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: Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume.
problem_activity: Narrative
The purpose of this activity is for students to connect written multiples of 10 to base-ten representations. Students notice a connection between how the numbers are said, written, and represented with tens. For example, “70” has the word “seven” as it is said, the digit “7” when it is written, and is represented with seven tens. Each number name is written under the number in this activity. Students are not expected to spell number names.
MLR8 Discussion Supports.
Invite students to begin partner interactions by repeating the question, “How did you match the towers of 10 to the written numbers?” This gives both students an opportunity to produce language.
Advances: Conversing
Required Materials
Materials to Gather
Connecting cubes
Materials to Copy
It's a Match (10-90) words, numbers, pictures
Launch
Groups of 2
Give each student a blackline master and access to connecting cubes.
Activity
Read the task statement from the blackline master.
5 minutes: independent work time
3 minutes: partner discussion
Monitor for students who count the number of towers, match correctly, and can explain how they knew.
Student Response
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Activity Synthesis
Invite previously identified students to share.
“How did you know which representations matched?” (I counted by ten and found the number. I said 10, 20, 30, 40, 50, and found 50.)


aligns: no