few_shots: Example:
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.


Mathematical concept/skill options: 
A. Write and interpret numerical expressions.
B. Generate and analyze patterns.
C. Analyze patterns and relationships.
D. Use properties of operations to generate equivalent expressions.
E. Use the four operations with whole numbers to solve problems.
F. Work with radicals and integer exponents.
G. Solve systems of equations.
H. Represent and solve problems involving multiplication and division.
I. Perform arithmetic operations on polynomials.
J. Understand the relationship between zeros and factors of polynomials.
K. Understand properties of multiplication and the relationship between multiplication and division.
L. Solve real-life and mathematical problems using numerical and algebraic expressions and equations.
M. Solve problems involving the four operations, and identify and explain patterns in arithmetic.
N. Use polynomial identities to solve problems.
O. Apply and extend previous understandings of arithmetic to algebraic expressions.
P. Rewrite rational expressions.
Q. Interpret the structure of expressions.
R. Add and subtract within 20.
S. Analyze and solve linear equations and pairs of simultaneous linear equations.
T. Represent and analyze quantitative relationships between dependent and independent variables.
U. Solve equations and inequalities in one variable.
V. Create equations that describe numbers or relationships
W. Reason about and solve one-variable equations and inequalities.
X. Represent and solve equations and inequalities graphically.
Y. Understand solving equations as a process of reasoning and explain the reasoning.
Z. Understand and apply properties of operations and the relationship between addition and subtraction.
AA. Gain familiarity with factors and multiples.
AB. Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from.
AC. Work with addition and subtraction equations.
AD. Multiply and divide within 100.
AE. Work with equal groups of objects to gain foundations for multiplication.
AF. Represent and solve problems involving addition and subtraction.
AG. Write expressions in equivalent forms to solve problems.
AH. Understand the connections between proportional relationships, lines, and linear equations.


Your response:
AB

Now, assign the following problem or activity to one or more relevant mathematical concepts/skills it teaches.
shot_info: im_task_001477

K
options: Summarize, represent, and interpret data on a single count or measurement variable.

Develop understanding of statistical variability.

Use the rules of probability to compute probabilities of compound events in a uniform probability model.

Understand independence and conditional probability and use them to interpret data.

Use random sampling to draw inferences about a population.

Use probability to evaluate outcomes of decisions.

Draw informal comparative inferences about two populations.

Summarize and describe distributions.

Investigate patterns of association in bivariate data.

Make inferences and justify conclusions from sample surveys, experiments, and observational studies.

Understand and evaluate random processes underlying statistical experiments.

Summarize, represent, and interpret data on two categorical and quantitative variables.

Interpret linear models.

Investigate chance processes and develop, use, and evaluate probability models.

Calculate expected values and use them to solve problems.
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.)


correct_option_index: 9