Problem 10 - Algebra 1: Concepts and Skills

Question

SCHOOL ENROLLMENT The table shows the number of students (in millions) enrolled in school in the United States by age. Make a table showing the total number of students enrolled for each given year. $$ \begin{array}{|c|c|c|c|c|c|} \hline \text { Age } & {1980} & {1985} & {1990} & {1995} & {2000} \\ \hline 14-15 \text { years old } & {7282} & {7362} & {6555} & {7651} & {8100} \\\ \hline 16-17 \text { years old } & {7129} & {6654} & {6098} & {6997} & {7600} \\\ \hline 18-19 \text { years old } & {3788} & {3716} & {4044} & {4274} & {4800} \\\ \hline \end{array} $$ Did the total enrollment increase for each 5 year period? Explain.

Step-by-Step Solution

Answer

The total enrollment number for each year is calculated as sum of enrollments for each age group. By comparing these total numbers for each 5-year period, we can determine if the total enrollment increased for each 5-year period.

Step 1: Calculate total enrollments for each year

For each year mentioned (1980, 1985, 1990, 1995, and 2000), sum up the number of enrolled students in the three age groups. Use addition operations for this, adding up the number of 14-15 years old students, 16-17 years old students, and 18-19 years old students separately for each year.

Step 2: Organize the data in a table

After carrying out the calculations, create a new table where each row represents a year and the total number of students enrolled in that year, summing up across all the three age groups.

Step 3: Analyze the trend

Locate whether the total number of enrolled students increased for each five-year period by comparing the totals for each subsequent five-year period. If the total enrollment for a later year is greater than the total enrollment for the earlier year, then there has been an increase in total enrollment in that five-year period.

Key Concepts

School Enrollment

School enrollment data is a valuable record that provides insights into the number of students attending schools over a series of years. These records can show changes and patterns in education participation, helping to understand shifts in demographic engagement, policy impacts, and resource requirements.
For each given year and age group, such as those from 14-19 years old, schools track how many students enroll. This corresponds to a specific dataset highlighting, for example, how many 14-15 year-olds are enrolled from 1980 to 2000.
The purpose of breaking down statistics by age and year is to paint a picture over time:

• Comparing figures can lead to insights into whether enrollment is growing, shrinking, or stabilizing in any particular age group.
• It also helps in understanding which age demographic may require more educational resources or policy attention.

Thus, maintaining and analyzing enrollment data is crucial for educational planning and policy making.

Addition

Addition is a mathematical operation that combines two or more numbers to find their total. This is an essential skill when analyzing data like school enrollment figures.
When we calculate total enrollments, for example, we sum up the number of students from different age groups in each year.
To perform the addition successfully in data analysis:

• Identify the relevant numbers from each category, e.g., numbers of students in specific age groups.
• Add these numbers together to get a sum that represents the overall total for that year.
• Repeat this process for all subsequent years, subsequently getting a comprehensive picture of enrollment trends.

Mastering addition in data contexts allows for accurate aggregations and helps simplify further analysis, building a base for data-driven decision-making.

Trends Analysis

Trends analysis involves examining data over a period to identify any patterns or shifts that may occur. This is particularly useful with school enrollment data, as trends can highlight changes in education demographics or demand over time.
By analyzing trends:

• One can determine whether enrollment numbers are increasing or decreasing over substantial periods, such as every five years.
• Trends can pinpoint significant changes resulting from external factors such as policy modifications, population growth, or changes in schooling preferences.
• They enable educational planners to forecast future enrollment needs and plan accordingly.

In examining our data set, comparing the sums of each year's total enrollments reveals shifts: did numbers steadily rise, drop, or fluctuate inconsistently? By recognizing and understanding these trends, educational stakeholders can make informed, strategic decisions to improve educational delivery and capacity planning.