Unit Title: Scientific Notation: Using Exponents to Make Meaning of the World Around Us!
Conceptual Lens: Mathematical/Scientific, Researcher
Unit Strands:
- Converting Between Scientific Notation and Standard Form
- Operations with Scientific Notation
- Real-World Applications with Scientific Notation
Web:
Generalizations:
- Exponents can be used to simplify very large or very small numbers.
- We can compare small or large numbers more easily when they are written with exponents.
- We can perform operations on small or large numbers more easily when they are written with exponents.
- Technology uses Scientific Notation to reduce the number of digits displayed.
Guiding Questions:
F = factual questions
C = conceptual questions
D = debatable questions
- What are some careers that use Scientific Notation? (F)
- Where can we see Scientific Notation in the technology we use? (F)
- How can we convert numbers from Scientific Notation to Standard Form and vise versa? (C)
- How can we perform operations with numbers written in Scientific Notation? (C)
- How can we compare numbers in Scientific Notation? (C)
- What kinds of numbers should be written in Scientific Notation? (D)
Critical Content:
- Each time the decimal is moved on spot, the number is multiplied or divided by 10.
- Scientific Notation must be written with the first factor being greater than 1 but less than 10.
- Scientific Notation must be written as a factor multiplied by a power of 10.
- When adding two numbers in Scientific Notation, make the exponents the same by moving the decimal, then add the factors.
- When subtracting two numbers in Scientific Notation, make the exponents the same by moving the decimal, then subtract the factors.
- When multiplying two numbers in Scientific Notation, add the exponents and multiply the factors.
- When dividing two numbers in Scientific Notation, subtract the exponents and divide the factors.
Key Skills:
- Convert from Scientific Notation to Standard Form and vise versa.
- Add, subtract, multiply and divide numbers in Scientific Notation.
- Given two numbers in either form, determine which number is larger or smaller.
Assessment with Scoring Guide:
What: Use exponents to simplify, compare, and perform operations with very large and very small numbers.
Why: …in order to make meaning of these numbers that are often found in the real-world.
How: You are a mathematician working at NASA. Your job is to research the distances from Earth to all of the other planets. Then, complete the following:
- Write the distances in Scientific Notation
- Order the distances from least to greatest
- How many times greater is…
- The distance from Earth to Saturn than the distance from Earth to Mars?
- The distance from Venus to Pluto than the distance from Venus to Earth?
- Explore the distance from our galaxy to others. Compare some of the distances you find to the distances in our Solar System. Explain your findings.
Suggested Learning Experiences:
Two are described in detail below.
Unit Overview:
Scientific Notation is a tool that is used by people in many different careers to simplify very large or very small numbers. In this unit, students make connections between Scientific Notation and the Laws of Exponents. Students have just completed the unit on exponents, and are familiar with how to add, subtract, multiply, and divide expressions that contain exponents. After making the connection, students are able to apply their new knowledge to real-world problems. Students come up with generalizations about the kinds of numbers that are being converted into Scientific Notation.
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Lesson #1: Converting Numbers in Scientific Notation
Before This Lesson:
This lesson will be the second day of this unit. Before this lesson, students will have seen numbers in Scientific Notation. They will understand that the first factor must be greater than 1 but less than 10, and they will understand that the factor is multiplied by a power of 10.
Standards:
- EE.3: Use numbers expressed in the form of a single digit times and 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.
- EE.4: Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities.
Objectives:
- Students will be able to convert numbers in Standard Form into Scientific Notation.
- Students will be able to convert numbers in Scientific Notation into Standard Form.
Resources and Materials:
- Teacher
- Cards with numbers in both Standard Form and Scientific Notation
- Whiteboard/Marker
- Student
- Pencil/Paper
Learning Tasks:
- Matching Activity: The teacher will give groups of students cards with numbers on them. Half of the cards will have certain numbers in Standard Form, while the other half of the cards will have the same numbers in Scientific Notation. Their task is to match up the Standard Form with the Scientific Notation.
- See-Think-Wonder: After students have matched up cards with their group members, explain the ‘See-Think-Wonder’ activity to students. Allow students to explore their thinking with the previous activity. They will be looking at pairs of numbers (one in Standard Form, and one in Scientific Notation). Students will write down their thoughts for each of the 3 ‘stages’ in this routine.
- Class Discussion: The teacher will lead a class discussion over the previous activities. The teacher will put ideas and thoughts on the board to make thinking visible for students.
- Procedure: The teacher will first ask groups to come up with a ‘procedure’ for going from Scientific to Standard and vise versa. They will once again be focusing on the pairs they formed with the cards in the initial matching activity. Give students plenty of time to come up with this process. At the end of class, share out ideas. End the lesson by solidifying a process for converting these numbers (if one of the groups doesn’t come up with a legitimate process, the teacher will have to show them).
Assessment:
- Students will be informally assessed during the matching activity. The teacher will walk around and observe the pairs of numbers students are grouping together.
- Students will be more formally assessed during the See-Think-Wonder activity. The teacher will collect the notes that students write down for each ‘stage’ in the routine. The teacher will informally assess as well by listening to students during their discussion.
Social Media:
- https://www.youtube.com/watch?v=Dme-G4rc6NI&t=33s
- https://twitter.com/g_brgmn/status/862125418589147136
- https://twitter.com/GAM4ths/status/877937172157931521
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Lesson #2: Comparing Numbers in Scientific Notation
Before This Lesson:
This lesson would be the 4th or 5th day of the unit. The comparing would take place after students have learned how to convert, but before they have learned how to perform operations with numbers in Scientific Notation.
Standards:
- EE.3: Use numbers expressed in the form of a single digit times and 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.
- EE.4: Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities.
