Distance/Scientific Notation

Day 5 - Math Lesson

 

Lesson objectives:

·         Students will be able to use the distance formula to figure out distances of two objects.

·         Students will be able to translate large or small numbers into scientific notation.

·         Students will be able to check their answers by plugging their answers back into the equation.

 

Content:

In this lesson students will be introduced to the distance formula as well as to scientific notation. We will practice how to use both of these as well as apply them to situations they are learning about in their science class. By the end of the lesson students will understand and know how to find distances and how they can write large numbers in a shorter form.

 

Materials:

·         Attached distance worksheet

·         Attached supplementary worksheet (for students to show work)

 

Lesson Introduction: Address in the Universe

·         Have students write down on a piece of paper their street address. While students do this write the street address of the school on the board. Next tell students to write the city they live in. Do the same for the school on the board.  Have students write the state they live in, then the country. Ask students to continue working on their address individually. Tell them to identify the next biggest areas in which we live. After giving students a few minutes to finish their address in the universe bring the class together to help identify and finish up the schools address on the board.

·         When finished it should look something like this:

  §  <street address>

             <city>,<state>

            <country>

            <continent>

           <hemisphere>

            <Earth>

          <Solar System>

           <Milky Way>

         <Local Group>

           <Universe>

·         Discuss with the students how small we are compared to the vastness of the Universe and how huge and magnificent our God must be to create something so huge.

    o   Start discussion by looking at the address that they wrote above. How many people live on your street? In your city? State? Etc. Could you see our class from a different planet, from the outside of the universe? How big must   our God be to create something so huge?

·         Introduce what they will be working on for the day, finding distances of far off objects in space and being able to write them in a form that will make it easier to read rather then writings huge numbers.

 

Procedure:

1)      Remind students about the Division Property of Equality. (If you divide each side of the equation by the same nonzero number, the two sides remain equal.)

2)      Have students get into pairs and take turns describing to each other each stage of solving multiplication equations.

  §  You may want to use the equation 24=X3, or another equation you may come up with.

3)      Bring class together and go over how to solve the equation as a class.

  §  Need to get X by itself

  §  Divide both sides by the same number (in this case 3)

  §  Get the answer of X = 8

  §  Have student plug the answer back into the equation to make sure it works.

4)      Introduce the distance equation. d=rt or d=st (distance=rate x time or distance=speed x time).

5)      Do some examples together as a class for finding distance.

  §  An airplane is traveling at 600 mph. How many miles would it travel in 2.5 hours? (1,500 miles)

  §  A turtle’s rate/speed is .25 mph. If the turtle travels for 5 hours how far would it go? (1.25 miles)

  §  A dragonfly can fly at a rate/speed of 18 mph. If the dragonfly travels for 5 hours how far would it go? (90 miles)

6)      Give each student the distance worksheet and supplementary worksheet and have them work through the problems individually. (NOTE: Only have students work on the first column. They will work on the other columns later on in the unit.) When they have had enough time to finish the worksheet, have them get into small groups and go over their answers to make sure they got the same answers. If their answers are different have them discuss and find an answer that they can agree on.

7)      Introduce to the class scientific notation. Discuss how it’s a way of writing very large or very small numbers in a more condensed way to make it easier to read. This is often used by scientists who deal with these kinds of numbers.

8)      Tell students that a number expressed in scientific notation needs to be written as a product of a number that is at least 1 but less then 10, and a power of ten. Also tell students that the decimal part of a number written in scientific notation is often rounded to the hundredths place.

9)      Do some examples on the board. (You can use these examples or examples of your own.)

  §  Write 4,500,000,000 on the board and have students write it in scientific notation.

                                                               i.      Answer: 4.5 x 10^9

  §  Write 1,000,000,000,000 on the board and have students write it in scientific notation.

                                                               i.      Answer: 1.0 x 10^12

  §  Write 7.9 X 10^5 on the board and have students write it in standard form.

                                                               i.      Answer: 790,000

  §  Write 3.0 X 10^9 on the board and have students write it in standard form.

                                                               i.      Answer: 3,000,000,000

10)   When students have a good understanding of how to do scientific notation have them pull out the worksheet they were working on earlier with distances and write the answers they found under the scientific notation column. (NOTE: Have students work only on the scientific notation column. They will work on the other columns later on in the unit.)

 

Closure:

·         Go back to the address activity the students did at the beginning of the lesson. Talk about how far away all of these other objects in space are from us and how many different things make up the universe. Discuss the vastness of the universe and how unfathomable not only the size of the universe is, but also our God, because God created the unfathomable universe?

·         Tie how we found the distances of various stars in space and how in science today they have learned/will learn about different characteristics of stars.

 

Extension:

Have students choose three stars that they did not already have in class from the list on the cosmobrain.com website that they would be interested in finding the speeds of. Have students write down these stars and the distance they are from the sun. Have students use the speed of the fastest spaceship which is approximately 72,000 km/h to solve the equations. Students should figure out the amount of time it would take them to get to these stars from the sun. Have students write the numbers in scientific notation. You may have students do more then three or the students can choose to do more then three stars if so desired.

 

Evaluation:

1)      Observe students during opening activity as well as group work. Teacher may take notes if desired and use them to assess student work and what needs to be worked on or gone over again.

2)      Grade the worksheet using the answer key attached and look over student work on supplementary worksheet that students worked on in class. You may also use the attached answer key for this as well.

 

Resources:

1)      Bailey, Day, Frey, Howard, Hutchens, McClain, et al. (2004). Mathematics: Applications and concepts. Columbus: Glencoe/McGraw-Hill.

           ·          This book was used to help generate examples for the board and worksheet. It also supplied the extension activity.

2)      These websites were used to find information for the distance worksheet.

           ·         Carter, L. (2003, August 25). Curious about astronomy: How far is each planet from the Earth?. Retrieved November 6, 2009, from http://curious.astro.cornell.edu/question.php?number=564

           ·         Soares, E. (2002). The nearest stars. Retrieved November 6, 2009, from http://www.cosmobrain.com/cosmobrain/res/nearstar.html

3)      Soares, E. (2002). The nearest stars. Retrieved November 6, 2009, from http://www.cosmobrain.com/cosmobrain/res/nearstar.html

 

 

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