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)


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

Understand and evaluate random processes underlying statistical experiments.

Use probability to evaluate outcomes of decisions.

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

Draw informal comparative inferences about two populations.

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

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

Investigate patterns of association in bivariate data.

Develop understanding of statistical variability.

Interpret linear models.

Use random sampling to draw inferences about a population.

Calculate expected values and use them to solve problems.

Summarize and describe distributions.

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

Investigate chance processes and develop, use, and evaluate probability models.
problem_activity: Activity
The mathematical purpose of this activity is for students to collect, represent, and interpret data using a histogram. For most groups of high school students, the distribution of handspans should be approximately normal. If the distribution for your group is not approximately normal, display the distribution from the student response provided in these materials as the data from another class and ask students to comment on that distribution.
Making statistical technology available gives students an opportunity to choose appropriate tools strategically (MP5).
Launch
Tell students that they will measure the distance from their thumb to smallest finger when their hand is stretched, rounded to the nearest tenth of a centimeter, and then tell you the measurement.
Speaking, Reading: MLR5 Co-Craft Questions.
Use this routine to orient students to the situation. Display the image and the first sentence of this problem, without revealing the questions that follow. Ask students to create a list of mathematical questions that could be asked about the situation. Invite students to compare their questions before revealing the remainder of the task. Listen for and amplify any questions related to how far students’ hands can reach, along with those curious about organizing and interpreting data from the class. This will help students create the language of mathematical questions before feeling pressure to produce solutions.
Design Principle(s): Maximize meta-awareness; Support sense-making
Representation: Access for Perception.
Read the directions for taking the measurements aloud. Demonstrate measuring your own hand and how to estimate the measurement to the nearest tenth of a centimeter. Students who both listen to and read the information will benefit from extra processing time.
Supports accessibility for: Language; Conceptual processing
Student Facing
[IMG]
On many piano keyboards, the distance from one white key to the next is 2.39 centimeters. How many of your classmates could reach two notes that are 9 keys apart (21.5 cm) on a keyboard using only one hand?
Stretch your fingers apart as wide as you can and measure the farthest distance from your thumb to smallest finger. Round your measurement to the nearest tenth of a centimeter.
Your teacher will collect the measurements from the class. Draw a dot plot or histogram from the class data.
[IMG]
Describe the distribution you drew using terms such as: symmetric, approximately symmetric, skewed left, skewed right, approximately uniform, uniform, bell-shaped, or bimodal. Estimate the center of your distribution.
How would you use your distribution to determine how many people in the class can reach the two notes 9 keys apart?
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
The purpose of this discussion is for students to recognize an approximately symmetric and bell-shaped histogram in context. Display a histogram representing the class data for all to see. If possible, display the distributions from other classes and combine the measurements from all the classes to see a distribution with more data. Select students to share their descriptions of the distributions they drew. Ask each student selected to explain their reasoning for that shape.
Here are some questions for discussion:
“What is the shape of the distribution?” (Approximately symmetric and bell-shaped.)
“What is the center of the distribution? Explain your reasoning.” (It is about 21 cm because the two middle bars appear in the center of the data and the middle of them is approximately 21 cm.)
“How did you estimate how many students could reach the keys?” (I found the total number of students with a measurement of 21.5 cm or more.)
“Do you think having a measurement of 21.5 cm or above would allow you to play the notes on the keyboard? Explain your reasoning.” (I do not think that everyone with a measurement of 21.5 cm would be able to play the notes because they might not have the same stretch while they are actually playing.)
“Does the data look like it could be modeled with a normal distribution?” (Yes. I think a normal distribution would model it well because the data is bell-shaped and approximately symmetric.)
Sketch the normal curve on the classroom data for all to see (either by hand or with technology). Ask, “Does the normal curve model the data well?” (Yes, it models the data well, but not exactly.) Note: for this discussion, the sample data provided should be sufficient. If you choose to include class data, you can do so by changing entries in Column A, but do not delete any.


correct_option_index: 5