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: 
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).

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


Answer: 
No. This task does not involve an equation in two variables. There is only 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_neg_0

HS_1

im_task_001160_neg_0

HS_2
standard_description: Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie?
problem_activity: Narrative
The purpose of this activity is for students to use a method of their choice, likely multiplication or division, to solve a contextual problem about equal sharing of the longest noodle ever made. The numbers in this activity are larger than the numbers students have worked with in previous lessons on division. Students estimate the number of feet of noodle each person ate at the record breaking event. The numbers and context were chosen to encourage students to consider what they know about the meaning of division, to make a reasonable estimate, and to reason about the meaning of the quotient in the context of the situation presented (MP2).
Monitor and select students with the following strategies to share in the synthesis:
Students use multiplication or division to estimate that each person will get about 25 feet of noodle.
Students can explain why 25 feet of noodle for each person is a low estimate.
Launch
“What kind of noodles do you like to eat?” (ramen, spaghetti, fettucini, chicken noodle soup)
30 seconds: partner discussion
“About how long is one of the noodles you like to eat?” (about 1 foot long)
Groups of 2
Activity
5 minutes: independent work time
5 minutes: partner discussion
As students work, consider asking “What do the numbers in your calculations mean, in terms of the situation?”
Student Facing
A Chinese food company cooked a single noodle measuring about 10,119 ft. It served 400 people.
If the noodle was shared equally, estimate how many feet of noodle each person was served.
Is your estimate lower or higher than the actual length of noodle each person ate? Explain your reasoning without calculating the actual length.
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
Ask selected students to share in the given order (or use the provided student solutions if needed).
“How are the methods for estimating the amount of noodle each person gets the same?”(They both start by giving each person 10 feet of noodle. Then they give more until they have both given 25 feet to each person. They both find multiples of 400.)
“How are they different?” (One thinks of the process as division and one uses just multiplication.)
“How do you know the estimate of 25 feet is too low?” (Because there was still some of the noodle left. There are 119 feet left over.)


aligns: yes