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: Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.  For example, if the function h(n) gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function.
problem_activity: Activity
First, students examine several examples of functions and non-functions from the perspective of “Can we figure out . . . ?” Then, they decide which of the functions can be represented by a given expression.
Launch
Allow quiet think time to consider the situations in the first question and answer yes or no. Ensure students understand which ones are functions, and which are not. Then, give students time to complete the table.
Student Facing
For each question, answer yes or no.
It is 50 miles to Tucson. Can we figure out how many kilometers it is to Tucson?
It is 200 kilometers to Saskatoon. Can we figure out how many miles it is to Saskatoon?
A number is -3. Can we figure out its absolute value?
The absolute value of a number is 8. Can we figure out the number?
A circle has a diameter of 8 cm. Can we figure out its circumference?
A circle has a circumference of
\(10\pi\)
cm. Can we figure out its diameter?
A square has a side length of 6 units. Can we figure out its perimeter?
A rectangle has a perimeter of 30 meters. Can we figure out its width?
Which of the relationships are functions?
For each function definition in the table, match it with the situation, write a statement explaining which variable depends on which, and write an example using function notation. An example is done for you.
{"table": [{"_attributes": {"border": "1"}, "thead": [{"tr": [{"th": [{"_attributes": {"scope": "col"}, "_value": "function definition"}, {"_attributes": {"scope": "col"}, "_value": "situation"}, {"_attributes": {"scope": "col"}, "_value": "statement"}, {"_attributes": {"scope": "col"}, "_value": "example"}]}]}], "tbody": [{"tr": [{"td": [{"span": [{"_attributes": {"class": ["math"], "data-png-file-id": "23857"}, "_value": "\\(m(x) = 0.62x \\)"}]}, {"_value": "You know kilometers and want to find miles."}, {"_value": "Distance in miles depends on distance in kilometers, or, distance in miles is a function of distance in kilometers."}, {"span": [{"_attributes": {"class": ["math"], "data-png-file-id": "23898"}, "_value": "\\(m(100)=62\\)"}]}]}, {"td": [{"p": [{"span": [{"_attributes": {"class": ["math"], "data-png-file-id": "23943"}, "_value": "\\(f(x) = x \\boldcdot \\pi\\)"}]}, {}]}, {}, {}, {}]}, {"td": [{"p": [{"span": [{"_attributes": {"class": ["math"], "data-png-file-id": "23991"}, "_value": "\\(g(x) = 1.6x\\)"}]}, {}]}, {}, {}, {}]}, {"td": [{"p": [{"span": [{"_attributes": {"class": ["math"], "data-png-file-id": "24038"}, "_value": "\\(h(x) = 4x\\)"}]}, {}]}, {}, {}, {}]}, {"td": [{"p": [{"span": [{"_attributes": {"class": ["math"], "data-png-file-id": "24087"}, "_value": "\\(k(x) = |x|\\)"}]}, {}]}, {}, {}, {}]}]}]}]}
Student Response
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Activity Synthesis
Invite students to share their responses in the table, and how they know. Emphasize that there are many correct examples one could choose—the thing to understand is how function notation communicates an input and output to the function (or a value of the independent variable and corresponding value of the dependent variable.)


aligns: no