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?


Mathematical concept/skill options: 
A. Use place value understanding and properties of operations to perform multi-digit arithmetic. (A range of algorithms may be used.)
B. Understand place value.
C. Understand the place value system.
D. Extend the counting sequence.
E. Work with numbers 11–19 to gain foundations for place value.
F. Use place value understanding and properties of operations to perform multi-digit arithmetic.
Grade 4 expectations in this domain are limited to whole numbers less than or equal to 1,000,000.
G. Perform operations with multi-digit whole numbers and with decimals to hundredths.
H. Generalize place value understanding for multi-digit whole numbers.
Grade 4 expectations in this domain are limited to whole numbers less than or equal to 1,000,000.
I. Use place value understanding and properties of operations to add and subtract.


Your response:
{
  "explanation": "This set of problems asks students to perform multiplication, which is an operation, on multi-digit whole numbers.",
  "answer": "G"
}

Now, assign the following problem or activity to one or more relevant mathematical concepts/skills it teaches.
shot_info: fl_problem_000674

5
options: Extend understanding of fraction equivalence and ordering.
Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.

Use equivalent fractions as a strategy to add and subtract fractions.

Apply and extend previous understandings of multiplication and division to multiply and divide fractions.

Develop Understanding of fractions as numbers.
Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, and 8.

Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.
Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.

Understand decimal notation for fractions, and compare decimal fractions.
Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.
problem_activity: Narrative
The purpose of this activity is for students to apply what they have learned in this section to compare a number to the product of that number with a fraction. There are two cases where the fraction has a value of 1. Students may identify that the value of the fraction is 1 and use what they know about multiplying a number by 1. They may also use their knowledge of how to multiply fractions and the calculations for these products have been made simpler so that students can find the product to make the comparison. For the other problems, the numbers are sufficiently complex that the most efficient way to compare is to think about the size of the factors.
MLR1 Stronger and Clearer Each Time.
Synthesis: Before the whole-class discussion, give students time to meet with 2–3 partners to share and get feedback on their response to whether the expressions are
\(<\)
,
\(>\)
, or
\(=\)
. Invite listeners to ask questions, to press for details and to suggest mathematical language. Give students 2–3 minutes to revise their written explanation based on the feedback they receive.
Advances: Writing, Speaking, Listening
Launch
Groups of 2
Activity
1–2 minutes: quiet think time
10–12 minutes: partner work time
For the expressions
\(\frac{1}{4} \times \frac{5}{5}\)
and
\(\frac{10}{10} \times \frac{1}{2}\)
monitor for students who calculate the products and for students who reason about the size of the factors.
Student Facing
Write
\(<\)
,
\(>\)
, or
\(=\)
in each blank to make true statements.
Choose one problem and explain or show your reasoning.
\(567 \, \underline{\hspace{0.7cm}} \,345 \times 567\)
\(\frac{4}{5} \times 851 \, \underline{\hspace{0.7cm}} \, 851\)
\(\frac{1}{4} \, \underline{\hspace{0.7cm}} \, \frac{5}{5} \times \frac{1}{4}\)
\(\frac{103}{104} \, \underline{\hspace{0.7cm}} \, \frac{103}{104} \times \frac{103}{104}\)
\(\frac{99}{8} \times \frac{23}{22} \, \underline{\hspace{0.7cm}} \, \frac{99}{8}\)
\(\frac{10}{10} \times \frac{1}{2} \, \underline{\hspace{0.7cm}} \, \frac{1}{2}\)
\(\frac{100}{7} \times \frac{9}{13} \, \underline{\hspace{0.7cm}} \, \frac{9}{13}\)
Student Response
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Activity Synthesis
Invite students to share their solution for comparing
\(\frac{10}{10} \times \frac{1}{2}\)
and
\(\frac{1}{2}\)
.
“How do you know that
\(\frac{10}{20} = \frac{1}{2}\)
?” (If you cut the half into 10 equal pieces then you get 10 pieces and there are 20 in the whole.)
“Can you use the equation
\(\frac{10}{10} = 1\)
to see that
\(\frac{10}{10} \times \frac{1}{2} = \frac{1}{2}\)
?” (Yes, because 1 times any number is that same number.)
Invite students to share their solution for comparing
\(\frac{103}{104}\)
and
\(\frac{103}{104} \times \frac{103}{104}\)
.
“Did you find the product to compare?” (No, the numbers are big so it would have taken a long time.)
“What did you do to compare the numbers?” (I know that
\(\frac{103}{104}\)
is less than 1, it’s
\(1 - \frac{1}{104}\)
. So when I multiply it by any number I get less than that number.)


correct_option_index: 2