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:
Thought: 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: Understand place value.

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.)

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.

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

Extend the counting sequence.

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

Understand the place value system.
problem_activity: Narrative
The purpose of this activity is for students to solve multi-step distance problems using centimeters, meters, and kilometers. This gives students an opportunity to think about which units are most helpful for communicating a distance (MP6). When the distance is short, like the length of a single footstep, centimeters or meters both work well. For a longer distance, like the distance a person walks in a day, it is reasonable to use meters or kilometers, but the number of centimeters is very large and more difficult to visualize.
To add movement or make this activity interactive, consider providing groups of 2 or 4 with a centimeter ruler or meter stick to measure their or a classmate’s step before working on the task. While students could use the measurements of their own steps to complete the table, the arithmetic may be more complex and, as a result, it may be harder to observe patterns.
Engagement: Provide Access by Recruiting Interest.
Optimize meaning and value. Invite students to share the places they could walk in the classroom, at home, in the community, and so on, that would be equivalent to the distances presented in the chart.
Supports accessibility for: Conceptual Processing; Visual-Spatial Processing
Required Materials
Materials to Gather
Metersticks
Launch
Groups of 2 or 4
“If someone wants to measure the length of one of their footsteps, which unit do you think they should use? Millimeters, centimeters, meters, or kilometers?”
Highlight that millimeters are too small and kilometers are too large. Both centimeters and meters make sense and the first part of this activity will use those two units of measure.
“There are 100 centimeters in a meter. About how many steps are in 1 meter?” (2 or 3)
“There are 1,000 meters in a kilometer. About how many steps are in a kilometer?” (2,000 or 3,000)
Give students access to a meter stick.
Activity
5 minutes: independent work time
5 minutes: small-group work time
Monitor for students who use the following strategies when determining how many kilometers Lin walks during the day:
multiply 50 centimeters by 8,500 steps to determine the distance in centimeters that Lin walked and divide 425,000 by 100,000
multiply 0.5 meters by 8,500 steps to determine the distance in meters that Lin walked and then divide 4,250 by 1,000
Student Facing
Lin has a watch that counts the number of steps she takes during the day and displays those steps in centimeters, meters, or kilometers.
Here is a list of activities Lin did on Monday. Next to each activity, write whether it would make sense to display the distance in cm, m, or km.
walked to her friend’s desk
walked to the front of the classroom
walked from her classroom to the bus
ran twice around the playground
The table shows the amount of steps Lin’s watch displayed for each activity. If each of her steps is 50 centimeters, how many centimeters and meters did Lin walk for each activity?
|               activity               | number of steps | distance (cm) | distance (m) |
|--------------------------------------|-----------------|---------------|--------------|
|     walked to her friend’s desk      |        5        |               |              |
| walked to the front of the classroom |       12        |               |              |
| walked from her classroom to the bus |       250       |               |              |
|   ran twice around the playground    |      1,000      |               |              |
At the end of the day, Lin’s watch displayed 8,500 steps. Would it make sense for her watch to record the distance in centimeters, meters, or kilometers? Why?
How many kilometers did Lin walk that day?
[IMG]
Student Response
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Activity Synthesis
“How did you determine how many kilometers Lin walked during the day?”
Ask previously selected students to share their solutions.
Display student work or write these equations for all to see:
\(8,\!500 \times 50= 425,\!000\)
\(8,\!500 \times 0.5 = 4,\!250\)
“How does each of these equations represent the situation?” (
\(8,\!500 \times 50= 425,\!000\)
represents 8,500 steps that are each 50 centimeters long so that would be a total of 425,000 centimeters.
\(8,\!500 \times 0.5 = 4,\!250\)
represents 8,500 steps that are each 0.5 meter long so that would be a total of 4,250 meters.)
“What is the same about these equations?” (They have the same number of steps. They are both multiplication equations.)
“What is different about these equations?” (One multiplies the number of steps by 50 centimeters and one multiplies the number of steps by 0.5 meter. The products are different. 4,250 is 100 times smaller than 425,000 because it represents meters instead of centimeters.)
Display:
\(425,\!000 \div 100,\!000= 4.25\)
\(4,\!250 \div 1,\!000 = 4.25\)
“How does each of these equations represent the situation?” (They both represent the number of kilometers that Lin walked. 425,000 is the distance she walked in centimeters so if you divide it by 100,000, you get the number of kilometers she walked. 4,250 is the distance in meters that she walked so we only have to divide by 1,000 to figure out how many kilometers she walked.)
Display: 4.25 km, 4,250 m, 425,000 cm
“Which of these do you think best communicates how far Lin walked this day?” (4.25 kilometers because I can picture how long a kilometer is.)


correct_option_index: 8