What we like about this task
- Addresses standards: 6.RP.A.1, 6.RP.A.2, MP.5, and MP.6
- Provides a simply stated, yet mathematically rich task
- Requires students to understand the concept of a ratio (6.RP.A.1) and a rate (6.RP.A.2)
- Builds understanding of ratios through the use of precise mathematical language (e.g., every, per) (MP.6)
In the classroom:
- Enables students to consider multiple correct descriptions of the same ratio by using "Choose all that apply"
- Orders answer choices intentionally, placing a similar - but incorrect - choice (c) after a correct one (a)
- Gives students the opportunity to thoughtfully select the method they will use to solve the task (e.g., table of equivalent ratios, plotting points in the coordinate plane, double number line diagrams, equations) (MP.5)
This task was designed to include specific features that support access for all students and align to best practice for English Language Learner (ELL) instruction. Go here to learn more about the research behind these supports. This lesson aligns to ELL best practice in the following ways:
- Provides opportunities for students to practice and refine their use of mathematical language.
- Allows for whole class, small group, and paired discussion for the purpose of practicing with mathematical concepts and language.
- Includes a mathematical routine that reflects best practices to supporting ELLs in accessing mathematical concepts.
- Provides opportunities to support students in connecting mathematical language with mathematical representations.
- Prompts teachers to write essential ideas/concepts/language on the board as a reference for students.
Making the Shifts
How does this task exemplify the instructional Shifts required by CCSSM?
Focus Belongs to the major work of sixth grade Coherence Provides foundational work for learning about proportional relationships in grade 7 (see Molly's Run) Rigor
Conceptual Understanding: primary in this task
Procedural Skill and Fluency: secondary in this task
Application: secondary in this task
Ty took the escalator to the second floor. The escalator is 12 meters long, and he rode the escalator for 30 seconds. Which statements are true? Select all that apply.
- He traveled 2 meters every 5 seconds.
- Every 10 seconds he traveled 4 meters.
- He traveled 2.5 meters per second.
- He traveled 0.4 meters per second.
- Every 25 seconds, he traveled 7 meters.
Illustrative Mathematics Commentary and Solution
This task is part of a joint project between Student Achievement Partners and Illustrative Mathematics to develop prototype machine-scorable assessment items that test a range of mathematical knowledge and skills described in the CCSSM and begin to signal the focus and coherence of the standards.
This task is part of a set of three assessment tasks that address various aspects of the RP domain and help distinguish between 6th and 7th grade expectations.
While simply constructed, 6.RP The Escalator addresses aspects of both 6.RP.A.1 "Understand the concept of a ratio” and 6.RP.A.2 “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." The simple extension of a traditional multiple choice item to a "choose all that apply" allows us to ask questions about the same context from the different perspectives afforded by the different RP standards in 6th grade.
The mathematics in "6.RP The Escalator" is more complex than it appears. The distractors are placed in a particular order. Students might choose (c) after (correctly) choosing (a) because they look similar. The three correct answers are purposefully interrupted by an incorrect choice, and (e) is included for students who subtract rather than divide.
Especially in 6th grade, the cognitive load associated with making sense of units in proportional relationships is heavy; this task engages MP.6, Attend to precision.
As part of an assessment, this would be a one-point task: (a), (b), and (d) are all correct.
As noted in the Commentary above, this task is the first in a set of three tasks. It's interesting to view the two grade six tasks side-by-side, as this task focuses primarily on conceptual understanding of ratios and rates, while Riding at a Constant Speed focuses primarily on application of ratio and rate reasoning to solve problems. The third task in this set, Molly's Run, illuminates the heightened expectations of this domain for grade 7 (i.e., students work with ratios specified by rational numbers).
For more insight into the expectations for ratio and rate reasoning in grade six, read pages 5–7 of the progression document, 6–7, Ratios and Proportional Relationships.
For more analysis on this task from an assessment perspective, read the Cognitive Complexity section on the Illustrative Mathematics site.