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: 
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_pos_0

K

fl_problem_001097_neg_0

7

fl_problem_001894_neg_0

HS_0
standard_description: Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.
problem_activity: Warm-up
In this warm-up, students are prompted to compare function values. To do so, they need to interpret statements in function notation and connect their interpretations to the graph of the function.
Previously, students recognized that if a point with coordinates
\((2,20)\)
is on the graph of a function, the 2 is an input and the 20 is a corresponding output. Here, they begin to see the second value in a coordinate pair more abstractly, as
\(f(2)\)
when the input is 2, or as
\(f(4)\)
when the input is 4.
Launch
Give students 1–2 minutes of quiet think time. Follow with a whole-class discussion.
Some students might be unfamiliar with drones. If needed, give a brief explanation of what they are.
Student Facing
[IMG]
Here is a graph that represents function
\(f\)
, which gives the height of a drone, in meters,
\(t\)
seconds after it leaves the ground.
[IMG]
Decide which function value is greater.
\(f(0)\)
or
\(f(4)\)
\(f(2)\)
or
\(f(5)\)
\(f(3)\)
or
\(f(7)\)
\(f(t)\)
or
\(f(t+1)\)
Student Response
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Activity Synthesis
Invite students to share how they compared each pair of outputs. If not mentioned in students’ explanations, point out that for each pair, what we are comparing are the vertical values of the points on the graph at different horizontal values. Even though the statements don’t tell us the values of, say
\(f(3)\)
and
\(f(7)\)
, and the vertical axis shows no scale, we can tell from the graph that the function has a greater value when
\(t\)
is 3 than when
\(t\)
is 7.
Tell students that the coordinates
\((0, f(0))\)
represent the starting point of the drone. Ask students, “What are the coordinates of the points when the drone starts leveling off? When it starts to descend? When it lands?” (
\((2, f(2)), (5,f(5))\)
, and
\((7,f(7))\)
, respectively.)
Highlight that the coordinates of each point on a graph of a function are
\((x, f(x))\)
.
Discuss with students how they compared
\(f(t)\)
and
\(f(t+1)\)
(in the last question). Make sure students see that the
\(f(t+1)\)
could be less than, equal to, or greater than
\(f(t)\)
, depending on the value of
\(t\)
.
If
\(t\)
is 2, then
\(t+1\)
is 3. From the graph, we can see that
\(f(2)\)
is equal to
\(f(3)\)
because the graph has the same vertical value when
\(t\)
is 2 and 3.
If
\(t\)
is 5, then
\(t+1\)
is 6. From the graph, we can see that
\(f(5)\)
is greater than
\(f(6)\)
because the graph has a greater vertical value when
\(t\)
is 5 than when
\(t\)
is 6.


aligns: yes