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 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 following problem or activity enable students to learn the full intent of the following concept or skill?

shot_info: im_task_001477_neg_0

K

fl_problem_001097_neg_0

7

fl_problem_001894_neg_0

HS_0
standard_description: Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output. (Function notation is not required in Grade 8.)
problem_activity: Activity
In this activity, students choose a graphing window to tell a particular story.
Launch
Continue access to graphing technology. Students may be ready to dive into the activity without much assistance, or may need to engage in a notice and wonder to familiarize themselves with the context and the information encoded in the equation and the graph.
Student Facing
Suppose
\(y=0.50d + 4\)
represents the cost of renting a car,
\(y\)
, as a function of miles driven,
\(d\)
. Here’s a graph representing the function.
[IMG]
What is the graphing window used for the given graph?
Find a graphing window so that:
It gives the impression that the charge per mile driven is very high and the total rental cost gets really expensive really fast.
It gives the impression that the charge for every mile driven is close to nothing and the total rental cost will be pretty low even if the car is driven many miles.
Student Response
Teachers with a valid work email address can
click here to register or sign in
for free access to Student Response.
Activity Synthesis
Invite selected students to share their responses. Questions for discussion:
“What adjustments to the graphing window make the cost seem lower? What adjustments make the cost seem higher?” (The graph in the second question make the cost seem lower, because the graph looks quite flat and close to the horizontal axis. The graph is the first question make the cost seem higher, because the graph looks quite steep.)
“For each situation, how did you decide whether to make the graph look flatter or steeper?” (I thought about whether the situation suggested the function should be increasing slowly or quickly.)
“What were some strategies to make the graph look flatter?” (Keep the domain the same or smaller, and make the range larger.)
“What were some strategies to make the graph look steeper?” (Keep the range the same, and make the domain larger.)
“In most graphing technology, you can zoom in or zoom out. Why might you want to set a specific graphing window, instead of zooming in or out?” (Zooming in or out often doesn’t change the overall shape of the graph, because the domain and range are being scaled by the same amount. Choosing a specific graphing window allows you more control over what is shown.)


aligns: no