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:
{
  "explanation": "This task involves representing addition with objects such as number cards and dice.",
  "answer": "A"
}

Example 2:
Problem/activity:
Task
 Arrange the fractions in order from least to greatest. Explain your answer with a picture.
 $\frac{1}{5}, \frac{1}{7}, \frac{1}{3} $
 $\frac{2}{5}, \frac{2}{7}, \frac{2}{3} $
 $\frac{5}{6}, \frac{3}{6}, \frac{1}{6} $
 $\frac{5}{12}, \frac{8}{12}, \frac{4}{12} $

Standard options: 
A. Understand a fraction as a number on the number line; represent fractions on a number line diagram.
Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, and 8.
B. Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size.
Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, and 8.
C. Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b.
Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, and 8.


Your response:
{
  "explanation": "By arranging the fractions in this problem, students learn to compare fractions by reasoning about their size.",
  "answer": "B"
}

Example 3:
Problem/activity:
Problem 1
Solve using the standard algorithm. If you get stuck, use an area model and/or the partial products algorithm to help. Then assess the reasonableness of your answer.
a.
$$5,803\times46$$
b.
$$63\times2,116$$
Problem 2
Dunkin' introduced a croissant doughnut in 2014. In the first three months of its debut, they sold 7,870 dozen of them per day. How many croissant doughnuts were sold in the first three months?


Standard options: 
A. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.
B. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.
C. Fluently multiply multi-digit whole numbers using the standard algorithm.


Your response:
{
  "explanation": "This set of problems involves multi-digit whole numbers because the numbers in each problem are four and two digit integers, and the mathematical calculations involved in both problems focus on multiplication. The first problem explicitly asks the student to solve its subproblems using the standard algorithm.",
  "answer": "C"
}

Now, assign the following problem or activity to one or more relevant standards it aligns with.
shot_info: im_task_001477

K

im_task_000157

3

fl_problem_000674

5
options: Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers.

Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true.

Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.

Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams.
problem_activity: Optional activity
This activity is optional due to time considerations. The purpose of this activity is for students to reason about whether given values make an inequality true and justify their answers using inequality statements and graphs (MP3). Students explored this concept in the previous activity, so they should work to articulate how they check if a number is a solution to an inequality statement and an inequality on a number line.
Students will play a game to practice this skill. The game’s goal is for one student to guess a mystery number using as few inequalities as possible. To create a class competition, keep track of how many inequalities each group uses for each number and display scores after each round. The winning group is the group with the lowest score.
Launch
Arrange students in groups of 4. As students read the game instructions with their group, give each group 1 set of inequalities and 1 set of numbers, pre-cut from the blackline master. Review the game instructions as a whole class. Students will play 1 round and then pause to reflect and plan strategies for the next rounds. Allow students 10 minutes of game time followed by a whole-class discussion.
Once student groups have completed one round of game play, pause the game and ask groups to reflect on their strategies. Groups should make a plan before continuing to the second round of the game. Post or ask these questions to guide a short discussion:
“Clue givers, how did you decide which inequalities would be the most helpful for your detective?”
“Clue givers, did you work together to decide which 3 clues to give or did you decide independently?”
“Detective, were some inequalities more helpful than others as you tried to guess the mystery number? If so, what made an inequality more helpful?”
Action and Expression: Internalize Executive Functions.
Begin with a small-group or whole-class demonstration of how to play the game. Check for understanding by inviting students to rephrase directions in their own words.
Supports accessibility for: Memory; Conceptual processing
Student Facing
Your teacher will give your group two sets of cards—one set shows inequalities and the other shows numbers. Place the inequality cards face up where everyone can see them. Shuffle the number cards and stack them face down.
To play:
One person in your group is the detective. The other people will give clues.
Pick one number card from the stack and show it to everyone except the detective.
The people giving clues each choose an inequality that will help the detective identify the unknown number.
The detective studies the inequalities and makes three guesses.
If the detective does not guess the right number, each person chooses another inequality to help.
When the detective does guess the right number, a new person becomes the detective.
Repeat the game until everyone has had a turn being the detective.
Student Response
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Anticipated Misconceptions
Some groups may misunderstand the directions, thinking that each person giving clues is supposed to take a different number card from the stack. Explain to them that there is only one unknown number per round and everyone gives clues about this same number. When a new person becomes the detective, that is when a new number card is drawn.
Activity Synthesis
Once all students have had a turn as the detective, start a whole-class discussion. Ask groups to share their most successful strategies for choosing helpful clue inequalities as well as strategies for using those clues to guess the mystery number. Emphasize how students can check that a value is or is not a solution to an inequality: both symbolic statements (substitute the value and check that the resulting statement is true) and on the number line (plot the value to test and make sure that it falls within a shaded region).
Speaking: MLR8 Discussion Supports.
To support all students to participate in the discussion, provide students with sentence frames, such as “One strategy I used to choose a clue was _____” or “One way that I checked that a value was a solution to the inequality (number line representation) was to _____.” Ask them to complete one of the sentences in writing or share a completed response verbally with a partner.
Design Principle(s): Maximize meta-awareness


correct_option_index: 1