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: 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).

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.

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.

Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem.

Fluently add and subtract within 5.
problem_activity: Narrative
The purpose of this activity is for students to make sense of a questionless Put Together/Take Apart, Both Addends Unknown story problem. In this activity, students are asked to show what Lin’s apples could have looked like. The focus of this activity is for students to show the two groups of apples, rather than on answering specific questions about how many red apples and how many yellow apples Lin had. While students may notice that there is more than one possible solution to the story problem, that is not highlighted until the next lesson.
When students explain to a partner how they have represented the apples they reason abstractly and quantitatively (MP2).
MLR8 Discussion Supports.
Use multimodal examples to show the meaning of “some of” and “the rest of.” Use verbal descriptions along with gestures, drawings, or concrete objects to show the groupings.
Advances: Listening, Representing
Required Materials
Materials to Gather
Connecting cubes
Two-color counters
Launch
Groups of 2
Give students access to connecting cubes and 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
Monitor for students who accurately retell the story. Choose at least one student to share with the class.
“Use objects or drawings to show what Lin’s apples could look like.”
Activity
3 minutes: independent work time
“Share how you showed Lin’s apples with your partner. Tell your partner how your objects or drawings show Lin’s apples.”
30 seconds: quiet think time
2 minutes: partner discussion
Monitor for students who use two-color counters to show 8 apples, some red and some yellow. Monitor for students who show different decompositions of 8, such as 5 and 3 and 4 and 4.
Student Facing
Lin picked 8 apples at the orchard.
Some of the apples were yellow.
The rest of the apples were red.
Student Response
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Activity Synthesis
Invite previously selected students to share.
As each student shares, ask:
“How many apples did Lin pick?”
“Where do you see the red apples that Lin picked?”
“Where do you see the yellow apples that Lin picked?”
“_____ used red and yellow counters to show Lin’s apples. What could I do if I wanted to draw a picture to show Lin’s apples?” (You could draw 4 red apples and 4 yellow apples. You could draw some circles. You could write r for red and y for yellow.)


correct_option_index: 1