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: Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. For example, given the rule “Add 3” and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way.
problem_activity: Narrative
In this optional activity, students investigate patterns in multiples of 15 and analyze and describe features of the digits in the tens and ones place. The activity also prompts them to consider why those features exist and to predict whether a given number could be a multiple of 15. The goal here is not to elicit clear justifications, but rather to encourage students to use their understanding of place value and numbers in base-ten to reason more generally about patterns in numerical patterns.
This activity uses
MLR5 Co-craft Questions
. Advances: writing, reading, representing
Launch
Groups of 2
MLR5 Co-Craft Questions
Display only the opening sentence and list of numbers, without revealing the question(s).
“Write a list of mathematical questions that could be asked about this situation.”
2 minutes: independent work time
2–3 minutes: partner discussion
Invite several students to share one question with the class. Record responses.
“What do these questions have in common? How are they different?”
Reveal the task (students open books), and invite additional connections.
“Let’s see what patterns we can find when we count by 15.”
Activity
“Take a few quiet minutes to work on the activity. Afterwards, discuss your responses with your partner.”
5 minutes: independent work time
5 minutes: partner discussion
Monitor for:
the different patterns students notice
the different ways they explain the patterns
the ways students reason about whether 250 could be a number being called out
Student Facing
Elena counted by 15 and recorded the numbers she counted:
15
30
45
60
75
90
Write the next four numbers she’d record if she kept going.
What patterns do you see? Describe as many as you can.
Choose one pattern that you noticed and explain why you think it happens.
Could 250 be a number that Elena calls out if she continued to count by 15? Explain or show your reasoning.
Student Response
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Advancing Student Thinking
To answer the last question, students may try to count up by 15 and see if they would reach 250. Encourage students to see if any of the patterns they noticed could help them answer the question.
Activity Synthesis
Invite students to share the patterns they noticed and their explanations for the patterns. Record them for all to see.
Select other students to share their explanation on whether 250 could be a number that Elena calls said. Highlight explanations that make use of the structure in the numbers.


correct_option_index: 0