few_shots: Example 1:
Problem/activity:
Task
Materials
One 10-frame per pair of students (see example below)
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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: Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers).

Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages. Recognize that there are data sets for which such a procedure is not appropriate. Use calculators, spreadsheets, and tables to estimate areas under the normal curve.

Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets.

Represent data with plots on the real number line (dot plots, histograms, and box plots).
problem_activity: Activity
The mathematical purpose of this activity is for students to collect, represent, and interpret data using a histogram. For most groups of high school students, the distribution of handspans should be approximately normal. If the distribution for your group is not approximately normal, display the distribution from the student response provided in these materials as the data from another class and ask students to comment on that distribution.
Making statistical technology available gives students an opportunity to choose appropriate tools strategically (MP5).
Launch
Tell students that they will measure the distance from their thumb to smallest finger when their hand is stretched, rounded to the nearest tenth of a centimeter, and then tell you the measurement.
Speaking, Reading: MLR5 Co-Craft Questions.
Use this routine to orient students to the situation. Display the image and the first sentence of this problem, without revealing the questions that follow. Ask students to create a list of mathematical questions that could be asked about the situation. Invite students to compare their questions before revealing the remainder of the task. Listen for and amplify any questions related to how far students’ hands can reach, along with those curious about organizing and interpreting data from the class. This will help students create the language of mathematical questions before feeling pressure to produce solutions.
Design Principle(s): Maximize meta-awareness; Support sense-making
Representation: Access for Perception.
Read the directions for taking the measurements aloud. Demonstrate measuring your own hand and how to estimate the measurement to the nearest tenth of a centimeter. Students who both listen to and read the information will benefit from extra processing time.
Supports accessibility for: Language; Conceptual processing
Student Facing
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On many piano keyboards, the distance from one white key to the next is 2.39 centimeters. How many of your classmates could reach two notes that are 9 keys apart (21.5 cm) on a keyboard using only one hand?
Stretch your fingers apart as wide as you can and measure the farthest distance from your thumb to smallest finger. Round your measurement to the nearest tenth of a centimeter.
Your teacher will collect the measurements from the class. Draw a dot plot or histogram from the class data.
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Describe the distribution you drew using terms such as: symmetric, approximately symmetric, skewed left, skewed right, approximately uniform, uniform, bell-shaped, or bimodal. Estimate the center of your distribution.
How would you use your distribution to determine how many people in the class can reach the two notes 9 keys apart?
Student Response
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Activity Synthesis
The purpose of this discussion is for students to recognize an approximately symmetric and bell-shaped histogram in context. Display a histogram representing the class data for all to see. If possible, display the distributions from other classes and combine the measurements from all the classes to see a distribution with more data. Select students to share their descriptions of the distributions they drew. Ask each student selected to explain their reasoning for that shape.
Here are some questions for discussion:
“What is the shape of the distribution?” (Approximately symmetric and bell-shaped.)
“What is the center of the distribution? Explain your reasoning.” (It is about 21 cm because the two middle bars appear in the center of the data and the middle of them is approximately 21 cm.)
“How did you estimate how many students could reach the keys?” (I found the total number of students with a measurement of 21.5 cm or more.)
“Do you think having a measurement of 21.5 cm or above would allow you to play the notes on the keyboard? Explain your reasoning.” (I do not think that everyone with a measurement of 21.5 cm would be able to play the notes because they might not have the same stretch while they are actually playing.)
“Does the data look like it could be modeled with a normal distribution?” (Yes. I think a normal distribution would model it well because the data is bell-shaped and approximately symmetric.)
Sketch the normal curve on the classroom data for all to see (either by hand or with technology). Ask, “Does the normal curve model the data well?” (Yes, it models the data well, but not exactly.) Note: for this discussion, the sample data provided should be sufficient. If you choose to include class data, you can do so by changing entries in Column A, but do not delete any.


correct_option_index: 3