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: Use the structure of an expression to identify ways to rewrite it. For example, see x^(4) – y^(4 )as (x^(2))^(2 )– (y^(2))^(2), thus recognizing it as a difference of squares that can be factored as (x^(2 )– y^(2))(x^(2 )+ y^(2)).
problem_activity: Activity
The goal of this activity is for students to be introduced to the idea that variability is important when analyzing and comparing data sets. Students will compare data sets, and make a decision as to which data set represents a better scenario. This activity prepares students to calculate variability in order to compare data sets in a later lesson. Monitor for students who calculate any
statistics
to inform their decisions. Make note of the students who only calculate a measure of center vs. students who calculate both a measure of center and a measure of variability.
Making statistical technology available gives students an opportunity to choose appropriate tools strategically (MP5).
Launch
Students will work individually. Tell them to use statistics to inform their decision.
Student Facing
In order from least to greatest, here are the prices per gallon of gas at two different gas stations over the past 7 days.
Station A:
2.38, 2.68, 2.82, 2.86, 2.99, 3.26, 3.59
Station B:
2.84, 2.85, 2.88, 2.95, 2.98, 3.03, 3.05
Suppose that these gas stations were the closest to your house, but not near each other. Which gas station would you go to for gas? Explain your reasoning.
Student Response
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Activity Synthesis
The purpose of this discussion is to understand that the variability is worth paying attention to. If any students chose to compute the mean, median, IQR, MAD, or range for the two stations, ask them to share their results and how those values help them decide. Interestingly, the mean is the same for the gas stations. But any measure of variability shows that the prices at station B are more stable and predictable than the prices at station A. If no students suggest computing measures of center and variability and comparing them, be prepared to demonstrate.
Here are the summary statistics for each set of data:
For Station A:
Mean: 2.94
Five-number summary: 2.38, 2.68, 2.86, 3.26, 3.59
Range: 1.21
IQR: 0.58
MAD: 0.29
For Station B:
Mean: 2.94
Five-number summary: 2.84, 2.85, 2.95, 3.03, 3.05
Range: 0.21
IQR: 0.18
MAD: 0.07
If time permits, discuss which measures are helpful. Here are sample questions:
“Was the mean helpful in deciding the gas station from which you would purchase gas?”(No, because both means were the same.)
“How did the range (or IQR, MAD, five-number summary) help you decide which gas station you would go to?” (Whichever gas station had the highest range [or IQR, MAD] is the gas station I chose.)
“In the real world, how would you use the gas prices at each gas station to make a decision?” (I would think about which one generally had lower prices and choose that one, or I would see which one had more predictably cheaper prices and choose that one.)


aligns: no