few_shots: 
Example 1:
Problem/activity:
Task
Materials
One 10-frame per pair of students (see example below)
[IMG]
Counters, 10 per pair of students
Decks of number cards 0-5 (with 4 of each number) or two 0-5 dice
Setup
This activity is done in pairs. The students sit side by side with 10-frame and deck of cards or dice. If they have cards, the cards are shuffled and placed face down in front of them.
Action
Player 1 flips a card or rolls the die. They place that many counters on the 10-frame. Player 2 flips a card or rolls the die. They place that many more counters on the 10-frame next to the counters already on the ten frame. The students count the total together.
A recording sheet can be added when the students have been introduced to equations and number sentences. For those students who can handle higher numbers, a deck of 0-10 cards and two 10-frames can be used.
This game can also be played alone.


Concept/skill: 
Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem.

Answer: 
No. Though this task involves addition, it does not involve any word problems.

Example 2:
Problem/activity:
For each pair of numbers, determine if the values are equivalent. Explain your reasoning for each one.
a.
$$-0.25$$
and
$$\frac{1}{-4}$$
b.
$$-\left ( \frac{1}{4} \right )$$
and
$$\frac{-1}{-4}$$
c.
$$\frac{-1}{4}$$
and
$$-\frac{1}{4}$$


Concept/skill: 
Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.

Answer: 
No. The expressions shown in this problem do not involve multiplying fractions with other fractions, nor whole numbers with fractions.

Example 3:
Problem/activity:
Find the general solution for:
$${\mathrm{cos}\left({\pi\over2}+x\right)=\mathrm{tan}{\pi\over4}}$$


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.

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

shot_info: im_task_001477_neg_0

K

fl_problem_001097_neg_0

7

fl_problem_001894_neg_0

HS_0
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