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: 
Represent addition and subtraction with objects, fingers, mental images, drawings (Drawings need not show details, but should show the mathematics in the problem. (This applies wherever drawings are mentioned in the Standards.)), sounds (e.g., claps), acting out situations, verbal explanations, expressions, or equations.

Answer: 
Yes. This task involves representing addition with objects such as number cards and dice.

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_pos_0

K

fl_problem_001097_neg_0

7

fl_problem_001894_neg_0

HS_0
standard_description: Use data from a sample survey to estimate a population mean or proportion; develop a margin of error through the use of simulation models for random sampling.
problem_activity: Warm-up
The purpose of this warm-up is to elicit the idea that there are different ways to collect and represent data. This will be useful when students examine statistical designs in a later activity. While students may notice and wonder many things about these images, how the data are represented (or misrepresented) is the important discussion point.
Through articulating things they notice and things they wonder about the headlines and graph, students have an opportunity to attend to precision in the language they use to describe what they see (MP6). They might first propose less formal or imprecise language, and then restate their observation with more precise language in order to communicate more clearly.
Launch
Display the image and headlines for all to see. Ask students to think of at least one thing they notice and at least one thing they wonder. Give students 1 minute of quiet think time, and then 1 minute to discuss the things they notice and wonder with their partner, followed by a whole-class discussion.
Student Facing
A graph and 2 headlines from a website are shown.
What do you notice? What do you wonder?
[IMG]
“80% of Dentists Recommend Acme Toothpaste”
“Pythagoras Brand Rulers Measure 20% Better”
Student Response
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Activity Synthesis
Ask students to share the things they noticed and wondered. Record and display their responses for all to see. If possible, record the relevant reasoning on or near the image or statement. After all responses have been recorded without commentary or editing, ask students, “Is there anything on this list that you are wondering about?” Encourage students to respectfully disagree, ask for clarification, or point out contradicting information.
Display a wider view of the graph that shows more of the story.
[IMG]
Ask, “How does having the whole graph tell a different story than just having the part of the graph from 1998 to 2012?” (In the whole graph, you can see that the slope of the line is positive over the 112 years represented in the graph, and you could find other 12-year periods in which the slope is negative, positive, or close to zero.) If time allows, follow up by asking, “Does the dashed line appear to be a line of best fit or is it something else? Explain your reasoning.” (The dashed line does not appear to be a line of best fit. It just seems to connect the first point in the graph to the last point. This could be misleading since the line of best fit would have a greater slope than the dashed line, and would be a little lower on the graph.)
Here are some questions for discussion:
“Why is the dentist headline potentially misleading?” (It does not mention if they recommend other brands as well. For example, dentists might just recommend using any toothpaste at all and this brand works just as well as any other brand.)
“Why is the ruler headline misleading?” (It does not mention what it is that Pythagoras rulers measure better than.)


aligns: no