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
Teachers with a valid work email address can
click here to register or sign in
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:
C

Now, assign the following problem or activity to one or more relevant standards it aligns with.
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options: Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.

Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠0, and use rate language in the context of a ratio relationship. For example, “This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar.” “We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger.” (Expectations for unit rates in this grade are limited to non-complex fractions.)

Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. For example, “The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak.” “For every vote candidate A received, candidate C received nearly three votes.”
problem_activity: Optional activity
In this Fermi problem, students estimate the total volume occupied by all of the breakfast cereal purchased in a year in the United States.
Monitor for different approaches to solving the problem, and select students to share during the discussion. In particular, look for:
A range of estimates
Different levels of precision in reporting the final estimate
Different arrangements of boxes
Launch
Arrange students in groups of 1–4. 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.
Before starting, ask students to come up with a guess about the answer and poll the class. Record all guesses.
Ask students to brainstorm the information they need to answer the question. Give the information provided when students ask for it, or provide access to internet-enabled devices so that students can find the information they need.
Vital information to have on hand includes:
Every year, people in the U.S. buy 2.7 billion boxes of breakfast cereal.
A “typical” cereal box has dimensions of 2.5 inches by 7.75 inches by 11.75 inches.
Representation: Internalize Comprehension.
Represent the same information through different modalities by using physical objects to represent abstract concepts. Some students may benefit by starting with an image, video, or a typical size cereal box to support visualization.
Supports accessibility for: Conceptual processing; Visual-spatial processing
Student Facing
Imagine a warehouse that has a rectangular floor and that contains all of the boxes of breakfast cereal bought in the United States in one year.
If the warehouse is 10 feet tall, what could the side lengths of the floor be?
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 not think about
how
the boxes are packed. That is, they may make a volume calculation and then perform division. (Ask these students to think about how the boxes are placed in the warehouse.)
Students may struggle with unit conversions. (Encourage them to go step by step: How many inches are in a foot? How many square inches are in a square foot? How many cubic inches are in a cubic foot?)
Activity Synthesis
Invite students or groups to share different solution approaches. Consider asking students to create a visual display and conducting a gallery walk. Highlight strategies that include keeping careful track of the information used including:
What is the volume of each box?
How are the boxes arranged for storage?
How are the dimensions of the warehouse floor determined?
Make sure to discuss why different people have different estimates.
Some students may just calculate volume and not think of how the boxes are packed. (This is OK as the amount of empty space will not be large unless the boxes are placed haphazardly.)
Students may place the boxes in a different way.
Students may or may not take account of the small amount of space in the warehouse that is not filled by the boxes.
There are an infinite number of rectangles with suitable area to serve as the floor of the warehouse. Note, however, that having an appropriate area (e.g., 36,000,000 square feet) is
not
sufficient. For example, we could not have a warehouse that is 1 inch wide and 432,000,000 feet long. In general, if one of the dimensions is too small, it increases the amount of wasted space.


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