Image description: A cartoon illustration shows a doctor pointing to a screen with alternating images of sick children.
Narration: Do you ever get sick the first week back to school, perhaps with a cold? Do you get the flu shot in hopes of not contracting a flu virus? How do viruses and diseases spread? How quickly can people become infected? The answers to these last two questions are very important to scientists and disease prevention. Looking at patterns and applying mathematics can help provide the answers.
The common cold is a virus. It grows additively. Let’s look at an example.
Image description: An illustration of a virus appears and the word Additively appears.
Narration: Suppose Ms. Hopkins has a class of 30 students. On the first day of school, one child has a cold. Each day, two more children catch the cold.
Image description: An illustrated image of 5 rows of 6 students appears. Students are faded to black as the narration describes how many students contract the virus each day.
Narration. The pattern shows the number of children in the class that catch the cold. 1, 3, 5, 7, 9, 11, 13, etcetera. When a pattern is an additive pattern, it adds the same value to the previous term to form the next term in the pattern.
Image description: A table appears illustrating the pattern. The table has eight columns and two rows. The top row is labeled “Day” and increases from 0 to seven in increments of one. Plus 1 appears between each number 1-7 on the top row. The bottom row is labeled “Number of sick children” and the eight columns are 1, 3, 5, 7, 9, 11 and 13. The common difference of plus 2 appears below the bottom row. 2 is highlighted and the words common difference appear. 5 minus 3 equals 2 is shown to illustrate an example of how to find the common difference.
Narration: For this cold pattern, as each day passes, the value of 2 is added to the previous term to form the next term. This value of 2 is known as the common difference. If you take one term in the pattern and subtract the previous term, you will find the common difference. Additive patterns are also known as arithmetic sequences.