few_shots: 
Example:
Concept/skill: 
Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles.

Problem/activity:
Find the general solution for:
$${\mathrm{cos}\left({\pi\over2}+x\right)=\mathrm{tan}{\pi\over4}}$$


Answer: 
No. This problem does not directly teach how side ratios in right triangles lead to definitions of trigonometric ratios. Instead, it involves solving a trigonometric function.

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

shot_info: fl_problem_001894_neg_0

HS_0
standard_description: Develop a probability distribution for a random variable defined for a sample space in which probabilities are assigned empirically; find the expected value. For example, find a current data distribution on the number of TV sets per household in the United States, and calculate the expected number of sets per household. How many TV sets would you expect to find in 100 randomly selected households?
problem_activity: Narrative
In this optional activity, students investigate patterns in multiples of 15 and analyze and describe features of the digits in the tens and ones place. The activity also prompts them to consider why those features exist and to predict whether a given number could be a multiple of 15. The goal here is not to elicit clear justifications, but rather to encourage students to use their understanding of place value and numbers in base-ten to reason more generally about patterns in numerical patterns.
This activity uses
MLR5 Co-craft Questions
. Advances: writing, reading, representing
Launch
Groups of 2
MLR5 Co-Craft Questions
Display only the opening sentence and list of numbers, without revealing the question(s).
“Write a list of mathematical questions that could be asked about this situation.”
2 minutes: independent work time
2–3 minutes: partner discussion
Invite several students to share one question with the class. Record responses.
“What do these questions have in common? How are they different?”
Reveal the task (students open books), and invite additional connections.
“Let’s see what patterns we can find when we count by 15.”
Activity
“Take a few quiet minutes to work on the activity. Afterwards, discuss your responses with your partner.”
5 minutes: independent work time
5 minutes: partner discussion
Monitor for:
the different patterns students notice
the different ways they explain the patterns
the ways students reason about whether 250 could be a number being called out
Student Facing
Elena counted by 15 and recorded the numbers she counted:
15
30
45
60
75
90
Write the next four numbers she’d record if she kept going.
What patterns do you see? Describe as many as you can.
Choose one pattern that you noticed and explain why you think it happens.
Could 250 be a number that Elena calls out if she continued to count by 15? Explain or show your reasoning.
Student Response
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Advancing Student Thinking
To answer the last question, students may try to count up by 15 and see if they would reach 250. Encourage students to see if any of the patterns they noticed could help them answer the question.
Activity Synthesis
Invite students to share the patterns they noticed and their explanations for the patterns. Record them for all to see.
Select other students to share their explanation on whether 250 could be a number that Elena calls said. Highlight explanations that make use of the structure in the numbers.


aligns: no