## Does the Decimal Point Really Make a Difference?

### Sharla ShultsBay District Schools

#### Description

What's the problem with cheeseburgers advertised for .99 cents each or colas for .89 cents each? Students study the decimal dilemma and discover major math mistakes in the real world.

#### Objectives

The student refines vocabulary for interpersonal, academic, and workplace situations, including figurative, idiomatic, and technical meanings.

The student locates, gathers, analyzes, and evaluates written information for a variety of purposes, including research projects, real-world tasks, and self-improvement.

Understands the relative size of integers, rational numbers, irrational numbers, real numbers and complex numbers.

Understands concrete and symbolic representations of real and complex numbers in real-world situations.

#### Materials

-Copies of documents found in the associated file prepared for class discussion and formative assessment (See Teacher Preparation for list.)
-Student calculators (optional) – FCAT style

#### Preparations

1. Have folders ready for distribution at the beginning of class.

2. Download and duplicate copies of the following documents found in the associated file:
a) Warm-Up Activity #2 – one per student
b) Warm-Up Activity #2 Answer Key – one copy for teacher use
c) Discover the Decimal Dilemma Response Sheet – one per student
d) Discover the Decimal Dilemma Response Sheet Answer Key – one teacher’s copy
e) The Decimal Dilemma Problem Solving – one per student
f) The Decimal Dilemma Problem Solving Answer Key – one copy for teacher use

3. Refer to the associated file for Group Activity Advertisements that demonstrate major mathematical errors. Download, print, number on the back from 1 to 8, laminate, and cut out the advertisements.

4. Set up overhead projector for class discussion.

5. Download, print, and make transparencies of Sample Decimal Dilemma Problem and Sample Decimal Dilemma Problem Corrected found in the associated file.

6. Secure a set of classroom calculators, FCAT style. Scientific calculators are not necessary.

7. Prepare extra worksheets as needed for students having difficulty with basic arithmetic skills. These reflect areas of difficulty as demonstrated in problem solving with decimals.

#### Procedures

Day 7 of the unit The Math Connection

Step #1, #2, #15, and #16 are for teachers using the Unit Plan. For a stand-alone lesson of decimals in the real world, please begin with Step #2 and end with Step #14.

NOTE UNIT PLAN: Letters should be arriving during this week. Since the letters will be coming in to the school, don’t forget to make a teacher’s copy to keep in a separate folder. This is a backup in the event students’ folders or materials are misplaced. Also, keep a checklist as the letters arrive. Distribute copies of the Rough Draft Comments Sheets to students to complete as they receive their letters. This document is found in the associated file of the lesson To Whom It May Concern to be duplicated as needed. Instruct students to write thank you notes to the contact persons for taking the time to answer the letters and make copies for the portfolio.

1. With student assistance, distribute student folders at the beginning of the class period.

2. Return the Rising and Falling Fractions Problem Solving practice sheets with feedback on weak areas for students to add to folders. Especially note to students any areas of weakness in arithmetic skills. Tell students to be mindful of any additional practice sheets attached. Remind students to place the problem-solving practice sheets in their folders and take home the attached sheets for extra practice.

3. Distribute the Warm-Up Activity #2 and tell students to work with partners in answering general questions about decimals they encounter in the real world. Hold a class discussion covering the information gathered.

NOTE: Following is some general information to share with students referencing the decimal dilemma that demonstrates the decimal really makes a difference!
· The most common types of mistakes involving infants and children are written orders in which a MISPLACED DECIMAL POINT results in drug doses several orders of magnitude higher than intended.
Misplaced Decimal Point Often Cause For Drug Errors In Kids Http://sns.mcall.tribune.com/features/health/sns-health-childmedication.story
(See Weblinks below for link to this Website.)
· Common mistakes include: transposition of digits (for example, reading 6238 as 6328); misreading of repeated digits (for example, reading 62238 as 62338); misreading of tables (for example, referring to a wrong line or a wrong column); INCORRECTLY POSITIONING A DECIMAL POINT; overlooking signs (especially near sign changes).
First Steps in Numerical Analysis: http://mpec.sc.mahidol.ac.th/numer/STEP2.HTM
(See Weblinks below for link to this Website.)
· A zero should always be placed before a DECIMAL if the prescription is for an amount LESS THAN 1.
Medication Mistakes – SecurityWorld.com: http://www.securityworld.com/library/family/medicationmistakes.html
(See Weblinks below for link to this Website.)

4. Divide the class into groups of 3 or 4 students per group depending on the size of the class. Be sure to create a way that they can be grouped effectively.

