few_shots: 
Example 1:
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.

Problem/activity:
Task
Materials
One 10-frame per pair of students (see example below)
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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.


Answer: 
Yes. This task involves representing addition with objects such as number cards and dice.

Example 2:
Concept/skill: 
Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.

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
$$-\frac{1}{4}$$


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

Problem/activity:
Find the general solution for:
$${\mathrm{cos}\left({\pi\over2}+x\right)=\mathrm{tan}{\pi\over4}}$$


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, determine whether the following problem or activity can enable students to understand the concepts or skills in the provided description.

shot_info: im_task_001477_pos_0

K

fl_problem_001097_pos_0

7

fl_problem_001894_pos_0

HS_0
standard_description: Apply properties of operations as strategies to add and subtract. (Students need not use formal terms for these properties.) Examples: If 8 + 3 = 11 is known, then 3 + 8 = 11 is also known. (Commutative property of addition.) To add 2 + 6 + 4, the second two numbers can be added to make a ten, so 2 + 6 + 4 = 2 + 10 = 12. (Associative property of addition.)
problem_activity: Narrative
The purpose of this activity is for students to solve a Put Together/Take Apart, Both Addends Unknown story problem about dates stuffed with cheese or almonds in more than one way. In the activity synthesis, students share their solutions. As students share, record their drawings and solutions systematically, as shown:
1 cheese, 7 almond
2 cheese, 6 almond
3 cheese, 5 almond
4 cheese, 4 almond
5 cheese, 3 almond
6 cheese, 2 almond
7 cheese, 1 almond
Only record solutions that students find for the problem. Leave an empty space if a combination isn’t shared.
In the lesson synthesis, students discuss whether a solution of 3 dates stuffed with cheese and 5 dates stuffed with almonds is the same solution as 5 dates stuffed with cheese and 3 dates stuffed with almonds. The purpose of the question is for students to think about and discuss what decompositions of numbers mean in context (MP2, MP6). There is no correct answer to the question. Some students may determine that both solutions are the same because they both showed 5 and 3 while other students may determine that the solutions are different because there are different numbers of dates stuffed with cheese and dates stuffed with almonds (MP3).
Representation: Internalize Comprehension.
Synthesis: Reiterate the fact that in this problem there is more than one answer. Make a connection between the solutions that were found and that they all add up to the same total number of dates.
Supports accessibility for: Conceptual Processing
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.
Read and display the task statement.
“Tell your partner what happened in the story.”
30 seconds: quiet think time
1 minute: partner discussion
“What are we trying to figure out?” (How many of the dates were stuffed with cheese and how many of the dates were stuffed with almonds?)
30 seconds: quiet think time
1 minute: partner discussion
“Show your thinking using drawings, numbers, words, or objects.”
Activity
2 minutes: quiet work time
2 minutes: partner discussion
“Write an expression to show how many of the dates were stuffed with cheese and how many were stuffed with almonds.”
1 minute: independent work time
“As you walk around, look to see if you can find other ways to solve the story problem.”
5 minutes: gallery walk
Student Facing
Andre and his older brother have 8 dates.
They stuff some of the dates with cheese.
They stuff the rest of the dates with almonds.
How many of the dates did they stuff with cheese?
Then how many of the dates did they stuff with almonds?
Expression: _______________________________
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Student Response
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Activity Synthesis
Invite students to share their solution or solutions they found during the gallery walk. Record student solutions as explained in the activity narrative.
“What do you notice? What do you wonder?” (2 and 6 is there but not 6 and 2. When it’s 4 and 4, there are the same number of cheese dates and almond dates. The first numbers are getting bigger and the second numbers are getting smaller.)
“Are there any other ways that we can solve the problem? What makes you think that?”
Record each student solution with an equation.


aligns: no