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: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.)

Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2.
problem_activity: Narrative
This Info Gap activity gives students an opportunity solve problems about data represented on line plots. In both sets of cards, there is a partially complete line plot and some missing data.
For the first set of cards, the problem card has the missing data and the data card has a partially complete line plot. Monitor for students who:
request all the information on the data card and create a complete line plot which they may use to answer the question
only request the information they need to answer the question about the heaviest apricot and the most common weight
For the second set of cards, the problem card has the partially complete line plot and the data card has information to determine the missing data. Here students will likely need to communicate with each other as the information about the most common weight is vital to solve the problem, but the student with the problem card may not think to ask about this.
The Info Gap allows students to refine the language they use and ask increasingly more precise questions until they get the information they need (MP6).
Representation: Access for Perception.
Provide appropriate reading accommodations and supports to ensure student access to written directions, word problems, and other text-based content.
Supports accessibility for: Conceptual Processing, Memory
Required Materials
Materials to Copy
Info Gap: Picking Fruit
Required Preparation
Create a set of cards from the blackline master for each group of 2.
Launch
Groups of 2
MLR4 Information Gap
Recall, if necessary, the steps of the info gap routine.
“I will give you either a problem card or a data card. Silently read your card. Do not read or show your card to your partner.”
Distribute the first set of cards.
Remind students that after the person with the problem card asks for a piece of information, the person with the data card should respond with: “Why do you need to know (restate the information requested)?”
Activity
8–10 minutes: partner work time
After students solve the first problem, distribute the next set of cards. Students switch roles and repeat the process with Problem Card 2 and Data Card 2.
Student Facing
Your teacher will give you either a problem card or a data card. Do not show or read your card to your partner.
Pause here so your teacher can review your work.
Ask your teacher for a new set of cards and repeat the activity, trading roles with your partner.
Student Response
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Activity Synthesis
“What kinds of questions were the most useful to ask?”
(Card 1: I asked for the heaviest apricot and then realized it was one of the ones on my card. Then I asked for the most common weight and could solve the problem.
Card 2: I needed to find out what the rest of the apricot weights were. I tried asking for that but my partner did not have that information. My partner told me she had some information about the heaviest apricot and the most common weight and once I found that out I was able to solve the problem.)
Invite students to share their strategy for solving one of the problems.
Consider asking “Did anyone solve the problem in a different way?”


correct_option_index: 1