few_shots: 
Example 1:
Problem/activity:
Find the general solution for:
$${\mathrm{cos}\left({\pi\over2}+x\right)=\mathrm{tan}{\pi\over4}}$$


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

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:
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 following problem or activity enable students to learn the full intent of the following concept or skill?

shot_info: fl_problem_001894_pos_0

HS_0

im_task_000870_neg_0

HS_1

im_task_001160_neg_0

HS_2
standard_description: Read and write numbers to 1000 using base-ten numerals, number names, and expanded form.
problem_activity: Narrative
The purpose of this activity is for students to analyze their completed food waste journals. Students begin the activity by sharing their food journal with a partner and discuss a few things they notice. Then they use the data from the journal and their experience with multiplying and dividing large numbers in this unit to estimate how much food waste they might produce in a month and in a year. They compare those results to the national average and discuss some possible reasons for the difference.
Launch
Groups of 2
“Share your food waste journal with a partner. As you look over your journals, what do you notice?”
“What is the same? What is different?”
Activity
10 minutes: independent work time
2 minutes: partner discussion
Student Facing
Use your food waste journal to answer the questions. Be prepared to share.
How many pounds of food waste did you or your family produce in a week?
If you produce about the same food waste each week as recorded in the food waste journal, how much would you produce in a month? In a year?
The average person produces 219 pounds of food waste per year in the United States. With your partner, discuss reasons for the differences between your data and the national average.
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
See lesson synthesis


aligns: no