few_shots: Example:
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: fl_problem_000674

5
options: Use place value understanding to round multi-digit whole numbers to any place.
Grade 4 expectations in this domain are limited to whole numbers less than or equal to 1,000,000.

Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.
Grade 4 expectations in this domain are limited to whole numbers less than or equal to 1,000,000.

Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. For example, recognize that 700 ÷ 70 = 10 by applying concepts of place value and division.
Grade 4 expectations in this domain are limited to whole numbers less than or equal to 1,000,000.
problem_activity: Narrative
This optional activity gives students additional opportunities to compare multi-digit numbers by reasoning about the value of the digits in different places. It also prompts students to generalize the relative size of two numbers based on their understanding of place value. Students practice constructing logical arguments (MP3) as they explain whether it is possible for
\(4 \underline{\phantom{5}},\!300\)
to be less than
\(3 \underline{\phantom{5}},\!400\)
, or for
\( \underline{\phantom{5}}4,\!300\)
to be less than
\( \underline{\phantom{5}}3,\!400\)
.
Required Materials
Materials to Gather
Materials from a previous activity
Required Preparation
Each group of 2 needs a set of cards from the previous activity.
Launch
Groups of 2
Give each group a card with a digit between 0 and 9 for each group
Activity
“Use the digit on the card to complete the comparison statements in the first problem and decide if they are true.”
4–5 minutes: group work time
Pause to collect responses from all the groups.
“Is the first comparison statement true for all digits?” (Yes, because if the digits are the same, we can just compare 999 to 500.)
Repeat the question with all statements. Record responses in a chart such as shown:
{"table": [{"_attributes": {"border": "1", "class": ["c-table-spread"]}, "thead": [{"tr": [{"th": [{"_attributes": {"scope": "row"}, "_value": "statement"}, {"_attributes": {"scope": "col"}, "_value": "true"}, {"_attributes": {"scope": "col"}, "_value": "false"}]}]}], "tbody": [{"tr": [{"td": [{"span": [{"_attributes": {"class": ["math", "math-repaired"]}, "_value": "\\( \\underline{\\phantom{00}} \\ , 999 > \\underline{\\phantom{00}} \\ , 500\\)"}]}, {"_value": "all digits"}, {}]}, {"td": [{"span": [{"_attributes": {"class": ["math", "math-repaired"]}, "_value": "\\(15,2 \\underline{\\phantom{00}}0 > 15, \\underline{\\phantom{00}}02\\)"}]}, {"_value": "0, 1, 2"}, {"br": [{}], "_values": ["3, 4, 5, 6,", "7, 8, 9"]}]}, {"td": [{"span": [{"_attributes": {"class": ["math", "math-repaired"]}, "_value": "\\(4 \\underline{\\phantom{00}},700 < 7 \\underline{\\phantom{00}} ,400 \\)"}]}, {"_value": "all digits"}, {}]}, {"td": [{"span": [{"_attributes": {"class": ["math", "math-repaired"]}, "_value": "\\(1 \\underline{\\phantom{00}}5,000 > 5 \\underline{\\phantom{00}}1,000\\)"}]}, {}, {"_value": "all digits"}]}]}]}]}
“Why are the statements in parts a and c true no matter what digit is used?” (Sample response:
In part a, both numbers are missing the first digit, in the thousands place. Since the missing digit is the same, we’re comparing the hundreds, and 999 is always greater than 500.
In part c, the missing digit is in the thousands place of both numbers, but the digits in the ten-thousands place need to be compared first, and 4 ten-thousand is always less than 7 ten-thousand.)
“Why is the statement in part d false no matter what digit is used?” (Ten-thousand is never greater than 50 thousand.)
“Take a few quiet minutes to work on the last two problems independently.”
5 minutes: independent work time
Student Facing
Each of the following pairs of numbers is missing the same digit but in different places.
Your teacher will assign a digit to you. Use it as the missing digit and decide if each comparison statement is true.
\(\large \boxed{\phantom{0}} \ , \boxed{9} \ \boxed{9} \ \boxed{9} > \boxed{\phantom{0}} \ , \boxed{5} \ \boxed{0} \ \boxed{0}\)
\(\large \boxed{1} \ \boxed{5} \ , \boxed{2} \ \boxed{\phantom{0}} \ \boxed{0} > \boxed{1} \ \boxed{5} \ , \boxed{\phantom{0}} \ \boxed{0} \ \boxed{2}\)
\(\large \boxed{4} \ \boxed{\phantom{0}} \ , \boxed{7} \ \boxed{0} \ \boxed{0} < \boxed{7} \ \boxed{\phantom{0}} \ , \boxed{4} \ \boxed{0} \ \boxed{0}\)
\(\large \boxed{1} \ \boxed{\phantom{0}} \ \boxed{5} \ , \boxed{0} \ \boxed{0} \ \boxed{0} > \boxed{5} \ \boxed{\phantom{0}} \ \boxed{1} \ , \boxed{0} \ \boxed{0} \ \boxed{0}\)
Here are two numbers, each with the same missing digit.
\(\large \boxed{4} \ \boxed{\phantom{0}} \ , \boxed{3} \ \boxed{0} \ \boxed{0} \qquad \qquad \boxed{3} \ \boxed{\phantom{0}} \ , \boxed{4} \ \boxed{0} \ \boxed{0}\)
Choose a digit to complete the numbers and show where they would be on the number line.
[IMG]
Is it possible to fill in the two blanks with the same digit to make each statement true? If you think so, give at least one example of what the digits could be. If not, explain why it is not possible.
\(\large \boxed{4} \ \boxed{\phantom{0}} \ , \boxed{3} \ \boxed{0} \ \boxed{0}\)
is less than
\(\large {\boxed{3}} \ \boxed{\phantom{0}} \ , \boxed{4} \ \boxed{0} \ \boxed{0}\)
.
\(\large \boxed{\phantom{0}} \ \boxed{4} \ , \boxed{3} \ \boxed{0} \ \boxed{0}\)
is less than
\(\large \boxed{\phantom{0}} \ \boxed{3} \ , \boxed{4} \ \boxed{0} \ \boxed{0}\)
.
Student Response
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Activity Synthesis
Select students to share their responses to the last two problems.
Highlight explanations that make it clear that:
\(4 \underline{\phantom{5}},\!300\)
will always be greater than
\(3 \underline{\phantom{5}},\!400\)
because 4 ten-thousand is always greater than 3 ten-thousands.
\( \underline{\phantom{5}}4,\!300\)
will always be greater than
\( \underline{\phantom{5}}3,\!400\)
because, given the first digit is the same, the digits to compare are the thousands, and 4 thousands is always greater than 3 thousands.


correct_option_index: 1