few_shots: 
Example:
Concept/skill: 
Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles.

Problem/activity:
Find the general solution for:
$${\mathrm{cos}\left({\pi\over2}+x\right)=\mathrm{tan}{\pi\over4}}$$


Answer: 
No. This problem does not directly teach how side ratios in right triangles lead to definitions of trigonometric ratios. Instead, it involves solving a trigonometric function.

Now, determine whether the following problem or activity can enable students to understand the concepts or skills in the provided description.

shot_info: fl_problem_001894_neg_0

HS_0
standard_description: Fluently divide multi-digit numbers using the standard algorithm.
problem_activity: Problem 1
a.   Estimate whether the following sums will be more or less than 1.
i.
$${{3\over4}+{2\over4}}$$
ii.
$${{5\over6}+{3\over6}}$$
b.   Solve for the actual sums in Part (a) above.
Problem 2
Cary computes
$$\frac{9}{10} + \frac4{10}$$
using a different strategy. Here is her reasoning:
[IMG]
“First I broke
$$\frac4{10}$$
into
$$\frac1{10}$$
and
$$\frac3{10}$$
. Then I added
$$\frac9{10}$$
and
$$\frac1{10}$$
to get to 1, then added the other
$$\frac3{10}$$
to get
$$1\frac3{10}$$
.
So
$$\frac{9}{10} + \frac4{10} = 1\frac3{10}$$
."
a.   Is Cary’s calculation correct? Explain.
b.   Will Cary’s strategy always work? If not, give an example of a calculation for which Cary can’t use this strategy.
c.   Use Cary’s strategy to find
$$\frac45+\frac35$$
.
Problem 3
a.   Estimate whether the following differences will be more or less than 1.
i.
$${1{1\over3}-{2\over3}}$$
ii.
$${1{3\over8}-{5\over8}}$$
b.   Solve for the actual differences in Part (a) above.
Problem 4
Corrado computes
$$1\frac15 - \frac25$$
using a different strategy. Here is his reasoning:
[IMG]
“First I broke
$$\frac25$$
into
$$\frac15$$
and
$$\frac15$$
. Then I subtracted
$$\frac15$$
from
$$1\frac15$$
to get to 1, then subtracted the other
$$\frac15$$
to get
$$\frac45$$
.
So
$$1\frac15 - \frac25 = \frac45$$
."
a.   Is Corrado’s calculation correct? Explain.
b.   Will Corrado’s strategy always work? If not, give an example of a calculation for which Corrado can’t use this strategy.
c.   Use Corrado’s strategy to find
$$1\frac2{12}-\frac5{12}$$
.


aligns: no