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.
• “Esta es una imagen de una colmena de abejas. ¿Cuántas abejas creen que hay en la imagen?” // “This is an image of a bee hive. How many bees do you think are in the image?” “¿Qué estimación sería muy alta?, ¿muy baja?, ¿razonable?” // “What is an estimate that’s too high?” “Too low?” “About right?”
• 1 minute: quiet think time

• “Discutan con su pareja cómo pensaron” // “Discuss your thinking with your partner.”
• 1 minute: partner discussion
• Record responses.

• “¿Alguien hizo una estimación menor que 100? ¿Alguien hizo una estimación mayor que 1,000?” // “Is anyone’s estimate less than 100? Is anyone’s estimate greater than 1,000?”
• “Basándose en esta discusión, ¿alguien quiere ajustar su estimación?” // “Based on this discussion, does anyone want to revise their estimate?”
• “¿Qué otros insectos o bichos conocen o han visto?” // “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: “¿Quisiste decir 2.4 pulgadas?” // “Did you mean 2.4 inches?” “¿El 30 representa cuántos meses vive una termita reina?” // “Does 30 represent how many months a queen termite lives?”

• Groups of 2
• “Un entomólogo es un científico que estudia los insectos. Hoy vamos a aprender algunos hechos sobre unos insectos” // “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.
• “¿Hubo algún número que solo podía representar un hecho posible sobre las termitas, las hormigas o las abejas melíferas?” // “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.)
• “¿Hubo algún número que podía representar varios hechos sobre los insectos?” // “Was there a number that could represent many facts about the insects?” (487, 1794, 6905)
• “Definitivamente, ¿qué no podía ser 487?” // “What could 487 definitely not be?” (Sample response: The length of any of the insects in millimeters.)
• “En la siguiente actividad, vamos a estudiar a las abejas y vamos a investigar cómo cambia una población de abejas con el tiempo. El estudio de los cambios en la población es un trabajo que hacen muchos científicos en varias disciplinas” // “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
• “Las abejas viven en colmenas. En el calentamiento vimos una foto del interior de una colmena. El número de abejas que hay en una colmena puede cambiar durante el año. Por ejemplo, cuando en el verano florecen muchas flores, la población de abejas crece. En el invierno, la población es mucho más pequeña” // “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.”
• “A los apicultores y a los entomólogos les interesa saber cuántas abejas hay en una colmena y cómo cambia esta cantidad con el tiempo. Un entomólogo es un científico que estudia los insectos” // “Beekeepers and entomologists are interested in knowing how many bees are in a hive over time. An entomologist is a scientist who studies insects.”
• “La tabla muestra información acerca del número de abejas que hay en una colmena en particular. Veamos la primera fila. ¿Qué información obtenemos sobre la colmena?” // “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.
• “¿Qué observan? ¿Qué se preguntan?” // “What do you notice? What do you wonder?”
• 30 seconds: quiet think time
• Share responses.
• “¿Cómo podríamos averiguar el número de abejas que había a principios de junio?” // “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.
• “Usen la información dada para completar la tabla” // “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

• “¿Cómo decidieron qué operación usar para completar cada celda?” // “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.)
• “¿Cómo encontraron el número de abejas que había en la colmena a principios del mes?” // “How did you find the number of bees in the hive at the beginning of the month?”
• “¿Qué otras preguntas matemáticas podemos hacer?” // “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?)