and write these strategies into their mathematician’s journal.

 Conduct a whole group discussion about the different

approaches to the Coke v. Sprite problem. Allow students to write in their mathematician’s journal again after the whole group discussion. Students can record any new strategies they’d like to explore.

 It is not important for students to solve the Coke v. Sprite problem right now. This problem can be revisited at the end of this task unit and solved in students’ mathematician’s journal.

Optional Activity: Blind taste test.

Using frozen lemonade concentrate, create a several concentrations of lemonade, ranging from 10% - 50% lemonade concentrate. Have a student taste each concentration and describe what the student

Mathematician Journal

Prompts:

What

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5 liked or disliked about each concentration of lemonade. Discuss the

different concentrations and the relevance to the juice makers, preferences to taste, and implications with cost.

Teacher note: The objective with the optional activity is for students to consider a different application where different concentrations of solutions are applied. Students can discuss how higher

concentrations of lemonade would be more costly to the juice makers, and possibly to the consumers. Students may indicate that taste is a more important factor to consider. Students can also discuss how pure lemonade concentrate could be sold so that the consumer can create their own concentration of lemonade to suit their individual taste. One of the inconveniences with this option is that consumers would have to make their own lemonade from the concentrate.

EXPLORE

Teacher provides

guidance for the explorations to prepare students with the

knowledge and skills to engage in the task. Students will self-assess on the prior knowledge and skills assumed for the unit

Number of hours:1

Exploration: Mixture Problems (Handout #1):

The goal of this activity is for students to identify the different concentrations of specific solutions in mixtures. Students will be working with percentages to solve these mixture problems.

 Students work in pairs to complete the Mixture Problems (Handout #1)

 Discussion Questions:

o What strategy did you use to solve each problem?

o Did you use a different strategy for each problem? If so, how did your strategy help you solve each problem?

 Facilitate a whole group discussion to explore the three mixture problems on Handout #1. Have students explore the different methods/strategies for solving each problem.

 If students liked a different strategy that was presented in the whole group discussion, have them record the new strategy into their mathematician’s journal.

Student Tutorials if needed:

Resources/Tutorial/Remediation (Handout #2)

This handout lists a series of links to online resources students can access for additional help and support with the mathematics involved in this task unit.

Prompts:

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6 EXPLAIN

Teacher introduces the main task of the unit and

prepares students to in small group independent work...

Number of Hours 0.5

USA Today Article

http://content.usatoday.com/communities/driveon/post/2011/06/e15- e10-ethanol-alcohol-pollution-engine-damage-labels-gas-station-pump-epa/1

This article presents some of the concerns and controversies with the increased use of ethanol alcohol as a gasoline additive.

Title: Ethanol Gasoline Mixture Problem (Handout #3)

 Have students read the USA Today Article to begin classroom discussions about ethanol gasoline and the reasons behind using ethanol as a gasoline additive.

 Working in pairs, have students work through theEthanol Gasoline Mixture Problem (Handout #3)

 The teacher may need to encourage students to develop a strategy for solving this problem first.

 Students will need to develop a plan of action for solving this task. Rough drafts of student work will be submitted as formative assessments.

 Review the self- and peer-evaluation rubrics with the students. Discuss expectations for group collaboration and teamwork. If necessary, model or provide examples of this 21st century skill.

 The summative assessment will be an oral presentation and a poster of the completed task along with justification of the work.

Prompts:

Why do you think there would be a need to create different concentrations of ethanol gasoline? What do you think are some of the implications and consequences of having different concentrations of ethanol gasoline? ELABORATE The student groups are working independently with teacher consultations. Number of Hours 2

 Facilitate group work and discussions. Do students have a clear strategy for solving this task? Are students recording their strategy so that others can understand their thinking?

 Provide students with the self- and peer-evaluation rubrics (Handout #4) so groups are aware of expectations.

 Provide students with the Final Presentation Rubric (Handout #5) so groups are aware of expectations.

Formative Assessments:

 Rubric of self- and peer-evaluation. (Handout #4)

 Mathematician Journal Prompts

 Drafts of student work

 Group discussions

Prompts:

What are your observations as you work through this task? What are your findings? What

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7 Anticipated Products and Artifacts:

 Student-created posters presenting their strategy and solution for the Ethanol Gasoline Mixture Problem (Handout #3)

Differentiation:

 Teacher can provide students with different concentrations of ethanol gasoline to create. For the new concentration of ethanol gasoline, first ask students to predict how much of the 20% ethanol gasoline and how much of the 5% ethanol gasoline to create this new concentration. Have students explain their thinking before they begin their actual calculations.

 Teacher can also introduce a new gas station, Gas Station C, which sells E85 ethanol gasoline, which consists of 85% ethanol and 15% gasoline. Using the three available concentrations of ethanol gasoline, ask students to create different concentrations of ethanol gasoline.

