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: Correctly name shapes regardless of their orientations or overall size.
problem_activity: Narrative
The purpose of this activity is for students to find the missing value in addition and subtraction equations. This activity is optional because determining the missing value of an equation is not required by the standards. Students may “just know” some of the answers or they may use counting forward or backward (MP7) or they may draw a picture.
MLR8 Discussion Supports.
Invite students to read their completed equations aloud.
Advances: Listening, Speaking
Required Materials
Materials to Gather
Connecting cubes or two-color counters
Launch
Groups of 2
Give students access to connecting cubes or two-color counters.
Display the student book.
“What do you notice? What do you wonder?” (The equations have a number missing. Why are there numbers missing?)
30 seconds: quiet think time
1 minute: partner discussion
Share responses.
“FIll in the missing part of each equation.”
Activity
10 minutes: partner work time
Monitor for students who use two-color counters or connecting cubes.
Monitor for students who draw pictures.
Student Facing
Fill in the missing part of each equation.
\(3 - \underline{\hspace{1.1 cm}} = 2\)
\(2 + \underline{\hspace{1.1 cm}} = 2\)
\(5 - \underline{\hspace{1.1 cm}} = 2\)
\(1 + \underline{\hspace{1.1 cm}} = 2\)
\(5 - \underline{\hspace{1.1 cm}} = 3\)
\(2 + \underline{\hspace{1.1 cm}} = 3\)
\(4 - \underline{\hspace{1.1 cm}} = 3\)
\(0 + \underline{\hspace{1.1 cm}} = 3\)
\(5 - \underline{\hspace{1.1 cm}} = 4\)
\(3 + \underline{\hspace{1.1 cm}} = 4\)
\(4 - \underline{\hspace{1.1 cm}} = 4\)
\(2 + \underline{\hspace{1.1 cm}} = 4\)
\(1 + \underline{\hspace{1.1 cm}} = 5\)
\(4 + \underline{\hspace{1.1 cm}} = 5\)
\(5 - \underline{\hspace{1.1 cm}} = 5\)
\(3 + \underline{\hspace{1.1 cm}} = 5\)
Student Response
Teachers with a valid work email address can
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Activity Synthesis
Invite previously identified students to share.


aligns: no