Making a PB&J Using Rational Equations

Rational Expressions and Rational Equations can be tough for students of any age to grasp, let alone if they are nestled within a word problem. The goal of this exercise is to connect the students with the material by engaging in a real-life problem...making peanut butter and jelly sandwiches (denoted PB&J henceforth).

What You Will Need:

--A loaf of bread

--Peanut Butter

--Jelly

--Two plastic knives

--Two volunteers

How It will Work:

Two volunteers will be timed while each making a peanut butter and jelly sandwich (see below for what constitutes completion). Two make the problem less tedious, have your students record times in seconds as opposed to minutes. Thus, a student who completes a PB&J in 1min and 15 seconds should have a recorded time of 75seconds. After each students has their time recorded, students will calculate the amount of time it should take both volunteers to make one PB&J. After calculated, a test will be performed with both volunteers working together to make one PB&J.

What Constitutes A PB&J Sandwich:

What seems obvious is not. We must have a benchmark for what constitutes a completed PB&J in order to compare the two times. We will say that a PB&J is complete after

1) One piece of bread is completely spread with peanut butter

2) One piece of bread is completely spread with jelly

3) Both pieces of bread are stacked on top of one another

4) The lid for both the jelly and the peanut butter have been sealed back on

5) The knife has been washed/wiped off.

Steps:

Step 1: Choose Two Volunteers

Step 2: Explain what each volunteer will do and what constitutes a finished PB&J sandwich.

Step 3: Have first volunteer make a PB&J and record their time.

Volunteer One Can Make a PB&J in ______seconds

Step 4: Have second volunteer make a PB&J and record their time.

Volunteer One Can Make a PB&J in ______seconds

Step 5: Have the class calculate how long it should take both volunteers to make one PB&J if they work together.

Step 6: Work out the proposed solution for your students on an overhead (see example below)

Step 7: Test the proposed time by timing both volunteers making one PB&J

Worked Out Example

Recorded Time Of Volunteer 1: ____75______seconds

Recorded Time Of Volunteer 2: ____80______seconds

Combined Time Should Be

1/75 + 1/80 = 1/x
LCD = 1200x
1200x(1/75 + 1/80) = 1200x(1/x)
16x + 15x = 1200
31x = 1200
x = 39 seconds (rounded up)