few_shots: Example:
Problem/activity:
Task
Cruz and Erica were both getting ready for soccer.
Cruz ran 1 lap around the school.
Erica ran 3 laps around the playground.
Erica said,
I ran more laps, so I ran farther.
Cruz said,
4 laps around the school is 1 mile, but it takes 12 laps around the playground to go 1 mile. My laps are much longer, so I ran farther.
Who is right? Draw a picture to help you explain your answer.


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. Develop Understanding of fractions as numbers.
Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, and 8.
E. Apply and extend previous understandings of multiplication and division to multiply and divide fractions.
F. 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.


Your response, in json format:
{
  "explanation": "In this problem, students learn to recognize equivalent fractions. That is, three laps around the playground is 3/12 mile, which is equivalent to 1/4, which is one lap around the school.",
  "answer": "B"
}

Now, assign the following problem or activity to one or more relevant mathematical concepts/skills it teaches.
shot_info: im_task_000212

4
options: Use place value understanding and properties of operations to perform multi-digit arithmetic. (A range of algorithms may be used.)

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.

Extend the counting sequence.

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

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

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

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 the place value system.

Understand place value.
problem_activity: Narrative
The purpose of this activity is for students to make sense of and then use exponential notation to represent large numbers, namely 1 million and 1 billion. Students should be encouraged to say the names of the numbers in a way that makes sense to them. Contexts, in the form of human populations, are provided for each of the large numbers to help students conceptualize the magnitude of the number. Students recognize that the purpose of exponential notation is to write large numbers efficiently and recognize how many factors of ten are in a given number.
When students relate 1 million and 1 billion to products of 10 and powers of 10 they look for and make use of base-ten structure (MP7).
MLR2 Collect and Display.
Circulate, listen for and collect the language students use as they use exponential notation to represent large numbers. On a visible display, record words and phrases such as: million, thousands, billion, powers of 10, exponential notation, represent, times, multiply by ten, number of zeros. Invite students to borrow language from the display as needed, and update it throughout the lesson.
Advances: Conversing, Reading
Launch
Groups of 2
Activity
3–5 minutes: independent work time.
3–5 minutes: partner discussion
Monitor for students who:
call 1,000,000,000 a thousand million or a million thousands
make up names such as a zillion
know that 1,000,000,000 is called a billion
Student Facing
About 1,000,000 people live in Delaware.
How do you say this number?
How many thousands is this? Explain or show your reasoning.
Write the number using powers of 10.
How many times would you need to extend the diagram from the warm-up to get 1,000,000 tiny segments? Explain or show your reasoning.
In 1997, the population of India was about 1,000,000,000.
How would you say this number?
How many millions is this? How many thousands is it? Explain or show your reasoning.
Write the number using powers of 10.
How many times would you need to extend the diagram from the warm-up to get 1,000,000,000 tiny segments? Explain or show your reasoning.
Student Response
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Activity Synthesis
Ask previously selected students to share their names for 1,000,000,000 in the given order.
“How many millions are in this number? How do you know?” (A thousand because there are 3 more zeros and that means multiplying by 10 three times.)
“How do you write this number using powers of 10? Why?” (
\(10^9\)
because there are 9 factors of 10.)
“This number is called a billion.”
“Using powers of 10, can you write a number that is bigger than a billion?” (Yes,
\(10^{10}\)
,
\(10^{11}\)
,
\(10^{100}\)
.)
“Why are powers of 10 useful for representing really big numbers?” (I would not want to write 100 zeros. I would also have to count all those zeros to see how big the number is.)


correct_option_index: 7