few_shots: 
Example 1:
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.

Example 2:
Concept/skill: 
Solve quadratic equations in one variable.

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


Answer: 
Yes. This task shows one quadratic equation with one variable, x.

Example 3:
Concept/skill: 
Construct a tangent line from a point outside a given circle to the circle.

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 $P$.


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, 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

im_task_000870_pos_0

HS_1

im_task_001160_neg_0

HS_2
standard_description: Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left.
problem_activity: Optional activity
In this activity, students use the measurements they just gathered to create their scale floor plans. Each student selects one of the paper options, decides on a scale to use, and works individually to create their drawing.
Support students as they reason about scale, scaled lengths, and how to go about creating the drawing. Encourage all to pay attention to units as they calculate scaled lengths. Ask students to think about the different ways that we can write a scale. If they struggle, remind students that a scale can be written in different units or written without units.
Action and Expression: Internalize Executive Functions.
Chunk this task into more manageable parts to support students who benefit from support with organizational skills in problem solving. For example, invite students to draw one section of the room at a time and monitor students to ensure they are making progress throughout the activity.
Supports accessibility for: Organization; Attention
Launch
Distribute at least three different types of paper for each group, which could include:
\(8\frac12 \times 11\)
printer paper
\(11 \times 17\)
printer paper
Centimeter graph paper
\(\frac14\)
-inch graph paper
\(\frac15\)
-inch graph paper
Ask each group member to select a paper for their drawing. Encourage variation in paper selections. Explain that they should choose an appropriate scale based on the size of their paper, the size of the classroom, and their chosen units of measurement. This means that the floor plan must fit on the paper and not end up too small (e.g., if the paper is
\(11 \times 17\)
inches, the floor plan should not be the size of a postcard).
Give students quiet time to create their floor plan. If the classroom layout is fairly complex, consider asking students to pause after they have completed a certain portion of the drawing (e.g., the main walls of the classroom) so their work may be checked. Alternatively, give them a minute to share their drawing-in-progress with a partner and discuss any issues.
Student Facing
Your teacher will give you several paper options for your scale floor plan.
Determine an appropriate scale for your drawing based on your measurements and your paper choice. Your floor plan should fit on the paper and not end up too small.
Use the scale and the measurements your group has taken to draw a scale floor plan of the classroom. Make sure to:
Show the scale of your drawing.
Label the key parts of your drawing (the walls, main openings, etc.) with their actual measurements.
Show your thinking and organize it so it can be followed by others.
Student Response
Teachers with a valid work email address can
click here to register or sign in
for free access to Student Response.
Student Facing
Are you ready for more?
If the flooring material in your classroom is to be replaced with 10-inch by 10-inch tiles, how many tiles would it take to cover the entire room? Use your scale drawing to approximate the number of tiles needed.
How would using 20-inch by 20-inch tiles (instead of 10-inch by 10-inch tiles) change the number of tiles needed? Explain your reasoning.
Student Response
Teachers with a valid work email address can
click here to register or sign in
for free access to Extension Student Response.
Anticipated Misconceptions
Some students may pick a scale and start drawing without considering how large their completed floor plan will be. Encourage students to consider the size of their paper in order to determine an appropriate scale before they start drawing.
Activity Synthesis
Small-group and whole-class reflections will occur in the next activity.


aligns: no