Part 1: Lesson Description

Making Informed Purchase Decisions: Understanding Unit Costs and Ratios to Get  a “Good Buy”

Abstract

This lesson takes the learner through a series  of exercises where the ability to understand  ratios and calculate unit cost will help the learner make optimal, well-reasoned, cost-effective  purchasing decisions.  The target audience is the adult learner (preferably with school-age children) working in the Grade D range (6th-8th grade) and with RP Domain (Ratios and Proportional Relationships).  Learners will benefit by seeing the relationship that mathematical concepts have to their everyday lives by using mathematical reasoning to make better  purchasing decisions.  Mastery of this material will help learners demonstrate readiness for higher-level algebraic concepts.

Learner Audience / Primary Users

• Adult learners demonstrating  6th-8th grade math and reading  level competencies.

Educational Use

• Curriculum / Instruction

Language

• English

Material Type

• Instructional Material
• Lesson Plan
• Homework and Assignments
• Images and Illustrations

Keywords

• Designers for Learning
• Adult Education
• Math
• Unit Price
• Unit Cost
• Ratios
• Consumer Math
• Purchasing Decisions

Time Required for Lesson

• 60 minutes

Targeted Skills

Key skills covered in this lesson include:

• Employability (Resource Management, Planning)
• Life (Resource Management, Planning)
• Career (Resource Management, Planning)

Learning Objectives

By the end of this lesson, the learner should be able to:

• Define unit price.
• Calculate unit price for a desired purchase item.
• Identify a preferred purchase based on unit price calculations.
• Describe several short and long-term benefits of using unit price calculations to make purchase decisions.

College & Career Readiness Standards (CCRS) Alignment

• Level:  Adult Education
• Grade Level:  D
• Subject:  Mathematics
• Domain:  RP: Ratios and proportional relationships
• Standards and Description:

• Expressions and Equations Use properties of operations to generate equivalent expressions.  Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients. (7.EE.1)
• Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related.  For example, a + 0.05a = 1.05a means that “increase by 5%” is the same as “multiply by 1.05.” (7.EE.2)  [Also see A.SSE.2, A.SSE.3, A.SSE.3a, A.CED.4]
• Solve real-life and mathematical problems using numerical and algebraic expressions and equations.
• Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically.  Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies.  For example:  If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation. (7.EE.3)

Prior Knowledge

• The learner should be able to apply basic addition, subtraction, multiplication and division functions using a basic calculator.
• The learner should be able to read and write at a 6th-8th grade level.

Required Resources

• Paper shopping circulars
• Internet access (recommended, but optional)
• Computer/projector
• Printouts of worksheets for classroom practice and homework
• Basic Calculator
• Notebook Paper
• Pencils

Lesson Author & License

• Lesson Authors: Team Members: Ruth Coleman, Cindy Francies, Jennifer Schneider
• License: Creative Commons License; Creative Commons CC BY 4.0 license is requested.

Part 2: Lesson

Instructional Strategies and Activities

Warm-Up

Time: 10 minutes

• Break the class into groups of no more than 4.
• Prompt them to discuss their experiences grocery shopping:
• Do they like it? Why or why not?
• What’s confusing about it? (If anything)
• When prompted with sales circulars, ads and coupons, how do they figure out what to buy?
• Are they confident that they are making good choices?

• After approximately 5 minutes of discussion, ask each group to report on their shared experiences.
• Some prompting questions:
• If they were more confident in their math skills, would they be more confident shoppers?
• How would spending grocery money more wisely improve their quality of life?

Introduction

Time: 15 minutes

First five minutes:  Lesson Overview

Provide learners with lesson objectives:

Instructor:  Restate each objective and share an overview:

• Define unit price.
• Calculate unit price for a desired purchase item.
• Identify a preferred purchase based on unit price calculations.
• Describe several short and long-term benefits of using unit price calculations to make purchase decisions.

Example:

• Over the next hour, we’re going to work through these issues together.
• We’ll start with defining our key term: unit cost.
• We will spend time exploring how to calculate unit cost.
• We’ll also work through some exercises and will play a game to help us practice.

