|Lesson Plan Title/Info:||Lesson Plan - Unit 1: Lesson 05: Pumping Powers of Ten (Place Value, Scientific Notation, and Exponent Rules) Is Number 5 Of 13 In Unit Plan - Unit 1: Health and Fitness (Number Operations and Data Collection)|
|Creator:||Myrtle Holland: firstname.lastname@example.org|
|Grade Level:||Seventh Grade|
1. How are place value and powers of ten related?
2. Why is being able to read and write numbers in scientific notation and decimal notation important?
1. Ask students to discuss what they think 10^2 means. (10 times 10, 100, the exponent tells how many zeros, etc.) Then ask students what they think (1/10)^2 means.(1/100, one hundredth). Ask students what 10^0 means. (Most may say 0 so go into the idea that the exponent tells the number of zeros, so if we have no zeros-- what number is that? An informal proof of how any number raised to the zero power is always one may be an possible extension) Also discuss 10^1 and just 10.
2. Pass out the power of ten charts or handout 2 (choose your preferred handout) for students to complete. If they follow the pattern, students should see that the decimal numbers (numbers less than one but greater than zero) have exponents that are negatives, therefore going back to the (1/10)^2 example also means 10^-2. Review the answers to the chart to make sure students have the correct answers.
3. Have students record the pattern in their notebook along with examples.
Place Value Power of Ten Activity
Using index cards make two sets of cards for each group of four students. One set has the powers of ten from 10^4 to 10^-5 (one on each card). The other set has the digits zero through nine.
Display the number 81,462.39057. Students will mix up the digit cards and place them face down in a stack. One card at time will be turned over and the group will find and display the correct power of ten place value card. Have students go through the first time together. Then using the same cards, have two students pick a card and the other two give the place value. Students would then switch and do the same activity.
To review the whole group, place a similar number on the board and using larger cards (so all students can see), have students compete in teams to be the first to display the correct place value card.
|Activating Prior Knowledge:||
Review expanded notation:
23.45= (2 x 10) + (3 x 1) + ( 4 x 0.1) +(5 x 0.01)
Using the power of ten chart, rewrite the notations with powers of ten.
Do several other examples: Ex.: (0.0195)
|Specialized Vocabulary Development:||
Words to add to the word wall and student notebooks:
powers of ten
(suggested time from
Investigation of scientific notation.
Using a computer and projector, go to this website http://micro.magnet.fsu.edu/primer/java/scienceopticsu/powersof10/ and watch the video that show the sizes of the Milky Way (light years) down to the quarks of a carbon atom (attometers). The sizes are in scientific notation and show the reasoning for writing numbers with very large values and very small values (magnitudes) in scientific notation.
(Break if 45 minute class)
1. Refer to the expanded notation example done earlier. Discuss that the form with powers of ten is an example of a number written in scientific notation.
2. Put these examples on the board.
2.3 X 10 ^4
1.93 X 10 ^ 2
5.0 X 10 ^-3
8.0401 X 10^ -2
3. Discuss the place values represented and which examples are greater than one and less than one. Some students may say all the examples are all greater than one, but discuss that these forms are in scientific notation.
4. Discuss what scientific notation looks like: 1. A number between 1 and 10 and 2. the number times a power of ten.
Work on converting numbers in standard (decimal) notation to scientific notation.
Discuss with students the largest significant place value in each example.
24,000; 0.03; 102,000; 0.124;
24,000 --- 2.4 x 10 ^4 (ten-thousands)
0.03 --- 3 x 10^-2 (hundredths)
102,000 --- 1.02 x 10^5 (hundred-thousands)
0.124 --- 1.24 x 10^-1 (tenths)
5. Ask students to brainstorm methods for writing in scientific notation.
Possibilities: Record the methods for student reference.
Converting to standard (decimal) notation.
1. Have students discuss how to convert 3.45 x 10^ 5 and 6. 02 x 10^ -3 back to standard (decimal) notation. Record suggestions.
(Class Break if not on block schedule.)
