Summary
In this lesson, students will look for patterns then formalize rules for multiplying and dividing numbers written in scientific notation and use this to analyze and interpret information about the solar system. Being able to express and interpret numbers in scientific notation is prerequisite knowledge to this lesson. This is the second lesson in the "Notation for NASA" lesson duo.
Essential Question(s)
How can we use very large or small numbers?
Learning Objectives
Multiply and divide numbers using scientific notation.
Describe the role of gravity in the solar system.
Determine the scale properties of objects in the solar system.
Snapshot
Engage
Students recall what they know to identify the fictional statement hidden among the given scientific facts.
Explore
Students analyze math problems to find patterns and generalize the rules for multiplying and dividing numbers in scientific notation.
Explain
Students formalize their understanding of multiplying and dividing numbers in scientific notation.
Extend
Students apply what they have learned by planning their mission to space.
Evaluate
Students reflect on how they feel and what they think about their learning.
Materials
Lesson Slides (attached)
Fiction in the Facts posters (attached; one set per class; print one-sided)
Constellation Stations signs (attached; multiple sets per class; print one-sided)
Note Catcher handout (attached; one per student; print two-sided)
Guided Notes handout (attached; one per student; print two-sided)
Guided Notes (Model Notes) document (attached)
Mission Analysis handout (attached; one per student; print two-sided)
Model Sketch handout (optional; attached; one per student)
Scientific calculators (one per student)
Pencils
Paper
Sticky notes or index cards (optional; one per student)
Student devices with internet access (optional)
Preparation
During the Engage phase of the lesson, students will visit five different posters identifying the false statement from each poster and writing their reasoning on a piece of paper. Dedicate space in your classroom to hang the five pages from the attached Fiction in the Facts posters and ensure that there is enough space to comfortably read each poster. If space is limited, consider using the hallway.
During the Explore phase of the lesson, students will visit two types of stations to observe patterns for multiplying and dividing numbers in scientific notation. The attached Constellation Stations signs is a two-page file. The first page (Libra) has multiplication examples while the second page (Aries) has division examples. To avoid overcrowding at one station, plan for enough stations and make enough copies such that 2–3 students are the most at any one station. These signs could be hung on the wall or placed on a counter depending on your space. Consider printing the Libra page in one color and the Aries page on another color to quickly identify them.
Engage
25 Minute(s)
After introducing the lesson title on slide 2, transition through slides 3–4 to introduce the essential question and lesson objectives.
Show slide 5 and introduce the Fiction in the Facts strategy. Let students know that they will all begin at one poster, dividing the class into relatively even groups, and then stay with their group to visit all five posters. At each poster, they should:
Read all three statements, all related to space.
Discuss which one they think is fiction.
Individually record their own answer and reasoning in 1–2 sentences.
Move to slide 6 and have students get out a piece of paper. Have students create a table so they can record the number of the poster, the number of the corresponding false statement, and their reasoning.
Display slide 7 and have students find a poster. Tell students that their challenge is to use what they know about space and their reasoning skills to figure out which statement at each station does not belong. Let students know that the discussion is meant to help them think more deeply, but they may disagree and record different decisions. Each student is responsible for their own response.
Have students write the number of the poster on their paper. Tell students they have approximately two minutes at each poster, and then have them begin.
After all groups have visited each station, have students return to their seats. Bring the class together for a whole-group discussion. Show slide 8, displaying the three statements from Poster 1 and ask the class which statement they thought was fiction. Ask for volunteers to share their reasoning. Then transition to slide 9 to reveal the false statement.
Repeat this for each poster using slides 10–17. Use this time to spotlight strong reasoning, clarify any misconceptions, and build energy for what is coming next in the lesson.
Explore
20 Minute(s)
Display slide 18 and introduce the students to the Painting a Picture strategy. Give each student a copy of the attached Note Catcher handout. Tell students that there are two different constellation-themed stations: Libra for multiplication and Aries for division. Explain that they are expected to take their handout to the Libra and Aries stations and record the examples before independently reflecting on what they notice and attempting to write a rule for the operation at their station.
Move to slide 19 and have students find a station. Give students approximately 5 minutes, then have them move to a station with a different name/operation. If students have not answered all of the reflection questions during this time, still have students move to the next station. They can still later participate in the discussion later even if they do not currently have each reflection question answered.
After another 5 minutes, transition to slide 20 and have students return to their seats. Have students share and compare with a neighboring partner what they noticed and what “picture” they painted on how to multiply and divide numbers in scientific notation. Give pairs approximately 5 minutes to discuss, then ask for volunteers to share their findings with the class. Create a list of observations (students’ responses) for the class to see. Ask students if they observed any similarities or differences between multiplying and dividing numbers in scientific notations. If any observations are inaccurate, record them as well.