Objectives:
- Students will be able to determine which number is greater given two numbers in Scientific Notation.
- Students will be able to determine which number is greater given one number in Scientific Notation and one number in Standard Form.
Resources and Materials:
- Teacher
- Computer/Video with Speakers
- Worksheets
- Student
- Pencil/Paper
- Laptop
Learning Tasks:
- Video: Start by showing students the ‘Powers of 10’ video (Link #2 under Media). This video will give students an idea of how massive some of the numbers are that we are dealing with.
- Group Discussion: Have students discuss in groups the following questions after the video:
- What stood out to you about the video?
- What questions do you have after watching the video?
- How is this video related to our current unit on Scientific Notation?
- Research: Give students a prompt that requires them to compare the mass of planets. They can collect data on the masses of planets however they’d like by researching online. Students will research in groups of 2 or 3.
- Comparisons: Have students come up with 3 significant comparisons that they find interesting. (For example, maybe students discover that Jupiter is 2.5 times more massive than all of the planets in our solar system combined)
- Share Out: Students will share out BOTH their findings and their math work. Students will need to show the class how they came up with the comparisons.
Assessment:
- Students will turn in their worksheet after they have researched the planet masses. Their work must also show the math behind the comparisons.
- ***Note: Students have not yet performed operations formally with Scientific Notation. However, some students may figure out the process of adding, subtracting, multiplying and dividing with Scientific Notation during this activity.
Social Media:
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Bobby –
Great job on all of this, but I especially like your What-Why-How assessment. You definitely captured what Erickson, et al, were demonstrating, and I find it helpful to see another example of it in action. Good work!!
– Angie
Bobby,
I enjoyed reading through your lesson dealing with scientific notation. Two of my favorite things about scientific notation are:
* E Notation – I believe someone mentioned this in your discussion post
* Fermi Questions – Uses scientific notation to do huge estimates http://www.physics.uwo.ca/science_olympics/events/puzzles/fermi_questions.html
Great job on your unit.
-GB
Wow! This is so cool! I have heard of Fermi Questions but never knew what they were or where they came from. I will have to explore this website!
Bobby, I love your lessons. Taking something like scientific notation and making it more interesting. I think the flow of your lessons are great. Here is some interesting scientific notation activities to consider on pinterist:
https://www.pinterest.com/explore/scientific-notation/
Thanks Cory! This will especially help with the assessment piece. The Scientific Notation Maze looks like an interesting worksheet that could be given as a homework assignment or an extended exit slip.
Hi Bobby,
Great job on bringing in real world concepts into your lesson. Growing up I wanted to be an astronaut so I would have loved being in your class and learning about the planets. It is fascinating information that I think the students will really be interested in.
So I have always wanted to try this strategy with partner work and never really done it in my class. Your lesson reminded me of it. So in your case, you would hand each student a notecard as they came into your classroom with either standard or scientific notation of a certain number written on it. It is their job to find the student who has the matching card (the opposite of either standard or scientific) and that is their partner for the day for the activity you are doing. I have read about this idea before and never actually tried it but something I want to do sometime as it is so feasible with a lot of mathematics topics.
Hey Kristyn! What a great idea! I have heard about a similar activity that is actually used on the first day of school. You get a 52-card deck of playing cards. Shuffle the deck, and hand one card to each student as they walk in the room for the first time. The students are to sit with someone who has a card that shares the same characteristic as theirs. Some students will sit with students who have the same color card, others will sit with the same number/value, others will sit with the same suit, etc. It leads to a good discussion that allows all students to participate in the class conversation.
This would be a great activity for my students with scientific notation. Thanks!
Good suggestions, guys! I love the idea of matching up the different forms of scientific notation as the students enter. I tried a similar activity with a Geometry class, giving them features of particular geometric shapes and asking them to find other students with the same shape (i.e. a student with formula for area of circle and 1/2*diameter=radius would connect b/c they’re both related to circles). I then had the students work in those groups on the day’s activity. (Easy way to create random groupings!)
I haven’t heard the playing card option before, but it reminded me of the WODB that you suggested on my post, Bobby. Once again, there are multiple ways to be “correct,” which is great!
Bobby,
I really like that your learning experiences start on day two. I think it will be very valuable for your students to head into these lessons with some base knowledge. Having students use that knowledge as a building block to build their own conversion rules will be a super powerful connection as they create their own mathematics! Way to bring space into the scientific notation lesson. Students love space and relating it to math will be something I hope they latch on to. A cool extension to your second lesson would be to ask students what other situations they might use scientific notation to express and have them present their ideas and maybe a poster outlining where they would use scientific notation, how they would use it and why it would be helpful.
Great lessons!!
Hey Amy! Thanks for the input! I think a project after the unit is a great idea. Students can research and choose topics that incorporate scientific notation (such as cells or organisms) and create a presentation. As you said, they could even create posters and we could have some kind of gallery walk. It could even be open to the public!
Bobby, I love the context that you provided for the unit… so fun to think about NASA and how they use scientific notation to talk about huge distances. I really like the sequence of tasks you have in your first lesson, especially with the See, Think, Wonder, and the task where students create a procedure for “translating” from standard form to scientific form. Having students discover this instead of telling them should be a very valuable experience! Another easy option for assessment would be to do an exit ticket at the end of the lesson (or entrance ticket at the beginning of class the next day) that has students use the procedure they created or learned about in the lesson.
Thanks Courtney! Sometimes I’m hesitant with having students discover a formula or procedure without me telling them first. While it usually leads to deep understanding, sometimes students completely miss the point. I am hoping at least one student in each of the groups can make the connection between scientific notation and standard form. If not, I will have to go back and reteach this topic. We shall see!