few_shots: 
Example:
Concept/skill: 
Fluently multiply multi-digit whole numbers using the standard algorithm.

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?


Answer: 
Yes. 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.

Now, determine whether the following problem or activity can enable students to understand the concepts or skills in the provided description.

shot_info: fl_problem_000674_pos_0

5
standard_description: Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational.
problem_activity: Warm-up
This Math Talk encourages students to think about exponent rules and to rely on properties of exponents to mentally solve problems. The understandings elicited here will be helpful later in the lesson when students use graphs to approximate the value of
\(2^x\)
for various negative rational exponents.
The final question is the first time students see an exponent that is a negative fraction. To use their prior knowledge to evaluate this expression, students need to look for and make use of structure (MP7).
Launch
Display one problem at a time. Give students quiet think time for each problem and ask them to give a signal when they have an answer and a strategy. Keep all problems displayed throughout the talk. Follow with a whole-class discussion.
Representation: Internalize Comprehension.
To support working memory, provide students with sticky notes or mini whiteboards.
Supports accessibility for: Memory; Organization
Student Facing
Evaluate mentally.
\(9^2\)
\(9^{\text-2}\)
\(9^{\frac12}\)
\(9^{\text-\frac12}\)
Student Response
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Activity Synthesis
Ask students to share their strategies for each problem. Record and display their responses for all to see. To involve more students in the conversation, consider asking:
“Who can restate
\(\underline{\hspace{.5in}}\)
’s reasoning in a different way?”
“Did anyone have the same strategy but would explain it differently?”
“Did anyone solve the problem in a different way?”
“Does anyone want to add on to
\(\underline{\hspace{.5in}}\)
’s strategy?”
“Do you agree or disagree? Why?”
If this strategy is not mentioned, consider asking students how they would use (9
1/2
)
-1
or (9
-1
)
1/2
to evaluate the last expression. If the results of the pre-assessment showed that students need extra practice with exponent rules, highlight any student strategies that leverage these rules and carefully record student thinking for all to see.
Speaking: MLR8 Discussion Supports.
Display sentence frames to support students when they explain their strategy. For example, "First, I _____ because…” or "I noticed _____ so I….” Some students may benefit from the opportunity to rehearse what they will say with a partner before they share with the whole class.
Design Principle(s): Optimize output (for explanation)


aligns: no