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# Art Class, Variation 1

## Task

The students in Ms. Baca’s art class were mixing yellow and blue paint. She told them that two mixtures will be the same shade of green if the blue and yellow paint are in the same ratio.

The table below shows the different mixtures of paint that the students made.

A | B | C | D | E | |

Yellow | 1 part | 2 parts | 3 parts | 4 parts | 6 parts |

Blue | 2 part | 3 parts | 6 parts | 6 parts | 9 parts |

- How many different shades of paint did the students make?
- Some of the shades of paint were bluer than others. Which mixture(s) were the bluest? Show work or explain how you know.
- Carefully plot a point for each mixture on a coordinate plane like the one that is shown in the figure. (Graph paper might help.)
- Draw a line connecting each point to (0,0). What do the mixtures that are the same shade of green have in common?

## IM Commentary

Giving the amount of paint in "parts" instead of a specific standardized unit like cups might be confusing to students who do not understand what this means. Because this is standard language in ratio problems, students need to be exposed to it, but teachers might need to explain the meaning if their students are encountering it for the first time.

## Solution

- The students made two different shades: mixtures A and C are the same, and mixtures B, D, and E are the same.
- To make A and C, you add 2 parts blue to 1 part yellow. To make mixtures B, D, and E, you add 3/2 parts blue to 1 part yellow. Mixtures A and C are the bluest because you add more blue paint to the same amount of yellow paint.
- See the figure.
- If two mixture are the same shade, they lie on the same line through the point (0,0).

## Art Class, Variation 1

The students in Ms. Baca’s art class were mixing yellow and blue paint. She told them that two mixtures will be the same shade of green if the blue and yellow paint are in the same ratio.

The table below shows the different mixtures of paint that the students made.

A | B | C | D | E | |

Yellow | 1 part | 2 parts | 3 parts | 4 parts | 6 parts |

Blue | 2 part | 3 parts | 6 parts | 6 parts | 9 parts |

- How many different shades of paint did the students make?
- Some of the shades of paint were bluer than others. Which mixture(s) were the bluest? Show work or explain how you know.
- Carefully plot a point for each mixture on a coordinate plane like the one that is shown in the figure. (Graph paper might help.)
- Draw a line connecting each point to (0,0). What do the mixtures that are the same shade of green have in common?

## Comments

Log in to comment## Andrew says:

almost 4 yearsSorry - looks like my comment was unnecessary as you've address the opaqueness issue by using milk!

## Janna says:

over 4 yearsI did this ask with a group of grade 7 students with a high EL population. I re-wrote it to make it a lesson for the entire class period. Students were allowed to use some optional hint cards to answer some of the questions. I changed the Y axis to represent the Yellow paint. The lesson began with mixing ratios of colored yellow and blue water to demonstrate the idea of different shades. The first mix was Y:B = 1:2, then 1:7 to show a much more aqua shade of green. Then we made the mixtures again, doubling each (2:4 and 2:14 respectively) to represent proportional mixtures. Then they were posed the Art Class task. I found that students still saw the 4 cups (1:2, 2:4, 1:7, 2:14) of colored water as 4 different shades of green as opposed to 2 different shades since the colored water looked a bit darker with a bigger serving. Next time, I will use colored milk to eliminate this problem. In general students really struggled to see the big ideas and are not used to these types of tasks, but it was worth while and a good challenge for me & the students.

## Andrew says:

almost 4 yearsI think it was a great idea to visually demonstrate the notion of different shades! Even though it is more expensive, next time try using paint instead of colored water - this way the depth of the liquid has less affect on it's appearance.

## Kristin says:

over 4 yearsThat's a great idea! I think I'm going to try that myself to see if it works.