EVALUATE

Working groups submit products or make

presentations

Number of Hours 0.5

Rubric(s) for teacher and/or audience for presentation Mix It Up Rubric for Final Presentation (Handout #5)

 Select and sequence student presentations based upon the strategies students used. Sequence the presentations so that students can make connections between the different approaches to this task.

 Watch the Coke v. Sprite video again and ask students to solve the problem in their mathematician’s journal and justify their response. http://blog.mrmeyer.com/?p=9553

 Students can conduct research on the implications and consequences of increased use of ethanol gasoline as well as increased concentrations of ethanol in gasoline.

 Possible Discussion Questions:

o What is the main source of ethanol alcohol and what are the implications of increased ethanol production for use in gasoline?

o What are the implications on the land that is currently used for food production?

o Is it truly more economical to use ethanol gasoline? Why or why not?

Prompts:

What is the practical use of

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8 Map the Unit

What do students need to know and be able to do to complete the task/project/problem successfully? How and when will they assess their own necessary knowledge and skills? How will they remediate their own gaps or weaknesses in knowledge and skills? Look at each major task for the unit and analyze the tasks necessary to produce a high-quality product.

Task: Go to appropriate websites to explore specific skills needed.

KNOWLEDGE AND SKILLS NEEDED

Assumed already learned

Students will self-assess

Will be taught during the unit

1. Operation with percents X X

2. Modeling the word problem X X

3. Solving systems of linear equations X X

4.

5.

6.

What project tools will student’s use?

 Know/need to know lists X Daily goal sheet

X Mathematician’s Journals

 Briefs/Memos X Task lists

 Planning Calendar

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9 HO#1

Mixture Problems

1. A one gallon beverage contains 5% fruit juice. How much pure (100%) fruit juice is in the one gallon beverage?

2. A solution is created by mixing 3 gallons of 5% juice with 2 gallons of 15% juice. How much pure juice is in the new solution? What is the concentration of juice in this new solution?

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10 HO#2

Resourses/Tutorial/Remediation

http://illuminations.nctm.org/ActivityDetail.aspx?ID=154

http://www.purplemath.com/modules/mixture2.htm

http://www.purplemath.com/modules/mixture.htm

http://www.purplemath.com/modules/systlin4.htm

http://www.purplemath.com/modules/systlin5.htm

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11 HO #3

Ethanol Gasoline Mixture Problem

How can you create solutions with various concentrations?

 Gas Station A sells 20% ethanol gasoline, which is a mixture consisting of 20% ethanol, 80% gasoline.

 Gas Station B sells 5% ethanol gasoline, which is a mixture consisting of 5% ethanol, 95% gasoline.

From the ethanol gasoline purchased at Gas Station A and Gas Station B, how can you create a 10% ethanol gasoline mixture (10% ethanol, 90% gasoline)?

From the ethanol gasoline purchased at Gas Station A and Gas Station B, how can you create concentrations of ethanol gasoline that is less than 5% ethanol?

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12 HO #4

Name____________________________

Partner Name_____________________

Peer Evaluation

The following is a list of statements to be answered by you about your partner. Think carefully about assigning values for each of the following statements.

Directions: Put an ‘X’ in the box that applies.

My partner… Strongly

Agree Agree Neutral Disagree

Strongly Disagree

Contributed positively to discussions

Did an equal portion of the workload

Helped to keep me focused on the task

Was respectful of my ideas and opinions

Is someone I would work with again

Self Evaluation

The following is a list of statements to be answered by you about yourself. Think carefully about assigning values for each of the following statements.

Directions: Put an ‘X’ in the box that applies.

I ,________________ ,(insert name here)… Strongly

Agree Agree Neutral Disagree

Strongly Disagree

Contributed positively to discussions

Did an equal portion of the workload

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13 HO #5 Mix It Up Rubric for Final Presentation

CATEGORY 4 3 2 1

Mathematical Concepts Explanation shows complete understanding of the

mathematical concepts used to solve the problem(s).

Explanation shows substantial understanding of the mathematical concepts used to solve the problem(s).

Explanation shows some understanding of the mathematical concepts needed to solve the problem(s).

Explanation shows very limited understanding of the underlying concepts needed to solve the problem(s) OR is not written.

Mathematical Reasoning Uses complex and refined mathematical reasoning.

Uses effective

mathematical reasoning

Some evidence of mathematical reasoning.

Little evidence of mathematical reasoning.

Working with Others Student was an engaged partner, listening to suggestions of others and working cooperatively throughout lesson.

Student was an engaged partner but had trouble listening to others and/or working cooperatively.

Student cooperated with others, but needed prompting to stay on-task.

Student did not work effectively with others.

Strategy/Procedures Typically, uses an efficient and effective strategy to solve the problem(s).

Typically, uses an effective strategy to solve the problem(s).

Sometimes uses an effective strategy to solve problems, but does not do it consistently.