Scientific Notation, Calculators and Exponent Rules
1. Give the students two large numbers and have students multiply them together using a calculator. (Ex.: 30,000,000,000 x 2,000,000,000) The answer will come out in scientific notation. (6E19) Discuss how this compares to the scientific notation form and what standard form would look like.
2. Have students write the two above numbers in scientific notation and as a multiplication problem. 3 x 10 ^ 10 times 2 x 10^9 = 6 x 10^19. Using the calculator, have students enter the scientific notation form of the numbers and see the product result.
3. Again have students multiply 100,000 by 200,000. Discuss result and again have students write out the multiplication problem in scientific notation. Again, have students enter the scientific notation form of the numbers and see the product result.
4. Using pair-share, have students discuss any possible patterns. (Multiply the first terms (numbers) and add the exponents to get the product).... 1 x 2 = 2 and 10^ 5 x 10 ^5 = 10^ 10 .... result - 2 x 10^10 and from example one: 3 x 2 = 6 and 10^10 x 10^9 = 10^ 19 ... result - 6 x 10^10.
5. To check to see if the pattern works for all products have student pairs make up problems to trade and check.
6. To check the pattern for all numbers (and emphasize that the bases must be the same) have students investigate using examples such as 2^3 x 2 ^4. Does this product equal 2^7?
7. Using the same method have students investigate division of large numbers. Ex.: 800,000,000 / 4,000,000. They should come up with the pattern that you divide the first terms and subtract the exponents. Do several examples to prove the point. Also have students explore the rule for other bases than 10. Ex: 3 ^ 5 / 3 ^ 3.
8. Have students record in their notebooks, the patterns of exponents that they found.
|Summarize/Debrief the Lesson
(suggested time from
To check for student understanding of this lesson, place students in groups of two and using the chart from http://www.enchantedlearning.com/subjects/astronomy/planets/ Have student pairs make a poster showing the following:
1. The distance of each planet from the sun in miles written in scientific notation.
2. Order (smallest to largest) the planets in our system by mass (kg) and by diameter (Km) using scientific notation.
3. Using scientific notation and the exponent rules, determine how many times heavier Jupiter is than Pluto. First round all decimal numbers (in scientific notation form) to the nearest whole number (Ex.: Venus - 4.87 x 10^24 rounds to 5 x 10^24.) and then determine the result. Answers should be in full sentences with both scientific and standard forms shown.
4. Rounding as you did in the previous section, pick two other planets and multiply their masses together. Answers should be in full sentences with both scientific and standards form shown.
5. Display the posters around the room for class discussion.
Other options for summarizing this lesson.
1. In order to do the following activity, go to the computer lab or use a computer and projector to display the studystack website (www.studystack.com). Show students how to get on-line and make their own study stacks. (Make one yourself using vocabulary from previous lessons for students to see and use. If there is time have students setup their own login names and passwords.)
2. Your best friend has been out of school for a few days because of health problems and you need to catch him/her up on the concept of scientific notation. Write a short lesson on scientific notation. In the lesson, you should include
a. Definitions of scientific notation, standard notation, and decimal notations, place value, powers of ten, and significant digits
b. Reasons for being able to read and write numbers in scientific notation and standard notations.
To make sure your friend practices, go to www.studystack.com and make a login name and password. Once you can get on, make a study stack of at least 10 cards that have definitions as well as examples of converting to and from scientific notation.
Give your friend the name of your study stack so that they can go and practice. Make sure that you save your study stack under the math category.
(Supply students with no Internet access at home time to make their stacks during school time or give them index cards to make their study stacks)
1. Please emphasize that the exponent rules only work with the same bases.
2 You should go to the study stack website and become familiar with the site. Make up one set that you can show students and if possible have them login and make their own practice set of cards.
3. To help special education students, pair them up with regular ed students. Perhaps have students make up problems for each other and them have them check each other’s answer. Also move around the room checking for understanding. Also the use of the Frayer model, notebook and word wall should help with all student retention and understanding.
4. To tier the lesson, you may want ot use only numbers from thousands to thousandths for students who struggle with place value.
interactive whiteboard (optional)
power of ten charts
|Duration:||90- 120 minutes|
|Date Created:||April 27, 2008|
|Date Modified:||July 04, 2008|
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