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.


Standard options: 
A. 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.
B. For any number from 1 to 9, find the number that makes 10 when added to the given number, e.g., by using objects or drawings, and record the answer with a drawing or equation.
C. Decompose numbers less than or equal to 10 into pairs in more than one way, e.g., by using objects or drawings, and record each decomposition by a drawing or equation (e.g., 5 = 2 + 3 and 5 = 4 + 1).
D. Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem.
E. Fluently add and subtract within 5.


Your response:
Thought: This task involves representing addition with objects such as number cards and dice.
Answer: A

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


Standard options: 
A. Solve real-world and mathematical problems involving the four operations with rational numbers. (Computations with rational numbers extend the rules for manipulating fractions to complex fractions.)
B. Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.
C. Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram.


Your response:
Thought: 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).
Answer: B

Example 3:
Problem/activity:
Find the general solution for:
$${\mathrm{cos}\left({\pi\over2}+x\right)=\mathrm{tan}{\pi\over4}}$$


Standard options: 
A. Prove the Pythagorean identity sin^(2)(θ) + cos^(2)(θ) = 1 and use it to find sin(θ), cos(θ),or tan(θ) given sin(θ), cos(θ), or tan(θ) and the quadrant of the angle.
B. Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems.


Your response:
Thought: 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. Solving this problem does not require use of the Pythagorean identity.
Answer: B

Now, assign the following problem or activity to one or more relevant standards it aligns with.
shot_info: im_task_001477

K

fl_problem_001097

7

fl_problem_001894

HS_0
options: Order three objects by length; compare the lengths of two objects indirectly by using a third object.

Express the length of an object as a whole number of length units, by laying multiple copies of a shorter object (the length unit) end to end; understand that the length measurement of an object is the number of same-size length units that span it with no gaps or overlaps. Limit to contexts where the object being measured is spanned by a whole number of length units with no gaps or overlaps.
problem_activity: Narrative
The purpose of this activity is for students to compare the length of two objects using a third object. When students decide if the teacher's desk will fit through the door or compare other large pieces of furniture, they will need to be precise about which lengths they are measuring as objects like the teacher's desk, a rug, and a bookcase, have a length, width, and in some cases a height (MP6). Next, they will need to select an appropriate third object to use to compare the lengths they have chosen. Teachers may choose to assign different questions for different groups to start with to facilitate student movement around the room. Teachers may also change any question that does not apply to their classroom.
MLR8 Discussion Supports.
Synthesis: For each observation that is shared, invite students to turn to a partner and restate what they heard using precise mathematical language.
Advances: Listening, Speaking
Engagement: Provide Access by Recruiting Interest.
Provide choice. Invite students to decide which problem to start with and the order to complete the task.
Supports accessibility for: Attention, Social-Emotional Functioning
Required Materials
Materials to Gather
Materials from a previous activity
Required Preparation
Each group needs measuring materials from the previous activity.
Launch
Groups of 2
Give students access to measuring materials.
“Have you ever seen someone move a large piece of furniture, like a couch, from one room to another? Is it easy to move big pieces of furniture? Why or why not?”
30 seconds: quiet think time
Share responses.
“I have been thinking about getting a new desk. If I do, I will have to move this desk out of the room. I am not sure if this desk will fit through the door. How can we check to see if it will fit?” (We could measure with a string.)
30 seconds: quiet think time
1 minute: partner discussion
Share responses.
“You are all going to check to see if my desk will fit through the door. You are also going to compare the length of some other objects in the room.”
Activity
15 minutes: partner work time
Monitor for a group that measures the width of the teacher's desk and one that measures the length.
Student Facing
Will the teacher’s desk fit through the door?
Show your thinking using drawings, numbers, or words.
Will a student desk fit through the door?
Show your thinking using drawings, numbers, or words.
Which is longer, the bookshelf or the rug?
Show your thinking using drawings, numbers, or words.
Which is longer, the file cabinet or the bookshelf?
Show your thinking using drawings, numbers, or words.
Which is shorter, the bookshelf or the teacher’s desk?
Show your thinking using drawings, numbers, or words.
Will the teacher’s desk fit next to the bookshelf?
Show your thinking using drawings, numbers, or words.
Student Response
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Activity Synthesis
Invite previously identified students to share.
For each student, ask: “How did they compare the length of the objects? What tool did they use? What part of each object did they measure?”


correct_option_index: 0