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: Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots. For example, from a line plot find and interpret the difference in length between the longest and shortest specimens in an insect collection.
problem_activity: Narrative
The purpose of this activity is for students to solve problems about a locker game by using the ideas of factors and multiples and by observing patterns in the numbers. The situation offers many possible explorations, but the questions around which lockers are touched and by how many people are designed to elicit understandings about multiplication.
Discussion about which lockers will be open or closed or by whom will likely move students away from thinking about factors and multiples and should not be the focus. The final question challenges students who are ready for more to look for additional patterns and generalize their observations. It is not expected that all students complete it. Students who are ready may simulate opening and closing the lockers in different ways, such as:
using actual lockers, if available
using a printed set of squares labeled 1 through 20
using two color counters and 10-frames, if available
using the head and tail sides of coins
MLR7 Compare and Connect
. Synthesis: Invite groups to prepare a visual display that shows the strategy they used to determine which lockers will be open. Encourage students to include details that will help others interpret their thinking. For example, specific language, using different colors, shading, arrows, labels, notes, diagrams or drawings. Give students time to investigate each other’s work. During the whole-class discussion, ask students, “Which students open or close locker 10? What about locker 20? What patterns do you notice about the number of factors for a locker number and whether it is open or closed?”
Advances: Representing, Conversing
Representation: Internalize Comprehension
. Support students in transferring their knowledge to a new context. Begin by asking, “Does this problem remind anyone of the concepts we have been studying?” Invite students to reference the vocabulary display, and continue to refer them to it throughout the lesson.
Supports accessibility for: Conceptual Processing, Language, Attention
Launch
Groups of 3–4
“Let’s solve some problems about a game you read about earlier, where students take turns opening and closing lockers.”
“Silently read and think about each question.”
1 minute: quiet think time
“Work in your group to answer each question. Consider the representations you created or saw earlier to help you think about the problems.”
Activity
15–20 minutes: group work time
Monitor for students who:
represent each contact with the lockers in a systematic way
represent the open and closed lockers in various ways
reason about factors and multiples and use the vocabulary in their explanations
Encourage students who use a pattern to answer the final question to share their explanation. Invite them to consider a situation with more lockers such as 50 or 100.
Student Facing
The 20 students in Tyler’s fourth-grade class are playing a game in a hallway with 20 lockers in a row.
Your goal is to find out which lockers will be touched as all 20 students take their turn touching lockers.
[IMG]
[IMG]
Which locker numbers does the 3rd student touch?
Which locker numbers does the 5th student touch?
How many students touch locker 17? Explain or show how you know.
Which lockers are only touched by 2 students? Explain or show how you know.
Which lockers are touched by only 3 students? Explain or show how you know.
Which lockers are touched the most? Explain or show how you know.
If you have time: Which lockers are still open at the end of the game? Explain or show how you know.
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
“Take a few minutes to share your answers with students in a different group.”
Invite students to share how they kept track of the number of touches for each locker.
See lesson synthesis.


aligns: no