If Internet is available, play the following Consumer Reports video (1:47) on how unit pricing helps a consumer save money when shopping.

Next five minutes:  Share a story to provide context, relevance and application.

Teacher will share a relatable story:

Example:

Last week I went shopping for my son’s birthday party.  He’s super excited and we wanted to make smart purchases.  We were all set.  We prepared our list.  It was quick and easy!

Here’s a few of the items we needed:

• Lots of Balloons
• Paper plates
• Napkins
• Juice Boxes
• Brownies

Off we went.  We started at the party store and I quickly realized this wasn’t go to be as easy as we thought.  We quickly found the aisle with balloons, but the options were so overwhelming!  There were packs of 25, packs of 50, packs of 100, even packs of 250!  The prices were all different.

How am I supposed to know which to buy?  Say I need 200 balloons.  Should I buy a pack of 250 and have extra?  Two packs of 100?  A bunch of smaller packs?  What would you do?  Have you ever been in a similar situation?

We need to understand unit cost and be able to calculate unit cost.

Ready?

[Teacher will ask group for similar examples and shared stories.  To motivate and establish relevance, teacher will explain that by working through this lesson students will be able to save money and make more informed purchase decisions.]

[Teacher can present story on a handout, with images and a shopping list for the party as well as examples of different pricing per package size.]

Next five minutes:  Introductory Activity:

Ask each learner to consider and share one experience where they had to (or may have to) make purchase decisions by comparing product prices that differ based on quantity.

Ask each learner to spend a few minutes looking through shopping circulars and identify different prices for an item based on quantity purchased.

Presentation / Modeling / Demonstration

Time: 15 minutes

Show the following Khan Academy two minute video on solving unit price.

If the internet and/or computer is unavailable, the instructor can demo on the board:

Calculating Unit Cost:

“Unit Cost” (or “Unit Price”) refers to the cost for one unit (item, pound, liter, etc.) of an item you intend to purchase.  So, when an item is sold by the pack or in bulk, the “Unit Cost” tells you what one item in the pack costs.

We calculate “Unit Cost” by dividing the total cost by the total quantity.  Unit Cost can’t help us with questions relating to quality, desired quantities or whether we have room to store 100-pack purchases, but “Unit Cost” does help us identify what is (and is not) and “good buy”.

For example, if juice boxes are 4 for $1.00, then they are $.25 each.  If brownies are 12.00 for a dozen, then they are $1.00 each.

Teacher will work through several unit cost calculation examples (on whiteboard).

Birthday party themed:

Example Item 1:  Granola Bars

1. A box (Box A) of 6 granola bars costs $3.60.  What is the unit cost of each granola bar in this box?
2. A box (Box B) of 10 granola bars costs $5.40.  What is the unit cost of each granola bar in this box?
3. A box (Box C) of 50 granola bars costs $10.00.  What is the unit cost of each granola bar in this box?

Question:  Which box is the better buy based on unit cost calculations?

Example Item 2:  Balloons

1. Pack A contains 20 balloons and costs $3.60.  What is the unit cost of each balloon in this pack?
2. Pack B contains 25 balloons and costs $4.00.  What is the unit cost of each balloon in this pack?
3. Pack C contains 50 balloons and costs $4.50.  What is the unit cost of each balloon in this pack?
4. Pack D contains 100 balloons and cost $8.00.  What is the unit cost of each balloon in this pack?

Question:  Which pack is the better buy based on unit cost calculations?

[These can be developed using Google Doc hand-outs and/or online worksheets/quizzes]

Additional Discussion Questions:

1. If you buy more (packs with greater amounts) do you have any use for the extra quantity?
2. Is the item perishable?  How might this impact your decision making process?
3. Does the item require significant storage space?  How might this impact your decision making process?
4. How might our answers and decisions change if, instead of granola bars or balloons, the item under discussion were cupcakes or ice-cream cups?
5. How might our answers and decisions change if, instead of granola bars or balloons, the item under discussion were paper plates or napkins?

