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)


Topic options: 
A. Geometry: students learn to classify geometric figures by their properties, and understand and compare the relationships between them. Students develop and use formulas to compute lengths, areas, and volumes, and they use transformations to generate new shapes and compare existing ones. Geometry can be studied with and without coordinates.
B. Modeling: students learn to choose and use appropriate mathematics and statistics to analyze real-world empirical situations, improve decisions, and report on their conclusions and the reasoning behind them.
C. Number & Operations - Fractions: students learn to understand fractions as numbers and may work with them using addition, subtraction, multiplication, and division.
D. Counting & Cardinality: students learn to know number names and the count sequence, count to tell the number of objects, and compare numbers.
E. Functions: students learn to define, use, and evaluate functions to model relationships between quantities.
F. Number & Operations in Base Ten: students learn to work with the base-ten system and build place value understanding.
G. Statistics & Probability: students learn to analyze and produce data distributions, and build understanding of univariate and bivariate data. They learn to interpret data, make statistical inferences, justify conclusions, understand rules of probability, and use probability to make decisions.
H. Ratios & Proportional Relationships: students learn to recognize, describe, represent, and reason with ratios, rates, proportional relationships, and percent.
I. Measurement & Data: students learn to work with data and measure attributes such as time, money, length, area, and volume. They may learn to compare measurements to operations and convert between different units of measure.
J. Number Systems and Quantity: students learn to understand the complex number system and reason quantitatively.
K. Operations & Algebra: students learn to solve problems using algebraic thinking and operations such as addition, subtraction, multiplication, and division. They may learn to identify and explain arithmetic patterns, evaluate or manipulate numerical expressions, and reason with equations and inequalities.


Your response:
A

Now, assign the following problem or activity to one or more relevant topics it teaches.
shot_info: im_lesson_009431

1
options: Number Systems and Quantity: students learn to understand the complex number system and reason quantitatively.

Statistics & Probability: students learn to analyze and produce data distributions, and build understanding of univariate and bivariate data. They learn to interpret data, make statistical inferences, justify conclusions, understand rules of probability, and use probability to make decisions.

Number & Operations in Base Ten: students learn to work with the base-ten system and build place value understanding.

Measurement & Data: students learn to work with data and measure attributes such as time, money, length, area, and volume. They may learn to compare measurements to operations and convert between different units of measure.

Number & Operations - Fractions: students learn to understand fractions as numbers and may work with them using addition, subtraction, multiplication, and division.

Operations & Algebra: students learn to solve problems using algebraic thinking and operations such as addition, subtraction, multiplication, and division. They may learn to identify and explain arithmetic patterns, evaluate or manipulate numerical expressions, and reason with equations and inequalities.

Functions: students learn to define, use, and evaluate functions to model relationships between quantities.

Geometry: students learn to classify geometric figures by their properties, and understand and compare the relationships between them. Students develop and use formulas to compute lengths, areas, and volumes, and they use transformations to generate new shapes and compare existing ones. Geometry can be studied with and without coordinates.

Modeling: students learn to choose and use appropriate mathematics and statistics to analyze real-world empirical situations, improve decisions, and report on their conclusions and the reasoning behind them.

Counting & Cardinality: students learn to know number names and the count sequence, count to tell the number of objects, and compare numbers.

Ratios & Proportional Relationships: students learn to recognize, describe, represent, and reason with ratios, rates, proportional relationships, and percent.
problem_activity: Problem 1
a.   Fill in the following blanks to make true statements. Use base ten blocks to help you.
1 thousand is the same as _______ hundreds.
1 hundred is the same as _______ tens.
1 ten is the same as _______ ones.
1 one is the same as _______ tenths.
b.   Below is an area model that represents 1 one. It is partitioned into tenths. Partition it to show what you would expect the next smallest unit to look like so that it continues the pattern in Part (a).
[IMG]
c.   Use what you notice in Part (a) and (b) to write a similar sentence that starts “1 tenth is the same as…”
Problem 2
The shaded part of this diagram represents 1 hundredth. We can write this as the fraction
$$\frac{1}{100}$$
or as the decimal
0.01.
[IMG]
Fill out the following table to represent each given number.
|                                                                                                  **            Diagram           **                                                                                                  | **            Unit Form           ** | **            Fraction Form           ** | **            Decimal Form           ** |
|--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|--------------------------------------|------------------------------------------|-----------------------------------------|
| |https://d21royfkw9g4l6.cloudfront.net/UXbX2I0Zc5A1kLpwT6BAA2_C9OM62.png|  |https://d21royfkw9g4l6.cloudfront.net/UXbX2I0Zc5A1kLpwT6BAA2_C9OM62.png| image:: https://d21royfkw9g4l6.cloudfront.net/UXbX2I0Zc5A1kLpwT6BAA2_C9OM62.png |             7 hundredths             |                                          |                                         |
| |https://d21royfkw9g4l6.cloudfront.net/UXbX2I0Zc5A1kLpwT6BAA2_C9OM62.png|  |https://d21royfkw9g4l6.cloudfront.net/UXbX2I0Zc5A1kLpwT6BAA2_C9OM62.png| image:: https://d21royfkw9g4l6.cloudfront.net/UXbX2I0Zc5A1kLpwT6BAA2_C9OM62.png |                                      |            $$\frac{32}{100}$$            |                                         |
| |https://d21royfkw9g4l6.cloudfront.net/UXbX2I0Zc5A1kLpwT6BAA2_C9OM62.png|  |https://d21royfkw9g4l6.cloudfront.net/UXbX2I0Zc5A1kLpwT6BAA2_C9OM62.png| image:: https://d21royfkw9g4l6.cloudfront.net/UXbX2I0Zc5A1kLpwT6BAA2_C9OM62.png |                                      |                                          |                  0.85                   |
| |https://d21royfkw9g4l6.cloudfront.net/xJTfKSJObLTngvzpCrjGcc_LY71VX.png|  |https://d21royfkw9g4l6.cloudfront.net/xJTfKSJObLTngvzpCrjGcc_LY71VX.png| image:: https://d21royfkw9g4l6.cloudfront.net/xJTfKSJObLTngvzpCrjGcc_LY71VX.png |                                      |                                          |                                         |
Problem 3
a.   Explain why
$${{1\over10}={10\over100}}$$
. Draw a picture to illustrate your explanation.
b.   Explain why
$${0.20 = 0.2}$$
. Draw a picture to illustrate your explanation.
Problem 4
Jani and Kai are representing a decimal number. Here are the area models they drew:
|                                                                                                                 Jani                                                                                                                 |                                                                                                                 Kai                                                                                                                  |
|--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|
| |https://d21royfkw9g4l6.cloudfront.net/pCjOWHyq93ljOqoarBpFRi_XAG8G1.png|  |https://d21royfkw9g4l6.cloudfront.net/pCjOWHyq93ljOqoarBpFRi_XAG8G1.png| image:: https://d21royfkw9g4l6.cloudfront.net/pCjOWHyq93ljOqoarBpFRi_XAG8G1.png | |https://d21royfkw9g4l6.cloudfront.net/IX0bwHJs13FGRL7TldfH6i_9P5SGX.png|  |https://d21royfkw9g4l6.cloudfront.net/IX0bwHJs13FGRL7TldfH6i_9P5SGX.png| image:: https://d21royfkw9g4l6.cloudfront.net/IX0bwHJs13FGRL7TldfH6i_9P5SGX.png |
a.   What value do you think Jani and Kai are trying to model? How do you know?
b.   Draw pictures to show what Kai might have drawn for each area model in Anchor Task 2.


correct_option_index: 4