few_shots: 
Example:
Concept/skill: 
Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual model.
Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.

Problem/activity:
Task
Cruz and Erica were both getting ready for soccer.
Cruz ran 1 lap around the school.
Erica ran 3 laps around the playground.
Erica said,
I ran more laps, so I ran farther.
Cruz said,
4 laps around the school is 1 mile, but it takes 12 laps around the playground to go 1 mile. My laps are much longer, so I ran farther.
Who is right? Draw a picture to help you explain your answer.


Answer: 
No. This task does not involve comparing decimals to hundredths. Instead, it involves fraction comparisons.

Now, determine whether the following problem or activity can enable students to understand the concepts or skills in the provided description.

shot_info: im_task_000212_neg_0

4
standard_description: Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output. (Function notation is not required in Grade 8.)
problem_activity: Activity
Students have already looked at measurement conversions that can be represented by proportional relationships, both in grade 6 and in previous lessons in this unit. This task introduces a measurement conversion that is not associated with a proportional relationship. The discussion should start to move students from determining whether a relationship is proportional by examining a table, to making the determination from the equation.
Note that some students may think of the two scales on a thermometer like a double number line diagram, leading them to believe that the relationship between degrees Celsius and degrees Fahrenheit is proportional. If not mentioned by students, the teacher should point out that when a double number line is used to represent a set of equivalent ratios, the tick marks for 0 on each line need to be aligned.
Launch
Arrange students in groups of 2. Provide access to calculators, if desired. Give students 5 minutes of quiet work time followed by students discussing responses with a partner, followed by whole-class discussion.
Representation: Internalize Comprehension.
Activate or supply background knowledge. Allow students to use calculators to ensure inclusive participation in the activity.
Supports accessibility for: Memory; Conceptual processing
Student Facing
The other day you worked with converting meters, centimeters, and millimeters. Here are some more unit conversions.
Use the equation
\(F =\frac95 C + 32\)
, where
\(F\)
represents degrees Fahrenheit and
\(C\)
represents degrees Celsius, to complete the table.
| temperature                       \((^\circ\text{C})\) | temperature                       \((^\circ\text{F})\) |
|--------------------------------------------------------|--------------------------------------------------------|
|                           20                           |                                                        |
|                           4                            |                                                        |
|                          175                           |                                                        |
Use the equation
\(c = 2.54n\)
, where
\(c\)
represents the length in centimeters and
\(n\)
represents the length in inches, to complete the table.
|             length (in)             | length (cm) |
|-------------------------------------|-------------|
|                 10                  |             |
|                  8                  |             |
| 3                       \(\frac12\) |             |
Are these proportional relationships? Explain why or why not.
Student Response
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Anticipated Misconceptions
Some students may struggle with the fraction
\(\frac95\)
in the temperature conversion. Teachers can prompt them to convert the fraction to its decimal form, 1.8, before trying to evaluate the equation for the values in the table.
Activity Synthesis
After discussing the work students did, ask, “What do you notice about the forms of the equations for each relationship?” After soliciting students’ observations, point out that the proportional relationship is of the form
\(y = kx\)
, while the nonproportional relationship is not.
Speaking: MLR8 Discussion Supports.
To provide a support students in producing statements when they compare and contrast equations with proportional and nonproportional relationships. Provide sentence frames such as: “I noticed that _____,” “What makes _____ different from the others is _____,” or “The patterns show _____.” Invite students to use these sentence frames when students comprehend orally the patterns they notice with proportional equations.
Design Principle(s): Support sense-making


aligns: no