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, in json format:
{
  "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: 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.

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.

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

Understand the place value system.

Understand place value.

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

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

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

Extend the counting sequence.
problem_activity: Narrative
The purpose of this activity is to introduce students to a new unit, the hundred. Students used connecting cubes to make tens in grade 1 and used tens and ones to count to and represent numbers within 120.
In an earlier unit, students were introduced to base-ten blocks and used base-ten diagrams to represent sums and differences within 100. Students build on this understanding as they use blocks to represent a starting number (96) and add ones until they reach a total value of 100. As students discover they have 10 tens, monitor for language they use to describe the total value of the blocks and the connections they make to their previous work with ones, tens, and three-digit numbers (MP7).
Engagement: Provide Access by Recruiting Interest.
Give the students a context to connect to their own lives. Tell the students that the base-ten blocks represent gum. The ones are single sticks of gum and the tens are packs of gum.
Supports accessibility for: Conceptual Processing, Attention
Required Materials
Materials to Gather
Base-ten blocks
Launch
Groups of 2
Give students access to base-ten blocks.
Display photo of 8 tens and 16 ones.
“Andre was using base-ten blocks to represent numbers. How many do you see? How do you see them?” (96. I see 8 tens and 16 ones. I see it as 9 tens and 6 ones.)
30 seconds: quiet think time
1 minute: partner discussion
Share responses.
Activity
“Work with a partner to follow along and see what Andre discovered as he adds more blocks.”
10 minutes: partner work time
Monitor for students who explain that the value is 100 by:
counting by 1 from 80 or by 1 from 96
counting by 10
Student Facing
How many do you see? How do you see them?
[IMG]
Andre added more blocks.
[IMG]
What is the value of Andre’s blocks now?
How many tens and ones are in this number?
Andre made the same number with the fewest amount of blocks possible. Draw a base-ten diagram to show what Andre’s number looks like now. Use your base-ten blocks to help.
Student Response
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Advancing Student Thinking
If students represent 100 with a diagram that includes tens and ones, consider asking:
“Can you explain how your diagram represents Andre’s total value using the fewest number of blocks possible?”
“Is there a way to represent the same amount without any ones?”
Activity Synthesis
Invite previously identified students to share how they know the value of Andre’s blocks is 100.
“If Andre used the fewest number of blocks, how many tens did he use?” (He had 10 tens.)
“What if Andre wanted to use the greatest amount of blocks to show this number? What would he do?” (He’d decompose all the tens to use only ones. He’d use 100 ones.)
“In this activity, you showed you know that 10 ones is the same as 1 ten. Just like 10 ones is the same as 1 ten, 10 tens is the same as 1 hundred.”
“A hundred is a unit that is made up of 10 tens.”


correct_option_index: 4