Painting a House (Understanding Ratios)
Task: Painting a House
Explore:
Suppose three people are painting a house. Kameron and Juan have paint guns and can paint a room in 6 minutes each. Teresa has a long paint brush and can paint a room in 18 minutes.
Answer the following questions.
1. It took the group 30 minutes to paint a house. How many rooms are in the house?
2. How long would it take them to paint two houses, one with 12 rooms and another with 16?
3. Bryan shows up for the next job. He paints as fast as Juan. The job took 36 minutes. How many rooms are in this house?
Allow students to show/articulate answers.
Discover (if students are unable to formulate an answer):
To assist studentts with the first question - start a table showing the number of rooms painted at given intervals of time
e.g.
| Painters | 6 min | 12 minutes | 18 minutes | 24 | 30 |
| Kameron | 6 min spent/6 min rate = 1 room | 2 | |||
| Juan | 6/6 = 1 room | 2 | |||
| Teresa | 6/18 = 1/3 room | 2/3 room | |||
| Total Rooms | 2 1/3 rooms | 2 2/3 |
To assist students with the second question - ask students to consider the total number of rooms to be painted and then encourage them to extend the table
To assist students with the third question - encourage the students to make a new table.
Learn:
Show how to convert the above table into multiple ratio tables. Then have the students seek out the following relationships in Teresa.
Horizontal: Each value in the "green" column is multiplied by a constant to get the corresponding value in the "red" column.  | Vertical: If the "green" value is multiplied by a number, then the "red" number is multiplied by the same number.  | Addition: If two numbers in the "green" column are added together, then the corresponding "red" numbers also are added together.  | |
| All three tables show that there will be 30 reds if there are 10 greens. | |||
Example
| Kameron's Room count | Time spent |
| 1 | 6 minutes |
| 2 | 12 minutes |
| 3 | 18 minutes |
| 4 | 24 minutes |
Vertically: 2 x 2 = 4 and 2 x 12 = 24
Addition: Kameron's 2 & 3 room count gives 5 rooms which equals the matching times of 12 + 18 minutes giving 30 minutes to paint 5 rooms.
Enrichment:
- Determine the team's painting rate of rooms per minute with and without Bryan's aid.
- Conclude the impact of adding Bryan.