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:
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.


Your response:
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.


Your response:
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: Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number.

Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. For example, “How old am I?” is not a statistical question, but “How old are the students in my school?” is a statistical question because one anticipates variability in students’ ages.

Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape.
problem_activity: Activity
Earlier, in the backpack example, students saw a distribution described in terms of where data points are clustered on a dot plot and which values have a large number of occurrences. The shape of that distribution was approximately symmetric. In this activity, they continue to analyze distributions in those terms, and try to identify and interpret the
center
and
spread
of a distribution that is not symmetric. The two distributions used here allow students to contrast a narrow spread and a wide spread and develop a deeper understanding of variability.
As students work, notice how students identify a general location for the center of a data set and the descriptions they use to talk about the spread (e.g., “wide,” “narrow,” or “something in between”). Identify students who connect the size of a spread to how different or alike the data points are; ask them to share later. Additionally, identify students who measure spread as the range of the entire data as well as those who use the distance to the center.
Launch
Arrange students in groups of 2. Give students 5–6 minutes of quiet work time for the first three sets of questions, and another 4–5 minutes to share their responses and then discuss the last two questions with a partner.
Students are asked to find a percentage. If necessary, briefly review how to find a percentage.
Representation: Internalize Comprehension.
Activate or supply background knowledge about calculating percentages. Allow students to use calculators to ensure inclusive participation in the activity.
Supports accessibility for: Memory; Conceptual processing
Representing, Writing: MLR5 Co-Craft Questions.
Invite pairs of students to create one or two mathematical questions that could be answered by the data displayed in the dot plot. Note questions that vary in complexity, making sure to have students share examples that ask about percent, center, or spread, if available. Allow students to ask clarifying questions of their peers regarding how the dot plot could be used to answer the questions, if needed. This will help students to make sense of the data using informal language prior to connecting their existing understanding to formal language.
Design Principle(s): Maximize meta-awareness; Support sense-making
Student Facing
Twenty-five sixth-grade students were asked to estimate how many hours a week they spend talking on the phone. This dot plot represents their reported number of hours of phone usage per week.
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How many of the students reported not talking on the phone during the week? Explain how you know.
What percentage of the students reported not talking on the phone?
What is the largest number of hours a student spent talking on the phone per week?
What percentage of the group reported talking on the phone for this amount of time?
How many hours would you say that these students typically spend talking on the phone?
How many minutes per day would that be?
How would you describe the
spread
of the data? Would you consider these students’ amounts of time on the phone to be alike or different? Explain your reasoning.
Here is the dot plot from an earlier activity. It shows the number of hours per week the same group of 25 sixth-grade students reported spending on homework.
[IMG]
Overall, are these students more alike in the amount of time they spend talking on the phone or in the amount of time they spend on homework? Explain your reasoning.
Suppose someone claimed that these sixth-grade students spend too much time on the phone. Do you agree? Use your analysis of the dot plot to support your answer.
Student Response
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Anticipated Misconceptions
Students may neglect to change the rate given (from minutes per week to hours per week, or to minutes per day) and may draw incorrect conclusions as a result. Ask them to think about the unit they are using in their responses.
Activity Synthesis
The purpose of the discussion is to help students find good ways to describe a distribution based on center and spread.
Select a few students to answer the questions about the first dot plot. Tell students that the “typical” value for the data is generally considered the center. Ask, “What would you consider the center for the two dot plots shown in this activity?”
Ask students how they thought about the spread of the data. If possible, select students who thought of spread as the range of the entire data and those who thought of it as an interval around the center. Ask students to share their interpretation of the what the spread means in the context of using the phone. Make sure to include previously identified students who connect spread to how alike or different the data points are.
Tell students that distributions are generally described using the center and spread. Select a few students to describe the distributions of the two data sets shown in this activity.


correct_option_index: 2