Multiplying Powers of 10
5 min
Teacher Prep
Setup
Narrative
This Warm-up gives students a chance to think about the different numbers that a diagram might represent. Students will see related diagrams that represent different powers of 10 in a following activity.
Launch
Give students 1 minute of quiet think time followed by a whole class discussion.
Student Task
Clare, Tyler, and Mai are looking at the diagram.
- Clare said she sees 100.
- Tyler says he sees 1.
- Mai says she sees 1001.
Whom do you agree with? Be prepared to explain your reasoning.
Sample Response
Sample response: I agree with all of them. There are 100 small squares and 1 big square. Each small square is 1001 of the large square.
Activity Synthesis (Teacher Notes)
The goal of this discussion is for students to share their reasoning. Survey the class to see who agrees with each person. Invite students to share their reasoning. Consider discussing the following questions:
- “Who can restate ’s reasoning in a different way?”
- “Did anyone agree with but would explain it differently?”
Standards
- 5.NBT.3.a·Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 × 100 + 4 × 10 + 7 × 1 + 3 × (1/10) + 9 × (1/100) + 2 × (1/1000).
- 5.NBT.A.3.a·Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., <span class="math">\(347.392 = 3 \times 100 + 4 \times 10 + 7 \times 1 + 3 \times (1/10) + 9 \times (1/100) + 2 \times (1/1000)\)</span>.
- 8.EE.1·Know and apply the properties of integer exponents to generate equivalent numerical expressions. <em>For example, 3² × 3<sup>-5</sup> = 3<sup>-3</sup> = 1/3³ = 1/27.</em>
- 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.1·Know and apply the properties of integer exponents to generate equivalent numerical expressions. <span>For example, <span class="math">\(3^2\times3^{-5} = 3^{-3} = 1/3^3 = 1/27\)</span>.</span>
- 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>
15 min
15 min
Knowledge Components
All skills for this lesson
No KCs tagged for this lesson
Multiplying Powers of 10
5 min
Teacher Prep
Setup
Narrative
This Warm-up gives students a chance to think about the different numbers that a diagram might represent. Students will see related diagrams that represent different powers of 10 in a following activity.
Launch
Give students 1 minute of quiet think time followed by a whole class discussion.
Student Task
Clare, Tyler, and Mai are looking at the diagram.
- Clare said she sees 100.
- Tyler says he sees 1.
- Mai says she sees 1001.
Whom do you agree with? Be prepared to explain your reasoning.
Sample Response
Sample response: I agree with all of them. There are 100 small squares and 1 big square. Each small square is 1001 of the large square.
Activity Synthesis (Teacher Notes)
The goal of this discussion is for students to share their reasoning. Survey the class to see who agrees with each person. Invite students to share their reasoning. Consider discussing the following questions:
- “Who can restate ’s reasoning in a different way?”
- “Did anyone agree with but would explain it differently?”
Standards
- 5.NBT.3.a·Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 × 100 + 4 × 10 + 7 × 1 + 3 × (1/10) + 9 × (1/100) + 2 × (1/1000).
- 5.NBT.A.3.a·Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., <span class="math">\(347.392 = 3 \times 100 + 4 \times 10 + 7 \times 1 + 3 \times (1/10) + 9 \times (1/100) + 2 \times (1/1000)\)</span>.
- 8.EE.1·Know and apply the properties of integer exponents to generate equivalent numerical expressions. <em>For example, 3² × 3<sup>-5</sup> = 3<sup>-3</sup> = 1/3³ = 1/27.</em>
- 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.1·Know and apply the properties of integer exponents to generate equivalent numerical expressions. <span>For example, <span class="math">\(3^2\times3^{-5} = 3^{-3} = 1/3^3 = 1/27\)</span>.</span>
- 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>