few_shots: 
Example:
Concept/skill: 
Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions.
Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.

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.


Answer: 
Yes. This task asks students to compare two fractions that are equal. The students need to explain why the two fractions are equal by drawing a picture, which involves using visual fraction models.

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_000212_pos_0

4
standard_description: Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems.
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.)


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