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: Describe objects in the environment using names of shapes, and describe the relative positions of these objects using terms such as above, below, beside, in front of, behind, and next to.

Identify shapes as two-dimensional (lying in a plane, “flat”) or three-dimensional (“solid”).

Correctly name shapes regardless of their orientations or overall size.
problem_activity: Narrative
The purpose of this activity is for students to learn stage 1 of the Match Mine center. Students use positional words to describe the location of pattern blocks within a larger shape. Students may initially describe the shapes generally or use positional words other than those introduced in the previous activity. Students need repeated experiences hearing positional words in order to develop precision with their language (MP6).
MLR8 Discussion Supports.
For each description that is shared, invite students to turn to a partner and restate what they heard using precise mathematical language, specifically positional words.
Advances: Listening, Speaking
Required Materials
Materials to Gather
Pattern blocks
Launch
Groups of 2
Give students access to pattern blocks.
“We are going to learn a new center called Match Mine. Let’s practice describing a shape together.”
Build a shape with 5 pattern blocks.
“How could we describe where the square is in this shape?” (The square is below the hexagon.)
“How could we describe where the triangle is?” (The triangle is next to the square.)
“One partner will build a shape using 5 pattern blocks. Then they will tell their partner about the shape and their partner tries to make the same shape.”
“Remember to use positional words that will help your partner put each pattern block in the right place.”
“Keep your shapes hidden while you build them. When your partner is done making the shape, check to see if they match.”
“Take turns building and describing shapes with your partner.”
Activity
8 minutes: partner work time
Monitor for students who describe the location of each pattern block using positional words.
Activity Synthesis
Display a shape made up of 5 pattern blocks, including a triangle.
“How would you tell your partner where to put the triangle?”


correct_option_index: 0