few_shots: 
Example 1:
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.

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.


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

Example 2:
Concept/skill: 
Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.

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
$$-\frac{1}{4}$$


Answer: 
Yes. This problem involves understanding fractions and division to divide rational numbers, such as 1, -4, 4, and -1. This problem also involves an understanding of multiplication: if p and q are integers, then -(p/q) = (-p)/q = p/(-q).

Example 3:
Concept/skill: 
Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems.

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


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, determine whether the following problem or activity can enable students to understand the concepts or skills in the provided description.

shot_info: im_task_001477_pos_0

K

fl_problem_001097_pos_0

7

fl_problem_001894_pos_0

HS_0
standard_description: Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units.
problem_activity: Problem 1
The table below shows the distance that Ms. Smith's fourth graders ran before stopping for a rest.
| Student | Distance (in miles) |
|---------|---------------------|
|   Joe   |  $${2{1\over2}}$$   |
| Arianna |  $${1{3\over4}}$$   |
|  Bobbi  |  $${2{1\over8}}$$   |
| Morgan  | $${1{{5\over8}}}$$  |
|  Jack   | $${2{{5\over8}}}$$  |
|  Sasha  |  $${2{1\over4}}$$   |
|  Tyler  |  $${2{2\over4}}$$   |
|  Jenny  |   $${{5\over8}}$$   |
|  Anson  |  $${2{2\over8}}$$   |
| Chandra |  $${2{4\over8}}$$   |
Using the information in the table, answer the following questions:
a.   What was the longest distance a student ran?
b.   What was the shortest distance a student ran?
c.   What was the most common distance that students ran?
Problem 2
Use the data from Anchor Task #1 to create a line plot.
Problem 3
a.   With a partner or group, gather a handful of round buttons from a diverse collection and use a ruler to measure the diameter of each button to the nearest eighth inch.
b.   Make a dot plot of button diameters, marking your scale in eighth-inch increments.
c.   What is the most common diameter in your collection? How does that compare with the collection from another group?
d.   Now measure the diameters of these same buttons to the nearest quarter inch.
e.   Make a dot plot of button diameters, marking your scale in quarter-inch increments.
f.   Describe the differences between the two dot plots you created. Which one gives you more information? Which one is easier to read?


aligns: no