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, assess whether the following problem or activity is 'aligned' with the given Common Core standard in Mathematics.

shot_info: im_task_000212_pos_0

4
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: Optional activity
If students investigated the answers to their questions in the previous activity, they need access to their findings. They can either work with the questions generated by their group, or everyone can work from a master list of questions compiled by the teacher.
If students have access to a spreadsheet program, they can use it to find the results (MP5). Students need to communicate their findings clearly in graphical displays (MP6). They can choose to illustrate all or some of the questions in their graphical displays. Encourage the students to be creative with their displays. For example, if students are examining the question “How many people would live on each continent?” they might sketch the continents and place stick figures on the continents to represent the class. They might also draw a bar graph showing the same information in a different way.
Launch
Students work in same groups of 2–4 from previous activity. Provide access to four-function calculators. If students are doing their own research, provide access to internet-enabled devices. If conducting a gallery walk at the end, provide access to tools for making a visual display.
To give students a sense of the magnitude of the world versus the classroom, consider zooming in from Earth to North America, the United States, your state, your city, and finally your school.
Invite students to work on the question or questions that are of most interest to them either from their own group work on from the compiled list.
Action and Expression: Internalize Executive Functions.
To support development of organizational skills, check in with students within the first 2–3 minutes of work time. Check to make sure students are beginning to choose characteristics about the world’s population that are available to find, and that they can calculate percentages for the class for those characteristics.
Supports accessibility for: Memory; Organization
Student Facing
Suppose your class represents all the people in the world.
Choose several characteristics about the world’s population that you have investigated. Find the number of students in
your
class that would have the same characteristics.
Create a visual display that includes a diagram that represents this information. Give your display the title “If Our Class Were the World.”
Student Response
Teachers with a valid work email address can
click here to register or sign in
for free access to Student Response.
Anticipated Misconceptions
Students may struggle with the difficult numbers for the percent of the world population with different characteristics. For example, there are about 1.2 billion people living in Africa. Ask them  to calculate
\(1.2 \div 7.4 \approx 0.162\)
. "What percent of the world population this is?" (16%). "If our class were the world, then about 16% of the class would live in Africa.  So how many students in our class would live in Africa?" (Since 16% of 25 is 4, that means that 4 students in our class would live in Africa.)
In some cases, there might be two acceptable answers to how many students in our class have a certain characteristic. About 10% of the world population is in Europe. For our class, we could have 2 students (8%) or 3 students (12%) that are in Europe. Either one is an acceptable answer. Make sure that students understand that 2.5 (10% of 25) is not a reasonable answer.
Activity Synthesis
Invite groups to share their displays. Consider doing a gallery walk and asking:
Were you surprised by any of your findings?
In what ways is the class actually representative of the world? (possibly gender distribution, religious adherence, etc.)
In what ways is it not? (age, place of residence, access to clean water, etc.)
Make sure to highlight the fact that having a small class limits the percentages that are possible. This can make deciding how many students in the class have a particular characteristic difficult. Consider asking:
What percentages are possible for students in the class? (0, 4, 8, . . . multiples of 4 up to 100)
There are 1 billion people living in the Americas. That’s a little more than 13.5% of the world population. If our class was the world, how many students in our class would be from the Americas? (3 students would be 12%, and 4 would be 16%. So 3 students is as close as we can get.)


aligns: yes