Guided Practice

Time: 10 minutes

Activity Option I:  Paper Jeopardy

Teacher breaks class down into groups of 3-4 students.

Play a Jeopardy like game.  Product categories.  Unit Cost Problems.

Jeopardy:

• Include downloadable/printable instructions and materials using Google Docs.
• Consider including an interactive version in Google Sheets.
• Alternatively - include a Bingo game with Google Doc print-outs/downloads and/or an online/interactive quiz.

Activity Option II: Online Unit Price Lesson and Game

The following website is a lesson on unit price.

• Math is Fun. [Website]. 2015. Retrieved fromhttp://www.mathsisfun.com/measure/unit-price.html

The following website is a unit price online game.

• Math is Fun. [Website]. 2015. Retrieved fromhttp://www.mathsisfun.com/measure/unit-price-game.html

• Break students down into groups of 4 and have them play game as a group.
• See which group gets the correct answer first (or take turns for point options).
• Assign points.

Evaluation

Time: 5 minutes

Activity/Option I:

• The instructor will use the whiteboard to work through sale options from circulars and calculate the Unit Cost.
• The instructor will present the problem, have students work on the problem independently.
• The instructor will check the students work for accuracy.

Activity/Option II:

• The instructor will use the exercises (listing unit sale prices) to calculate Total Cost.  Students will be given the unit cost to calculate the total purchase price.
• The instructor will initiate the exercise by demonstrating how to calculate total purchase price when given unit cost.
• The instructor will model the first example.  (Unit Cost multiplied by quantity equals Total Purchase Price).
• Students work through the remaining examples below.

What’s for Dinner? (Calculate Total Cost)

Application

Time: 5 minutes

The teacher will have a class-wide discussion of homework.  Prior to dismissal, the teacher will demonstrate one final example.

Homework:

• When shopping this coming week, calculate unit price for at least two purchase items.
• Make your purchase decision based on optimal unit cost as well as other considerations (including quality, brand-loyalty, quantity and storage capabilities).
• Describe 2 short-term and 2 long-term benefits of using unit price calculations to make purchase decisions.
• Evaluate your purchase decisions and discuss the impact incorporating unit-price calculations may have on future purchases.

Key Terms and Concepts

• Bulk
• Division
• Item
• Multiplication
• Product
• Purchase Decisions
• Purchase Price
• Quantity
• Ratio
• Sale Price
• Total Cost
• Unit Cost
• Unit Price

Supplemental Resources

Video:

The following video is a lecture about Ratios, Rates, and Unit Rates.

Websites:

The following website is a worksheet on calculating unit price.

• Study Zone. [Website]. 2001-6. Retrieved from http://www.studyzone.org/mtestprep/math8/a/unit_price7p.cfm

The following website provides an interactive activity to compare unit prices.

• PBS Learning Media. [Website]. 2016. Retrieved from http://whyy.pbslearningmedia.org/resource/4f5b0540-485c-4abc-8f73-7430563d83a8/comparing-unit-price/

References

Consumer Reports. (2012, June 19). Unit pricing helps you save money at the grocery store. [video]. Retrieved fromhttps://www.youtube.com/watch?v=KMe85qahPbk

Khan Academy. (2010, August 11).Solving unit price problem. [video]. Retrieved from https://www.youtube.com/watch?v=d7rAlcNHDUI

Math is Fun. [Website]. 2015. Retrieved fromhttp://www.mathsisfun.com/measure/unit-price.html

Math is Fun. [Website]. 2015. Retrieved fromhttp://www.mathsisfun.com/measure/unit-price-game.html

PBS Learning Media. [Website]. 2016. Retrieved from http://whyy.pbslearningmedia.org/resource/4f5b0540-485c-4abc-8f73-7430563d83a8/comparing-unit-price/

SkyhawksMath's channel. (2012, September 11). Ratios, Rates, and Unit Rates. [Video]. Retrieved fromhttps://www.youtube.com/channel/UC0HuqFIAjLxkygbb4xDF2UQ

Study Zone. [Website]. 2001-6. Retrieved from http://www.studyzone.org/mtestprep/math8/a/unit_price7p.cfm