options: 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.

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.

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

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.

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.

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.

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

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

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

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.
problem_activity: Warm-up
The purpose of this warm-up is for students to choose the more likely event based on their intuition about the possible outcomes of two chance experiments. The activities in this lesson that follow define probability and give ways to compute numerical values for the probability of chance events such as these.
Launch
Arrange students in groups of 2. Give students 1 minute of quiet work time followed by time to share their response with a partner. Follow with a whole-class discussion.
Student Facing
Which game would you choose to play? Explain your reasoning.
Game 1: You flip a coin and win if it lands showing heads.
Game 2: You roll a standard number cube and win if it lands showing a number that is divisible by 3.
Student Response
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Anticipated Misconceptions
Some students may have trouble comparing
\(\frac{1}{2}\)
and
\(\frac{2}{6}\)
. Review how to compare fractions with these students.
Some students may struggle with the wording of the second game. Help them understand what it means for a number to be divisible by a certain number and consider providing them with a standard number cube to examine the possible values.
Activity Synthesis
Have partners share their answers and display the results for all to see. Select at least one student for each answer provided to give a reason for their choice.
If no student mentions it, explain that the number of possible outcomes that count as a win and the number of total possible outcomes are both important to determining the likelihood of an event. That is, although there are two ways to win with the standard number cube and only one way to win on the coin, the greater number of possible outcomes in the second game makes it less likely to provide a win.


correct_option_index: 1