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: 
Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem.

Answer: 
No. Though this task involves addition, it does not involve any word problems.

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 and division and of fractions to multiply and divide rational numbers.

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


Concept/skill: 
Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles.

Answer: 
No. This problem does not directly teach how side ratios in right triangles lead to definitions of trigonometric ratios. Instead, it involves solving a trigonometric function.

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_neg_0

K

fl_problem_001097_pos_0

7

fl_problem_001894_neg_0

HS_0
standard_description: Represent addition, subtraction, multiplication, and conjugation of complex numbers geometrically on the complex plane; use properties of this representation for computation. For example, (-1 + Ö3i)^(3) = 8 because (-1 + Ö3i) has modulus 2 and argument 120°.
problem_activity: The estimated size for a population of rabbits and a population of coyotes in a desert habitat are shown in the table. The estimated population sizes were recorded as a part of a long-term study related to the effect of commercial development on native animal species.
{"table": [{"_attributes": {"class": ["table", "table-bordered"], "style": "width:100%"}, "tbody": [{"tr": [{"td": [{"em": [{"_value": "n"}], "_values": ["Years since initial count (", ")"]}, {"_value": "0"}, {"_value": "3"}, {"_value": "6"}, {"_value": "9"}, {"_value": "12"}, {"_value": "15"}, {"_value": "18"}, {"_value": "21"}, {"_value": "24"}]}, {"td": [{"em": [{"_value": "r"}], "_values": ["Estimated number of rabbits (", ")"]}, {"_value": "14,989"}, {"_value": "10,055"}, {"_value": "5,002"}, {"_value": "10,033"}, {"_value": "15,002"}, {"_value": "10,204"}, {"_value": "4,999"}, {"_value": "10,002"}, {"_value": "14,985"}]}, {"td": [{"em": [{"_value": "c"}], "_values": ["Estimated number of coyotes (", ")"]}, {"_value": "1,995"}, {"_value": "2,201"}, {"_value": "2,003"}, {"_value": "1,795"}, {"_value": "1,999"}, {"_value": "2,208"}, {"_value": "2,010"}, {"_value": "1,804"}, {"_value": "2,001"}]}]}]}]}
Below are sketches of each graph, with a curve fitted to the data.
[IMG]
[IMG]
Write the function for each situation and then calculate the two different numbers of years where the population estimate is about 13,000 for rabbits and 2,100 for coyotes.


aligns: no