Guided Lessons

# I Got The Power!

Do your students understand the power of 10? This lesson will allow your students to see the utility of the power of 10 in mathematics and come to a concrete conclusion of how 10 impacts the value of mathematical equations.

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Students will be able to identify and explain patterns in the number of zeros of the product when multiplying a number by powers of 10, identify and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10 and use whole number exponents to denote powers of 10.

(10 minutes)
• Review place value and order of operations.
• Remind students that our number system is a decimal system and it relies on groupings of 10s. Tell students that we also utilize a place value system, with the value of each digit depending on its position or place in the number.
• Write "1,000,000" on the board and ask students to identify at least one other way this number can be written. Possible answers include: writing the words “one million” or 10 x 10 x 10 x 10 x 10 x 10.
• Tell students that mathematicians created a shortcut for writing very large numbers, and that today they are going to explore this technique.
(15 minutes)
• Display the Exponent Chart on the board.
• Cover up a few of the fields or leave some of the fields blank and allow students to use the other fields to predict what will go in the fields that are covered.
• Once predictions have been made, allow students to verbally identify patterns in each column by discussing it with a partner.
• Allow students to share their patterns with the class.
• Using the chart, explain to students that mathematicians established our number system a long time ago and that any number raised to the power of zero would equal 1.
• Using the chart, explain to the students that any base number raised to the power of 1 is the base number.
• Using the chart, explain to students that any number raised to the power of 2 is the base number multiplied by itself.
• Ask the students if they are beginning to see a pattern. Let them know that it will make more sense as they proceed and continue to look for patterns.
• Allow students to use an online exponents calculator.
(30 minutes)
• Since students in elementary school are often fascinated by large numbers, such as a million, a zillion, and a trillion, this is a good opportunity to have them try to get an idea of just how big those numbers really are.
• Use an interactive whiteboard to complete the guided steps below:
• Write the following numbers on the board and have students use whole number exponents to denote powers of 10 and then identify patterns that they see:
``````1. 1,000,000,000
2. 1,000,000,000,000
3. 1,000,000,000,000,000
• Students should understand that the number of 0s in the number equals the value of the exponent.
• Write the following exponential notation numbers on the board and have students write the numbers in standard form and then identify patterns that they see:
``````1. 10^4
2. 10^5
3. 10^6
4. 10^7
• Students should understand that the exponent value equals the number of 0s in the number.
• Write the following on the board and have students use exponential notation to simplify the value and then identify patterns that they see:
``````1. 250
2. 2,500
3. 25,000
4. 250,000
• Students should understand that when simplifying values they should take any numbers before the zero and multiply it by the exponential notation which is the number 10 with an exponent that equals the amount of 0’s.
• Write the following on the board and have students multiplying a number by powers of 10 and then identify patterns that they see:
``````1. 36 x 10^1
2. 36 x 10^2
answer: 36 x (10x10)= 36 x 100=3,600
3. 36 x 10^3
answer: 36 x (10x10x10)= 36 x 1000=36,000
4. 36 x 10^4
• Students should understand that when multiplying a whole number by a power of 10, one converts the exponent into standard form, counts the number of zeros after the 1 and add the 0s to the end of the whole number.
• Write the following on the board and have students work on equations that emphasize placement of the decimal point when a decimal is multiplied or divided by a power of 10 and then identify patterns that they see:
``````1. 2.5 x 10^3
answer: 2.5 x (10 x 10 x 10)=
2.5 x 1,000 = 2.5000, then move decimal 3 places to the right
=2,500
2. 0.22 x 10^2
0.22 x 100= .22000, then move decimal places 2 places to the right
=22
3. 0.042 ÷ 10^2
0.042 x 100=.04200, then move decimal 2 places to the left
=.00042
4. 63.4 ÷ 10^3
63.4 ÷ 1,000 = 63.4000, then move decimal 3 places to the left
=.0634000
=.0634``````
• Students should understand that when multiplying a decimal by a power of ten and moving the decimal point one place to the right for each 0 after the 1 and when dividing a decimal by a power of ten and moving the decimal point one place to the left for each 0 after the 1.
(45 minutes)
• Pass out the I Got The Power worksheet.
• Ask students to use their notes from the guided practice to help them work independently to follow the instructions on the worksheet.
• Tell students that they are going to work independently to use whole number exponents to denote powers of 10, write the numbers in standard form, use exponential notation to simplify the value, multiplying a number by powers of 10, and decipher the placement of the decimal point when a decimal is multiplied or divided by a power of 10.
• Enrichment: Students can create a “test” bank of questions or worksheets and answers using a word processing program.
• Support: Provide struggling students with a peer tutor who can help explain the concepts in student friendly language.
• Students can use a word processor to create a worksheet or test bank of questions and answers.
• The students can video themselves answer the independent practice problems to be used for peer tutoring.
(20 minutes)
• Have students use the following prompts to write an explanation and provide an example of: a. using a whole number exponent to denote powers of 10, b. writing the numbers in standard form, c. using exponential notation to simplify the value of a number, and d. multiplying a number by powers of 10 and deciphering the placement of the decimal point when a decimal is multiplied or divided by a power of 10.
• If time permits, allow students to come to the whiteboard and explain their answers.
• Students can use a camera phone or tablet to record explanations of their answers in an effort to expand on their technological skills.
(10 minutes)
• Recap the components of this unit by reviewing the chart in the guided practice section or problems from their independent practice.
• Ask students why they think it is important to know this information.