Comparing Relationships with Tables

5 min

Teacher Prep
Setup
Students in groups of 2. Display the image for all to see. 2 minutes of quiet think time, followed by whole-class discussion. (Optional demonstration of the original lemonade.)

Narrative

This activity encourages students to reason about equivalent ratios in a context. During the discussion, emphasize the use of ratios and proportions in determining the effect on the taste of the lemonade. 

Launch

Arrange students in groups of 2. Give students 2 minutes of quiet think time.

Optionally, instead of the abstract recipe description, you could bring in a clear glass, measuring implements, and the lemonade ingredients. Pour the ingredients in the glass and introduce the task that way.

MLR8 Discussion Supports. Prior to solving the problems, invite students to make sense of the situations. Monitor and clarify any questions about the context.
Advances: Reading, Representing

Student Task

A lemonade recipe calls for the juice of 5 lemons, 2 cups of water, and 2 tablespoons of honey.

Invent four new versions of this lemonade recipe:

  1. One that would make more lemonade but taste the same as the original recipe.
  2. One that would make less lemonade but taste the same as the original recipe.
  3. One that would have a stronger lemon taste than the original recipe.
  4. One that would have a weaker lemon taste than the original recipe.

Sample Response

The base recipe has a ratio of number of lemons to cups of water to tablespoons of honey of 5:2:2. Sample responses:

  1. 10 lemons, 4 cups of water, 4 tablespoons honey
  2. 2122\frac12 lemons, 1 cup water, 1 tablespoon honey
  3. 8 lemons, 2 cups water, 2 tablespoons honey
  4. 2 lemons, 2 cups water, 2 tablespoons honey
Activity Synthesis (Teacher Notes)

Invite students to share their versions of the recipe with the class and record them for all to see. After each explanation, ask the class if they agree or disagree and how the new lemonade would taste. After recording at least 3 responses for each, ask students to describe any patterns they notice how the recipe was adjusted. If students do not mention ratios in their descriptions, be sure to ask them how the ratios changed in their new recipe.

Math Community
After the Warm-up, display the Math Community Chart and a list of 2–5 revisions suggested by the class in the previous exercise for all to see. Remind students that norms are agreements that everyone in the class shares responsibility for, so everyone needs to understand and agree to work on upholding the norms. Briefly discuss any revisions and make changes to the “Norms” sections of the chart as the class agrees. Depending on the level of agreement or disagreement, it may not be possible to discuss all suggested revisions at this time. If that happens, plan to discuss the remaining suggestions over the next few lessons.

Tell students that the class now has an initial list of norms or “hopes” for how the classroom math community will work together throughout the school year. This list is just a start, and over the year it will be revised and improved as students in the class learn more about each other and about themselves and math learners.

Standards
Building On
  • 6.RP.3·Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.
  • 6.RP.A.3·Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.

15 min

15 min