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: 
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 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_pos_0

HS_0
standard_description: Use coordinates to prove simple geometric theorems algebraically. For example, prove or disprove that a figure defined by four given points in the coordinate plane is a rectangle; prove or disprove that the point (1, Ö3) lies on the circle centered at the origin and containing the point (0, 2).
problem_activity: Task
Members of the seventh grade math group have nominated a member of their group for class president. Every student in seventh grade will cast a vote. There are only 2 candidates in the race, so a candidate must receive at least 50% of the vote to be elected. It is expected to be a tight race, so the math group wants to conduct a survey to gain information on their candidate’s prospects. They do not have the time to interview all seventh graders in the school (even if they could contact them) so they decide to interview a sample of 40 students from that grade. They obtain the seventh grade list of names from their school principal’s office and select the sample from this list. They plan to ask each sampled student whether they plan to vote for their candidate or the other candidate.
How should the students select the sample of 40 from the list if they want to have the best chance of obtaining a representative sample? Use the random number table provided below, a random number generator, or a software program to help select the sample of 40 students.
[IMG]
All of the 40 students selected from the list of seventh graders in the school responded to the survey. The results showed that 18 of the 40 students surveyed said they would vote for the math group’s candidate. The math group is puzzling over whether this provides enough information for them to feel confident about their candidate winning with 50% of the vote. To get a sense of how much this sample result of 18 out of 40 could vary in random samples of size $n = 40$, the math group decides to repeatedly simulate the sample selection process and compute the proportion of sampled students that would vote for their candidate for each repeated sample.
Because they are interested in whether their candidate can win with 50% of the vote, they decide to simulate assuming that the seventh grade class is divided 50-50 between the two candidates (50% voting for the math group candidate and the other 50% voting for the other candidate).
Carry out this simulation by taking samples of 40 students and recording the proportion of students in the sample that would vote for the math group’s candidate. Repeat the sampling process 100 times. To carry out the process, use a random number generator or a software program.
Draw a dot plot to represent the outcome of the 100 simulations.
How many times does the selected sample reflect that 18 or fewer students out of the 40 sampled would vote for the math group’s candidate?
If 50% of the class was going to vote for the math group’s candidate, then is the sample outcome of 18 out of 40 voting for the math group’s candidate a reasonably likely occurrence? In other words, is the 50% population percentage plausible given the observed sample proportion of 45%?
Using your answers to (i) and (ii), should the math group students conducting the poll be discouraged, or is it reasonable to think their candidate might win? Why or why not?
Now, the math group is puzzling over whether their 18 out of 40 provides enough information for them to think that the percentage who favor their candidate might be 60%. They decide to repeat the simulation only this time, they decide to simulate assuming that the seventh grade class is divided 60-40 between the two candidates (60% voting for the math group candidate and the other 40% voting for the other candidate).
Carry out this simulation by taking samples of 40 students and recording the proportion of students in the sample that would vote for the math group’s candidate. Repeat the sampling process 100 times. To carry out the process, use a random number generator or a software program.
Draw a dot plot to represents the outcome of the 100 simulations.
How many times does the selected sample reflect that 18 or fewer students out of the 40 sampled would vote for the math group’s candidate?
If 60% of the class was going to vote for the math group’s candidate, then is the sample outcome of 18 out of 40 voting for the math group’s candidate a reasonably likely occurrence? In other words, is the 60% population percentage plausible given the observed sample proportion of 45%?
Using your answers to (i) and (ii), should the math group students conducting the poll be discouraged, or is it reasonable to think their candidate might win 60% of the vote? Why or why not?


aligns: no