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 problem or activity shown below enable students to learn the full intent of the following concept or skill?

shot_info: im_lesson_009431_pos_0

1
standard_description: Use the structure of an expression to identify ways to rewrite it. For example, see x^(4) – y^(4 )as (x^(2))^(2 )– (y^(2))^(2), thus recognizing it as a difference of squares that can be factored as (x^(2 )– y^(2))(x^(2 )+ y^(2)).
problem_activity: Activity
Students have seen quadratic expressions in both standard form and factored form since the beginning of the unit. In this activity, they learn to distinguish the expressions by their forms and to refer to each form by its formal name. Refining their language about the different forms prepares students to be more precise in their thinking about the graphs of quadratic functions in later lessons (MP6).
Launch
Arrange students in groups of 2. Give students quiet work time and then time to share their work with a partner.
Writing, Conversing: MLR1 Stronger and Clearer Each Time.
Use this routine to help students improve their writing, by providing them with multiple opportunities to clarify their explanations through conversation. Give students time to meet with 1–2 partners to share their response to the final question, “Why do you think that form is called factored form?” Provide listeners with prompts for feedback that will help their partner add detail to strengthen and clarify their ideas. For example, students can ask their partner, “Can you say more about what each expression means?” or “I understand _____, but can you clarify . . .” Next, provide students with 2–3 minutes to revise their initial draft based on feedback from their peers.
Design Principle(s): Optimize output (for explanation)
Action and Expression: Internalize Executive Functions.
Provide students with a graphic organizer that can be used to brainstorm the activity. Include one column for standard form and one column for factored form. Include a space at the bottom of the organizer for student-generated notes or reminders about standard form and factored form.
Supports accessibility for: Language; Organization
Student Facing
The quadratic expression
\(x^2 + 4x + 3\)
is written in
standard form
.
Here are some other quadratic expressions. The expressions on the left are written in standard form and the expressions on the right are not.
Written in standard form:
\(x^2 – 1\)
\( x^2 + 9x\)
\(\frac12 x^2\)
\(4x^2 – 2x + 5\)
\(\text-3x^2 – x + 6\)
\(1 - x^2\)
Not written in standard form:
\((2x + 3)x\)
\((x+1)(x-1)\)
\(3(x-2)^2 +1\)
\( \text-4(x^2 + x) +7\)
\( (x+8)(\text{-}x+5)\)
What are some characteristics of expressions in standard form?
\((x+1)(x-1)\)
and
\((2x + 3)x\)
in the right column are quadratic expressions written in
factored form
. Why do you think that form is called factored form?
Student Response
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Student Facing
Are you ready for more?
What quadratic expression can be described as being both standard form and factored form? Explain how you know.
Student Response
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click here to register or sign in
for free access to Extension Student Response.
Activity Synthesis
Display the two columns of expressions for all to see. Solicit students’ ideas on the features of each form. Record their responses for all to see. Invite other students to express agreement or disagreement or to clarify their fellow students’ responses.
Define a quadratic expression in
standard form
explicitly as
\(ax^2 + bx + c\)
. Explain that we refer to
\(a\)
as the coefficient of the squared term
\(x^2\)
,
\(b\)
as the coefficient of the linear term
\(x\)
, and
\(c\)
as the constant term.
Ask students:
“How would you write
\((2x + 3)x\)
in standard form?” (
\(2x^2 + 3x\)
)
“The expression
\(2x^2 + 3x\)
only has two terms. Is it still in standard form?” (Yes, there is no constant term, which means
\(c\)
is 0.)
“How would you write
\(\text {-4}(x^2 + \frac14x) +7\)
in standard form?” (
\(\text {-4}x^2 - x + 7\)
)
“What are the values of the coefficients
\(a\)
and
\(b\)
?” (-4 and -1) “What about the constant term?” (7)
Then, clarify that a quadratic expression in
factored form
is a product of two factors that are each a linear expression. For example,
\((x+1)(x-1)\)
,
\((2x + 3)x\)
, and
\(x(4x)\)
all have two linear expressions for their factors. An expression with two factors that are linear expressions and a third factor that is a constant, for example:
\(2(x+2)(x-1)\)
, is also in factored form.
Tell students that each form gives us interesting or useful information about the function that the expression represents, and they will learn more about this in future lessons.


aligns: yes