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## Pink Walls?!?

By D. Assael, February 27, 2017

• Middle School

• Mathematics

### Lesson Time

Three 60 minute classes

### Introduction

The following lessons provide students an opportunity to be interior designers!  In this lesson, students will use measurements and surface area to create a budget for painting the classroom walls.  Students will have to create a plan for identifying how much wall space is to be painted (surface area!), what materials they will need, how much paint they will need and how they can maximize their budget.

### National Standards

7.G: Solve real-life and mathematical problems involving angle measure, area, surface area, and volume. l 7.G.6: Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.   7.G: Draw, construct, and describe geometrical figures and describe the relationships between them. l 7.G.1: Solve problems involving scale drawings of geometric       figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale.     7.NS: Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers.   SL.7.1 Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher led) with diverse partners on grade 7 topics, texts, and issues, building on others’ ideas and expressing their own clearly.   SL.7.5 Include multimedia components and visual displays in presentations to clarify claims and findings and emphasize salient points.     Standards for extension:   7.R.P: Analyze proportional relationships and use them to solve real-world and mathematical problems. l 7.R.P.1: Compute unit rates associated with ratios of fractions, including ratio of lengths, areas and other quantities measured in like or different units.

### Objectives

SWBAT use appropriate tools to measure the dimensions of the classroom. SWBAT calculate surface area SWBAT create a budget

### Resources

• Internet connection
• Home Depot, Lowes or other hardware website to determine price of items needed.
• Scale Drawing Examples:
If no Internet:  Have advertisements of hardware stores or information relating to the prices of items needed to paint a classroom.  Collect the advertisements from local newspapers and have them available for students to research the prices on their own.

### Materials

• Tape measures
• Rulers
• Graph paper
• Colored pencils
• Budget Template (attached)

### Vocabulary

Surface area: The sum of the areas of all the sides of a 3 dimensional figure.   Budget: A plan used to decide the amount of money that can be spent and how it will be spent Brainstorm: A spontaneous group discussion to produce ideas and ways of solving problems.

### Procedures

1. Introduction
1. Explain the following scenario to students:

1. Identifying the information
1. After explaining the scenario, present students with an opportunity to identify some information needed to tackle the scenario.
1.                                                i.     “What information will we need to know in order to create a detailed budget for painting the classroom?”
2.                                               ii.     Allow students to brainstorm all questions they believe they need answered.
3.                                              iii.     Allow students to work in small groups to combine questions and see if peers can answer some of the questions.
4.                                              iv.     Allow all ideas to be shared (record ideas board and in student notes),
5.                                               v.     Provide leading questions to help determine any information that students did not address themselves.
1. Ex: “Would we want 30 gallons of paint or would we want to determine how much wall space 1 gallon of paint covers to keep our budget low?”
2. From this scenario, the teacher must guide student inquiry to gather the information necessary to create the budget. “How might we create a budget for painting the classroom?” “What information do we need to know?”
1.                                                i.     From the teacher led questions, more student questions should arise.
3. Information we need (discovered by students or led by teacher)
1.                                                i.     Surface area of wall space to be painted
2.                                               ii.     Size of doors and windows
3.                                              iii.     Will we paint the ceiling?
4.                                              iv.     The amount of area 1 gallon of primer/paint covers
5.                                               v.     How many coats of primer/paint?
6.                                              vi.     Cost of paint
7.                                             vii.     Cost of brushes
8.                                            viii.     Do we need a ladder?
9.                                              ix.     Time commitment
10.                                               x.     Scale to use for drawing
11.                                              xi.     Any other relevant information for you specific classroom.
1. Using the list of necessary information that students created, begin finding the answers to the missing information that cannot be found in the classroom:  (Having a small group of students look this up and report back to the class may be an option) – All information should be recorded in student notebooks
1.                                                i.     Look up the cost of 1 gallon of primer
2.                                               ii.     Look up the cost of 1 gallon of paint (specific to brands and colors)
3.                                              iii.     Look up the cost of 1 paint brush
4.                                              iv.     Look up the cost of 1 roller paint brush
5.                                               v.     Look up the cost of blue painters tape cover
6.                                              vi.     Provide number of coats necessary to prime and paint walls (2 coats each)
7.                                             vii.     Look up the amount of area 1 gallon of primer/paint can
2. Using the list of necessary information that students created, begin finding the answers that can be found in the classroom using a tape measurer: (Having a small group of students look this up and report back to the class may be an option) – All information should be recorded in student notebooks
1.                                                i.     Dimension of the walls of the classroom.
2.                                               ii.     Dimension of any object on the walls that will not be painted (ie. White boards, bulletin boards, clock, etc.)
3.                                              iii.     Dimension of the windows and doors.

