Prior to this video clip students have been exploring exponentials in the context of the size changes of Alice in the story "Alice in
Wonderland." Students have been asked to translate the experiences of Alice into mathematical symbols. The investigation leads to discussions
over the differences between a constant growth rate and a constant growth factor. Being engaged in solving problems that require the use
of very large numbers prompts students to consider of the value of scientific notation to communicate the answer clearly.
In the first video clip below, students discuss their solutions to the problem "How many inches are in a light year?" As you watch the
video clip the first time, think about the following questions:
Focus Questions
How is the communication among students being structured?
What do students appear to be understanding about scientific notation and exponentials?
Listening to students share their ideas with their classmates can provide the teacher with information about student understanding.
What do the students seem to understand about scientific notation and exponents?
What might students still need to learn?
How can a teacher encourage students to listen to other students during small group discussion
Students need time individually to formulate their thinking. Following this time with small group discussion maximizes the number of
students who have an opportunity to verbalize their thinking (as seen in the video clip above). In addition to discussing solution methods
in small groups, students need opportunities to communicate their thinking to larger audiences. Presenting problems and solutions to the
class provides students with such an opportunity. When a small group of students prepares a presentation, group members have the opportunity
to listen to each other's ideas and evaluate their own solution methods. In the following video clip, a group of students shares their
solution method to the problem "About how many atoms are there in a kilogram of carbon?"
How can a teacher encourage students to listen to and engage with other students during small group discussion? During student
presentations?
Compare the language that the students use to your own. What are some of the differences? What words or phrases may be problematic
when working with exponents and scientific notation?
How might a teacher follow-up these investigations to have students formalize their thinking?
The National Council of Teachers
of Mathematics is a public voice of mathematics education, providing
vision, leadership, and professional development to support teachers
in ensuring mathematics learning of the highest quality for all
students. The views expressed or implied, unless otherwise noted,
should not be interpreted as official positions of the Council.
