few_shots: Example:
Problem/activity:
Narrative
The purpose of this activity is for students to create composite shapes and compose new shapes from composite shapes. For example, students may find that a rectangular prism can be made from four triangular prisms or from eight smaller cubes. Students then discover that they can combine two of the composed rectangular prisms to make a new rectangular prism.
Required Materials
Materials to Gather
Geoblocks
Launch
Groups of 4
Give each group geoblocks.
Display a large cube.
“This cube can be built from other shapes. See how many ways you can build a cube using other shapes.”
3 minutes: partner work time
Share responses.
Activity
“Choose a different shape. Try to find smaller shapes you can use to build that shape.”
5 minutes: partner work time
Student Response
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for free access to Student Response.
Activity Synthesis
Display a cube and a composite cube—for example, a cube composed of four small cubes and one rectangular prism.
Demonstrate putting the shapes together.
“What new shape did I make with the cube and the cube I made?”
“Put your shapes together to make a rectangular prism.”
Display a rectangular prism and two triangular prisms.
“Find these shapes. Put them together. What new shape can you make?” (a cube, a rectangular block)


Standard options: 
A. Partition circles and rectangles into two and four equal shares, describe the shares using the words halves, fourths, and quarters, and use the phrases half of, fourth of, and quarter of. Describe the whole as two of, or four of the shares. Understand for these examples that decomposing into more equal shares creates smaller shares.
B. Distinguish between defining attributes (e.g., triangles are closed and three-sided) versus non-defining attributes (e.g., color, orientation, overall size); build and draw shapes to possess defining attributes.
C. Compose two-dimensional shapes (rectangles, squares, trapezoids, triangles, half-circles, and quarter-circles) or three-dimensional shapes (cubes, right rectangular prisms, right circular cones, and right circular cylinders) to create a composite shape, and compose new shapes from the composite shape. (Students do not need to learn formal names such as “right rectangular prism.”)


Your response:
{
  "explanation": "This activity asks students to compose three-dimensional shapes, using geoblocks, to create composite shapes.",
  "answer": "C"
}

Now, assign the following problem or activity to one or more relevant standards it aligns with.
shot_info: im_lesson_009431

1
options: Summarize numerical data sets in relation to their context, such as by:
- Reporting the number of observations.
- Describing the nature of the attribute under investigation, including how it was measured and its units of measurement.
- Relating the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered.
- Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.

