## IM Commentary

The purpose of this task is to provide students with a first informal experience with the idea of equivalent ratios. The intuitive notion that making multiple batches of the same recipe results in the same bread as a single recipe helps motivate the idea that different ratios can be "the same" in some important way. Later, students will formalize the idea that *a* :* b* is equivalent to any ratio *sa* : *sb, *where *s *> 0*.*

The task statement shows different-sized blobs, so that cups are represented with larger blobs and teaspoons are represented with smaller blobs, although the blob sizes are not proportional in any way to actual cups and teaspoons. Note that a student might produce a correct drawing where all the blobs are the same size or the relative sizes of the units are not reflected in the diagram. The important thing is that the correct values are shown for each quantity in the ratio.

A possible followup task could be:

Another recipe calls for 2 cups of flour and 1 teaspoon of yeast.

- How much flour and how much yeast do you need for two batches of this bread?
- Compare two batches of this bread with one batch of the first bread recipe. Do you think these ratios are equivalent?

Students might say that since they make different kinds of bread since the amount of flour is different when the amount of yeast is the same, the ratios are not equivalent.

## Comments

Log in to comment## St. Christopher School says:

9 monthsThis is a good basic introduction to ratios and equivalent ratios. In the problem you talk about teaspoons of yeast and in the solution you talk about tablespoons of yeast.

## Bill says:

9 monthsThanks for catching that.