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
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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)


Mathematical concept/skill options: 
A. Reason with shapes and their attributes.
B. Understand similarity in terms of similarity transformations.
C. Use coordinates to prove simple geometric theorems algebraically.
D. Translate between the geometric description and the equation for a conic section.
E. Understand congruence and similarity using physical models, transparencies, or geometry software.
F. Analyze, compare, create, and compose shapes.
G. Identify and describe shapes (squares, circles, triangles, rectangles, hexagons, cubes, cones, cylinders, and spheres).
H. Understand congruence in terms of rigid motions.
I. Classify two-dimensional figures into categories based on their properties.
J. Draw, construct, and describe geometrical figures and describe the relationships between them.
K. Explain volume formulas and use them to solve problems.
L. Prove theorems involving similarity.
M. Prove geometric theorems.
N. Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.
O. Define trigonometric ratios and solve problems involving right triangles.
P. Apply trigonometry to general triangles.
Q. Visualize relationships between two-dimensional and three-dimensional objects.
R. Draw and identify lines and angles, and classify shapes by properties of their lines and angles.
S. Make geometric constructions.
T. Apply geometric concepts in modeling situations.
U. Solve real-world and mathematical problems involving area, surface area, and volume.
V. Graph points on the coordinate plane to solve real-world and mathematical problems.
W. Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres.
X. Understand and apply theorems about circles.
Y. Understand and apply the Pythagorean Theorem.
Z. Experiment with transformations in the plane.
AA. Find arc lengths and areas of sectors of circles.


Your response:
A

Now, assign the following problem or activity to one or more relevant mathematical concepts/skills it teaches.
shot_info: im_lesson_009431

1
options: Use random sampling to draw inferences about a population.

Interpret linear models.

Draw informal comparative inferences about two populations.

Summarize, represent, and interpret data on two categorical and quantitative variables.

Investigate patterns of association in bivariate data.

Understand and evaluate random processes underlying statistical experiments.

Use probability to evaluate outcomes of decisions.

Summarize and describe distributions.

Develop understanding of statistical variability.

Use the rules of probability to compute probabilities of compound events in a uniform probability model.

Calculate expected values and use them to solve problems.

Understand independence and conditional probability and use them to interpret data.

Summarize, represent, and interpret data on a single count or measurement variable.

Make inferences and justify conclusions from sample surveys, experiments, and observational studies.

Investigate chance processes and develop, use, and evaluate probability models.
problem_activity: Optional activity
This task is provided for optional, additional practice for understanding variability in context.
The mathematical purpose of this activity is to compare data sets, and to interpret the measures of center and measures of variability in the context of the problem.
Launch
Keep students in the same groups. Give students 5 minutes to work on the questions and follow with a whole-class discussion.
Action and Expression: Develop Expression and Communication.
To help get students started, display sentence frames such as “In this situation, a larger/smaller value for the standard deviation means _____.” or “Both dot plots are different because….”
Supports accessibility for: Language; Organization
Student Facing
For each situation, you are given two graphs of data, a measure of center for each, and a measure of variability for each.
Interpret the measure of center in terms of the situation.
Interpret the measure of variability in terms of the situation.
Compare the two data sets.
The heights of the 40 trees in each of two forests are collected.
mean: 44.8 feet, standard deviation: 4.72 feet
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mean: 56.03 feet, standard deviation: 7.87 feet
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The number of minutes it takes Lin and Noah to finish their tests in German class is collected for the year.
mean: 29.48 minutes, standard deviation: 5.44 minutes
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mean: 28.44 minutes, standard deviation: 7.40 minutes
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The number of raisins in a cereal with a name brand and the generic version of the same cereal are collected for several boxes.
mean: 289.1 raisins, standard deviation: 19.8 raisins
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mean: 249.17 raisins, standard deviation: 26.35 raisins
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Student Response
Teachers with a valid work email address can
click here to register or sign in
for free access to Student Response.
Student Facing
Are you ready for more?
One use of standard deviation is it gives a natural scale as to how far above or below the mean a data point is. This is incredibly useful for comparing points from two different distributions.
For example, they say you cannot compare apples and oranges, but here is a way. The average weight of a granny smith weighs 128 grams with a standard deviation of about 10 grams. The average weight of a navel orange is 140 grams with a standard deviation of about 14 grams. If we have a 148 gram granny smith apple and a 161 gram navel orange, we might wonder which is larger for its species even though they are both about 20 grams above their respective mean. We could say that the apple, which is 2 standard deviations above its mean, is larger for its species than the orange, which is only 1.5 standard deviations above its mean.
How many standard deviations above the mean height of a tree in forest A is its tallest tree?
How many standard deviations above the mean height of a tree in forest B is its tallest tree?
Which tree is taller in its forest?
Student Response
Teachers with a valid work email address can
click here to register or sign in
for free access to Extension Student Response.
Anticipated Misconceptions
Identify students who struggle making the connections between the summary statistics and the problem context. Ask them what information the standard deviation conveys. Tell them to focus less on the actual value of the standard deviation and more on which of the two distributions have a greater standard deviation and what that might mean.
Activity Synthesis
The purpose of this discussion is for students to explain the mean and the standard deviation in context.
For each set of graphs, select students read their answers for all three prompts. When necessary, prompt students to revise their language to include the terms shape, measure of center, and variability.
Speaking: MLR 8 Discussion Supports.
Use this routine to support whole-class discussion. For each observation that is shared, ask students to restate and/or revoice what they heard using precise mathematical language (shape, measure of center, and variability). Consider providing students time to restate what they hear to a partner, before selecting one or two students to share with the class. Ask the original speaker if their peer was accurately able to restate their thinking and to clarify, if necessary. Call students' attention to any words or phrases that helped clarify the original statement. This will provide more students with an opportunity to produce language as they explain the mean and standard deviation in context.
Design Principle(s): Support sense-making


correct_option_index: 12