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: Measure the length of an object twice, using length units of different lengths for the two measurements; describe how the two measurements relate to the size of the unit chosen.
problem_activity: Narrative
The purpose of this activity is for students to learn about the meter as a longer metric unit of length. Students measure longer lengths with a new tool, the meter stick. Students measure strips of tape of different lengths and choose between a centimeter ruler and a meter stick in order to measure each. In the synthesis, students share their measurements of each line and discuss how they chose which tool to use to measure (MP5). Students measure Strips D
–
G in this activity. Students measure the komodo dragon (Strip D) twice to experience measuring the same length with a ruler and a meter stick. They discuss and compare their measurements in the lesson synthesis.
MLR2 Collect and Display.
Direct attention to words collected and displayed from the previous lesson. Add “meter stick” to the collection. Invite students to borrow language from the display as needed, and update it throughout the lesson.
Advances: Conversing, Reading
Engagement: Provide Access by Recruiting Interest.
Synthesis: Optimize meaning and value. Invite students to share people they know or specific jobs they recognize that may use the measuring tools they have been exposed to. “When and why might someone use these measuring tools?”
Supports accessibility for: Conceptual Processing
Required Materials
Materials to Gather
Metersticks
Rulers (centimeters)
Launch
Groups of 3–4
Give each group a meter stick.
“We saw that measuring longer lengths with centimeters can be challenging. Luckily, there is a standard unit that is much larger than a centimeter that we can use. It’s called a
meter
.”
Show students a meter stick.
“This is called a meter stick. The length of one end to the other is 1 meter long. Just like we used centimeter cubes at first to measure centimeters. We can use the length of a meter stick to measure length in meters.”
“What do you notice about the meter stick?” (There are lots of little lines; the numbers go up to 100; every tenth number is bold)
30 seconds: quiet think time
Share responses.
“The meter stick makes it easier to measure longer lengths. We can use the meter stick to measure in meters or centimeters.”
“Find 50 cm on the meter stick.”
If time permits, find a few other markings.
Activity
“Now, let’s go back to our job as zookeepers and measure some even larger reptiles.”
“You are going to measure the komodo dragon again and 3 new reptiles."
“You may use any of the measuring tools you have used today. Be prepared to explain why you chose each tool.”
12 minutes: group work time
Monitor for the different ways students measure the ribbon snake and adult alligator including how they record their measurements in meters.
Student Facing
D: komodo dragon
[IMG]
E: adult alligator
[IMG]
F: adult cobra
[IMG]
G: ribbon snake
[IMG]
Measure the length of the komodo dragon in meters.
What is the same or different about your measurements for the komodo dragon from Activity 1 and Activity 2?
Measure each reptile in centimeters or meters. Don’t forget the units.
How long is an adult alligator?
How long is an adult cobra?
How long is a ribbon snake?
Student Response
Teachers with a valid work email address can
click here to register or sign in
for free access to Student Response.
Advancing Student Thinking
If students do not measure using the meter stick, or only report their measurements in centimeters, consider asking:
“About how many meters long is the __?”
“What is different about measuring the __ in meters (or meters and centimeters) rather than only centimeters?”
Activity Synthesis
“Which tools did you use to measure Strip G, the ribbon snake? Why did you choose this tool?” (We used the meter stick and took away 10 because it was so close.)
“What did you do when you found that Strip E, the adult alligator, was longer than 3 meters but shorter than 4 meters?” (We saw it was closer to 3 meters so we said it was about 3 meters. We used the meter stick 3 times and then the cm ruler for the rest.)


aligns: no