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: Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.
Grade 4 expectations in this domain are limited to whole numbers less than or equal to 1,000,000.

Find whole-number quotients and remainders with up to four-digit dividends and one-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.
Grade 4 expectations in this domain are limited to whole numbers less than or equal to 1,000,000.

Fluently add and subtract multi-digit whole numbers using the standard algorithm.
Grade 4 expectations in this domain are limited to whole numbers less than or equal to 1,000,000.
problem_activity: Narrative
The purpose of this activity is to examine subtraction cases in which non-zero digits are subtracted from zero digits. In some cases, students could simply look at the digit to the left of a 0 and decompose 1 unit of that number. But in other cases, the digit to the left is another 0 (or more than one 0), which means looking further to the left until reaching a non-zero digit. Students learn to decompose that unit first, and then move to the right, decomposing units of smaller place values until reaching the original digits being subtracted. The problems are sequenced from fewer zeros to more zeros to allow students to see how to successively decompose units.
Recording all of the decompositions can be challenging. For the last problem, two sample responses are given to show two different ways of recording the decompositions. The important point to understand is that because there are no tens, hundreds, or thousands to decompose, a ten-thousand must be decomposed to make 10 thousands. Then, one of the thousands is decomposed to make 10 hundreds, and so on, until reaching the ones place. Those successive decompositions can be lined up horizontally, but this can make it hard to see what happened first. A second way shows more clearly the order in which the decompositions happen, but it may be challenging to see which place the successive decomposed units are in.
To add movement to this activity, the second problem could be done as a gallery walk where each group completes one problem and then walk around the room to look for similarities and differences in others’ posters.
MLR8 Discussion Supports.
Display sentence frames to support partner discussion: “I noticed _____ so I . . .”, and “I wonder if . . . .”
Advances: Conversing, Representing
Representation: Develop Language and Symbols.
Maintain a visible display to record language that students can use to explain their work. Include important vocabulary, such as the name of each place value category, decompose, and exchange. Also include sentence frames, such as: “I looked at the _____ place and saw that I did not have enough ____ to subtract.” and “I exchanged one ______ for 10 _____.”
Supports accessibility for: Conceptual Processing, Language, Organization
Launch
Groups of 2–4
5 minute: independent think time
3 minute: partner share
Activity
“Take some time to think about the first problem and then discuss it with your partner.”
2 minutes: quiet think time
3 minutes: partner discussion
Pause for clarifying questions, as needed.
“Now, work with your partner to complete the next 2 problems.”
5 minutes: partner work time
Student Facing
Here are some numbers you saw earlier. Each number has at least one 0. From each number, 1,436 is being subtracted.
Make sense of the problems and explain to a partner.
a
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b
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Use the approach in the first problem to find these two differences:
a
[IMG]
b
[IMG]
Find the value of each difference. Be prepared to explain your reasoning. If you get stuck, try subtracting using the expanded form.
a
[IMG]
b
[IMG]
c
[IMG]
d
[IMG]
Student Response
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Advancing Student Thinking
Students may lose track of the units when multiple rounds of decompositions are required. Offer base-ten blocks and prompt students to show multiple decompositions when finding the value of
\(100 - 1\)
using a large square base-ten block that represents 100. Consider asking:
“How can you show subtraction of 1?” (Exchange it for 100 ones.)
“What if we could only exchange 1 unit for 10 units at a time?” (Exchange the hundred for 10 tens, then exchange 1 ten for 10 ones, so that we’d have 9 tens and 10 ones. Then, we can remove 1.)
“How would you show the subtraction of 1 from 100 using the standard algorithm?”
Activity Synthesis
Ask students to share responses and to demonstrate consecutive decomposing when multiple zeros are involved.
If needed, use expanded form to represent the decompositions students are explaining.


correct_option_index: 2