Narrative
In this lesson, students use number lines to visualize powers of 10, compare very large numbers, and make sense of orders of magnitude (MP2). They use the structure of a number line that is subdivided into 10 equal intervals to express large numbers as multiples of a power of 10, which naturally leads to the idea of scientific notation, which will be introduced in subsequent lessons (MP7).
In these materials, “multiple of a power of 10” does not necessarily mean an integer multiple of a power of 10. Students explore numbers of the form \(b \cdot 10^n\), where \(b\) is some decimal number. Eventually, when students are formally introduced to scientific notation, \(b\) is restricted to values between 1 and 10.
Lesson overview
 10.1 Warmup: Labeling Tick Marks on a Number Line (5 minutes)

10.2 Activity: Comparing Large Numbers with a Number Line (10 minutes)
 There is a digital applet in this activity.

10.3 Activity: The Speeds of Light (20 minutes)
 Includes "Are you Ready for More?" extension problem
 There is a digital applet in this activity.
 Lesson Synthesis
 10.4 Cooldown: Describe the Point (5 minutes)
Learning goals:
 Compare large numbers using powers of 10, and explain (orally) the solution method.
 Use number lines to represent (orally and in writing) large numbers as multiples of powers of 10.
Learning goals (student facing):
 Let’s visualize large numbers on the number line using powers of 10.
Learning targets (student facing):
 I can write a large number as a multiple of a power of 10.
 I can plot a multiple of a power of 10 on such a number line.
 I can subdivide and label a number line between 0 and a power of 10 with a positive exponent into 10 equal intervals.
Glossary:
 Access the complete Grade 8 glossary.
Standards:
 This lesson builds towards the standard: CCSS.8.EE.A.4MS.8.EE.4
IM 6–8 Math was originally developed by Open Up Resources and authored by Illustrative Mathematics, and is copyright 20172019 by Open Up Resources. It is licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0). OUR's 6–8 Math Curriculum is available at https://openupresources.org/mathcurriculum/.
Adaptations and updates to IM 6–8 Math are copyright 2019 by Illustrative Mathematics, and are licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).
Adaptations to add additional English language learner supports are copyright 2019 by Open Up Resources, and are licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).
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