Objective To introduce exponential notation for powers of 10 as a way of naming the values of places in our base-ten system. 1 Teaching the Lesson materials Key Activities ٗ Math Journal 1, p. 130 Students fill in a place-value chart that shows place-value headings expressed as powers ٗ Student Reference Book, p. 271 of 10. They use exponential notation to represent powers of 10. Study Link 5᭜8 ٗ Key Concepts and Skills ٗ Teaching Aid Master (Math • Read and write large numbers; identify the digits and their values. Masters, p. 388 or 389) ,Number and Numeration Goal 1] ٗ Transparency (Math Masters] p. 166; optional) • Use exponential notation to represent powers of 10. [Number and Numeration Goal 4] ٗ • Use expanded notation to represent powers of 10. [Number and Numeration Goal 4] calculator • Identify and describe patterns in a place-value table. [Patterns, Functions, and Algebra Goal 1] See Advance Preparation Key Vocabulary scientific notation • trillion • quadrillion • quintillion • sextillion • powers of 10 • exponent Ongoing Assessment: Recognizing Student Achievement Use a Math Log or Exit Slip. [Patterns, Functions, and Algebra Goal 1] 2 Ongoing Learning & Practice materials Students play Polygon Pair-Up to practice naming properties of polygons. ٗ Math Journal 1, p. 131 ٗ Students practice and maintain skills through Math Boxes and Study Link activities. Student Reference Book, p. 258 ,Study Link Master (Math Masters ٗ p. 167) Polygon Pair-Up Property Cards and ٗ Polygon Cards (Math Masters, pp. 496 and 497) 3 Differentiation Options materials ٗ ENRICHMENT EXTRA PRACTICE ELL SUPPORT Teaching Master (Math Masters, p. 168) ٗ Students investigate powers Students use exponential Students find various ways of 10 with a calculator. notation. of using the word power. 5-Minute Math, pp. 2, 3, and 7 calculator ٗ Additional Information Advance Preparation For Part 1, draw a place-value chart on the board like the one on journal Technology page 130, or use a transparency of Math Masters, page 166. Assessment Management System Math Log or Exit Slip See the iTLG. Lesson 5᭜9 361 Getting Started Mental Math and Reflexes Math Message Write large numbers through the billions on the board, Find the largest number you can in the World Tour and have volunteers read them aloud. Suggestions: section of your Student Reference Book. 396,467 3,654,987 5,123,467,890 283,950 17,834,567 8,312,945,607 Study Link 5᭜8 Follow-Up 712,945 527,000,348 3,980,246,571 The number in the place-value chart should be Ask questions such as: 92,106,954,873. Accept either of the following • What digit is in the millions place? ways to write the number: • What is the value of the digit x? ᭟ 92 billion, 106 million, 954 thousand, 873 • How many billions are there? ᭟ ninety-two billion, one hundred six million, nine hundred fifty-four thousand, eight hundred seventy-three 1 Teaching the Lesson ᭤ SMALL-GROUP Math Message Follow-Up ACTIVITY (Student Reference Book, p. 271) Divide students into small groups so they can compare answers. You might give them a few additional minutes to look for an even larger number. Then have the groups report their answers and write them in the place-value chart on the board. Discuss the answers. The largest numbers in the World Tour section of the Student Reference Book are found on page 271. The total population of the world is given in the table near the Student Page bottom of the page. Although this is not the largest number in the World Tour section, it is probably the largest number that most World Tour students will recognize at this time. Facts About the World Dimensions of the Earth Continents are large land masses. There are Equatorial circumference*: seven continents on the Earth, although Europe about 24,900 miles The largest number in the World Tour section is found in the and Asia are sometimes thought of as one (40,000 kilometers) Equatorial diameter**: continent. Most continents contain many about 7,930 miles other table on page 271. The approximate weight (mass) of Earth countries, but there are no countries at all (12,760 kilometers) 11 21 ء in Antarctica. Volume: 2.6 x 10 cubic miles (1.1 x 1012 cubic kilometers) is listed as 6.6 10 tons. This number is read as “6 point 6 A country is a territory and the people who live Weight (mass): 6.6 x 1021 tons 21 there under one