MATH-IN-CTE TECHNICAL ASSISTANCE

Math-in-CTE Lesson Plan Template

Lesson Title: Resisters in Parallel Lesson #2

Author(s): Phone Number(s): E-mail Address(es): Wayne Sellevaag 503 353-5910 x37620 sellevaagw@nclack.k12.or.us

Courtney Giddings 503 353-5870 x38620 giddingsc@nclack.k12.or.us

Occupational Area: Advanced Analog Class

CTE Concept(s): ENPF01.01 Understand and apply electrical theory and laws. ENPF02.01 Understand and apply circuit concepts and analysis techniques.

CTE Standard: ENPF01.01.01.01 Use ohms law formulas for current, voltage, resistance and power to solve electrical systems problems. ENPF01.01.01.00 Understand concepts of voltage, current, power, resistance, capacitance, and inductance. (Resistors in Series & Parallel) ENPF02.01.01.02 Build and test a variety of series and parallel circuits.

Math Concepts: Manipulation of equations

Common Core SS Math Standard: 7.EE.4. Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.

a. Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width? 8.EE.7. Solve linear equations in one variable.

b. Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms.

Lesson Objective:

Create equations to solve multi-step electronics problems using the basic series, parallel and ohm’s law formulas.

Series RT = R1 + R2

IT = IR1 = IR2

ET = ER1 + ER2

Using the standard Resistors in Parallel formula Rp = Ra x Rb / Ra + Rb

Ohm’s Law E = I * R ( Voltage = V or E)

MATH-IN-CTE TECHNICAL ASSISTANCE

Materials: Calculator and Student “Class Notes” Notebook

THE "7 ELEMENTS" TEACHER NOTES (and answer key)

1. Introduce the CTE Lesson. Explain the series, parallel combination circuit.

Series RT = R1 + R2

IT = IR1 = IR2

ET = ER1 + ER2

Then, resistors in parallel formula.

Rp = Ra x Rb Ra + Rb Because there are 2 current paths for these resistors in parallel, the total resistance Rp, will be smaller than the smallest resistor.

2. Assess students’ math awareness as it relates to the CTE lesson.

Review Ohm’s Law and the manipulation of the formula: E = I x R

EI

R or

ER

I

3. Work through the math example embedded in the CTE lesson.

1) Solve R2//R3

2) Re-draw the circuit and solve for RT

3) Solve for ERT

4) Solve IT = ERT / RT

5) Solve ER1 = IT * R1

6) Solve EAB = ET-ER1-ELED

7) Solve IR2 = EAB / R2

8) Solve IR3 = EAB / R3

9) The Check IT = IR2 + IR3 (same as step 4 above)

MATH-IN-CTE TECHNICAL ASSISTANCE

4. Work through related, contextual math-in-CTE examples.

Rp = Ra x Rb Ra + Rb Resisters in Series….Rt = R1 + R2 + R3

Resisters in Parallel

Rt = 1

1 + 1 + 1

R1 R2 R3

5. Work through traditional math examples.

Review basic math and solve.

1) -39 = -2v – 9

2) 127 = -6n + 7

3) 8v – 7 = 129

4) 5a – 2 = -22

5) 13 83

r

6. Students demonstrate their understanding.

Students work out and solve for the unknown in their class notebook. Teacher check-off correct answer.

7. Formal assessment.

If Et = 9v, R1=1000Ω, R2=1200Ω, R3=750Ω and a 2v LED IT = .00479A or 4.79mA