# Build a Better Barcode

 Author: Lakisha Edmondson Unit Title: Build a Better Barcode Grade: 9th Subject: Algebra l Estimated Duration: 5 days (50 minute periods) Unit Activities: Activity 1: Number Magic Activity 2: Simplifying Algebraic Expressions Activity 3: How Do Barcodes Work?  Background Knowledge:  Prior to this unit, Students should be able to simplify numerical expressions using the order of operations. Students should be able to write simple algebraic expressions using coefficients, variables, and constants. Students should be able to simplify algebraic expressions by combining like terms and using the distributive property. Date: July 2014
##### The Big Idea (including global relevance)

The BIG IDEA is that computerized barcoding has greatly simplified the distribution and pricing of products.  Barcodes, which have a mathematical formula embedded within them, have global relevance, as they make everyday life so much easier.  Imagine going back to a time when grocery items didn’t have UPC codes.  The barcode impacts retail, manufacturing, and distribution on a global level.  In fact, coding systems in general, are the way of the future—the banking industry, hospitals, and even dry cleaners use them.

##### The Essential Question

How can we create a barcode for our brand that contains a better algorithm for the check digit than our current UPC code?

##### Justification for Selection of Content

This unit relates to several Common Core State Standards for high school mathematics—Interpret the structure of expressions; Write expressions in equivalent forms to solve problems; Rewrite rational expressions.  In addition, simplifying algebraic expressions is one of the fundamental topics in beginning algebra that students must master in order to be successful in the course. Each year, at least 1/3 of my students demonstrate difficulty combining like terms and simplifying expressions.

##### The Challenge

The challenge for this unit is Barcodes for Your Brand:  Students will use their knowledge about simplifying algebraic expressions to encode their brand’s barcode with a new, efficient algorithm for the check digit.  Groups will check each other’s barcodes to make sure the algorithm actually works, then refine and redesign if needed.

##### The Hook

Students will be presented with a number “trick” that demonstrates the “magic” of numbers to get them excited about the lesson.  For example, instruct students to follow this series of steps (but make sure to tell them that if their math is incorrect, the “magic” won’t work!):

1.     Pick any number (keep it secret!).

3.     Multiply by 2.

4.     Subtract 4.

5.     Subtract 8.

I will then inform students that if they tell me their final number, I can “magically” tell them their starting number.  (The final number will be twice the amount of the starting number).

If students still don’t believe in the “magic,” tell them they will now all “magically” end with whatever number I want them to, no matter the beginning number.  Give the following instructions:

1.     Pick a number.

2.     Multiply by 2.

4.     Subtract 15.

5.     Divide by 2.

Everyone should end up with 5 as their final number!  Magic!

Demonstrate the algebra (simplifying expressions) behind the number magic so students make the connection between the steps and the end result.

##### Teacher's Guiding Questions
1. What are barcodes/UPC codes and what are they used for?
2. How do barcodes work?
3. How is math connected to barcodes?
4. What is a check digit?
5. What are some potential problems with our current barcode system?
6. How can we improve the barcode system?
7. How can we be sure that an algorithm works for all numbers?
8. How do number tricks work?
##### Engineering Design Process (EDP)

The engineering design process will be used during the challenge to create a barcode with a unique algorithm for the check digit.

Define problem: Students will work in teams to create a barcode with a unique algorithm embedded in the code. (Lesson 2, Activity 3)

Research: Students will research the history of barcodes and how they work. (Lesson 2, Activity 3)

Brainstorm solutions:  Students will discuss different ways to create a unique, efficient algorithm for their barcode (Lesson 2, Activity 3)

Choose a solution to develop:  Student teams will create an algorithm for their barcode. (Lesson 2, Activity 4)

Create a prototype: Teams will present their barcodes once finished creating the algorithm.  (Lesson 2, Activity 4)

Test and redesign:  Teams will test the barcodes to make sure they work in all cases.  Teams will make suggestions for improvements or corrections.  Teams will redesign codes.  Following the challenge, teams will present final barcodes to the class.  (Lesson 2, Activity 4)

CCSS:  A-SSE Interpret the structure of expressions.

