Mathematics Curriculum
Unit #8 Project
Title: Design on a Dime
Grade Level: 6 / Length of Time: 2 days
Project Summary:
This project utilizes skills learned in the Geometry Unit, as well as Ratios, Rates, and Proportions Unit. In this project, students will utilize what they know about surface area, unit rates, and percents to become wise consumers, and turn a profit. In this real-life scenario, students will act as painters. They will determine the surface area of a room to be painted, and utilize unit rates to determine the most cost effective way to purchase paint. Students may work independently, with a partner, or in collaborative groups to complete this project.
Learning Targets
Domain: Geometry
Cluster: Solve real-world and mathematical problems involving area, surface area, and volume.
Standard #s: / Standards:
6.RP.2 / Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V = l w h and V = b h to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems.
6.RP.3 / Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems.
Domain: Ratios and Proportional Relationships
Cluster: Understand ratio concepts and use ratio reasoning to solve problems.
Standard #s: / Standards:
6.RP.2 / Understand the concept of a unit rate a/b associated with a ratio a:bwith b ≠ 0, and use rate language in the context of a ratio relationship. For example, “This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar.” “We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger.”
6.RP.3 / Use ratio and rate reasoning to solve real-world and mathematicalproblems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.
b. Solve unit rate problems including those involving unit pricing andconstant speed. For example, if it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed?
Evidence of Learning
Rubric will assess:
Planning: Accuracy of calculations
Materials
Student Handout (1 pg.)
Assessment Rubric
Lesson Plans
Lessons / Timeframe
Present Project & Step 1 / One 40 min period
Steps 2 & 3 / 1 period
Curriculum Development Resources:
Design on a Dime
You are quite the designer! You just took on the challenge of repainting the room shown below. Painting can be fun, but there’s a catch. You are being paid $1,000 to paint the room, but you must purchase and pay for the paint yourself. In order to have the maximum amount of money left in your pocket, you need to determine the most cost effective way to purchase the paint.
The floor to ceiling height in this room is 12 ft.
You will be choosing paint from one of three companies: PaintMe, Prime Quality, or Two Brothers.The table below shows the price per container, and the coverage area for each company’s paint. You may purchase paint in different sized containers, but you must place an order with only one company.
Company / 8 oz / Gallon / 5-GallonPaintMe / $2.94/16 sq ft / $32.98/400 sq ft / $128.00/2,000 sq ft
Prime Quality / $3.07/18 sq ft / $34.56/425 sq ft / $142.95/2,600 sq ft
Two Brothers / $2.53/13 sq ft / $29.09/390 sq ft / $108.00/1,900 sq ft
1. Determine the amount of paint needed to paint the room.
2. Determine which brand and which container(s) will be the most cost-effective (will give you the most coverage for the least amount of money).
3. Calculate your profit after deducting the total paint cost, including 7% sales tax.
Teacher Resource Page
This project can be assigned as a group/partner project, or an individual project. It can be utilized as a learning experience, or as an assessment. If given as an assessment, ensure that the students fully understand the task, and are prepared to utilize what they have learned to problem solve. A rubric is attached for grading.
If it is a group/partner project, allow the students to have the time and space needed to devise strategies and plans to problem solve together before intervening. If/when necessary, provide just enough redirection and guidance needed to get them to utilize what they have learned about area, surface area, ratios, unit rates, and percents to complete each part of this project.
- In order to determine the amount of paint needed, the surface area of the walls to be painted must be calculated. Keep in mind that the ceiling, floor, windows, and door will not be painted.
- In order to determine which paint to use and the container size, the student should calculate the unit rate for each option. Additionally, if different sized containers are used, this further affects which brand is chosen.
3. Calculate your profit after deducting the total paint cost, including 7% sales tax.
Students should be mindful that they are splitting the profit with the other members of their group. So if this is a group project, you may consider increasing the initial payment.
Rubric
Category / 3 pts. / 2 pts. / 1 pts. / 0 pts.Paint Area /
- Did not include ceiling or floor
- Deducted window area
- Deducted door area
Paint Purchase /
- Calculated unit rates correctly
- Correctly calculated the amount of paint needed
- Found most cost-effective combination of container size & brand
Profit /
- Calculated total paint cost correctly
- Deducted tax correctly
Total: ______