few_shots: 
Example:
Concept/skill: 
Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions.
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: 
Yes. This task asks students to compare two fractions that are equal. The students need to explain why the two fractions are equal by drawing a picture, which involves using visual fraction models.

Now, assess whether the following problem or activity is 'aligned' with the given Common Core standard in Mathematics.

shot_info: im_task_000212_pos_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 lesson is for students to motivate a conceptual understanding of the
addition rule
. Monitor for students discussing counting people twice.
Launch
Arrange students in groups of 2. Give students quiet work time and then time to share their work with a partner.
Student Facing
The table displays information about people at a neighborhood park.
{"table": [{"_attributes": {"border": "1"}, "thead": [{"tr": [{"th": [{"_attributes": {"scope": "row"}}, {"_attributes": {"scope": "col"}, "_value": "wearing sneakers"}, {"_attributes": {"scope": "col"}, "_value": "not wearing sneakers"}, {"_attributes": {"scope": "col"}, "_value": "total"}]}]}], "tbody": [{"tr": [{"th": [{"_attributes": {"scope": "row"}, "_value": "wearing a hat"}], "td": [{"_value": "8"}, {"_value": "2"}, {"_value": "10"}]}, {"th": [{"_attributes": {"scope": "row"}, "_value": "not wearing a hat"}], "td": [{"_value": "3"}, {"_value": "12"}, {"_value": "15"}]}, {"th": [{"_attributes": {"scope": "row"}, "_value": "total"}], "td": [{"_value": "11"}, {"_value": "14"}, {"_value": "25"}]}]}]}]}
Andre says the number of people wearing sneakers or wearing a hat is 21, because there are a total of 10 people wearing a hat and a total of 11 people wearing sneakers. Is Andre correct? Explain your reasoning.
What is the probability that a person selected at random from those in the park is wearing sneakers or wearing a hat?
Student Response
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Activity Synthesis
The goal of this discussion is to use the context as a model to introduce a conceptual understanding of the addition rule. Ask previously identified students to explain why Andre counted some people twice when he stated that the number of people wearing sneakers or wearing a hat is 21.
Here are some questions for discussion.
“Why did Andre need to subtract 8 from 21 to get the correct answer?” (It needs to be subtracted because the 8 people that were wearing sneakers and wearing a hat were counted twice. We counted them twice when adding the column total for wearing sneakers and the row total for wearing a hat.)
“How could the number of people wearing sneakers or wearing a hat be represented using a Venn diagram?” (A Venn diagram could be made using two overlapping circles, one for wearing sneakers and one for wearing a hat. There would be 8 people in the middle where the two circles overlap. There would be an additional 3 people in the wearing sneakers circle representing those wearing sneakers but not a hat. There would also be an additional 2 people in the circle representing those wearing a hat but not sneakers.)
“What is the probability that a person selected at random is not wearing sneakers and not wearing a hat?” (
\(\frac{12}{25}\)
)


aligns: no