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: 
Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size.
 Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, and 8.

Problem/activity:
Task
 Arrange the fractions in order from least to greatest. Explain your answer with a picture.
 $\frac{1}{5}, \frac{1}{7}, \frac{1}{3} $
 $\frac{2}{5}, \frac{2}{7}, \frac{2}{3} $
 $\frac{5}{6}, \frac{3}{6}, \frac{1}{6} $
 $\frac{5}{12}, \frac{8}{12}, \frac{4}{12} $

Answer: 
Yes. By arranging the fractions in this problem, students learn to compare fractions by reasoning about their size.

Example 3:
Concept/skill: 
Fluently add and subtract multi-digit whole numbers using the standard algorithm.
Grade 4 expectations in this domain are limited to whole numbers less than or equal to 1,000,000.

Problem/activity:
Problem 1
Solve using the standard algorithm. If you get stuck, use an area model and/or the partial products algorithm to help. Then assess the reasonableness of your answer.
a.
$$5,803\times46$$
b.
$$63\times2,116$$
Problem 2
Dunkin' introduced a croissant doughnut in 2014. In the first three months of its debut, they sold 7,870 dozen of them per day. How many croissant doughnuts were sold in the first three months?


Answer: 
No. This set of problems does not directly involve adding or subtracting multi-digit whole numbers. Instead, it focuses on multiplying multi-digit whole numbers.

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

im_task_000157_pos_0

3

fl_problem_000674_neg_0

5
standard_description: Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally.
problem_activity: Task
Complete the table below. Is $\Delta x$ a constant?  If so, what constant is it? What do you notice about the 3rd column of the table?
| $x$ | $f(x)=128\cdot \left({\frac {1}{2}}\right)^x$ |               Successive quotients                |
|-----|-----------------------------------------------|---------------------------------------------------|
|  0  |                      128                      |                       ----                        |
|  1  |                      64                       | $\frac{f(1)}{f(0)}=\frac {64}{128} = \frac{1}{2}$ |
|  2  |                                               |               $\frac{f(2)}{f(1)}=$                |
|  3  |                                               |                                                   |
|  4  |                                               |                                                   |
Complete the table below. Is $\Delta x$ a constant?  If so, what constant is it? What do you notice about the 3rd column of the table?
| $x$ | $f(x)=128\cdot \left({\frac {1}{2}}\right)^x$ |                Successive quotients                 |
|-----|-----------------------------------------------|-----------------------------------------------------|
|  0  |                      128                      |                         ---                         |
|  2  |                      32                       | $\frac{f(2)}{f(0)} = \frac {32}{128} = \frac{1}{4}$ |
|  4  |                                               |                $\frac{f(4)}{f(2)}=$                 |
|  6  |                                               |                                                     |
|  8  |                                               |                                                     |
Let $f(x)=a \cdot b^x$. Let $x_0$ be any particular $x$-value. Show that if $x_0$ is increased by a constant, $\Delta x$, the successive quotient  $$\frac{f(x_0+ \Delta x)}{f(x_0)}$$ is always the same no matter what $x_0$ is.
Is b) an example of the result of c)? Explain.


aligns: no