few_shots: 
Example 1:
Problem/activity:
Task
Materials
One 10-frame per pair of students (see example below)
[IMG]
Counters, 10 per pair of students
Decks of number cards 0-5 (with 4 of each number) or two 0-5 dice
Setup
This activity is done in pairs. The students sit side by side with 10-frame and deck of cards or dice. If they have cards, the cards are shuffled and placed face down in front of them.
Action
Player 1 flips a card or rolls the die. They place that many counters on the 10-frame. Player 2 flips a card or rolls the die. They place that many more counters on the 10-frame next to the counters already on the ten frame. The students count the total together.
A recording sheet can be added when the students have been introduced to equations and number sentences. For those students who can handle higher numbers, a deck of 0-10 cards and two 10-frames can be used.
This game can also be played alone.


Concept/skill: 
Represent addition and subtraction with objects, fingers, mental images, drawings (Drawings need not show details, but should show the mathematics in the problem. (This applies wherever drawings are mentioned in the Standards.)), sounds (e.g., claps), acting out situations, verbal explanations, expressions, or equations.

Answer: 
Yes. This task involves representing addition with objects such as number cards and dice.

Example 2:
Problem/activity:
For each pair of numbers, determine if the values are equivalent. Explain your reasoning for each one.
a.
$$-0.25$$
and
$$\frac{1}{-4}$$
b.
$$-\left ( \frac{1}{4} \right )$$
and
$$\frac{-1}{-4}$$
c.
$$\frac{-1}{4}$$
and
$$-\frac{1}{4}$$


Concept/skill: 
Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.

Answer: 
No. The expressions shown in this problem do not involve multiplying fractions with other fractions, nor whole numbers with fractions.

Example 3:
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.

Now, does the problem or activity shown below enable students to learn the full intent of the following concept or skill?

shot_info: im_task_001477_pos_0

K

fl_problem_001097_neg_0

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fl_problem_001894_pos_0

HS_0
standard_description: 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
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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.)


aligns: yes