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: Distinguish between situations that can be modeled with linear functions and with exponential functions.
problem_activity: Activity
The mathematical purpose of this activity is for students to begin to understand the relationship between sample size and margin of error. Two characters collect samples and notice that their simulations result in very different margins of error. Students should begin to notice that a larger sample size should result in an estimate with a lesser margin of error.
Launch
Reading: MLR6 Three Reads.
Use this routine to support reading comprehension of this problem. Ask students to keep their books or devices closed and display only the task statement without revealing the questions that follow. Use the first read to orient students to the situation. After a shared reading, ask, “What is this situation about?” (two students found a proportion from a random sample). After the second read, students list any quantities that can be counted or measured, without focusing on specific values (proportions, margins of error, and number of simulations). During the third read, the question or prompt is revealed. Invite students to discuss possible strategies to answer the questions, referencing the relevant quantities named after the second read. This helps students connect the language and reasoning needed to solve a problem while maintaining the cognitive demand of the task.
Design Principle: Support sense-making
Representation: Internalize Comprehension.
Begin by providing students with questions to help them form generalizations about mean, sample size, standard deviation, and margin of error. For example, “When the mean changes, does the margin of error change? When the standard deviation changes, does the margin of error change?”
Supports accessibility for: Conceptual processing
Student Facing
Elena and Clare are each working on a project about how high school students are having trouble finding jobs. They each find the proportion of students without jobs from a random sample, then use a computer to do 1,000 simulations using the proportion they found and report the results.
Elena says, “The proportion of high school students without jobs is about 0.70 with a margin of error of 0.280.”
Clare says, “The proportion of high school students without jobs is about 0.74 with a margin of error of 0.138.”
Both students reported the margin of error based on 2 standard deviations from their simulations. What are the mean and standard deviation each student found? For at least one student, show your reasoning.
Clare and Elena try to figure out why Clare had such a smaller range of values in her report.
First they consider the proportion they used in the simulations. Elena says, “My simulation used 0.7 as the proportion since I found that proportion in my original sample.” Clare says, “My simulation used 0.75 as the proportion since I found that proportion in my original sample.” The students used different proportions in their simulations. Do you think this is why Clare has a smaller margin of error? Explain your reasoning.
They look for more differences in their initial sample and discover than Elena surveyed 10 people in her initial sample and Clare surveyed 40 people. Do you think this is why Clare has a smaller margin of error? Explain your reasoning.
Student Response
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Activity Synthesis
The purpose of this discussion is for students to think about the relationship between sample size and margin of error. Ask students,
“Why do you think Clare continues to get a smaller margin of error than Elena?” (She took a bigger sample so the samples are more likely to be representative of the population.)
“Elena had a sample size of 10 and Clare had a sample size of 40. Why do you think the sample size could have caused Clare’s margin of error to be less than Elena’s margin of error?” (Since there are more people included in each sample, the samples themselves capture more of the population variability, so each sample estimate is more likely to accurately reflect the population characteristic.)


aligns: no