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.


Standard options: 
A. 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.
B. For any number from 1 to 9, find the number that makes 10 when added to the given number, e.g., by using objects or drawings, and record the answer with a drawing or equation.
C. Decompose numbers less than or equal to 10 into pairs in more than one way, e.g., by using objects or drawings, and record each decomposition by a drawing or equation (e.g., 5 = 2 + 3 and 5 = 4 + 1).
D. Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem.
E. Fluently add and subtract within 5.


Your response, in json format:
{
  "explanation": "This task involves representing addition with objects such as number cards and dice.",
  "answer": "A"
}

Example 2:
Problem/activity:
Task
 Arrange the fractions in order from least to greatest. Explain your answer with a picture.
 $\frac{1}{5}, \frac{1}{7}, \frac{1}{3} $
 $\frac{2}{5}, \frac{2}{7}, \frac{2}{3} $
 $\frac{5}{6}, \frac{3}{6}, \frac{1}{6} $
 $\frac{5}{12}, \frac{8}{12}, \frac{4}{12} $

Standard options: 
A. Understand a fraction as a number on the number line; represent fractions on a number line diagram.
Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, and 8.
B. Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size.
Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, and 8.
C. Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b.
Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, and 8.


Your response, in json format:
{
  "explanation": "By arranging the fractions in this problem, students learn to compare fractions by reasoning about their size.",
  "answer": "B"
}

Example 3:
Problem/activity:
Problem 1
Solve using the standard algorithm. If you get stuck, use an area model and/or the partial products algorithm to help. Then assess the reasonableness of your answer.
a.
$$5,803\times46$$
b.
$$63\times2,116$$
Problem 2
Dunkin' introduced a croissant doughnut in 2014. In the first three months of its debut, they sold 7,870 dozen of them per day. How many croissant doughnuts were sold in the first three months?


Standard options: 
A. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.
B. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.
C. Fluently multiply multi-digit whole numbers using the standard algorithm.


Your response, in json format:
{
  "explanation": "This set of problems involves multi-digit whole numbers because the numbers in each problem are four and two digit integers, and the mathematical calculations involved in both problems focus on multiplication. The first problem explicitly asks the student to solve its subproblems using the standard algorithm.",
  "answer": "C"
}

Now, assign the following problem or activity to one or more relevant standards it aligns with.
shot_info: im_task_001477

K

im_task_000157

3

fl_problem_000674

5
options: Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions. For example, estimate the mean word length in a book by randomly sampling words from the book; predict the winner of a school election based on randomly sampled survey data. Gauge how far off the estimate or prediction might be.

Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences.
problem_activity: Optional activity
This activity is a follow-up to the context used in the activities Three Different TV Shows and Who's Watching What?, but also follows the ideas of sample means from this lesson.
In this activity, students continue to look at how variability in the sample means can be used to think about the accuracy of an estimate of a population mean. If the means from samples tend to be very spread out, then there is reason to believe that the mean from a single sample may not be especially close to the mean for the population. If the means from samples tend to be tightly grouped, then there is reason to believe that the mean from a single sample is a good estimate of the mean for the population (MP7).
Launch
Arrange students in groups of 2.
Tell students that, although the dot plots seem to have a similar shape, attention should be given to the scale of the horizontal axis.
Allow students 3–5 minutes of quiet work time followed by partner and whole-class discussions.
Action and Expression: Internalize Executive Functions.
Chunk this task into more manageable parts. After students have solved the first 2-3 population mean estimate problems, check-in with either select groups of students or the whole class. Invite students to share the strategies they have used so far as well as any questions they have before continuing.
Supports accessibility for: Organization; Attention
Student Facing
The other day you worked with 2 different samples of viewers from each of 3 different television shows. Each sample included 10 viewers. Here are the mean ages for 100 different samples of viewers from each show.
[IMG]
[IMG]
[IMG]
For each show, use the dot plot to estimate the
population
mean.
Trivia the Game Show
Science Experiments YOU Can Do
Learning to Read
For each show, are most of the sample means within 1 year of your estimated population mean?
Suppose you take a new random sample of 10 viewers for each of the 3 shows. Which show do you expect to have the new sample mean closest to the population mean? Explain or show your reasoning.
Student Response
Teachers with a valid work email address can
click here to register or sign in
for free access to Student Response.
Student Facing
Are you ready for more?
Market research shows that advertisements for retirement plans appeal to people between the ages of 40 and 55. Younger people are usually not interested and older people often already have a plan. Is it a good idea to advertise retirement plans during any of these three shows? Explain your reasoning.
Student Response
Teachers with a valid work email address can
click here to register or sign in
for free access to Extension Student Response.
Anticipated Misconceptions
Students may get confused about what the dot plots represent. Refer to the class dot plot of sample means from the reaction time activity to help them understand that a single dot on the dot plot represents a mean from a single sample. Each dot plot shows means from several different samples.
Activity Synthesis
The purpose of the discussion is to think about what the information in the given dot plots tells us about the accuracy of an estimate of a population mean based on the sample mean from a single sample.
Consider asking these questions for discussion:
“In the first dot plot for ‘Trivia the Game Show,’ what does the dot at 68 represent?” (There is a sample of 10 viewers that has a mean age of 68 years.)
“Based on the dot plot shown for ‘Learning to Read,’ do you think any 7 year olds were included in the data?” (Yes. Since one of the sample means is 6.8, there are probably a few 7 year olds and some 6 year olds in that sample.)
“Why is this kind of dot plot useful?” (It shows how variable the means from samples can be, so it gives a good idea of how accurate a sample mean might be as an estimate of a population mean.)
“Why might it be difficult to obtain a dot plot like this?” (Each dot represents a sample of 10. It might be hard to get 100 different samples of size 10.)
Representing, Speaking: MLR2 Collect and Display.
Create a visual display with the heading “Dot Plots of Sample Means.” As students respond to the discussion questions, write down the words and phrases students use on the visual display. Listen for and amplify words and phrases such as “each dot represents...,” “variability of the sample means,” and “population mean.” As students review the language collected in the visual display, encourage students to clarify the meaning of a word or phrase. For example, a phrase such as “each dot represents a sample” can be clarified by restating it as “each dot represents a sample mean.” This will help students make sense of dot plots of sample means as they draw conclusions about populations.
Design Principle(s): Support sense-making: Maximize meta-awareness


correct_option_index: 0