few_shots: 
Example:
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.”)

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)


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

Now, assess whether the following problem or activity is 'aligned' with the given Common Core standard in Mathematics.

shot_info: im_lesson_009431_pos_0

1
standard_description: Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each. For example, describe a context in which a total number of objects can be expressed as 5 × 7.
problem_activity: Activity
Having just seen an example of the meaning of
\(a\)
and
\(b\)
in an exponential expression
\(a \boldcdot b^x\)
, students now focus on interpreting these numbers using graphs. They graph the equations from the previous task, noticing that
\(a\)
is the vertical intercept of the graph while the number
\(b\)
determines how quickly the graph grows (since in these cases
\(b>1\)
). A larger value of
\(b\)
corresponds to a more rapid rate of growth for the bacteria population. The axes for the graphs have been labeled here, but in future activities, students will have to think strategically about how to label the axes to most effectively plot the points.
Making graphing technology available gives students an opportunity to choose appropriate tools strategically (MP5).
Launch
Display the equations from the previous activity for all to see (if they are not already visible).
Conversing: MLR8 Discussion Supports.
Use this routine to help students describe the meaning of variables in exponential expressions. Arrange students in groups of 2. Invite Partner A to share their observations for the first graph and Partner B to share their observations for the second graph. Provide sentence frames such as “I can connect the equation to the graph by….” and “I notice that….” Invite the listener to press for additional details referring to features of the graphs, such as the vertical intercept, specific points, and the steepness of the curve. This will help students justify how features of the graph can be used to identify matching equations.
Design Principle(s): Support sense-making; Cultivate conversation
Student Facing
Refer back to your work in the table of the previous task. Use that information and the given coordinate planes to graph the following:
a. Graph
\((t,n)\)
when
\(t\)
is 0, 1, 2, 3, and 4.
[IMG]
b. Graph
\((t,p)\)
when
\(t\)
is 0, 1, 2, 3, and 4. (If you get stuck, you can create a table.)
[IMG]
On the graph of
\(n\)
, where can you see each number that appears in the equation?
On the graph of
\(p\)
, where can you see each number that appears in the equation?
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 graphing the points, particularly finding the appropriate vertical (
\(n\)
or
\(p\)
) values. Ask them to find the coordinates of the grid points on the vertical axis and use that to estimate the vertical position of their points.
When calculating values by hand, many students may mistakenly write an expression like
\(100 \boldcdot 3^2\)
as
\(300^2\)
. Remind them that the expression
\(100 \boldcdot 3^2\)
means
\(100 \boldcdot 3 \boldcdot 3\)
.
Activity Synthesis
Make sure students recognize two key takeaways from this activity:
The vertical intercept of the graph is the initial bacteria population size. It is the size of the population when first measured, or when
\(t\)
, the number of hours since measurement, is 0.
The growth factor of the populations is represented by how quickly the graph increases.


aligns: no