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

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

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

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.

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.

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.

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.

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

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.
problem_activity: Problem 1
Bobbie is a sixth grader who competes in the 100-meter hurdles. In eight track meets during the season, she recorded the following times (to the nearest one hundredth of a second).
18.11    31.23    17.99    18.25    17.50    35.55    17.44    17.85
a.   What is the mean of Bobbie’s times for these track meets? What does the mean tell you in terms of the context?
b.   What is the median of Bobbie’s times? What does the median tell you in terms of the context?
c.   Explain why the mean is higher than the median.
d.   Which measure of center do you think best represents Bobbie’s 100-meter hurdle time? Explain your reasoning.
e.   The two times that were over 30 seconds were times when Bobbie fell on a hurdle. She decides to take those times out to get a sense of her typical time without falling. What is the new mean? The new median? How do those compare to the original mean and median?
Problem 2
At the University of North Carolina (UNC) in the mid-1980's, the average starting salary for a Geography major was over $100,000 (equivalent to almost $300,000 today).
At that same time, basketball star Michael Jordan was drafted into the NBA with one of the highest salaries in the league. He had just graduated from UNC with a degree in Geography.
a.   Explain why the mean is a misleading measure of center to represent the salary of geography students at UNC.
b.   What measure of center would better represent the salary of geography students at UNC? Explain your reasoning.
Problem 3
The data set below represents the morning commute time of eight colleagues in an office on the same day. The mean of the data set is 32.5 minutes and the median is 38 minutes.
45           32           38           20           5           40           38           42
There was a typo in the data set, and the input “5” was supposed to be “50.” The typo is corrected and the correct mean and median are found.
Without calculating, explain what impact the typo had on the mean and the median.


correct_option_index: 3