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.


Thought: 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.


Thought: 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.


Thought: 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: Activity
In this activity, students think a little more deeply about the data we would like to know and how that compares to the data we can collect easily and quickly (MP1). They are presented with a statistical question that does not have an obvious answer. Students are then asked to consider ways they might begin gathering data to answer the question, but are asked to realize that the data they could reasonably collect is not everyone addressed by the question. Following the activity, the discussion defines the terms
population
and
sample
.
Launch
Arrange students in groups of 2.
Set up the context by asking students, “Do people who are the only child have more pets?” then to provide a possible explanation for their answer. For example, maybe only children do have more pets because the family can better afford to take care of an animal with only 1 child. Maybe they do not because smaller families may live in smaller places and not have room for a lot of pets.
Give students 5 minutes of partner work time followed by 5 minutes of whole-class discussion.
Student Facing
Consider the question: Do people who are the only child
have more pets
?
Earlier, we used information about the people in your class to answer a question about the entire school. Would surveying only the people in your class give you enough information to answer this new question? Explain your reasoning.
If you had to have an answer to this question by the end of class today, how would you gather data to answer the question?
If you could come back tomorrow with your answer to this question, how would you gather data to answer the question?
If someone else in the class came back tomorrow with an answer that was different than yours, what would that mean? How would you determine which answer was better?
Student Response
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Activity Synthesis
The purpose of the discussion is to show the difference between the data we would like to have to answer the question and the data we have available.
Some questions for discussion:
“If we had all the time and money in the world and wanted to answer this question, who would we need to collect data from?” (Everyone in the world.)
“What would you do with the data collected from everyone to answer the questions?” (Find the mean and MAD of the data from the two sets and compare them like we did in previous lessons.)
“Why is it unreasonable to actually collect all the necessary data to answer the question?” (There are too many people to collect data from. There is not enough time to get to everyone in the world, and I cannot travel everywhere.)
“Since it may be difficult to guess an answer without doing
any
research, but we cannot get all of the data we want, what data could you get that would help estimate an answer?” (It would be good to ask a few people in different parts of the world and try to get different groups represented.)
Define population and sample. A
population
is the entire pool from which data is taken. Examples include (depending on the question) “all humans in the world,” “all 7th graders at our school,” or “oak trees in North America.” In this usage, it does not have to refer only to groups of people or animals. A
sample
is the part of the population from which data is actually collected. Examples (related to the population examples) include “5 people from each country,” “the first 30 seventh graders to arrive at our school,” or “8 oak trees from the forest near our school.”
Ask students, "What is the population for the question about only children and their pets?" (Everyone in the world.) Note that we would need data from everyone, including those who don't have pets or do have siblings.
Ask students, "What might be a sample we could use to answer the question?" (The students in our class, my neighbors, a few people from different countries.) After getting several responses, ask, "What might be the benefits and drawbacks of each of these samples?" (Some may be more convenient, but would not represent the population as well or vice-versa.)
Explain: While it is best to have data for the entire population, there are many reasons to use a sample.
More manageable. With very large populations, the amount of data can be hard to collect and work with, so a smaller subset may still be informative and easier to work with. Example: Find the average size of a grain of sand.
Necessary. Sometimes it is impossible to reach the entire population, so a sample is all that is available. Example: Find the average lifespan of tuna.
Speed. Sometimes a rough estimate is all that is needed and a sample of data is enough to estimate the population characteristic. Example: Out of curiosity, what is the median number of apps on smartphones.
Cost. Sometimes it is very costly to obtain the data needed, so a sample can reduce the cost. Example: Find the average amount of hydrogen in moon rocks.
Representation: Develop Language and Symbols.
Create a display of important terms and vocabulary. Invite students to suggest language or diagrams to include that will support their understanding of: populations and sample.
Supports accessibility for: Conceptual processing; Language
Representing, Speaking: MLR2 Collect and Display.
To help students make sense of the terms “sample” and “population”, draw a diagram of a few circles inside a larger circle on a visual display. Label the large outer circle “population” and the small inner circles “sample.” As students respond to the question “What is the population for the question about only children and their pets?”, write the population on the visual display. As students respond to the question “What might be a sample we could use to answer the question?”, write the samples in different inner circles on the visual display. Listen for and amplify words and phrases that define these terms, such as “part of” or “entire.” This will help students visualize a sample as part of a population and understand that there are multiple samples inside a population.
Design Principle(s): Support sense-making (for representation); Maximize meta-awareness


correct_option_index: 1