**Name of Project: How Efficient is Your Home?**/

**Duration: 3 Weeks**

**Subject/Course: Algebra 2**/

**Teacher(s): R. Flake**/

**Grade Level: 10-11**

**Other subject areas to be included, if any: Physics**

**Key Knowledge and Understanding**

(CCSS or other standards) / ACCRS

HS.N-CN.A.1. Know there is a complex number i such that i2 = −1, and every complex number has the form a + bi with a and b real.

HS.N-CN.A.2. Use the relation i2 = –1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.

**Mathematical Practices**

HS.MP.2. Reason abstractly and quantitatively.

HS.MP.6 Attend to precision.

HS.MP.7. Look for and make use of structure

Success Skills

(to be taught and assessed) / Critical Thinking/Problem Solving - Student will make choices regarding available technology. Students will solve problems regarding the efficiency of housing units. They will need to assess the situation and determine which operations should be used to successfully determine the efficiency / Self-Management – Students will manage time and focus on task at hand. Student will make use of log book to reflect on progress in learning the concepts involved and will reflect on progress in determining the efficiency of the housing unit, and in determining most efficient unit.

Collaboration – Students will be working in teams of two to determine the efficiency of the housing units. Students will also be working with the entire class as they compare efficiencies in their housing units. Students will consider the input from other students before making decisions regarding the most efficient unit.

Project Summary

(include student role, issue, problem or challenge, action taken, and purpose/beneficiary) / The student will assume the role of an intern at Arizona Public Service and will analyze the efficiency of two different housing units that are being developed in the region. The students will work in teams of two. Each team will design a working circuit that is a representation of the flow of electricity in the housing unit, determine the impedance of the circuit, determine the amount of current running through the unit, then graph the projected monthly electrical expenses for the unit, based on the findings.

The student team will compare their findings with other groups to determine which design is the most efficient of all the different housing circuit designs completed in the class.

**Driving Question**/ How is the efficiency and impedance determined in a circuit?

How can the efficiency of a circuit be improved?

How can energy usage be decreased in the home?

How are complex numbers used to calculate impedance?

What can be done to conserve energy in home?

Entry Event / Americans are some of the greatest consumers of energy in the world. Together, on average, we use nearly a million dollars in energy every minute – twenty four hours per day – every day.

When you save energy, you not only save money, you also reduce the demand for such fossil fuels as coal, oil, and natural gas. Less burning of fossil fuels also means lower emissions of carbon dioxide (CO2), the primary contributor to climate change, and other pollutants. The average American produces about 40,000 pounds of CO2 emissions per year.

To help the environment, to help the economy, and to help decrease our dependence on fossil fuels, it is essential for us to develop and use high efficiency appliances to reduce our consumption of energy. Developing more energy efficient homes can be an effective way to decrease our demand on energy resources.

To introduce the project, a representative from Arizona Public Service will come to the classroom and officially welcome each student as an intern at APS. He will give each student a welcome packet outlining their individual responsibilities. He will explain the project to the class and will explain how electric bills are calculated by the electric company.

In addition, the APS representative will explain the energy consumption of different household items that consume electricity and how these appliances can be made to be more efficient.

Products / Individual:

1. Efficiency rating for two housing developments

2. Learning log book

3. Complex Operations Exercises

4. A drawing of circuit which is designed online using a simulation. / Specific content and success skills to be assessed:

1. Know how to use distributive property of multiplication

2. Ability to add complex numbers

3. Ability to subtract complex numbers

4. Ability to multiply complex numbers

5. Ability to divide complex numbers

6. Ability to calculate the powers of i

7. Determine the conjugate of an expression

8. Ability to build simple circuits using online applet

Team:

Students will develop a linear equation to represent the electrical costs for their assigned housing units. Students will compare their findings with those of the other teams to determine which unit is the most electrically cost efficient. Students will prepare a power point presentation, including table and graphs, that justify their recommendation for the most cost efficient unit / Specific content and success skills to be assessed:

Ability to derive a linear equation

Be able to determine the impedance of an a/c circuit

Be able to graph the results of the study to show efficiency

Project DESIGN: OVERVIEW page 2

**Making Products Public**

(include how the products will be made public and who students will engage with during/at end of project) / During final presentations, the Arizona Public Service representative will be in attendance to observe the final presentations and provide feedback.

**Resources Needed**/ On-site people, facilities:

School maintenance personnel will be available to allow students to check voltage at different locations.

Equipment: Computers,

Materials:

Housing Unit Diagrams, Imaginary Numbers Practice Pages

Community Resources:

Representative from APS

**Reflection Methods**

(how individual, team, and/or whole class will reflect during/at end of project) / Journal/Learning Log.

Students will make daily entries into their learning logs to explain their learning and understanding. They will give examples of what they have learned and will write these reflections in their learning logs.

Whole-Class Discussion

Whole class discussions will take place daily as students explain their learning from the prior day. This will help to reinforce what was learned in prior classes. It will also be a time for those who may have struggled the day prior to learn concepts that may have been missed on the prior day.

Notes:

Project Design: student Learning Guide

Project:

**Driving Question:**

**Final Product(s)**

Presentations, Performances, Products and/or Services /

**Learning Outcomes/Targets**

knowledge, understanding & success skills needed

by students to successfully complete products /

**Checkpoints/Formative Assessments**

to check for learning and ensure

students are on track /

**Instructional Strategies for All Learners**

provided by teacher, other staff, experts; includes

scaffolds, materials, lessons aligned to learning outcomes and formative assessments

(individual and team) / Students will gain an understanding of simple a/c circuits. / Building circuits on simulation will give students a knowledge of circuits. Assessment will be determined by successful completion of circuit / Students will learn about a/c circuits through discovery as they build the circuits on the simulator.

Students will be able to perform operations with complex numbers / Complex operations exercise will serve as a formative assessment to ensure understanding. / Students will use the internet in the form of instructional video or other instructional sites to learn how to perform operations with complex numbers

Students will be able to graph complex numbers on a 3 dimensional graph / Graphs will be checked to determine mastery of graphing complex numbers / Students will use the internet in the form of instructional video or other instructional sites to learn how to graph complex numbers. Teacher instruction will be used when intervention is necessary

Students will be able to calculate the total impedance on a circuit. / Housing circuit diagrams will be checked to determine whether or not students have correctly calculated the total impedance. / Students will use peer to peer instruction to determine the total impedance. When necessary, the internet will be used to aid instruction. The teacher will also provide instructional support.

Student will be able to create a graph to display the cost of running the circuit vs. the amount of energy converted in the circuit. / Student graphs will be used to determine mastery of graphing ability. / This should be something students already know how to do. If not, teacher input will be provided to guide students in creating graphs.

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