In this activity, students apply their understanding of area from an earlier unit to find the total wall area to be painted. Later in the lesson, they will use this area to determine the amount of paint and the amount of time needed to apply two coats of paint.

To calculate the total wall area, students rely on a floor plan of a bedroom, a list of its features and measurements, and the drawings that show the view of each wall (from the Warm-up).

Because of the variations in the bedroom’s walls and features, keeping track of the shapes to be included or excluded from the area calculation may be challenging to students. For example, students may need to be reminded to:

• Include the 3 square feet of wall space above the door.
• Account for the south face of the short wall on the west end of the closet (which accounts for 4 square feet of paintable surface area).
• Account for the area above or below the window.

As students work, notice those who organize their work methodically and those who may need organizational support.

Select a few students to share their strategies and solutions for the total wall area. If possible, record their calculations near the relevant parts of the drawings, and display them for all to see. Discuss any disagreements or questions about the calculations or approaches. Make sure that the class agrees on the total square feet before students proceed to think about the amount of paint and time needed for the job in upcoming activities.

In this activity, students apply their understanding of rates and percentages to determine the amount of paint needed to paint a bedroom, the costs for buying paint in different-size containers, and how discounts affect the costs. Students use the area found in the “All the Walls” activity as the basis for their calculation. If the class did not complete that activity, the total wall area (300 square feet) will need to be provided.

There are several combinations of can sizes that would be enough for two coats of paint on all the walls. Some students might consider the possibility of spills or errors and opt to buy a larger quantity. This is perfectly valid as long as students can support and explain their choices. In making assumptions and connecting calculations to real-life considerations, students practice modeling with mathematics (MP4).

Focus the discussion on how students found the amounts of savings in each option given the discounts. Invite several students or groups to share their approaches. Highlight strategies that allow for efficient computation of 20% and 30% of the original prices.

Make sure students see that the cheapest option after discount may vary, depending on which purchasing options students listed initially. (For example, if students listed 7 quart-size containers and 1 gallon container plus 3 quarts as two purchasing options, the latter would be the cheaper of the two. If they also included 2 gallon-size containers, this would be the cheapest after discount.)

In this activity, students solve problems about the amount of time to paint an area, using their understanding of ratio, rate, and percentage along the way. Each problem can be approached in a number of ways, giving students additional opportunities to model with mathematics (MP4).

The last question requires students to consider the rate of painting of one person, determine the time needed to complete the painting at that rate, and find the difference between that amount of time and 150 minutes (the time it takes 2 people to do the work). No scaffolding is given, prompting students to make sense of problems and persevere in solving them (MP1).

Some students may use approximation when answering the first question (saying that the east wall does account for about 25% of the painting job), which would affect their calculations for the second question. Ask these students if the area of the east wall is exactly 25% of the total area. If they say that it is less than 25%, urge them to find out precisely how much less.

Invite students who thought their partner used a particularly efficient strategy on the first question to share. If most students reasoned that 3 square feet is 1% and then scaled it to 72 square feet to correspond to 24%, discuss how the problem can be solved more directly by calculating .

Then discuss the strategies used to answer the last question, in particular how students found the amount of painting time if they were painting the remaining walls on their own. Students are likely to start with one of two rates:

• 96 minutes to paint 72 square feet of area
• 96 minutes to paint 24% of the total area

Select students who used each rate to share. If one of these rates is not mentioned, ask students to discuss how it might be used to solve the problem.