options: 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.

Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. For example, “The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak.” “For every vote candidate A received, candidate C received nearly three votes.”

Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠0, and use rate language in the context of a ratio relationship. For example, “This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar.” “We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger.” (Expectations for unit rates in this grade are limited to non-complex fractions.)
problem_activity: Optional activity
This activity provides an opportunity for additional practice in solving equivalent ratio problems. Monitor for students solving the problems in different ways.
Launch
Give students 4 minutes of quiet work time and then have them discuss their solutions with a partner.
Representation: Internalize Comprehension.
Activate or supply background knowledge about equivalent ratios describing situations that happen at the same rate which can be displayed on double number lines. Allow students to use calculators to ensure inclusive participation in the activity.
Supports accessibility for: Memory; Conceptual processing
Writing: MLR5 Co-Craft Questions.
Before asking students to solve the given question, display only Lin's, Diego's and Elena's reading rates. Invite students think of possible mathematical questions about this situation. Keep in mind students do not need to answer their created questions. Students share and revise their questions with a partner and then with the whole class. Record questions shared with the class in a public space. This helps students connect mathematical language to get into the context of the problem as they reason about the three different quantities (i.e., number of pages read, number of pages in the book, and number of days reading).
Design Principle(s): Maximize meta-awareness​
Student Facing
Lin read the first 54 pages from a 270-page book in the last 3 days.
Diego read the first 100 pages from a 325-page book in the last 4 days.
Elena read the first 160 pages from a 480-page book in the last 5 days.
If they continue to read every day at these rates, who will finish first, second, and third? Explain or show your reasoning.
Student Response
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Student Facing
Are you ready for more?
The ratio of cats to dogs in a room is
\(2:3\)
. Five more cats enter the room, and then the ratio of cats to dogs is
\(9:11\)
. How many cats and dogs were in the room to begin with?
Student Response
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Activity Synthesis
Select students to present their solutions. Sequence solutions with diagrams first and then tables. Make sure students see connections between the different representations and ways of solving the problems.


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