Carpenter

You want to replace the carpet in your New York studio apartment with vinyl flooring. To ensure you have enough vinyl planks, you have drawn a scale drawing of your apartment. The vinyl planks are 36 inches by 6 inches, with 10 in a box. Based on the drawing, how many boxes will you need? 

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Ferris Wheel (Circumference)

Goat on a Rope (Area)

Gravel (Area with Unit Rates)

Alberto and Nia are going to the garden center to buy pea gravel for our yard. Alberto has created a blueprint for the yard design. They want gravel around the patio, firepit, pavers, and fountain. Each 50-lb bag of pea gravel we would like to buy will cover about 3 square feet. How many bags do they need?

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PacMan Mural (Area)

Andrew, an arcade owner, wants the alley behind the arcade to fit better with the theme of the building. He asks local artist Nia to create a Pac-Man mural to cover as much of the wall as possible. The space he wants covered is 9 feet high and 16 feet wide. The design she comes up with has a Pac-Man that fits the wall perfectly from top to bottom, two dots that are half the size of Pac-Man, and Pac-Man has a Pac-Man-shaped eye that is half the size of the dots. She leaves the background untouched to give the mural a “city” look. How much of the wall can still be seen?

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Pathway (Area)

Alberto from Scape that Land meets James, the city planner, at city hall to discuss the new path at the playground. In James' office, Alberto shows what his company can do for the city. He lays out rubber pavers on the desk for James to look at. These pavers are durable, safe, and easy to install. He puts them on the table for James to look at. They have three sizes and can stamp the town seal for a more personalized look. There are three designs they can do for the pathway. The space between the pavers can be grass, rocks, or sand. The space between the pavers will require maintenance. How much space is there between the pavers in each design?

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Sprinklers (Area)

James and Nia need to figure out the ideal location of sprinkler heads for their lawn. They want to use the fewest sprinklers possible while covering the most grass. They should only place the sprinklers on the edge of the grass; no area of the sprinklers should overlap another, and no sprinkler should hit the concrete around the lawn. One sprinkler can spray between 8 and 16 feet in 2-foot increments and can be set to full circle, half circle, or quarter circle. Where should they place them? How much of the lawn is covered?

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Delivery (Volume of Rectangular Prisms)

An emergency order has come in for ball bearing. General Electric needs as many as we can ship as fast as possible. We have the choice between the large or the medium boxes. Which boxes should we choose to fit the most ball bearings into the truck? How many boxes can you fit into the truck? How many ball bearings? How much space is left over or wasted inside the truck?

Extension: This is an emergency order, and we do not have the time to worry about efficiency. But for future reference, how efficient is this shipping method? What is the percent increase when choosing a box? What percent of the truck's volume are we utilizing?

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Clean Air (Volume of Rectangular Prisms)

Microbes small enough to be discharged from an infected person can stay in the air on dust particles, respiratory droplets, and water droplets. Air purifiers filter the air, helping to fight the spread of airborne diseases. The building supervisor has asked us to install new air purifiers for the entire building. We determined the dimensions of the whole building with a laser distance meter. The bigger unit purifies 7500 cubic feet and costs $1200. The smaller unit purifies 6000 cubic feet and costs $900. Which units should we buy?

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Shipment (Surface Area of Rectangular Prisms)

Your company sells classroom supplies, and one of the supplies you sell is classroom sets of Rubiks Cubes. As a company, you spend too much money on cardboard. The packaging needs to be more efficient. You will need to design new packaging. How do we stack them and put them in a box? How much cardboard does each arrangement require? Which arrangement will make the most efficient box and use the least amount of cardboard? You also must remember that a shipping box has double flaps at the bottom and double flaps at the top to close the box.

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Pool Tiles (Surface Area of Rectangular Prisms)

The pool in your backyard needs to be resurfaced. Instead of opting for plaster, you decide to tile the pool. Pool tiles shouldn't have to be replaced after installation, whereas plaster will only last about 7 to 10 years. Tiling the entire pool will be more expensive now, but it should save money over time. How much will the tiles cost you?

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Scandinavia (Area of Composites)

We are Sara’s Flags' geometry experts. Sara uses high-quality, weather-resistant fabric to make the flags, and it is our job to ensure that we have enough. We are adding the flags of Iceland, Norway, Sweden, Denmark, Finland, and the Faroe Islands to our catalog. We need you to calculate the amount of fabric each flag requires. We need to ensure we have the right amount of colored fabric when we start production. How much colored fabric do we need to make one of each flag? What are the ratios between the colors?

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Wedding Cake (Surface Area of Rectangular Prisms)

When you need a wedding cake, you go to Alberto’s bakery. Alberto makes every wedding cake exactly how the customer wants it. The customers, James and Nia, prefer square layers over circular ones. They want the bottom layer to be 5 inches tall, the middle layer 4 inches, and the top layer 3 inches. They want the layers to be 16, 14, and 12 inches wide. Once we have created the layers and stacked them, we need to cover them with fondant. How much fondant will we need?

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