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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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)


Concept/skill: 
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.”)

Answer: 
Yes. This activity asks students to compose three-dimensional shapes, using geoblocks, to create composite shapes.

Now, does the following problem or activity enable students to learn the full intent of the following concept or skill?

shot_info: im_lesson_009431_pos_0

1
standard_description: Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). For example, the expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for.
problem_activity: Activity
This task is analogous to a previous activity with positive exponents. The number line strongly encourages students to think about how to change expressions so they all take the form
\(b \boldcdot 10^k\)
, where
\(b\)
is between 1 and 10, as in the case of scientific notation. The number line also is a useful representation to show that, for example,
\(29 \boldcdot 10^\text{-7}\)
is about half as much as
\(6 \boldcdot 10^\text{-6}\)
. The last two questions take such a comparison a step further, asking students to estimate relative sizes using numbers expressed with powers of 10.
As students work, look for different strategies they use to compare expressions that are not written as a product of a number and
\(10^{\text-6}\)
. Also look for students who can explain how they estimated in the last two problems. Select them to share their strategies later.
Launch
Arrange students in groups of 2. Give students 5 minutes of quiet work time, followed by partner discussion and whole-class discussion. During partner discussion, ask students to share their responses for the first two questions and reach an agreement about where the numbers should be placed on the number line.
Action and Expression: Develop Expression and Communication.
Maintain a display of important terms and vocabulary. During the launch take time to review the visual display of rules for exponents.
Supports accessibility for: Memory; Language
Speaking: MLR8 Discussion Supports.
Display sentence frames to support students as they describe how they compared and estimated the difference in magnitude between the pairs of values
\(29⋅10^{\text-7}\)
and
\(6⋅10^{\text-6}\)
or
\(7⋅10^{\text-8}\)
and
\(3⋅10^{\text-9}\)
. For example, “First I ____ , then I ____ .” or “_____ is (bigger/smaller) because ______ .”
Design Principle(s): Optimize output (for explanation)
Student Facing
[IMG]
Label the tick marks on the number line.
Plot the following numbers on the number line:
A.
\(6 \boldcdot 10^{\text -6}\)
B.
\(6 \boldcdot 10^{\text -7}\)
C.
\(29 \boldcdot 10^{\text -7}\)
D.
\((0.7) \boldcdot 10^{\text -5}\)
Which is larger,
\(29 \boldcdot 10^{\text -7}\)
or
\(6 \boldcdot 10^{\text -6}\)
? Estimate how many times larger.
Which is larger,
\(7 \boldcdot 10^{\text -8}\)
or
\(3 \boldcdot 10^{\text -9}\)
? Estimate how many times larger.
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 have trouble comparing negative powers of 10. Remind these students that, for example,
\(10^\text{-5}\)
is 5 factors that are
\(\frac{1}{10}\)
and
\(10^\text{-6}\)
is 6 factors that are
\(\frac{1}{10}\)
, so
\(10^\text{-5}\)
is 10 times larger than
\(10^\text{-6}\)
.
Students may also have trouble estimating how many times one larger expression is than another. Offer these students an example to illustrate how representing numbers as a single digit times a power of 10 is useful for making rough estimations. We have that
\(9 \boldcdot 10^\text{-12}\)
is roughly 50 times as much as
\(2 \boldcdot 10^\text{-13}\)
because
\(10^\text{-12}\)
is 10 times as much as
\(10^\text{-13}\)
and 9 is roughly 5 times as much as 2. In other words,
\(\displaystyle \frac{9 \boldcdot 10^\text{-12}}{2 \boldcdot 10^\text{-13}} \approx \frac{10 \boldcdot 10^\text{-12}}{2 \boldcdot 10^\text{-13}} = 5 \boldcdot 10^{\text-12 - (\text-13)} = 5 \boldcdot 10^1 = 50\)
Activity Synthesis
Select previously identified students to explain how they used the number line and powers of 10 to compare the numbers in the last two problems.
One important concept is that it’s always possible to change an expression that is a multiple of a power of 10 so that the leading factor is between 1 and 10. For example, we can think of
\(29 \boldcdot 10^\text{-7}\)
as
\((2.9) \boldcdot 10 \boldcdot 10^\text{-7}\)
or
\((2.9) \boldcdot 10^\text{-6}\)
. Another important concept is that powers of 10 can be used to make rough estimates. Make sure these ideas are uncovered during discussion.


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