few_shots: 
Example:
Concept/skill: 
Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size.
 Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, and 8.

Problem/activity:
Task
 Arrange the fractions in order from least to greatest. Explain your answer with a picture.
 $\frac{1}{5}, \frac{1}{7}, \frac{1}{3} $
 $\frac{2}{5}, \frac{2}{7}, \frac{2}{3} $
 $\frac{5}{6}, \frac{3}{6}, \frac{1}{6} $
 $\frac{5}{12}, \frac{8}{12}, \frac{4}{12} $

Answer: 
Yes. By arranging the fractions in this problem, students learn to compare fractions by reasoning about their size.

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_000157_pos_0

3
standard_description: Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages. Recognize that there are data sets for which such a procedure is not appropriate. Use calculators, spreadsheets, and tables to estimate areas under the normal curve.
problem_activity: Warm-up
The mathematical purpose of this activity is for students to reason about the area under a normal curve using what they know about composition and decomposition of areas.
If students are using a table of values with
\(z\)
-scores for this lesson, this work will be essential to finding the desired areas in many cases.
Launch
Remind students that the phrase “the area under the curve” means the area between the
\(x\)
-axis and the curve.
Student Facing
The images show a normal curve with mean of 40 and standard deviation of 2.
The area under the curve to the left of 39 is 0.3085.
[IMG]
The area under the curve to the left of 43 is 0.9332.
[IMG]
Since it is a normal curve, we know that the total area under the curve is 1. Use the given areas to find the areas in question. Explain your reasoning for each.
Find the area under the curve to the right of 39.
Find the area under the curve between 39 and 43.
Find the area under the curve to the left of 40.
Find the area under the curve between 39 and 40.
Student Response
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Activity Synthesis
The purpose of this discussion is to make sure students can use the given areas to compose or decompose them to find additional areas. For each question, ask a student to explain how they reasoned about their answer. Highlight places where students used the symmetry of the distribution or cases where they could add or subtract known areas to find new areas.


aligns: yes