few_shots: 
Example 1:
Problem/activity:
Find the general solution for:
$${\mathrm{cos}\left({\pi\over2}+x\right)=\mathrm{tan}{\pi\over4}}$$


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.

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.

Example 2:
Problem/activity:
Task
Solve the quadratic equation
$$ x^2 = (2x - 9)^2 $$
using as many different methods as possible.


Concept/skill: 
Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line).

Answer: 
No. This task does not involve an equation in two variables. There is only one variable, x.

Example 3:
Problem/activity:
Task
Suppose $A$ is an angle with vertex $P$, as pictured below:
[IMG]
Draw a circle with center $P$ and with  radius $r \gt 0$.  Explain why the circle
meets each ray of angle $A$ in a single point.  Label these points $Q$ and $R$ respectively.
Draw circles with centers $Q$ and $R$ respectively and radius $r$.  These circles meet at $P$ and a second point to be labelled $B$.
Show that ray $\overrightarrow{PB}$  bisects angle $P$.


Concept/skill: 
Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). Copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line.

Answer: 
Yes. This task asks students to draw a ray that bisects an angle. The act of drawing circles and rays may involve compass and straightedge or dynamic geometric software.

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

shot_info: fl_problem_001894_neg_0

HS_0

im_task_000870_neg_0

HS_1

im_task_001160_pos_0

HS_2
standard_description: Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. For example, observe that 4 times a number is always even, and explain why 4 times a number can be decomposed into two equal addends.
problem_activity: Problem 1
Katia and Gerard are stocking shelves at the grocery store. Katia stocks 3 shelves with 7 boxes of cereal on each shelf. Gerard stocks 7 shelves with 3 boxes of cereal on each shelf.
Katia says they put the same number of cereal boxes on each shelf. Gerard says they didn’t, since they stocked a different number of boxes on each of a different number of shelves. Who do you agree with, Katia or Gerard? Explain.
Problem 2
Fill in the facts you know on the multiplication table below.
{"table": [{"_attributes": {"class": ["table", "table-bordered"], "style": "table-layout:fixed; width:100%"}, "tbody": [{"tr": [{"td": [{"_attributes": {"style": "background-color:#3399ff; text-align:center"}, "strong": [{"_value": "\u00d7"}]}, {"_attributes": {"style": "background-color:#99ccff; text-align:center"}, "strong": [{"_value": "1"}]}, {"_attributes": {"style": "background-color:#99ccff; text-align:center"}, "strong": [{"_value": "2"}]}, {"_attributes": {"style": "background-color:#99ccff; text-align:center"}, "strong": [{"_value": "3"}]}, {"_attributes": {"style": "background-color:#99ccff; text-align:center"}, "strong": [{"_value": "4"}]}, {"_attributes": {"style": "background-color:#99ccff; text-align:center"}, "strong": [{"_value": "5"}]}, {"_attributes": {"style": "background-color:#99ccff; text-align:center"}, "strong": [{"_value": "6"}]}, {"_attributes": {"style": "background-color:#99ccff; text-align:center"}, "strong": [{"_value": "7"}]}, {"_attributes": {"style": "background-color:#99ccff; text-align:center"}, "strong": [{"_value": "8"}]}, {"_attributes": {"style": "background-color:#99ccff; text-align:center"}, "strong": [{"_value": "9"}]}, {"_attributes": {"style": "background-color:#99ccff; text-align:center"}, "strong": [{"_value": "10"}]}]}, {"td": [{"_attributes": {"style": "background-color:#99ccff; text-align:center"}, "strong": [{"_value": "1"}]}, {"_attributes": {"style": "background-color:#ffffff; text-align:center"}}, {"_attributes": {"style": "background-color:#ffffff; text-align:center"}}, {"_attributes": {"style": "background-color:#ffffff; text-align:center"}}, {"_attributes": {"style": "background-color:#ffffff; text-align:center"}}, {"_attributes": {"style": "background-color:#ffffff; text-align:center"}}, {"_attributes": {"style": "background-color:#ffffff; text-align:center"}}, {"_attributes": {"style": "background-color:#ffffff; text-align:center"}}, {"_attributes": {"style": "background-color:#ffffff; text-align:center"}}, {"_attributes": {"style": "background-color:#ffffff; text-align:center"}}, {"_attributes": {"style": "background-color:#ffffff; text-align:center"}}]}, {"td": [{"_attributes": {"style": "background-color:#99ccff; text-align:center"}, "strong": [{"_value": "2"}]}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}]}, {"td": [{"_attributes": {"style": "background-color:#99ccff; text-align:center"}, "strong": [{"_value": "3"}]}, {"_attributes": {"style": "background-color:#ffffff; text-align:center"}}, {"_attributes": {"style": "background-color:#ffffff; text-align:center"}}, {"_attributes": {"style": "background-color:#ffffff; text-align:center"}}, {"_attributes": {"style": "background-color:#ffffff; text-align:center"}}, {"_attributes": {"style": "background-color:#ffffff; text-align:center"}}, {"_attributes": {"style": "background-color:#ffffff; text-align:center"}}, {"_attributes": {"style": "background-color:#ffffff; text-align:center"}}, {"_attributes": {"style": "background-color:#ffffff; text-align:center"}}, {"_attributes": {"style": "background-color:#ffffff; text-align:center"}}, {"_attributes": {"style": "background-color:#ffffff; text-align:center"}}]}, {"td": [{"_attributes": {"style": "background-color:#99ccff; text-align:center"}, "strong": [{"_value": "4"}]}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}]}, {"td": [{"_attributes": {"style": "background-color:#99ccff; text-align:center"}, "strong": [{"_value": "5"}]}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}]}, {"td": [{"_attributes": {"style": "background-color:#99ccff; text-align:center"}, "strong": [{"_value": "6"}]}, {"_attributes": {"style": "background-color:#ffffff; text-align:center"}}, {"_attributes": {"style": "background-color:#ffffff; text-align:center"}}, {"_attributes": {"style": "background-color:#ffffff; text-align:center"}}, {"_attributes": {"style": "background-color:#ffffff; text-align:center"}}, {"_attributes": {"style": "background-color:#ffffff; text-align:center"}}, {"_attributes": {"style": "background-color:#ffffff; text-align:center"}}, {"_attributes": {"style": "background-color:#ffffff; text-align:center"}}, {"_attributes": {"style": "background-color:#ffffff; text-align:center"}}, {"_attributes": {"style": "background-color:#ffffff; text-align:center"}}, {"_attributes": {"style": "background-color:#ffffff; text-align:center"}}]}, {"td": [{"_attributes": {"style": "background-color:#99ccff; text-align:center"}, "strong": [{"_value": "7"}]}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}]}, {"td": [{"_attributes": {"style": "background-color:#99ccff; text-align:center"}, "strong": [{"_value": "8"}]}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}]}, {"td": [{"_attributes": {"style": "background-color:#99ccff; text-align:center"}, "strong": [{"_value": "9"}]}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}]}, {"td": [{"_attributes": {"style": "background-color:#99ccff; text-align:center"}, "strong": [{"_value": "10"}]}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}]}]}]}]}
Problem 3
Solve.
a.
$$4 \times 8 =a $$
b.
$$18 = b \times 6$$
c.
$$c= 35 \div 7$$
d.
$$9 = 18 \div d$$


aligns: yes