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 and division and of fractions to multiply and divide rational numbers.

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


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

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

shot_info: im_task_001477_neg_0

K

fl_problem_001097_pos_0

7

fl_problem_001894_pos_0

HS_0
standard_description: Use data from a randomized experiment to compare two treatments; use simulations to decide if differences between parameters are significant.
problem_activity: Problem 1
Bobbie is a sixth grader who competes in the 100-meter hurdles. In eight track meets during the season, she recorded the following times (to the nearest one hundredth of a second).
18.11    31.23    17.99    18.25    17.50    35.55    17.44    17.85
a.   What is the mean of Bobbie’s times for these track meets? What does the mean tell you in terms of the context?
b.   What is the median of Bobbie’s times? What does the median tell you in terms of the context?
c.   Explain why the mean is higher than the median.
d.   Which measure of center do you think best represents Bobbie’s 100-meter hurdle time? Explain your reasoning.
e.   The two times that were over 30 seconds were times when Bobbie fell on a hurdle. She decides to take those times out to get a sense of her typical time without falling. What is the new mean? The new median? How do those compare to the original mean and median?
Problem 2
At the University of North Carolina (UNC) in the mid-1980's, the average starting salary for a Geography major was over $100,000 (equivalent to almost $300,000 today).
At that same time, basketball star Michael Jordan was drafted into the NBA with one of the highest salaries in the league. He had just graduated from UNC with a degree in Geography.
a.   Explain why the mean is a misleading measure of center to represent the salary of geography students at UNC.
b.   What measure of center would better represent the salary of geography students at UNC? Explain your reasoning.
Problem 3
The data set below represents the morning commute time of eight colleagues in an office on the same day. The mean of the data set is 32.5 minutes and the median is 38 minutes.
45           32           38           20           5           40           38           42
There was a typo in the data set, and the input “5” was supposed to be “50.” The typo is corrected and the correct mean and median are found.
Without calculating, explain what impact the typo had on the mean and the median.


aligns: no