few_shots: 
Example 1:
Concept/skill: 
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.

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.


Answer: 
Yes. This task involves representing addition with objects such as number cards and dice.

Example 2:
Concept/skill: 
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.

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} $

Answer: 
No. Completing this task does not involve representing fractions on a number line diagram.

Example 3:
Concept/skill: 
Fluently multiply multi-digit whole numbers using the standard algorithm.

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?


Answer: 
Yes. 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.

Now, determine whether the following problem or activity can enable students to understand the concepts or skills in the provided description.

shot_info: im_task_001477_pos_0

K

im_task_000157_neg_0

3

fl_problem_000674_pos_0

5
standard_description: Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1–100 with a common factor as a multiple of a sum of two whole numbers with no common factor. For example, express 36 + 8 as 4 (9 + 2).
problem_activity: Narrative
The purpose of this activity is for students to visualize and make sense of the context of problems they will solve in the next activity. They will also consider representations that can be used to model the quantities and actions in the situation (MP4) and try creating them. Students will not have time to make a complete representation, so the focus is on making sense of the situation and persevering in finding effective representations (MP1).
Required Materials
Materials to Gather
Coins
Index cards
Paper
Two-color counters
Launch
Groups of 3 or 4
Display the image of the lockers.
“In your small group, discuss what you notice and wonder about the picture.”
1 minute: quiet think time
1 minute: group discussion
Share and record responses. If students are not familiar with lockers, explain that lockers are used to hold students’ coats, books, and backpacks in some schools.
Activity
Read the problem aloud to students.
“Take some time on your own to make sense of the problem. You may want to try to visualize it or reread the problem.”
2 minutes: quiet think time
Give students access to two-color counters, index cards, coins, and other materials that may be helpful to them.
“Based on what you know, create a representation of the problem.”
5 minutes: independent work time
Monitor for and select 3 different representations that:
represent lockers in different ways
show instances of contact with lockers (or of opening and closing)
show correspondence between each student and the lockers touched
Student Facing
The picture shows lockers in a school hallway.
The 20 students in Tyler’s fourth-grade class are playing a game in a hallway that is lined with 20 lockers in a row.
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The first student starts with the first locker and goes down the hallway and opens all the lockers.
The second student starts with the second locker and goes down the hallway and shuts every other locker.
The third student stops at every third locker and opens the locker if it is closed or closes the locker if it is open.
This process continues until all 20 students in the class have touched the lockers.
Create a representation to show what you understand about this problem. Consider:
How does your representation show lockers?
How does your representation keep track of students who touch lockers?
How does your representation show which lockers are open or closed?
Student Response
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Activity Synthesis
While discussing each representation, ask students:
“Where are the lockers in this representation?” (Numbers or pictures used to indicate lockers)
“How can we tell if a locker is open or closed in this representation?” (Symbols or colors used to indicate open or closed)
“How does this representation show which student is touching the lockers?” (Students and their actions listed in a table or a T-chart)
“In the next activity, you will answer questions about the game. You may use your representation or one shared by a classmate to help you think through the problems.”


aligns: no