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: Geometric measurement: understand concepts of angle and measure angles.

Work with time and money.

Relate addition and subtraction to length.

Measure and estimate lengths in standard units.

Solve problems involving measurement and estimation of intervals of time, liquid volumes, and masses of objects.

Geometric measurement: recognize perimeter as an attribute of plane figures and distinguish between linear and area measures.

Tell and write time.

Describe and compare measurable attributes.

Represent and interpret data.

Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit.

Convert like measurement units within a given measurement system.

Classify objects and count the number of objects in each category.

Measure lengths indirectly and by iterating length units.

Geometric measurement: understand concepts of area and relate area to multiplication and to addition.

Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition.
problem_activity: Narrative
In this activity, students create a line plot using measurements to the nearest
\(\frac{1}{4}\)
and
\(\frac{1}{8}\)
inch. This task prompts students to use their understanding of fraction equivalence to plot and partition the horizontal axis.
Representation: Access for Perception.
Provide access to fraction strips that show fourths and eighths, and invite students to use them to answer question 4. Ask students to identify correspondences between the fraction strips and the horizontal axis of the line plot.
Supports accessibility for: Conceptual Processing, Visual-Spatial Processing
Launch
Groups of 2
“The table lists many different lengths.”
“What do you notice about the pencil lengths?” (Sample responses:
Some repeat more than one time.
The numbers are mixed numbers.
There are no whole numbers.)
1 minute: quiet think time
“There are some lengths that are more common or occur more often than others.”
“Tell a partner the length that is most common.” (
\(6\frac{3}{4}\)
)
Activity
Groups of 2
5 minutes: independent work time
Monitor for students who use equivalence to plot measurements to the nearest eighth inch.
“Share your line plots with your partner and make revisions as needed.”
2 minutes: partner discussion
Student Facing
Andre’s class measured the length of some colored pencils to the nearest
\(\frac{1}{4}\)
inch. The data are shown here:
\(1\frac{3}{4}\)
\(2\frac{1}{4}\)
\(5\frac{1}{4}\)
\(5\frac{1}{4}\)
\(4\frac{2}{4}\)
\(4\frac{2}{4}\)
\(6\frac{1}{4}\)
\(6\frac{3}{4}\)
\(6\frac{3}{4}\)
\(6\frac{3}{4}\)
[IMG]
Plot the colored-pencil data on the line plot.
[IMG]
Which colored-pencil length is the most common in the data set?
Write 2 new questions that could be answered using the line plot data.
Next, Andre’s class measured their colored pencils to the nearest
\(\frac{1}{8}\)
inch. The data are shown here:
\(1\frac{6}{8}\)
\(2\frac{2}{8}\)
\(5\frac{2}{8}\)
\(5\frac{3}{8}\)
\(4\frac{4}{8}\)
\(4\frac{4}{8}\)
\(6\frac{6}{8}\)
\(6\frac{6}{8}\)
\(6\frac{6}{8}\)
\(6\frac{3}{8}\)
Plot the colored-pencil data on the line plot.
[IMG]
Which colored-pencil length is the most common in the line plot?
Why did some colored-pencil lengths change on this line plot?
What is the difference between the length of the longest colored pencil and the shortest colored pencil? Show your reasoning.
Student Response
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Advancing Student Thinking
If students do not yet identify “most common” length as the length with the most data points on the line plot, consider asking: “Which measurement occurred more often than others?” and “Which pencil measurement was plotted most often?”
Activity Synthesis
“How many colored pencils were measured in Andre’s class?” (10, because there were ten data points and each represented a pencil that was measured.)
“What was the most common measurement in the first set of data? In the second set of data?” (In the first set of data:
\(6\frac{3}{4}\)
inches. In the second set of data:
\(6\frac{6}{8}\)
inches.)
“How did you use equivalence to help as you plotted measurement data in eighths of an inch?” (I know that two eighths are equivalent to one fourth and this helped to find eighths on the line plots.)
Use the line plot image to clearly label
\(\frac{1}{2}\)
,
\(\frac{1}{4}\)
and
\(\frac{1}{8}\)
with help from students.


correct_option_index: 8