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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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:
Thought: This activity asks students to reason how shapes can combine to make other shapes.
Answer: 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: Extend the counting sequence.

Use place value understanding and properties of operations to perform multi-digit arithmetic. (A range of algorithms may be used.)

Use place value understanding and properties of operations to perform multi-digit arithmetic.
Grade 4 expectations in this domain are limited to whole numbers less than or equal to 1,000,000.

Understand the place value system.

Understand place value.

Use place value understanding and properties of operations to add and subtract.

Work with numbers 11–19 to gain foundations for place value.

Perform operations with multi-digit whole numbers and with decimals to hundredths.

Generalize place value understanding for multi-digit whole numbers.
Grade 4 expectations in this domain are limited to whole numbers less than or equal to 1,000,000.
problem_activity: Problem 1
Josie makes 1.7 liters of lemonade. Josie’s mom tells her to split it evenly with her brother. How much lemonade, in liters, will Josie and her brother each get?
Problem 2
Here is how Mai used base-ten diagrams to calculate 0.62 ÷ 5. She started by representing 0.62.
[IMG]
She then made 5 groups, each with 1 tenth. There was 1 tenth left. She unbundled it into 10 hundredths and distributed the hundredths into 5 groups. Here is her diagram for 0.62 ÷ 5.
[IMG]
Mai should have a total of 12 hundredths, but her diagram shows only 10. Why?
She did not originally have thousandths, but in her diagrams each group has 4 thousandths. Why?
What value has Mai found for 0.62 ÷ 5?
Problem 3
Here is how Lin calculated 0.62 ÷ 5.
|                 Lin wrote the dividend, 0.62, and the divisor, 5.                  | She subtracted 5 groups of different amounts from 0.62, starting with 5 groups of 0.10, then 5 groups of 0.02. |                Lin wrote 0 to the right of the 2, which made 0.020.                | Lastly, she subtracted 5 times 0.004 from 0.020, which left no remainder.                          Then she added 0.100 + 0.020 + 0.004, which gave a quotient of 0.124. |
|------------------------------------------------------------------------------------|----------------------------------------------------------------------------------------------------------------|------------------------------------------------------------------------------------|--------------------------------------------------------------------------------------------------------------------------------------------------------------------------|
| .. image:: https://d21royfkw9g4l6.cloudfront.net/9FyZXfKqijxVpRgv2Bc6qf_CDWBZL.png |               .. image:: https://d21royfkw9g4l6.cloudfront.net/nxKMGc5DKRKgY6x2FVmo07_YDGM41.png               | .. image:: https://d21royfkw9g4l6.cloudfront.net/O3iHOw3zlpAkiFdwXHFNPB_NVXARD.png |                                            .. image:: https://d21royfkw9g4l6.cloudfront.net/91UkRicG3K9xdXGPqEsgOT_06NZSH.png                                            |
Lin put a 0 after the remainder of 0.02. Why? Why does this 0 not change the value of the quotient?
What value did Lin find for 0.62 ÷ 5?
Problem 4
Solve. Show or explain your work.
27 ÷ 6
0.84 ÷ 8
18.03 ÷ 6
3 ÷ 4


correct_option_index: 7