Display numerical data in plots on a number line, including dot plots, histograms, and box plots.
problem_activity: Activity
In a previous lesson, students had a primer on histograms—how they are drawn, how they differ from dot plots, and what information they can tell us. In this activity, students practice drawing a histogram for a given data set and using it to answer statistical questions. To help students understand the lengths involved in the data set, students are asked to draw various lengths used to group the worms in the first histogram.
As students organize the data set and draw their histogram, notice any challenges or questions students come across. If a question is raised by multiple groups, consider discussing it with the whole class. Also pay attention to how students use the histogram to identify a “typical” length—some might describe it in terms of the size of the bins (e.g., “a typical length is between 20 and 40 mm”); others might choose a value within a bin or a boundary between bins. Invite them to share their reasonings later.
Launch
Arrange students in groups of 2. Provide access to centimeter rulers.
Consider giving students a brief overview of the context for the problems in the activity. Tell students that there are nearly 6,000 species of earthworms in the world.  Some earthworms help the environment, while others (generally not native to the region in which they are found) may harm the environment.  Earthworms that are native to a particular region of the world are often raised, by farmers, in terrariums (a container or bin similar to an aquarium but it contains soil and leaves). The terrarium-raised earthworms provide bait for people who fish, provide food for various wildlife, and decompose food waste into soil.  Food waste and water are added to the terrariums as food for raising and growing worms.  Soil produced by the worms as they eat the food waste is often used as fertilizer.
Explain that the lengths of the worms in the bins provide information about the ages of the worms, which can be useful for the farmer. In this activity, students will organize the lengths of the earthworms in several terrariums or bins.
Give students 8–10 minutes of quiet work time, and then 3–4 minutes to discuss their work and complete the activity with a partner.
Action and Expression: Internalize Executive Functions.
Activate or supply background knowledge by demonstrating how to use a ruler to draw a line segment for a given length.
Supports accessibility for: Memory; Conceptual processing
Student Facing
An earthworm farmer set up several containers of a certain species of earthworms so that he could learn about their lengths. The lengths of the earthworms provide information about their ages. The farmer measured the lengths of 25 earthworms in one of the containers. Each length was measured in millimeters.
[IMG]
Using a ruler, draw a line segment for each length:
20 millimeters
40 millimeters
60 millimeters
80 millimeters
100 millimeters
Here are the lengths, in millimeters, of the 25 earthworms.
6
11
18
19
20
23
23
25
25
26
27
27
28
29
32
33
41
42
48
52
54
59
60
77
93
Complete the table for the lengths of the 25 earthworms.
{"table": [{"_attributes": {"border": "1"}, "thead": [{"tr": [{"th": [{"_attributes": {"scope": "col"}, "_value": "length"}, {"_attributes": {"scope": "col"}, "_value": "frequency"}]}]}], "tbody": [{"tr": [{"td": [{"_value": "0 millimeters to less than 20 millimeters"}, {}]}, {"td": [{"_value": "20 millimeters to less than 40 millimeters"}, {}]}, {"td": [{"_value": "40 millimeters to less than 60 millimeters"}, {}]}, {"td": [{"_value": "60 millimeters to less than 80 millimeters"}, {}]}, {"td": [{"_value": "80 millimeters to less than 100 millimeters"}, {}]}]}]}]}
Use the grid and the information in the table to draw a histogram for the worm length data. Be sure to label the axes of your histogram.
[IMG]
Based on the histogram, what is a typical length for these 25 earthworms? Explain how you know.
Write 1–2 sentences to describe the spread of the data. Do most of the worms have a length that is close to your estimate of a typical length, or are they very different in length?
Student Response
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for free access to Student Response.
Student Facing
Are you ready for more?
Here is another histogram for the earthworm measurement data. In this histogram, the measurements are in different groupings.
[IMG]
Based on this histogram, what is your estimate of a typical length for the 25 earthworms?
Compare this histogram with the one you drew. How are the distributions of data summarized in the two histograms the same? How are they different?
Compare your estimates of a typical earthworm length for the two histograms. Did you reach different conclusions about a typical earthworm length from the two histograms?
Student Response
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click here to register or sign in
for free access to Extension Student Response.
Anticipated Misconceptions
When determining frequencies of data values, students might lose track of their counting. Suggest that they use tally marks to keep track of the number of occurrences for each bin.
When drawing the histogram, students might mistakenly use bar graphs as a reference and leave spaces between the bars. Ask them to look at the bars in other histograms they have seen so far and to think about what the gaps might mean considering that the bars are built on a number line.
Activity Synthesis
Ask one or two students to display their completed histograms for all to see and briefly describe the overall distribution. Then, select a few other previously identified students to share their responses and explanations for the last two questions.
Focus the discussion on how identifying center and spread using a histogram is different than doing so using a dot plot. Discuss:
“In a histogram, are we able to see clusters of values in the distribution?”
“Can we see the largest and smallest values? Can we tell the overall spread?”
“How do we identify the center of a distribution?”
From the various estimates that students give for a typical earthworm length (and from earlier exercises), students should begin to see that identifying a typical value of a distribution is not a straightforward or precise process so far. Explain that in upcoming lessons they will explore how to describe a typical value and characterize a distribution more systematically.
Representing, Conversing: MLR7 Compare and Connect.
As the selected students show and describe their histograms, invite pairs to discuss: “What is the same and what is different?” about their own histograms and reasoning. This will help students better understand there are multiple valid ways for describing center and spread.
Design Principle(s): Maximize meta-awareness; Support sense-making


correct_option_index: 1