few_shots: 
Example 1:
Concept/skill: 
Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems.

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


Answer: 
Yes. An initial step when solving for x in this problem requires the use of the addition formula for cosine on the left side of the equation.

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_pos_0

HS_0

im_task_000870_pos_0

HS_1

im_task_001160_neg_0

HS_2
standard_description: Use addition and subtraction within 100 to solve word problems involving lengths that are given in the same units, e.g., by using drawings (such as drawings of rulers) and equations with a symbol for the unknown number to represent the problem.
problem_activity: Narrative
The purpose of this activity is to introduce the foot as a length unit in the U.S. customary system. Students learn that a foot is longer than an inch and is the same length as 12 inches. They use the length of 12-in rulers as a tool to measure lengths in feet by iterating the length of a ruler, or, more precisely, the length of 12 inches shown on the ruler. The experience iterating lengths of a ruler to measure a length in feet helps students build a mental benchmark for the approximate length of a foot that they can use to estimate lengths.
Students measure lengths of tape that represent realistic lengths of different types of fish. They measure each length to the nearest inch and to the nearest foot. In the synthesis, students discuss the difference in their measurements and relate the differences to the size of the length units (MP7).
MLR2 Collect and Displa
y. Circulate, listen for, and collect the language students use as they measure the length of each animal. Display measurement words and comparative language such as: “inches,” “feet,” “ruler,” “more than,” “less than,” “longer,” “shorter,” “smaller,” and so on. Invite students to borrow language from the display as needed, and update it throughout the lesson.
Advances: Conversing, Reading
Required Materials
Materials to Gather
Inch tiles
Rulers (inches)
Tape (painter's or masking)
Required Preparation
Tape strips of these lengths on the floor. Label each strip with the letter and fish name. It may be helpful to make multiple sets of these lines to keep the groups small.
Strip A, largemouth bass: 2 feet
Strip B, spiny dogfish shark: 4 feet
Strip C, catfish: 3 feet
Strip D, koi: 2 feet and 6 inches
Launch
Groups of 3–4
Give each student an inch ruler and access to inch tiles.
“You have measured the length of objects and the sides of shapes using inches. If you are measuring longer objects, like the fish in the warm-up, you might want to use a different unit.”
“A
foot
is a longer length unit in the U.S. Customary Measurement System. A foot is the same length as 12 inches.”
“When we measure a length that starts at 0 on the ruler and ends at the 12, we can say the length is 12 inches or we can say the length is 1 foot.”
“What are some things you see around the classroom that are about 1 foot long?"
30 seconds: quiet think time
Share responses.
Activity
Display the images of the fish.
“In previous lessons, we measured the lengths of different kinds of reptiles. In this lesson, you will be measuring the lengths of fish. What do you know about fish?”
Share responses.
“Let’s imagine we work at the aquarium and need to measure the lengths of these fish. The tape on the floor represents their lengths.”
“Look at the tape strips on the floor. Use your rulers to measure each length first in feet. Then measure the length in inches using the rulers or your inch tiles.”
10 minutes: group work time
As needed, pause after students have measured their first fish in feet and invite students to share how they used their rulers to measure in feet.
Student Facing
Work with your group to measure the tape strips around the classroom in feet. Then measure the length in inches.
Tape A
largemouth bass
[IMG]
Length in feet: __________
Length in inches: __________
Tape B
spiny dogfish shark
[IMG]
Length in feet: __________
Length in inches: __________
Tape C
catfish
[IMG]
Length in feet: __________
Length in inches: __________
Tape D
koi
[IMG]
Length in feet: __________
Length in inches: __________
What did you notice about the number of feet compared to the number of inches when you measured the tape strips?
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 measure lengths in feet by lining up multiple rulers or iterating the same ruler without considering gaps that may be caused by the lengths of the ruler before the 0 in or after the 12 in mark, point out these gaps on the ruler and consider asking:
“Can you show me how you measured the length of the ______ in feet?”
“Did you measure the length without any gaps? How do you know?”
“How would you revise the way you measure to make sure you have no gaps or overlaps?”
Activity Synthesis
“What did you notice about your measurements when you switched from measuring in feet to measuring in inches?” (The numbers are smaller for the number of feet. I had to count more inches than feet.)
“Why are our measurements in feet so much smaller than our measurements in inches?” (Feet are longer, so you don't need as many to measure the length of the tape. It takes more inches to cover the same length.)


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