government. The number of (6.0 x 10 metric tons) times 10 to the 21st power.” countries in the world often changes as countries Total world water area: about 139,433,000 square miles split apart or join with other countries. At this (361,129,000 square kilometers) time, there are about 200 countries in the world. *Circumference is the distance around a circle or sphere. Numbers written in this form are said to be in scientific Population is the number of people who **Diameter is the distance live in a certain region. Population growth is measured by a straight line passing from one side of a notation. the change in the population every year after circle or sphere, through the This is how the number looks, written out: all births and deaths are accounted for. center, to the other side. The population growth rate is the increase (or decrease) in population per year, written as a percent. 6 600 000 000 000 000 000 000 The world’s population is now increasing by about 200,000 , , , , , , , people per day, or about 75 million people per year. Over the last 40 years, the world’s population has about doubled. It reached ion ion ion ion ion ion ill ill ill ill ill ill the 6 billion mark in 1999. World population is expected to reach tr b about 9 billion people by the year 2050. int m sext qu thousand The Continents quadr Percent of World Area Percent of Continent Population* Population (sq miles) Land Area Write this 22-digit number on the board, including the labels for North America 509,000,000 8.0% 8,300,000 14.8% South America 367,000,000 5.8 6,800,000 12.1 Europe 799,000,000 12.5 4,100,000 7.3 thousands, millions, billions, and so on. Point out the place-value Asia 3,797,000,000 59.5 16,700,000 29.8 Africa 874,000,000 13.7 11,500,000 20.5 group names that are used for numbers larger than billions, Australia 32,000,000 0.5 3,300,000 5.9 Antarctica 0 0.0 5,400,000 9.6 namely trillions, quadrillions, quintillions, and sextillions. World Totals 6,378,000,000 100.0% 56,100,000 100.0% (about 6.4 billion) *Data are for the year 2004. World population growth rate for the year 2004: about 1.2% per year Ask students to read the number by using the name labels written Student Reference Book, p. 271 beside the commas. 6 sextillion, 600 quintillion 362 Unit 5 Big Numbers, Estimation, and Computation ᭤ WHOLE-CLASS Introducing Exponential ACTIVITY Notation for Powers of 10 Links to the Future (Math Journal 1, p. 130) The discussions of exponential notation and scientific notation are exposures to the topics. They will be revisited more formally in In preparation for later work with scientific notation, it is useful later grades. The use of exponential notation to show how place-value headings can be expressed as powers of is a Grade 5 Goal, and the use of scientific 10 using exponential notation. notation is a Grade 6 Goal. 1. Review the place-value headings that students are familiar with on journal page 130—ones, tens, hundreds, and so on. Ask them to write the standard numerals in Row 1 of the place-value chart. 2. Review the relationship between the value of each place and the place to its right. The value of each place is 10 times the value of the place to its right. Students complete the 10-times-as-much pattern in Row 2. 3. Tell students that numbers like 100, 1,000, and 10,000 are called powers of 10. They are numbers that can be expressed as products whose factors are 10. Have students fill in Row 3 of the chart on their journal page. 4. Instead of repeating the factor 10, we can use the shorthand introduced in the Math Message Follow-Up. For example, ”can be written as 102 (read “10 to the second power 10 ء 10 can be written as 103 (read 10 ء 10 ء or “10 squared”). 10 “10 to the third power” or “10 cubed”). The raised digit, called the exponent, tells how many times 10 is used as a factor. Ask students to fill in Row 4 of the chart on their journal page. Student Page 130 Date Time LESSON 5 ᭜ 9 Hundred Ten and Powers ofPlace Value 10 Millions Thousands Hundreds Tens Ones Thousands Thousands 1,000,000 100,000 10,000 1,000 100 10 1 10 [100,000s] 10 [10,000s] 10 [1,000s] 10 [100s] 10 [10s] 10 [1s] 10 [tenths] ء 10 ء 10 ء 10 ء 10 ء 10 10 10 ء 10 10 ء 10 ء 10 10 ء 10 ء 10 ء 10 10 ء 10 ء 10 10 ء 10 ء 10 6 4 1 10 105 10 103 102 10 100 Fill in this place-value chart as follows: 1. Write standard numbers in Row 1.