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: 
Construct a tangent line from a point outside a given circle to the circle.

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, 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_neg_0

HS_2
standard_description: Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept. For example, in a linear model for a biology experiment, interpret a slope of 1.5 cm/hr as meaning that an additional hour of sunlight each day is associated with an additional 1.5 cm in mature plant height.
problem_activity: Task
Is there an association between the weight of an animal’s body and the weight of the animal’s brain? 1. Make a scatterplot using the following data.
{"table": [{"caption": [{"_value": "Body and brain weight by animal. Source:", "a": [{"_attributes": {"class": ["newWindow"], "href": "http://mste.illinois.edu/malcz/DATA/BIOLOGY/Animals.html"}, "_value": "http://mste.illinois.edu/malcz/DATA/BIOLOGY/Animals.html"}]}], "tbody": [{"tr": [{"th": [{"_value": "Animal"}, {"_value": "Body Weight (kg)"}, {"_value": "Brain Weight (g)"}]}, {"td": [{"_value": "Mountain beaver"}, {"_value": "1.35"}, {"_value": "8.1"}]}, {"td": [{"_value": "Cow"}, {"_value": "465"}, {"_value": "423"}]}, {"td": [{"_value": "Grey wolf"}, {"_value": "36.33"}, {"_value": "119.5"}]}, {"td": [{"_value": "Goat"}, {"_value": "27.66"}, {"_value": "115"}]}, {"td": [{"_value": "Guinea pig"}, {"_value": "1.04"}, {"_value": "5.5"}]}, {"td": [{"_value": "Asian elephant"}, {"_value": "2547"}, {"_value": "4603"}]}, {"td": [{"_value": "Donkey"}, {"_value": "187.1"}, {"_value": "419"}]}, {"td": [{"_value": "Horse"}, {"_value": "521"}, {"_value": "655"}]}, {"td": [{"_value": "Potar monkey"}, {"_value": "10"}, {"_value": "115"}]}, {"td": [{"_value": "Cat"}, {"_value": "3.3"}, {"_value": "25.6"}]}, {"td": [{"_value": "Giraffe"}, {"_value": "529"}, {"_value": "680"}]}, {"td": [{"_value": "Gorilla"}, {"_value": "207"}, {"_value": "406"}]}, {"td": [{"_value": "Human"}, {"_value": "62"}, {"_value": "1320"}]}, {"td": [{"_value": "African elephant"}, {"_value": "6654"}, {"_value": "5712"}]}, {"td": [{"_value": "Rhesus monkey"}, {"_value": "6.8"}, {"_value": "179"}]}, {"td": [{"_value": "Kangaroo"}, {"_value": "35"}, {"_value": "56"}]}, {"td": [{"_value": "Golden hamster"}, {"_value": "0.12"}, {"_value": "1"}]}, {"td": [{"_value": "Mouse"}, {"_value": "0.023"}, {"_value": "0.4"}]}, {"td": [{"_value": "Rabbit"}, {"_value": "2.5"}, {"_value": "12.1"}]}, {"td": [{"_value": "Sheep"}, {"_value": "55.5"}, {"_value": "175"}]}, {"td": [{"_value": "Jaguar"}, {"_value": "100"}, {"_value": "157"}]}, {"td": [{"_value": "Chimpanzee"}, {"_value": "52.16"}, {"_value": "440"}]}, {"td": [{"_value": "Mole"}, {"_value": "0.122"}, {"_value": "3"}]}, {"td": [{"_value": "Pig"}, {"_value": "192"}, {"_value": "180"}]}]}]}]}
Do there appear to be outliers in this data? Which animals appear to be outliers? Explain how you identified these outliers.
Removing the outliers from the data set, make a new scatterplot of the remaining animal body and brain weights.
Does there appear to be a relationship between body weight and brain weight? If yes, write a brief description of the relationship.
Take a piece of uncooked spaghetti and use that spaghetti to informally fit a line to the data. Attempt to place your line so that the vertical distances from the points to the line are as small as possible.
How well does the spaghetti line appear to fit the data? Explain.


aligns: no