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


Standard options: 
A. Prove the Pythagorean identity sin^(2)(θ) + cos^(2)(θ) = 1 and use it to find sin(θ), cos(θ),or tan(θ) given sin(θ), cos(θ), or tan(θ) and the quadrant of the angle.
B. Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems.


Your response:
Thought: 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. Solving this problem does not require use of the Pythagorean identity.
Answer: B

Now, assign the following problem or activity to one or more relevant standards it aligns with.
shot_info: fl_problem_001894

HS
options: Summarize numerical data sets in relation to their context, such as by:
- Reporting the number of observations.
- Describing the nature of the attribute under investigation, including how it was measured and its units of measurement.
- Relating the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered.
- Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.

Display numerical data in plots on a number line, including dot plots, histograms, and box plots.
problem_activity: Activity
In this activity, students use their understanding of spreadsheets to compute useful statistics from data sets. In the associated Algebra 1 lesson, students will learn alternative methods for computing these values.
Launch
If students need a reminder about how to use a spreadsheet as a calculator, demonstrate how to do basic calculations such as =A1+A2, =SUM(A1:A10), =(A1+A2)/A3, and =COUNT(A1:A50) or =LENGTH(A1:A50) in GeoGebra.
Student Facing
Here is a list of the number of pages for fiction books on a shelf.
15
243
426
175
347
186
236
394
170
412
242
479
185
254
186
278
277
278
486
207
378
251
458
360
440
181
349
482
382
Describe a method to find the mean of these values. (Do not calculate the value yet.)
Input the data into a spreadsheet in the same column. In another column, write a spreadsheet formula that will compute the value of the mean for the values in the column. What is the mean number of pages in these books?
The first book on the list with 15 pages was a recording error and should have been 158 pages. You need to compute the new mean using 158 instead of 15. Would you rather compute the new mean by hand or use a computer? Explain your reasoning.
What is the new mean number of pages in these books with the updated value of 158 pages for the first book in the list?
Another book is found and added to the shelf. This new book has 519 pages. How would you update your spreadsheet formula to include this new value?
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
Select students to share their responses and methods for finding the mean from a list of values in a spreadsheet. The purpose of the discussion is to point out the advantage of using a spreadsheet to calculate statistics, especially for very large sets of data. For further discussion, consider asking these questions:
"Which part of the process for finding the mean for these values took the most time?" (Typing the values into the spreadsheet and making sure they are correct.)
"Often large data sets are collected electronically and automatically added to a spreadsheet. When there are thousands of data values in a spreadsheet, what other advantages do you think might be helpful when using technology to compute the mean?" (It may be difficult to understand the data when there are so many values, so using the spreadsheet to calculate the mean can help in understanding what is typical. It would definitely be faster to use the spreadsheet to calculate the mean than doing it by hand.)
"What other statistics would be useful and easier to calculate using a spreadsheet?" (If the data set is large or the numbers are difficult to understand at a glance, the median, quartiles, interquartile range, mean absolute deviation, maximum, and minimum should all be easy for a computer to find from a list.)


correct_option_index: 0

1