After students have shared all observations, ask if there is anything on the list that they disagree with or would like explained further. Ideally, this list should form the basis of the rules for multiplying and dividing numbers in scientific notation. If there are still misconceptions, they can be addressed during the Explain portion.
Explain
25 Minute(s)
Display slide 21 and give each student a copy of the attached Guided Notes handout. Resume the discussion from the Explore phase of the lesson, specifically focusing on the patterns and rules students had around multiplying numbers in scientific notation. Use the slide and their list of observations to discuss how to multiply numbers in scientific notation. Ask students to fill in the spaces in their Guided Notes as you progress. Use the attached Guided Notes (Model Notes) document as needed.
Give each student a calculator. Express to them that this is a great time for them to use this tool as a time-saver since you know that they know how to multiply. The focus of the lesson today is to understand how to quickly multiply and divide numbers written in scientific notation, so using this tool will allow them to focus their attention on learning these new skills.
Show slide 22 and follow the steps to go through the example: (2.5 × 102) · (8.1 × 105). After multiplying the coefficients and adding the exponents, you have 20.25 × 107. Ask students if this is written in scientific notation and how they know. Ask guiding questions, if needed, to help students realize that it is not since there is more than one nonzero digit in front of the decimal point.
Transition through slides 23–24 to explain how to correctly rewrite a number in scientific notation. Display slide 25 and then lead the class through completing the previous example by rewriting the previous result in scientific notation.
Direct students’ attention to the back of their handout and move to slide 26. Have students practice multiplying numbers in scientific notation. The notes are structured so that examples (a) and (c) can be used as whole-class practice and examples (b) and (d) can be used for students to work individually and informally assess their progress. All examples can be done together as a whole class or individually, depending on the needs of the students.
Transition through slides 27–30 to reveal each final product. Give students time to check and correct their work as needed. Use this time to answer any questions they may have.
Show slide 31 and discuss how to divide numbers in scientific notation. Display slide 32 and have students practice dividing numbers in scientific notation. Transition through slides 33–36 in the same way as you did the previous examples with slides 27–30.
Extend
30 Minute(s)
Display slide 40 and give each student a copy of the attached Mission Analysis handout. Have students get out their Mission Report handout from the previous lesson or a device. Explain to students that because of their excellent work on their Mission Reports, their missions have been approved! Inform students that their next task is to now plan for their mission: calculating distances, modeling how gravity affects motion, and solving real-world problems NASA teams face when planning space travel.
Show slide 41 and have students work in pairs to complete the activity. Encourage students to imagine themselves as real NASA mission planners as they apply their scientific knowledge and mathematical reasoning to help plan the mission.
Once students complete their mission planning, move to slide 44. Have students take out a piece of notebook paper and answer the reflection questions on the slide:
How did using scientific notation help you understand the scale of space?
What surprised you the most about the distances, sizes, or gravity that you calculated?
As time allows, ask for volunteers to share their responses with the class.
Evaluate
10 Minute(s)
Have students use the How Am I Feeling? What Am I Thinking? strategy to reflect on both their emotional and cognitive responses to the lesson.
Provide each student with a sticky note, index card, or piece of paper and display slide 45. Instruct them to draw a line dividing it into two sections. On one side of their paper, have them draw a picture, symbol, or emoji that represents how they feel about the content they explored, whether that’s confidence, curiosity, confusion, excitement, or another emotion.
On the other side of their paper, have students write a sentence expressing what they are thinking about regarding the lesson. This could include something they now understand better, a question they still have, a surprising discovery, or a personal insight.
Once they finish their reflection, have students place their notes on a designated board, wall, or collection area. Collect and review their responses to better understand their learning and emotional state. Use this insight to inform your next steps in instruction and support.
Resources
Lora. (2022, August 9). Aries. [Illustration]. Noun Project. https://thenounproject.com/icon/aries-5126164/
Lora. (2022, August 9). Libra. [Illustration]. Noun Project. https://thenounproject.com/icon/libra-5126161/
K20 Center. (n.d.). Fiction in the facts. Strategies. https://learn.k20center.ou.edu/strategy/60
K20 Center. (n.d.). How am I feeling? What am I thinking? Strategies. https://learn.k20center.ou.edu/strategy/187
K20 Center. (n.d.). I notice, I wonder. Strategies. https://learn.k20center.ou.edu/strategy/180
K20 Center. (n.d.). Painting a picture. Strategies. https://learn.k20center.ou.edu/strategy/1331
K20 Center. (2025, May 29). Aeronautical Engineering for NASA. [Video]. YouTube. https://www.youtube.com/watch?v=rYT3JoJDh9E
