This is the second of two lessons that help students make sense of equivalent ratios through physical experiences. In this lesson, students mix different numbers of batches of a recipe for green water by combining blue and yellow water (created ahead of time with food coloring) to see if they produce the same shade of green. They also change the ratio of blue and yellow water to see if it changes the result. The activities here reinforce the idea that scaling a recipe up (or down) requires scaling the amount of each ingredient by the same factor (MP7). Students continue to use discrete diagrams as a tool to represent a situation.
For students who do not see color, the lesson can be adapted by having students make batches of dough with flour and water. 1 cup of flour to 5 tablespoons of water makes a very stiff dough, and 1 cup of flour to 6 tablespoons of water makes a soft (but not sticky) dough. In this case, doubling a recipe yields dough with the same tactile properties, just as doubling a colored-water recipe yields a mixture with the same color. The invariant property is stiffness rather than color. The principle that equivalent ratios yield products that are identical in some important way applies to both types of experiments.
- Comprehend and respond (orally and in writing) to questions asking whether two ratios are equivalent, in the context of color mixtures.
- Draw and label a discrete diagram with circled groups to represent multiple batches of a color mixture.
- Explain equivalent ratios (orally and in writing) in terms of the amounts of each color in a mixture being multiplied by the same number to create another mixture that is the same shade.
Let’s see what color-mixing has to do with ratios.
Mix blue water and yellow water; each group of 2 students will need 1 cup of each. To make colored water, add 1 teaspoon of food coloring to 1 cup of water. It would be best to give each mixture to students in a beaker or another container with a pour spout. If possible, conduct this lesson in a room with a sink.
Note that a digital version of this activity is available at this link: https://ggbm.at/Hcz2rDHc. It is embedded in the digital version of the student materials, but if classrooms using the print version of materials have access to enough student devices, it could be used in place of mixing actual colored water.
- I can explain the meaning of equivalent ratios using a color mixture as an example.
- I can use a diagram to represent a single batch, a double batch, and a triple batch of a color mixture.
- I know what it means to double or triple a color mixture.