1. Calculating the surface area of the room
1. After the room’s dimensions have been measured (in inches and feet) present another question to students so that they can problem solve:
1.                                                i.     “How do we determine how much area will be painted?”
3.                                              iii.     Allow students an opportunity to work in small groups to discuss their thoughts.
4.                                              iv.     Have groups share out their thoughts.
2. Explain that surface area is the sum of the areas of all the sides of a 3-dimensional figure.
3. Have students find the surface area of all the wall space
4. Have students find the area of all the objects on the walls that will not be painted.
5. Have students subtract the surface area of the walls in the classroom and subtract the total area of all the objects on the walls not to be painted.

1. Scale drawings
Provide some real life examples/bring some items in of scale            drawings:
1. Blue prints of buildings
2. Paintings of objects
3. Floor plans
1. Scale models
Provide some real life examples/bring some items in of scale models:
1. Toy cars (if you have any to bring in to show off, do so!)
2. Model airplanes (if you have any to bring in to show off, do so!)
3. Model buildings (souvenirs from major landmarks and attractions, ie. Eiffel Towner, Empire State building, etc.)
4. Explain scale: The relationship between drawing’s or model’s dimensions and the actual dimensions of the object being modeled
5. Teach how to use the scale to find dimensions of scale drawings:
Finding a part/demension of a scale drawing/model: Step 1: Write the scale       Step 2: Create a proportion with the missing part       Step 3: Solve the proportion   Cross-Multiplication OR Equivalent Fractions Ex. You are creating a scale drawing of your bedroom and you are using the scale of    1 ft: 4 cm. If the measure of a wall is 26 feet long, how long will the corresponding wall be in the model?   Step 1:   Step 2:   Step 3: Cross-Multiplication: Equivalent Fractions:
1. Using the following process, on a separate sheet of graph paper, have students create a scale drawing of the walls of the classroom:
1.                                                i.     Students determine the measurement of their models using their chosen scale. Have students determine the best scale to use in relation to the materials they will be working with. (Have students explain why they chose their scale).
1. Example: 1 foot = 2 inches
2.                                               ii.     Include appropriate scale measurement for walls, windows, doors, etc.
3.                                              iii.     Students may color walls to match the desired color scheme selected in groups.
1. Putting together a budget
1. Have students create their budget for the painting project.
1.                                                i.     Groups of 3-4
2.                                               ii.     All members must participate the “painting” (this should add some more details for the budget creation),
3.                                              iii.     Based on how much area is being painted and how much area a gallon of primer/paint can cover, have students calculate the necessary amount of paint/primer to purchase.
1. Have students make calculations on a the back of their budget report
4.                                              iv.     Students should fill out a their budget on the provided budget report template.

1. Present
1. Have students set up scale drawings and do a gallery walk!

### Assessment

Students will have to write a proposal for the re-painting of the classroom via a budget.
• Budget:
• Cost of paint
• Cost of paint brushes
• Scale drawing of all walls of the classroom to be painted (Optional: Provide scale 2 feet = 1 inch)
• Scale provided on drawing
• All objects (whiteboards, bulletin boards, windows, doors, etc) counted for and appropriately drawn to scale.

### Enrichment Extension Activities

#1: Making the scale model
1. Using measurements calculated, have groups create their own scale model of the classroom (no furniture necessary)
2. Use cardboard boxes to cut out necessary wall sizes
3. Glue white paper on model’s walls
4. Make sure students have some way of representing the objects on the walls not to be painted.
5. Color paper the desired color scheme selected by your group
6. Glue all walls together on top of a cardboard base
#2: Have students create a plan to redesign their bedroom!
• Using surface area, how could you maximize the space in your bedroom?
• Would you like to buy new furniture?
• Would it help if you door opened out of your bedroom instead of into your bedroom?
•  How could you re-arrange your current furniture to maximize your space?

### Teacher Reflection

It might be powerful to have an administer come into the class room and "act out" the debate over whether or not we can re-paint the classroom.