few_shots: Example 1:
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.


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.


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.


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.


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: Understand the relationship between numbers and quantities; connect counting to cardinality.

Count to answer “how many?” questions about as many as 20 things arranged in a line, a rectangular array, or a circle, or as many as 10 things in a scattered configuration; given a number from 1–20, count out that many objects.
problem_activity: Narrative
The purpose of this activity is for students to identify examples of circles and triangles. The geometric terms
circle
and
triangle
are formally introduced, though some students may already be familiar with the terms and may have heard or used them in previous lessons. This activity exposes students to a wider variety of circles and triangles than they may have seen previously, which encourages students to expand their concepts of the shapes. Students may incorrectly identify some shapes as triangles or circles, particularly distactors, such as a shape that looks like a triangle but has 4 sides. These shapes can be discussion points and are expected throughout kindergarten. Students distinguish between defining and non-defining attributes of shapes in grade 1.
MLR8 Discussion Supports.
To support the transfer of new vocabulary to long term memory, invite students to chorally repeat these words in unison 1–2 times: circles, triangles.
Advances: Listening, Speaking
Representation: Access for Perception.
Synthesis: Students might need extra support determining that the oval and the pizza slice shapes are not circles or triangles. Hold up a triangle and circle next to the shapes to visually show that the oval and pizza slice shapes do not match the triangle and circle.
Supports accessibility for: Visual-Spatial Processing
Required Materials
Materials to Gather
Colored pencils or crayons
Required Preparation
Each student needs at least 2 different colored crayons or colored pencils.
Launch
Groups of 2
Give each student access to 2 different color crayons or colored pencils.
Display the image from the book.
“Mai put her shapes into 2 groups. What do you notice? Why do you think Mai put these shapes together?”
30 seconds: quiet think time
Share responses.
“What can we name each group?”
30 seconds: quiet think time
30 seconds: partner discussion
Share responses.
“We can call this group
circles
. All of the shapes in this group are circles. We can call this group
triangles
because all of the shapes in this group are triangles.”
“What do you know about circles?”
30 seconds: quiet think time
30 seconds: partner discussion
Share and record responses.
“What do you know about triangles?”
30 seconds: quiet think time
30 seconds: partner discussion
Share and record responses.
Display student workbook.
“Color all of the circles that you find with 1 color. Then color all of the triangles that you find with another color.”
Activity
4 minutes: independent work time
“Choose 1 triangle that you colored in. Tell your partner 1 thing that you know about that shape.”
30 seconds: quiet think time
30 seconds: partner discussion
“Write a number to show how many triangles you colored. Write a number to show how many circles you colored.”
1 minute: independent work time
“Did you color more triangles or more circles? How do you know?”
30 seconds: quiet think time
30 seconds: partner discussion
Student Facing
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Student Response
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Activity Synthesis
Display shape from student book or draw shape:
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“Did you color this shape? Why or why not?” (I didn’t color the shape. It looks like a triangle but one of the sides is round.)
Display shape from student book or draw shape:
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“Did you color this shape? Why or why not?” (I didn’t color this shape. It looks like a circle but it is stretched out.)


correct_option_index: 1