A-SSE Write expressions in equivalent forms to solve problems.

A-APR Perform arithmetic operations on polynomials.

A-APR Rewrite rational expressions.

##### ACS (Real world applications; career connections; societal impact)

Applications:  Barcodes are used every day in the real-world—in grocery stores, retail chains, healthcare settings, the postal system, manufacturing, event ticketing, and the list goes on and on.

Career connections:  Software engineer, systems analyst, quality auditor, electrical engineer, computer engineer, inventory control manager

Societal impact:  Barcodes have a significant impact on society.  From product identification, tracking, to inventory, to branding, pricing to coding, barcodes have simplified many different aspects of society.

##### Unit Activities

Lesson 1:  The Magic Behind Numbers and Expressions (2 days)

In this lesson, students will experience number “magic” and learn how it relates to simplifying algebraic expressions.

Activity 1: Number Magic (1 day)

Activity 2: Simplifying Algebraic Expressions (1 day)

Lesson 2:  Branding with Barcodes (3 days)

In this lesson, students will learn how UPC codes work.  Then, they will use what they know about simplifying expressions to develop their own barcode with a better check digit algorithm than the current one.

Activity 3: How Do Barcodes Work? (1 day)

Activity 4: Barcodes for Your Brand (2 days)

##### Where the CBL and EDP appear in the Unit

CBL and EDP appear in Lesson 2, Activity 4

##### Misconceptions

--When using the distributive property, students may forget to distribute to all terms inside of the parentheses.

--Students may forget to use the order of operations when simplifying expressions.

--When simplifying rational expressions, students may forget to divide all terms by the coefficient.

http://teachers.egfi-k12.org/lesson-cracking-the-code/

##### Pre-Unit Assessment Instrument

Pre-Assessment Simplifying Expressions

##### Post-Unit Assessment Instrument

Post- Assessment Simplifying Expressions

##### Results: Evidence of Growth in Student Learning

Results: PREPOST UNIT 1

The results demonstrate that 50/55 (91%) students scored higher on the post-test than they did on the pre-test.  In addition, the overall mean on the pre-test was 1.8 versus a mean score of 5.8 on the post-test.

##### How to Make This a Hierarchical Unit

B) To teach this unit at a lower grade level, address the following standards:

CCSS: 6.EE Apply and extend previous understandings of arithmetic to algebraic expressions.

7.EE Use properties of operations to generate equivalent expressions.

##### Reflection

Overall, I feel that this unit was successful.  Students were engaged, interested, and motivated to complete the challenge.  Although not every group was able to successfully complete the challenge, results on the post-test indicate substantial student growth on the academic content. (91% of the students demonstrated improvement on the post-test) .  I selected the content for this unit because barcodes have such relevance.  They make everyday life so much easier--imagine going back to a time when grocery items didn’t have UPC codes!  The barcode impacts retail, manufacturing, and distribution on a global level.  My students enjoyed testing the check digit of UPC codes of various products, but struggled to create their own algorithms.  Students really liked working in teams during the challenge activity.

If I re-taught this unit, I would change a few things:

1. I would allow a bit more time for the research on barcodes, so that more students could find the algorithm for UPC codes.  If that wasn’t possible, I could direct them all to the same website.

2. It took 10 class days, which was longer than anticipated.  I would cut back on some of the in class work and assign it for homework in order to shorten this time length.

3. I would give more emphasis to the EDP.  Perhaps instead of putting all drafts on the same worksheet (in an effort to conserve paper), each draft or revision could be done on a different sheet, with a different color.  This would ensure that students perform several revisions, and allow the teacher to see quickly, from the color, which draft students were working on.

4. I made need to issue more constraints on the challenge, or at least be more specific.  For instance, I could tell students that may only use numbers that result in a single digit.  Or, provide a flow-chart for different situations (if-then…ie.if a double digit, then use the first digit…) that may be encountered in their algorithm.

5.Do a bit more research on my part to find out why the check digit algorithm didn’t work for some of the products we tested.