Unit 3, Lesson 17
Painting a Room
Grade 6
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This Warm-up familiarizes students with the context of painting the walls of a room, which is used throughout this lesson. Students are given drawings of the four walls of a bedroom. They are prompted to think about what information they would need if they were to paint all the walls and buy the paint.
Display the drawings of the four walls for all to see. (If possible, provide access to a color version of the drawings to support students in making sense of the features of the room.) Read aloud the statement and the question (or invite students to do so). Give students 1–2 minutes of quiet think time.
Here are drawings of the four walls of a bedroom.
If you are asked to paint all the walls and buy enough paint for the job, what information would you need?
Invite students to share the information they would need and questions they would ask. Consider recording and displaying their responses for all to see. If any students have had experience painting a room, invite them to share any considerations that may be important but have not been mentioned.
Tell students that they will think more about the area to be painted, the necessary amount of paint, and the time needed to paint the walls of a bedroom.
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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).
Tell students that if they are painting the bedroom, they would need to determine how much paint is needed and how much it would cost. Remind students (or tell them, if they did not do the “All the Walls” activity) that the paintable wall area of the bedroom is 300 square feet.
Explain that paint can be purchased in 1-quart or 1-gallon containers. Ask students how the two units of volume relate to one another. If needed, remind students that there are 4 quarts in a gallon.
Arrange students in groups of 2. Give students 5–6 minutes of quiet work time on the first two questions and then time to discuss their responses and reasoning with their partner. Then pause for a brief whole-class discussion.
Invite students to share some possible combinations of container sizes to purchase to have enough paint for the project. Make sure students recognize that the wall area of 300 square feet needs to be doubled because two coats of paint are required. Then ask students to share the cost of each option they mentioned.
Explain that hardware stores would sometimes have a sale on paint. Tell students that they will now look at how the paint costs would change when some discounts are applied. Give students a few minutes to work on the last question independently or with their partner.
Paint can be purchased in 1-quart or 1-gallon containers. The paint chosen for the room costs $12 a quart and $38 a gallon.
Which container sizes and how many could you buy to have enough paint for the room? Name at least two options.
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.)
Help us improve by sharing suggestions or reporting issues.
Here is the floor plan for the bedroom that needs to be painted.
A floor plan for a bedroom that closely resembles the shape of a rectangle with the top side labeled "North," the bottom side labeled "South," the right side labeled "East," and the left side labeled "West."
Here is some information about the room and the job:
How many square feet need to be covered with paint? Show your reasoning. Organize your work so that it can be followed by others.
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.