few_shots: 
Example:
Problem/activity:
Stage 1: Money
 Required Preparation
 Materials to Copy
 Blackline Masters
 Would You Rather Stage 1 Spinner
 Would You Rather Stage 1 Recording Sheet
 
 Narrative
 The first partner spins to get a group of coins. They write a question that compares the amount they spun to a different group of coins that they make up.

Concept/skill: 
Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using $ and ¬¢ symbols appropriately. Example: If you have 2 dimes and 3 pennies, how many cents do you have?

Answer: 
Yes. In this activity, students write word problems that compare coin amounts.

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

shot_info: im_center_000269_pos_0

2
standard_description: Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.
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