# Lesson 10

Representing Large Numbers on the Number Line

### Lesson 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 \(b \boldcdot 10^n\), where \(b\) is some decimal number. Eventually, when students are formally introduced to scientific notation, \(b\) is restricted to values between 1 and 10.

### Learning Goals

Teacher Facing

- 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.

### Student Facing

Let’s visualize large numbers on the number line using powers of 10.

### Learning Targets

### Student Facing

- 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.
- I can write a large number as a multiple of a power of 10.