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: 
Construct a tangent line from a point outside a given circle to the circle.

Answer: 
No. This task does not involve drawing lines that are tangent to circles. The only line that may be drawn is the ray between points P and B.

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

shot_info: fl_problem_001894_neg_0

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im_task_000870_neg_0

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im_task_001160_neg_0

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standard_description: Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.
problem_activity: Activity
When students are finding values to aid in their method, consider allowing them to research typical values online at hardware websites or search for values that would be useful. If these tools are not available, some values are provided here.
Values that may be useful for students:
Typical (modern) shower heads have a flow rate of 1.9 to 2.5 gallons per minute. Older shower heads (pre-1992) could have flow rates up to 5.5 gallons per minute.
Bath tubs hold approximately 120 to 180 gallons of water when completely filled to the top.
The interior of a typical bath tub has an approximate width of 30 to 32 inches, length of 55 to 60 inches, and depth of 18 to 24 inches.
There are approximately 230 cubic inches in 1 gallon of water.
1 liter of water is 1,000 cubic centimeters.
1 liter is approximately 0.26 gallons
1 inch is 2.54 centimeters.
Typical showers last approximately 11 minutes although during a drought, it is recommended to reduce the time to about 5 minutes. During normal circumstances, some people appreciate much longer showers.
After students have made good progress in the activity, tell them to make a display (e.g. poster) to share their method and results.
This activity can take the rest of the class period, if desired.
Launch
Arrange students in groups of 2–4. Tell them either that they should research relative information and provide access to internet enables devices or tell them that they can ask for information they need.
Action and Expression: Internalize Executive Functions.
To support development of organizational skills, check in with students within the first 2–3 minutes of work time. Check to make sure students have a valid method for comparing the water usage for a bath and a shower prior to allowing them to research typical values of measurements.
Supports accessibility for: Memory; Organization
Student Facing
Describe a method for comparing the water usage for a bath and a shower.
Find out values for the measurements needed to use the method you described. You may ask your teacher or research them yourself.
Under what conditions does a bath use more water? Under what conditions does a shower use more water?
Student Response
Teachers with a valid work email address can
click here to register or sign in
for free access to Student Response.
Activity Synthesis
Allow students to share their displays possibly through a gallery walk or ask them to present to the class. After students have had a chance to explore their work, ask them to share ideas they saw that were interesting and any methods they considered but did not use.
Writing, Representing: MLR7 Compare and Connect.
Use this routine when students present their visual displays. Ask students to consider how comparisons were made between water usage of baths and showers. Draw students’ attention to the relationships between quantities in each situation (e.g., How does the rate of water flow from the shower affect water usage? How does tub size affect the comparison?). Emphasize language used to make sense of strategies used to calculate and compare water usage.
Design Principle(s): Maximize meta-awareness; Support sense-making


aligns: no