few_shots: Example:
Problem/activity:
For each pair of numbers, determine if the values are equivalent. Explain your reasoning for each one.
a.
$$-0.25$$
and
$$\frac{1}{-4}$$
b.
$$-\left ( \frac{1}{4} \right )$$
and
$$\frac{-1}{-4}$$
c.
$$\frac{-1}{4}$$
and
$$-\frac{1}{4}$$


Mathematical concept/skill options: 
A. Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers.
B. Reason quantitatively and use units to solve problems.
C. Apply and extend previous understandings of numbers to the system of rational numbers.
D. Represent complex numbers and their operations on the complex plane.
E. Perform arithmetic operations with complex numbers.
F. Compute fluently with multi-digit numbers and find common factors and multiples.
G. Represent and model with vector quantities.
H. Perform operations on vectors.
I. Use properties of rational and irrational numbers.
J. Use complex numbers in polynomial identities and equations.
K. Extend the properties of exponents to rational exponents.
L. Know that there are numbers that are not rational, and approximate them by rational numbers.
M. Perform operations on matrices and use matrices in applications.
N. Apply and extend previous understandings of multiplication and division to divide fractions by fractions.


Your response:
Thought: This problem involves understanding fractions, multiplication, and division.
Answer: A

Now, assign the following problem or activity to one or more relevant mathematical concepts/skills it teaches.
shot_info: fl_problem_001097

7
options: Use place value understanding and properties of operations to add and subtract.

Understand place value.

Understand the place value system.

Use place value understanding and properties of operations to perform multi-digit arithmetic. (A range of algorithms may be used.)

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.

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.

Extend the counting sequence.

Work with numbers 11–19 to gain foundations for place value.

Perform operations with multi-digit whole numbers and with decimals to hundredths.
problem_activity: Narrative
The purpose of this activity is for students to connect story problems to the equations that represent them and to solve different types of story problems. Students identify equations with a symbol for the unknown that match a story problem and justify their decisions by describing how the equations represent the quantities and any actions in the story problem (MP4). When students analyze and connect the quantities and structures in the story problems and equations, they are thinking abstractly and quantitatively (MP2) and making use of structure (MP7).
MLR8 Discussion Supports.
Display sentence frames to support discussion as students explain their reasoning to their partner: “I noticed ___ , so I matched . . .” Encourage students to challenge each other when they disagree.
Advances: Conversing, Representing
Required Materials
Materials to Gather
Base-ten blocks
Materials from a previous lesson
Materials to Copy
Equations for Different Types of Word Problems
Required Preparation
Create a set of cards from the blackline master for each group of 2
–
4.
Each group of 2
–
4 needs a set of cards from the previous lesson.
Launch
Groups of 2
–
4
Give each group the story problems (Cards A–I) from the Story Problem and Diagram Cards.
Give one set of Equation Cards to each group of students.
Give each group access to base-ten blocks.
“Take turns reading the story problems. After one person reads, work together to find an equation that matches. When you think you have found a match, explain to your group why the cards match.”
“If you think that more than one card could match the story, explain the match to your group.”
As needed, demonstrate the activity with a student volunteer.
“When your group finishes, choose 2 story problems from Cards F, G, H, or I and solve them.”
Activity
6 minutes: partner work time
Monitor for students who explain why more than one equation may match a story and how the equations match the quantities in the context of the story problem.
4 minutes: independent work time
Student Facing
Match each story problem with an equation. Explain why the cards match.
Choose 2 story problems and solve them. Show your thinking.
Student Response
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Advancing Student Thinking
Students may believe that only one equation could match each story. Encourage
students to describe how equations match any actions in the story and whether any other equations show the same actions. If there are no actions in the story, ask students to explain why one or more cards shows the relationship between the parts and the whole. Consider providing the tape diagrams from the previous activity to support students in their explanations.
Activity Synthesis
Invite students to share a match for each story.
Consider asking:
“How does the equation match the story problem?”
“Is there another equation that could match the story problem? Explain why or why not.”


correct_option_index: 0