few_shots: Example:
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} $

Mathematical concept/skill options: 
A. Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.
Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.
B. Extend understanding of fraction equivalence and ordering.
Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.
C. Use equivalent fractions as a strategy to add and subtract fractions.
D. Apply and extend previous understandings of multiplication and division to multiply and divide fractions.
E. Understand decimal notation for fractions, and compare decimal fractions.
Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.
F. Develop Understanding of fractions as numbers.
Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, and 8.


Your response:
{
  "explanation": "This problem involves understanding fractions as numbers by comparing their quantities.",
  "answer": "F"
}

Now, assign the following problem or activity to one or more relevant mathematical concepts/skills it teaches.
shot_info: im_task_000157

3
options: Understand the place value system.

Use place value understanding and properties of operations to perform multi-digit arithmetic. (A range of algorithms may be used.)

Perform operations with multi-digit whole numbers and with decimals to hundredths.

Use place value understanding and properties of operations to add and subtract.

Use place value understanding and properties of operations to perform multi-digit arithmetic.
Grade 4 expectations in this domain are limited to whole numbers less than or equal to 1,000,000.

Work with numbers 11–19 to gain foundations for place value.

Extend the counting sequence.

Generalize place value understanding for multi-digit whole numbers.
Grade 4 expectations in this domain are limited to whole numbers less than or equal to 1,000,000.

Understand place value.
problem_activity: Narrative
The purpose of this activity is for students to play a game that enables them to practice using strategies and algorithms to subtract within 1,000. Students decide whether they will try to make the smallest or greatest difference, then spin a paper clip on a spinner to generate two three-digit numbers. Students use their choice of strategy or algorithm to subtract the numbers.
When students use place value to create a pair of numbers with a specific type of difference, they are looking for and making use of structure (MP7).
Required Materials
Materials to Gather
Paper clips
Pencils
Materials to Copy
Greatest Difference, Smallest Difference
Required Preparation
Each group of 2 will need a paper clip.
Launch
Groups of 2
Give each group 1 copy of Greatest Difference, Smallest Difference.
“Take a minute and read the directions to the game with your partner.”
1 minute: partner work time
Play one round of the game against the class to illustrate how the game should be played.
“Are there any questions about the game?”
Answer any questions students have about the game.
Activity
“Now, take some time and play the game with your partner.”
7–10 minutes: partner work time
Student Facing
Decide with your partner whether you will try to make the greatest difference or smallest difference.
Take turns spinning and recording a digit in the hundreds, tens, or ones place. Continue until your numbers are complete.
Find the difference.
Compare your values.
Write a comparison using >, <, or =.
Play again.
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Student Response
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Activity Synthesis
Display: 601 and 398
“If these were the numbers you made, how would you find the difference and why?” (Sample responses: I would count up because 398 is so close to 400. I would use an algorithm because I know that if I follow the steps it would work every time.)


correct_option_index: 1