few_shots: 
Example 1:
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.

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.


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

Example 2:
Concept/skill: 
Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.

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
$$-\frac{1}{4}$$


Answer: 
Yes. This problem involves understanding fractions and division to divide rational numbers, such as 1, -4, 4, and -1. This problem also involves an understanding of multiplication: if p and q are integers, then -(p/q) = (-p)/q = p/(-q).

Example 3:
Concept/skill: 
Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems.

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


Answer: 
Yes. An initial step when solving for x in this problem requires the use of the addition formula for cosine on the left side of the equation.

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_001477_pos_0

K

fl_problem_001097_pos_0

7

fl_problem_001894_pos_0

HS_0
standard_description: Summarize numerical data sets in relation to their context, such as by:
- Reporting the number of observations.
- Describing the nature of the attribute under investigation, including how it was measured and its units of measurement.
- Relating the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered.
- Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.
problem_activity: Problem 1
You would like to know whether the number of minutes that a train is delayed correlates to the number of violent acts that occur on the platform or in the train.
Which would result in the most reliable data?
Delay trains, on purpose, by 5 minutes, 10 minutes, and 20 minutes and track the number of violent acts reported to the MBTA police. Compare this information to when the trains are not delayed.
Use data about delayed trains and look at the report data for the MBTA police—connecting the times of each.
Ask a sample of ridership about number of violent acts witnessed and ask respondents to identify the station and the approximate time these acts took place.
Which of these is an observational study, which is a survey, and which is an experiment? How do you know?
Problem 2
To determine if higher speed limits cause more traffic fatalities, researchers compared the number of traffic deaths on randomly selected stretches of highway within 65 mph speed limits to the number of traffic deaths on an equal number of randomly selected stretches of highway with 75 mph speed limits.
Problem 3
For each part below, determine 1) if the type of study described is a survey, observational study, or experimental study, and 2) if the study is good or bad, and why.
Why are students missing so much school in the district? A district administrator selects 300 student names at random from the enrollment list and sends a letter to each student’s home. The letter includes a page to be returned to their school signed by a parent or guardian. The page asks, “How many days has your student missed school this year?” and “What are the reasons for missing school on those days?”
Why are students missing so much school in the district? A district administrator chooses one of the elementary schools in the district and asks the principal to provide information about the number of absences and the excuse notes provided to the school.
Do voters in the district favor a sales tax increase of 1% to fund the parks and recreation department? A politician sends a letter to 300 voters in the district asking, “Would you pay extra money on your essential groceries to hire more government workers to plant flowers around the town?”
Do voters in the district favor a sales tax increase of 1% to fund the parks and recreation department? A politician sends a letter to 300 voters selected at random in the district asking, “Would you be in favor of a 1% increase in sales tax to fund the parks and recreation department in town?”


aligns: no