options: Number Systems and Quantity: students learn to understand the complex number system and reason quantitatively.

Ratios & Proportional Relationships: students learn to recognize, describe, represent, and reason with ratios, rates, proportional relationships, and percent.

Geometry: students learn to classify geometric figures by their properties, and understand and compare the relationships between them. Students develop and use formulas to compute lengths, areas, and volumes, and they use transformations to generate new shapes and compare existing ones. Geometry can be studied with and without coordinates.

Number & Operations - Fractions: students learn to understand fractions as numbers and may work with them using addition, subtraction, multiplication, and division.

Functions: students learn to define, use, and evaluate functions to model relationships between quantities.

Number & Operations in Base Ten: students learn to work with the base-ten system and build place value understanding.

Operations & Algebra: students learn to solve problems using algebraic thinking and operations such as addition, subtraction, multiplication, and division. They may learn to identify and explain arithmetic patterns, evaluate or manipulate numerical expressions, and reason with equations and inequalities.

Counting & Cardinality: students learn to know number names and the count sequence, count to tell the number of objects, and compare numbers.

Modeling: students learn to choose and use appropriate mathematics and statistics to analyze real-world empirical situations, improve decisions, and report on their conclusions and the reasoning behind them.

Measurement & Data: students learn to work with data and measure attributes such as time, money, length, area, and volume. They may learn to compare measurements to operations and convert between different units of measure.

Statistics & Probability: students learn to analyze and produce data distributions, and build understanding of univariate and bivariate data. They learn to interpret data, make statistical inferences, justify conclusions, understand rules of probability, and use probability to make decisions.
problem_activity: Narrative
This warm-up prompts students to examine a diagram representing equal groups of non-unit fractions. The understandings elicited here allow students to discuss the relationship between the product of a whole number and a unit fraction and that of a whole number and a non-unit fraction with the same denominator.
Launch
Groups of 2
Display the image.
Activity
“What do you notice? What do you wonder?”
1 minute: quiet think time
1 minute: partner discussion
Share and record responses.
Student Facing
What do you notice? What do you wonder?
[IMG]
Student Response
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Activity Synthesis
If no students notice or wonder about equal groups, ask, “What groups do you see and how do you see them?” (4 wholes, each whole has
\(\frac{2}{3}\)
shaded)
“How many thirds do you see?” (8 thirds)
“How are these diagrams different than those we've seen so far in this unit?” (Previously, each whole has only one shaded part. These have two shaded parts each.)
“Today, we will think about situations that involve equal groups but now each group has non-unit fractions.”


correct_option_index: 3