Representing Large Numbers on the Number Line
5 min
Teacher Prep
Setup
Narrative
This Warm-up prompts students to visualize and make sense of numbers expressed as a product of a single digit and a power of 10, in preparation for working with scientific notation.
Expect student responses to include a variety of incorrect or partially-correct ideas. It is not important that all students understand the correct notation at this point, so it is not necessary to extend the time for this reason.
Launch
Arrange students in groups of 2. Give students 1 minute of quiet work time and then 2 minutes to compare their number line with their partner's. Tell partners to try to come to an agreement on how to label the number line. Follow with a whole-class discussion.
Student Task
Label the tick marks on the number line. Be prepared to explain your reasoning.
Sample Response
The tick marks should be labeled: 0, 1⋅106,2⋅106,3⋅106,4⋅106,5⋅106,6⋅106,7⋅106,8⋅106,9⋅106,107.
Activity Synthesis (Teacher Notes)
The goal of this discussion is for students to see how to correctly label this number line. Begin by inviting selected students to explain how they labeled the number line. Record and display their responses on the number line for all to see. As students share, use their responses, correct or incorrect, to guide students to the understanding that the first tick mark is 1⋅106, the second is 2⋅106, and so on.
If not uncovered in students' explanations, ask the following questions to make sure students see how to label the number line correctly:
- “How many equal parts is 107 being divided into?” (10)
- “If the number at the end of this number line were 20, how would we find the value of each tick mark?” (Divide 20 by 10)
- “Can we use the same reasoning with 107 at the end?” (Yes)
- “What is 107÷10?” (106) “What does this number represent?” (The distance between two tick marks)
- “Can we write 106 as 1⋅106?” (Yes).
- “If the first tick mark is 1⋅106, then what is the second tick mark?” (2⋅106)
Standards
- 8.EE.3·Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other. <em>For example, estimate the population of the United States as 3 × 10<sup>8</sup> and the population of the world as 7 × 10<sup>9</sup>, and determine that the world population is more than 20 times larger.</em>
- 8.EE.A.3·Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other. <span>For example, estimate the population of the United States as <span class="math">\(3 \times 10^8\)</span> and the population of the world as <span class="math">\(7 \times 10^9\)</span>, and determine that the world population is more than <span class="math">\(20\)</span> times larger.</span>
10 min
20 min
Knowledge Components
All skills for this lesson
No KCs tagged for this lesson
Representing Large Numbers on the Number Line
5 min
Teacher Prep
Setup
Narrative
This Warm-up prompts students to visualize and make sense of numbers expressed as a product of a single digit and a power of 10, in preparation for working with scientific notation.
Expect student responses to include a variety of incorrect or partially-correct ideas. It is not important that all students understand the correct notation at this point, so it is not necessary to extend the time for this reason.
Launch
Arrange students in groups of 2. Give students 1 minute of quiet work time and then 2 minutes to compare their number line with their partner's. Tell partners to try to come to an agreement on how to label the number line. Follow with a whole-class discussion.
Student Task
Label the tick marks on the number line. Be prepared to explain your reasoning.
Sample Response
The tick marks should be labeled: 0, 1⋅106,2⋅106,3⋅106,4⋅106,5⋅106,6⋅106,7⋅106,8⋅106,9⋅106,107.
Activity Synthesis (Teacher Notes)
The goal of this discussion is for students to see how to correctly label this number line. Begin by inviting selected students to explain how they labeled the number line. Record and display their responses on the number line for all to see. As students share, use their responses, correct or incorrect, to guide students to the understanding that the first tick mark is 1⋅106, the second is 2⋅106, and so on.
If not uncovered in students' explanations, ask the following questions to make sure students see how to label the number line correctly:
- “How many equal parts is 107 being divided into?” (10)
- “If the number at the end of this number line were 20, how would we find the value of each tick mark?” (Divide 20 by 10)
- “Can we use the same reasoning with 107 at the end?” (Yes)
- “What is 107÷10?” (106) “What does this number represent?” (The distance between two tick marks)
- “Can we write 106 as 1⋅106?” (Yes).
- “If the first tick mark is 1⋅106, then what is the second tick mark?” (2⋅106)
Standards
- 8.EE.3·Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other. <em>For example, estimate the population of the United States as 3 × 10<sup>8</sup> and the population of the world as 7 × 10<sup>9</sup>, and determine that the world population is more than 20 times larger.</em>
- 8.EE.A.3·Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other. <span>For example, estimate the population of the United States as <span class="math">\(3 \times 10^8\)</span> and the population of the world as <span class="math">\(7 \times 10^9\)</span>, and determine that the world population is more than <span class="math">\(20\)</span> times larger.</span>