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.


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: Count to 120, starting at any number less than 120. In this range, read and write numerals and represent a number of objects with a written numeral.
problem_activity: Narrative
The purpose of this activity is for students to learn stage 2 of the Write Numbers center. Like the last stage of this center, students take turns writing the next one, two, or three numbers. The player who writes the last number on the board wins. Students may choose to count forward or backward. In this stage, students count by 10 starting at numbers other than 10.
MLR8 Discussion Supports.
Revoice student ideas to demonstrate and amplify mathematical language use. For example, revoice the student statement “the first number changes” as “the number in the tens place increases by one.”
Advances: Speaking
Required Materials
Materials to Gather
Dry erase markers
Sheet protectors
Materials to Copy
Write the Number Stage 2 Gameboard
Required Preparation
Put each gameboard in a sheet protector.
Launch
Groups of 2
Give each group a gameboard and a dry erase marker.
“We are going to learn a new way to do the Write Numbers center.”
Display the gameboard.
“You and your partner will practice writing numbers. Just like the last time we played this game, you will fill in the number path on the gameboard. You can decide to start with the smaller number and count forward, or start with the larger number and count backward. On each turn, you can decide whether you would like to write one, two, or three numbers on the gameboard. The person who writes the last number on the board is the winner.”
“Today you will not write every number in the sequence. You will count by ten and write each number you say.”
Demonstrate playing one round with the students.
“Now you will play with your partner.”
Activity
10 minutes: partner work time
Activity Synthesis
“What do you notice about each number on the gameboard?” (They all have the same amount of ones. The tens go up by one in each number.)


correct_option_index: 0