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 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_pos_0

7

fl_problem_001894_pos_0

HS_0
standard_description: Identify whether the number of objects in one group is greater than, less than, or equal to the number of objects in another group, e.g., by using matching and counting strategies (include groups with up to ten objects).
problem_activity: Narrative
The purpose of this activity is for students to learn stage 3 of the Less, Same, More center. Students draw groups that have more, fewer, or the same number of images as a given group. Consider using a sheet protector or laminating the mats for students to use with dry erase markers. Otherwise, make multiple copies of the mats for each group.
MLR8 Discussion Supports.
If necessary, invite students to repeat their reasoning to describe their comparison to a partner using mathematical language: “Can you say that again using the words more/fewer/the same?”
Advances: Listening, Speaking
Required Materials
Materials to Gather
Sheet protectors
Materials to Copy
Less, Same, More Mat
Image Cards Grade K
Required Preparation
Each group of 2 needs a set of cards from the blackline master.
Launch
Groups of 2
Give students the mats and cards.
“We are going to learn a new way to play the Less, Same, More center. It is called Less, Same, More, Drawings.”
“First, draw a card and place it at the top of the mat. Figure out how many things are on the card.”
Point to each square as you explain: “Draw three groups in the squares below. Draw one group that has fewer things, one group that has the same number of things, and one group that has more things.”
“Switch mats with your partner. Check to be sure you agree with the groups your partner made.”
“Choose one of the groups you drew to describe with a sentence using ‘more,’ ‘fewer,’ or ‘the same number’.”
“When you are finished, place a new card at the top of your mat and draw groups that have more, fewer, and the same number in the squares.”
Activity
10 minutes: partner work time
Activity Synthesis
Display the card with 5 dots in a number cube arrangement:
[IMG]
“Draw a group that has fewer images.”
1 minute: independent work time
“How many images are in the group you drew?”
Share responses.
“Did all of our groups have the same number of things? Why?” (No, some people drew groups with 2 things and some people drew groups with 4 things. 4 and 2 are both less than 5.)
“Did all of our groups have fewer than 5 things?” (Yes.)


aligns: yes