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 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: 
Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems.

Answer: 
Yes. An initial step when solving for x in this problem requires the use of the addition formula for cosine on the left side of the equation.

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_pos_0

K

fl_problem_001097_pos_0

7

fl_problem_001894_pos_0

HS_0
standard_description: Organize, represent, and interpret data with up to three categories; ask and answer questions about the total number of data points, how many in each category, and how many more or less are in one category than in another.
problem_activity: Narrative
The purpose of this activity is for students to think of questions that can be answered using the data representation they create as they collect data from the class. Although there are two different sets of data, all of the questions students ask should be able to be answered using either data set. Questions are compiled during the synthesis and will be used in the following activity.
If necessary, use the provided blackline master instead of collecting data from the class. Cut the blackline master in half and give half the class data from Group A and the other half data from Group B.
Required Materials
Materials to Copy
Favorite Special Class Data
Launch
Groups of 2
“We are going to take another survey and ask questions about the data.”
Decide on a survey question the class would like to answer and three possible responses.
“Record the title of the data representation and each category.”
Demonstrate recording the titles.
Divide the class into Group A and Group B. Each partnership should have one person from each group.
“Group A is going to take the survey first. If you are in Group B, record the data in your book as I record it for all to see.”
Ask students in Group A the survey question and record the data on the table using tally marks and numbers.
“Now Group B is going to take the survey and Group A will record the data.”
Ask students in Group B the survey question and record the data on the table using tally marks and numbers.
Activity
“Now, think of as many questions as you can that can be answered using your data representation. Record your questions in your book if you would like.”
5 minutes: independent work time
Student Facing
Our favorite __________________________________________________
| category 1                     \(\phantom{\hspace{2.5cm} \\ \hspace{2.5cm}}\) | category 2                     \(\phantom{\hspace{2.5cm} \\ \hspace{2.5cm}}\) | category 3                     \(\phantom{\hspace{2.5cm} \\ \hspace{2.5cm}}\) |
|-------------------------------------------------------------------------------|-------------------------------------------------------------------------------|-------------------------------------------------------------------------------|
|                \(\phantom{\hspace{2.5cm} \\ \hspace{2.5cm}}\)                 |                                                                               |                                                                               |
Student Response
Teachers with a valid work email address can
click here to register or sign in
for free access to Student Response.
Advancing Student Thinking
If students make statements instead of questions, consider asking:
“What is the question you want your partner to answer?”
“How could you finish this question, ‘How many students chose _____?’”
Activity Synthesis
Share and record the students’ questions about their data.
“Now we will ask our partner some of these questions.”


aligns: yes