The purpose of this activity is for students to use rounding skills to make sense of numbers in the context of insect populations. Students use given numerical facts about insects to determine what a variety of numbers could represent. For many of the numbers, several choices are possible. For example, students may say that 1,794 represents the number of days a queen ant lives or the number of eggs a queen bee lays in a day. When students determine a quantity that a number could represent in a situation, they model with mathematics (MP4).

• Invite previously selected students to share their responses and reasoning.
• “Was there any number that could represent only one possible fact about termites, ants, or honey bees?” (2.4 represents the length of an ant in millimeters, and 530,097 represents the size of a termite colony.)
• “Was there a number that could represent many facts about the insects?” (487, 1794, 6905)
• “What could 487 definitely not represent?” (The length of any of the insects in millimeters because those lengths were all less than 487.)
• “In the next activity, we are going to look at bees and investigate how a bee population changes over time. Studying population changes is something that many scientists do in many fields.”

The purpose of this activity is for students to investigate how a bee population changes over time. Population modeling is an important application of mathematics in many fields of study such as demography, biology, and infectious diseases. Students use a simplified model to show population change over time by using the number of individuals added and subtracted during each month.

In this activity, students are given some of the numbers and are to reason whether they need to add or subtract to fill in the missing information. When students model a situation using a representation such as an equation, they model with mathematics (MP4).

• “How did you decide which operation to use to complete each cell?” (If I had the starting number, I could add the new bees and subtract the bees that left the hive to get the number in the next month.)
• “How did you find the number of bees in the hive at the beginning of the month?” (After I added the number of new bees and subtracted the number of bees that left for a month, that gave me the beginning number of bees for the next month.)
• “What other mathematical questions can we ask about the bee population?” (How many total bees were born? How many total bees left the hive? What month had the most or fewest bees?)