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, in json format:
{
  "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, in json format:
{
  "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, in json format:
{
  "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: Explain why addition and subtraction strategies work, using place value and the properties of operations. (Explanations may be supported by drawings or objects.)

Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.

Add and subtract within 1000, 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. Understand that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds.

Add up to four two-digit numbers using strategies based on place value and properties of operations.

Mentally add 10 or 100 to a given number 100–900, and mentally subtract 10 or 100 from a given number 100–900.
problem_activity: Narrative
The purpose of this activity is for students to learn stage 5 of the Target Numbers center. Students subtract two-digit numbers to get as close to 0 as possible. For the introduction of this stage, invite students to count by 10 to 100 and represent their count with base-ten blocks. Then, they take turns rolling the 3 cubes to get a number to subtract. They choose one of the numbers on the cubes to represent the tens and a different number to represent the ones. Students subtract their tens and ones from the starting number. The difference becomes the first number in the next equation. The player who gets closest to 0 in 6 rounds, without going below 0, is the winner.
Required Materials
Materials to Gather
Base-ten blocks
Number cubes
Materials to Copy
Target Numbers Stage 5 Recording Sheet
Required Preparation
Each group of 2 students will need 3 number cubes.
Each group of 2 students will need base-ten blocks to represent at least 20 tens and 18 ones
.
Launch
Groups of 2
Give each student a copy of the recording sheet.
Give each group 3 number cubes and access to base-ten blocks.
“We are going to learn a new way to play Target Numbers. You and your partner will start with 100 and race to see who can reach a number less than 10 first.”
“Instead of using cards to decide whether to take away tens or ones, you will use number cubes to create a two-digit number and then subtract that number.”
“First, represent 100 with base-ten blocks."
As needed, invite students to count by 10 to 100 using the base-ten blocks or invite student to share how they might represent 100 with the blocks.
"When it’s your turn, roll all 3 number cubes. Pick 1 number to represent the tens and one number to represent the ones. Then show the subtraction with your blocks and write an equation on your recording sheet.”
“Take turns rolling and subtracting until the first person reaches a number less than 10.”
As needed, demonstrate a round with a student volunteer.
Activity
10
–
15 minutes: partner work
Activity Synthesis
Display equation:
\(73 - \underline{\hspace{1 cm}} = \underline{\hspace{1 cm}}\)
Draw or display number cubes showing 4, 2, and 5.
“What two-digit numbers could you create with this roll that would make you need to decompose a ten to subtract? How do you know?” (Sample response: 24 because if you subtract by place, there are only 3 ones, so you would need to decompose to take away 4 ones.)
“What two-digit numbers could you create that wouldn’t require decomposing a ten? How do you know?” (Sample response: 52 because if you subtract by place there are 3 ones and you can take away 2 ones from 3 ones.)
“What number would you create to try to get below 10 the fastest? Explain. (54 because it’s the number that lets you take away the most tens and ones.)


correct_option_index: 1