Lesson 23

The purpose of an Estimation Exploration is to practice the skill of estimating a reasonable answer based on experience and known information. Students consider a picture of bees to familiarize them with a context that will be used later in the lesson.

• Groups of 2
• Display image.
• “This is an image of a bee hive. How many bees do you think are in the image?” “What is an estimate that’s too high?” “Too low?” “About right?”
• 1 minute: quiet think time

• “Discuss your thinking with your partner.”
• 1 minute: partner discussion
• Record responses.

• “Is anyone’s estimate less than 100? Is anyone’s estimate greater than 1,000?”
• “Based on this discussion, does anyone want to revise their estimate?”
• “What are some other insects or bugs you know or have seen?”

In this activity, students use rounding skills to make sense of numbers in the context of insect population. 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.

The work here offers students many opportunities to attend to precision (MP6). For instance, students may say that 2.4 represents the length of an ant or 30 represents how long a queen termite lives. Urge students to clarify the quantities they stated: “Did you mean 2.4 inches?” “Does 30 represent how many months a queen termite lives?”

• Groups of 2
• “An entomologist is a scientist who studies insects. Today, we’ll learn some facts about a few insects.”
• Read facts aloud. Clarify new words if needed.

• 2 minutes: independent work time
• 8 minutes: partner work time
• Monitor for students who:
  • think of multiple quantities that the same number might represent
  • use estimation in their reasoning

• 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 be?” (Sample response: The length of any of the insects in millimeters.)
• “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. ”

In this activity, students 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 at each time interval:

\(\displaystyle \text{new population} = \text{old population} + \text{inflow} – \text{outflow}\)

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.

• Groups of 2
• “Bees live in hives. We saw a picture of the inside of a hive in the warm-up. The number of bees in one hive can change throughout the year. For example, in the summer, when there are lots of flowers blooming, the population grows. In the winter, the population is a lot smaller.”
• “Beekeepers and entomologists are interested in knowing how many bees are in a hive over time. An entomologist is a scientist who studies insects.”
• “The table shows information about the number of bees in one particular hive. Look at the first row. What information do we get about the beehive?” (There were 20,000 to start with, 9378 bees were born or added, and 342 bees left.)
• Display the table in the activity.
• “What do you notice? What do you wonder?”
• 30 seconds: quiet think time
• Share responses.
• “How might we find out the number of bees at the beginning of June?”
• 30 seconds: quiet think time
• 1 minute: partner discussion
• Share responses.
• “Use the given information to complete the table.”

• 10 minutes: independent work time
• 2 minutes: partner discussion
• Monitor for students who:
  • use the standard algorithm to add and subtract the numbers
  • are able to explain why they used addition or subtraction

• “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 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?”
• “What other mathematical questions can we ask?” (How many total bees were born? How many total bees left the hive? What month had the most or fewest bees?)