5. Distribute one Discover the Decimal Dilemma Response Sheet per student. (See Associated File.) Each set of questions corresponds to an advertisement. (See Associated File for sample ads.) Inform students that one advertisement per set of questions is distributed per group. Explain that each group starts on the same number on the response sheet that corresponds to the number of the advertisement given to the group. (Advertisements have been numbered on the back from 1 to 8.)

6. Distribute one advertisement per group and allow a few minutes for each group to study the ad and find the major math mistake involving decimals.

7. Using the Discover the Decimal Dilemma Response Sheet, students answer the questions as a team with each member recording on his own sheet.

8. Rotate advertisements throughout the groups until all groups have studied each example and recorded the responses.

9. Monitor students’ progress throughout the entire group activity and lend assistance as needed.

10. Hold a class discussion on the information gathered, going over each problem explicitly, and record important notes on the overhead or board. This provides an excellent opportunity for student feedback regarding the understanding of decimal problem solving in the real world. Emphasize to the students that the importance of this activity is to enhance problem-solving skills and sets the stage for the individual problem solving activity to follow.

NOTE: If time allows, have each group select a member to discuss and explain their responses to the last advertisement reviewed.

11. Collect all advertisements and instruct students to place the completed response sheets in their folders.

12. Optional: Use the Transparency Sample Decimal Dilemma Problem and the Transparency Sample Decimal Dilemma Problem Corrected (see Associated File) to demonstrate to students additional errors that exist within the decimal dilemma.

13. Tell students: Now, let’s practice! Distribute The Decimal Dilemma Problem Solving practice sheets. (See Associated File.) Tell students to take out one sheet of paper to use for additional workspace as needed. Remind students to show work. Allow students to use calculators in the problem solving, but be careful that a clear understanding of the arithmetic skills is already in place. Use teacher discretion whether to utilize this as an independent activity or perform with a partner or in groups. If students are working in groups, create a way that they can be partnered or grouped effectively.

14. As students are engaged in the problem solving, continue to monitor students’ progress with arithmetic skills and lend assistance as needed. This provides the necessary feedback for determining the additional practice needs regarding problem solving with decimals.

15. While students are completing the problem solving, collect students’ folders. The added documents of today’s lesson include the Rising and Falling Fractions Problem Solving, Warm-Up Activity #2, the Discover the Decimal Dilemma Response Sheets and The Decimal Dilemma Problem Solving practice sheets.

16. Collect students’ The Decimal Dilemma Problem Solving practice sheets at the end of the class period to be returned the following day. Check students’ problem solving skills using the Discover the Decimal Dilemma Problem Solving Answer Key found in the associated file.* Identify any students struggling with the problem solving due to the inadequacy of understanding decimals. Attach additional practice work sheets as needed to the decimals problem solving activity sheets and return to students the next day to take home for extra practice. (Check out [Pre-Algebra Step by Step] by Sharron Vogt. 1996. Frank Schaffer Publications, Inc. This book contains explanations instead of just a lot of problems. There is often one or more pages of instruction to every page of practice. The explanations are unique, creative and effective.)

*Note: If deemed necessary, adapt the checklist provided in the associated file of Rising and Falling Fractions to record the results for decimals.

#### Assessments

This assessment aligns with the part of the standard only dealing with decimal representation in real-world situations. Students understand the meaning of decimal placement by comparison of values and concrete and symbolic representations of rational numbers by equivalent representations as demonstrated on the Decimal Dilemma Problem Solving practice sheet. (See Associated File.)

Students analyze and evaluate the information from the text within the real world math problems presented for solving. Students demonstrate understanding by correctly solving the problems.

Students are formatively assessed using the answer key provided in the associated file. Vocabulary is embedded throughout the lesson plan allowing students to refine vocabulary for interpersonal, academic and workplace situations.

The standards and Goal 3 Standards addressed will be modeled and formatively assessed throughout this unit and will be summatively assessed at the completion of the unit.

#### Extensions

This is Lesson 7 of 10 in the unit The Math Connection addressing [When Are We Ever Going to USE This MATH?]

The Beacon Unit Plan associated with this lesson can be viewed by clicking on the link located at the top of this page or by using the following URL: http://www.beaconlearningcenter.com/search/details.asp?item=2947. Once you select the unit’s link, scroll to the bottom of the unit plan page to find the section, “Associated Files.” This section contains links to the Unit Plan Overview, Diagnostic and Summative Assessments, and other associated files (if any).

Misplaced Decimal Point Often Cause For Drug Errors In Kids
Newsroom: Patient Safety News

Scroll down to Step 4 – Mistakes
First Steps in Numerical Analysis

Medication Mistakes
The Education Station

Basic Aspects of Decimals and Operations
Math Tutorials: Decimals

From Understanding Place Value to Operations
Math.com: Decimals

When Are We Ever Going to USE This Math?
The Math Connection