few_shots: 
Example:
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.


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.

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

Now, does the problem or activity shown below enable students to learn the full intent of the following concept or skill?

shot_info: im_task_000212_neg_0

4
standard_description: Describe events as subsets of a sample space (the set of outcomes) using characteristics (or categories) of the outcomes, or as unions, intersections, or complements of other events (“or,” “and,” “not”).
problem_activity: Warm-up
The mathematical purpose of this activity is for students to match bivariate data with its context. Students should think about whether they might expect a strong correlation or not as well as whether the relationship has a positive or negative correlation. Monitor for students who discuss linear relationships or variability in the data.
Launch
Arrange students in groups of two to four. Provide access to the scatter plots and contexts for the warm-up.
Student Facing
Match the variables to the scatter plot you think they best fit. Be prepared to explain your reasoning.
{"table": [{"_attributes": {"border": "1"}, "thead": [{"tr": [{"th": [{"_attributes": {"scope": "row"}}, {"_attributes": {"scope": "col"}, "span": [{"_attributes": {"class": ["math", "math-repaired"], "data-png-file-id": "50"}, "_value": "\\(x\\)"}], "_value": "variable"}, {"_attributes": {"scope": "col"}, "span": [{"_attributes": {"class": ["math", "math-repaired"], "data-png-file-id": "29"}, "_value": "\\(y\\)"}], "_value": "variable"}]}]}], "tbody": [{"tr": [{"th": [{"_attributes": {"scope": "row"}, "_value": "1."}], "td": [{"_value": "daily low temperature in Celsius for Denver, CO"}, {"_value": "boxes of cereal in stock at a grocery in Miami, FL"}]}, {"th": [{"_attributes": {"scope": "row"}, "_value": "2."}], "td": [{"_value": "average number of free throws shot in a season"}, {"_value": "basketball team score per game"}]}, {"th": [{"_attributes": {"scope": "row"}, "_value": "3."}], "td": [{"_value": "measured student height in feet"}, {"_value": "measured student height in inches"}]}, {"th": [{"_attributes": {"scope": "row"}, "_value": "4."}], "td": [{"_value": "average number of minutes spent in a waiting room"}, {"_value": "hospital satisfaction rating"}]}]}]}]}
A
[IMG]
B
[IMG]
C
[IMG]
D
[IMG]
Student Response
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Anticipated Misconceptions
Students may struggle with matching the pairs of variables with a scatter plot. Encourage students to think about how related the variables are and how the
\(y\)
variable might change as the
\(x\)
variable increases.
Activity Synthesis
The goal of this discussion is for students to discuss how the characteristics of the scatter plots allowed them to determine the context. For each context, select groups to share their match and reasoning. Select groups who used linear model and variability in their small group discussions.
Here are some questions for discussion.
“How did the concept of linear relationships help you to make a match?” (For the height in inches and the height in feet, I knew that the data would be very linear. I chose scatter plot A because it was the only one that appeared linear. I did wonder why scatter plot A was not perfectly linear. Maybe it had to do with rounding or measurement error.)
“How did you use the concept of linearity to help you to make a match?” (First, I expected the temperature and cereal context relationship to be totally random rather than linear at all, so that fit with scatter plot C. Second, I knew that problem 3 matched with scatter plot A, because I knew it should be almost perfectly linear. For a given height in feet, there is only one height in inches.)
“Which matches were the most difficult? What helped you figure them out?” (It was hardest to find the matches for scatter plots B and D because they were pretty scattered. I noticed that the data in scatter plot D displayed a negative relationship, so I looked for a context that would have a negative relationship. It makes sense that customer satisfaction decreases as wait time increases.)


aligns: no