few_shots: 
Example:
Concept/skill: 
Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems.

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


Answer: 
Yes. An initial step when solving for x in this problem requires the use of the addition formula for cosine on the left side of the equation.

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_pos_0

HS_0
standard_description: Understand a fraction as a number on the number line; represent fractions on a number line diagram.
Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, and 8.
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