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: Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, 3^(2) × 3^(–5) = 3^(–3) = 1/3^(3) = 1/27.
problem_activity: Warm-up
The purpose of this warm-up is for students to reason about powers of positive and negative numbers. While some students may find the numeric value of each expression to make a comparison, it is not always necessary. Encourage students to reason about the meaning of the integers, bases, and exponents rather than finding the numeric value of each expression.
Launch
Display one problem at a time. Give students up to 1 minute of quiet think time per problem and tell them to give a signal when they have an answer and a strategy. Follow with a whole-class discussion.
There may be some confusion about how negative numbers interact with exponents. Tell students that exponents work the same way for both positive and negative bases. In other words,
\((\text- 3)^2 = \text- 3 \boldcdot \text- 3\)
.
Students may also struggle to interpret the notation difference between two expressions such as
\((\text- 4)^2\)
and
\(\text- 4^2\)
. Tell students that the interpretation of the first expression is
\((\text- 4)^2 = \text- 4 \boldcdot \text- 4\)
and the interpretation of the second expression is
\(\text- 4^2 = \text- 1 \boldcdot 4 \boldcdot 4\)
.
Student Facing
Is each statement true or false? Be prepared to explain your reasoning.
\(3^5 < 4^6\)
\(\left(\text- 3\right)^2 < 3^2\)
\(\left(\text- 3\right)^3 = 3^3\)
\(\left( \text- 5 \right) ^2 > \text- 5^2\)
Student Response
Teachers with a valid work email address can
click here to register or sign in
for free access to Student Response.
Activity Synthesis
Poll students on their response for each problem. Record and display their responses for all to see. If all students agree, ask 1 or 2 students to share their reasoning. If there is disagreement, ask students to share their reasoning until an agreement is reached. After the final problem, ask students if the same strategies would have worked if all of the bases were 10 to highlight the idea that powers with a base of 10 behave the same as those with bases other than 10.
To involve more students in the conversation, consider asking:
“Do you agree or disagree? Why?”
“Who can restate ___’s reasoning in a different way?”
“Does anyone want to add on to _____’s reasoning?”


aligns: yes