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)


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: Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them.
problem_activity: Task
In ''Building an explicit quadratic function'' a particular quadratic function was rewritten by completing the square. The quadratic function used was $q(x) = 2x^2 + 4x - 16$ and this function was rewritten as $$ q(x) = 2\left(x+1\right)^2 - 18 = 2\left((x+1)^2 - 9\right). $$ Some of the advantages to this form are that the $x$-coordinate of the vertex of the graph of $q$ can be found more easily and the two roots of $q$ can also be found readily. The right hand side of this equation can be seen as a horizontal translation by $-1$, then squaring, then a vertical translation by $-9$, and finally a multiplicative scaling by $2$. The goal of this task is first to employ the same technique on a general quadratic function and then derive the quadratic formula. To assist in this process, we first rewrite the equation above: $$ \frac{q(x)}{2} = \left(x+1\right)^2 - 9. $$
Let $f$ be a quadratic function, so we have $$ f(x) = ax^2 + bx + c. $$ Here $a,b,c$ are real numbers and we assume that $a$ is non-zero.
Following the lead of our example problem, we begin by dividing out the leading coefficient:
Multiplying $f(x)$ by $\frac{1}{a}$ gives $$ \frac{f(x)}{a} = x^2 + \frac{b}{a}x + \frac{c}{a}. $$ We wish to write this as the square of a linear function $x + d$ plus a constant. Find numbers $d$ and $k$ so that $\frac{f(x)}{a} = (x+d)^2 + k$.
Using the values for $d$ and $k$ found in part (b), rewrite $f(x) = ax^2 + bx + c$ as $$ \frac{f(x)}{a} = \left(x+d\right)^2 + k. $$ Why do the expressions $f(x)$ and $\frac{f(x)}{a}$ have the same roots?
Explain how to deduce the quadratic formula for the roots of $f$ from part (c).


aligns: yes