few_shots: Example:
Problem/activity:
Task
 Arrange the fractions in order from least to greatest. Explain your answer with a picture.
 $\frac{1}{5}, \frac{1}{7}, \frac{1}{3} $
 $\frac{2}{5}, \frac{2}{7}, \frac{2}{3} $
 $\frac{5}{6}, \frac{3}{6}, \frac{1}{6} $
 $\frac{5}{12}, \frac{8}{12}, \frac{4}{12} $

Mathematical concept/skill options: 
A. 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.
B. 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.
C. Use equivalent fractions as a strategy to add and subtract fractions.
D. Apply and extend previous understandings of multiplication and division to multiply and divide fractions.
E. 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.
F. Develop Understanding of fractions as numbers.
Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, and 8.


Your response:
Thought: This problem involves understanding fractions as numbers by comparing their quantities.
Answer: F

Now, assign the following problem or activity to one or more relevant mathematical concepts/skills it teaches.
shot_info: im_task_000157

3
options: Use polynomial identities to solve problems.

Work with addition and subtraction equations.

Write and interpret numerical expressions.

Rewrite rational expressions.

Work with radicals and integer exponents.

Use properties of operations to generate equivalent expressions.

Use the four operations with whole numbers to solve problems.

Generate and analyze patterns.

Multiply and divide within 100.

Work with equal groups of objects to gain foundations for multiplication.

Understand the relationship between zeros and factors of polynomials.

Analyze patterns and relationships.

Analyze and solve linear equations and pairs of simultaneous linear equations.

Interpret the structure of expressions.

Understand the connections between proportional relationships, lines, and linear equations.

Understand properties of multiplication and the relationship between multiplication and division.

Create equations that describe numbers or relationships

Apply and extend previous understandings of arithmetic to algebraic expressions.

Solve equations and inequalities in one variable.

Perform arithmetic operations on polynomials.

Write expressions in equivalent forms to solve problems.

Represent and solve problems involving multiplication and division.

Understand and apply properties of operations and the relationship between addition and subtraction.

Add and subtract within 20.

Solve systems of equations.

Solve problems involving the four operations, and identify and explain patterns in arithmetic.

Represent and solve problems involving addition and subtraction.

Reason about and solve one-variable equations and inequalities.

Gain familiarity with factors and multiples.

Represent and analyze quantitative relationships between dependent and independent variables.

Understand solving equations as a process of reasoning and explain the reasoning.

Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from.

Represent and solve equations and inequalities graphically.

Solve real-life and mathematical problems using numerical and algebraic expressions and equations.
problem_activity: Warm-up
The purpose of this Math Talk is to elicit strategies and understandings students have for expressing total lengths and areas, given some dimensions. These understandings help students develop fluency and will be helpful later in this lesson when students will need to be able to combine like terms to express a total length and express an area of a rectangle in different ways using the distributive property. In this activity, students have an opportunity to notice and make use of structure (MP7) because there are opportunities to invoke the distributive property and to replace expressions with equivalent expressions.
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.
Student Facing
A rectangle is partitioned into smaller rectangles. Explain why each of these expressions represents the area of the entire rectangle.
[IMG]
\(7(7+7+4+4)\)
\(7(2 \boldcdot 7 + 2 \boldcdot 4)\)
\(7^2+7^2+4 \boldcdot 7+4 \boldcdot 7\)
\(2(7^2) + 2 (4 \boldcdot 7)\)
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?”


correct_option_index: 17