Comparing Data Objective To guide students as they look up and compare numerical data, including geographical measurements. www.everydaymathonline.com epresentations etoolkit Algorithms Practice EM Facts Workshop Game Family Letters Assessment Management Common Core State Standards Curriculum Focal Points Interactive Teacher s Lesson Guide Teaching the Lesson Ongoing Learning & Practice Differentiation Options Key Concepts and Skills Read and write large numbers. [Number and Numeration Goal 1] Develop the meaning of percent as per 100. [Number and Numeration Goal 5] Compare large numbers. Use a table of information. [Data and Chance Goal 2] Key Activities Students use the World Tour section of the Student Reference Book to look up population, area, and climate data for countries and capitals of Europe. They identify the maximum and minimum values for each count or measure. They compare counts and measures by comparing the initial digits of the numbers. Materials Math Journal 1, p. 134 Student Reference Book, pp. 279 281, 294 (optional), 297, 301, and 304 Study Link 5 10 Math Masters, p. 426 (optional) slate Updating the World Tour Math Journal 1, pp. 171 173, 178, and 179 Student Reference Book, pp. 276, 277, 279 281, 297, 302 305 Math Masters, pp. 419 421 (optional) Students continue their World Tour by traveling from Cairo, Egypt, to Budapest, Hungary. They update their Route Map and complete the Country Notes for Hungary. Students who are keeping a Route Log update it. Solving Addition and Subtraction Number Stories Math Journal 1, pp. 134A and 134B Students solve addition and subtraction number stories. Math Boxes Math Journal 1, p. 135 Students practice and maintain skills through Math Box problems. Ongoing Assessment: Recognizing Student Achievement Use Math Boxes, Problems 2a 2d. Study Link Math Masters, p. 172 Students practice and maintain skills through Study Link activities. Advance Preparation For the optional Readiness activity in Part 3, make a place-value mat by taping together Math Masters, pages 492 and 493. READINESS Playing Number Top-It Student Reference Book, p. 255 Math Masters, pp. 492, 493, and 506 per partnership: 4 each of number cards 0 9 (from the Everything Math Deck, if available) tape Students practice comparing numbers. EXTRA PRACTICE Playing High-Number Toss Student Reference Book, p. 252 Math Masters, p. 487 per partnership: 1 six-sided die Students practice comparing numbers. Teacher s Reference Manual, Grades 4 6 pp. 230, 261 264 Lesson 373
Getting Started Mental Math and Reflexes Write pairs of numbers on the board. Students record the larger number on their slates. Suggestions: 3,482 and 3,982 3,982 35,281 and 34,975 35,281 984,063 and 984,065 984,065 6,005 and 6,500 6,500 78,004 and 78,400 78,400 1,239,462 and 1,239,362 1,239,462 8,600 and 8,599 8,600 238,756 and 209,899 238,756 5,400,780 and 5,410,780 5,410,780 Math Message Find the table listing the tallest mountains on page 304 in your Student Reference Book. Which digits tell you that Everest is taller than K-2? ten thousands thousands hundreds tens ones Study Link 5 10 Follow-Up Have students compare their rounded numbers for the census data. Ask which 20-year span showed the greatest growth. 1980 to 2000 1 Teaching the Lesson Math Message Follow-Up (Student Reference Book, p. 294 (optional); p. 304) WHOLE-CLASS World Tour Unit feet Largest Oceans and Seas Average Depth (feet) Pacific Ocean 64,186,300 12,925 Atlantic Ocean 33,420,000 11,730 Indian Ocean 28,350,500 12,598 Arctic Ocean 5,105,700 3,407 South China Sea 1,148,500 4,802 Caribbean Sea 971,400 8,448 Mediterranean Sea 969,100 4,926 Bering Sea 873,000 4,893 Gulf of Mexico 582,100 5,297 Okhotsk Sea 537,500 3,192 Largest Deserts Sahara Africa 3,500,000 Gobi Asia 500,000 Libyan Africa 450,000 Patagonia S. America 300,000 Rub al Khali Asia 250,000 Kalahari Africa 225,000 Great Sandy Australia 150,000 Great Victoria Australia 150,000 Chihuahua N. America 140,000 Tallest Mountains Height (feet) Everest Nepal Tibet 29,028 K-2 (Godwin-Austen) Kashmir 28,250 Kanchenjunga Nepal India 28,208 Lhotse I (Everest) Nepal Tibet 27,923 Makalu I Nepal Tibet 27,824 Lhotse II (Everest) Nepal Tibet 27,560 Dhaulagiri I Nepal 26,810 Manaslu I Nepal 26,760 Cho Oyu Nepal Tibet 26,750 Nanga Parbat Kashmir 26,660 Longest Rivers Length (miles) Africa 4,160 Nile Amazon S. America 4,000 Chang (Yangtze) Asia 3,964 Huang (Yellow) Asia 3,395 Ob-Irtysh Asia 3,362 Congo Africa 2,900 Lena Asia 2,734 Niger Africa 2,590 Parana S. America 2,485 Mississippi N. America 2,340 Largest Freshwater Lakes Superior N. America 31,700 Victoria Africa 26,828 Huron N. America 23,000 Michigan N. America 22,300 Tanganyika Africa 12,700 Baykal Asia 12,162 Great Bear N. America 12,096 Malawi (Nyasa) Africa 11,150 Continent Student Reference Book, p. 304 Highest/Lowest Elevation Points Highest/ Lowest Point Elevation (feet) Africa Mt. Kilimanjaro, Tanzania 19,340 Lake Assal, Djibouti 512 Antarctica Vinson Massif 16,864 Bentley Subglacial Trench 8,327 Asia Mt. Everest, Nepal Tibet 29,028 Dead Sea, Israel Jordan 1,312 Australia Mt. Kosciusko, New S. Wales 7,310 Lake Eyre, South Australia 52 Europe Mt. El brus, Russia 18,510 Caspian Sea, Russia-Azerbaijan 92 N. America Mt. McKinley (Denali), Alaska 20,320 Death Valley, California 282 22,834 S. America Mt. Aconcagua, Argentina Valdés Penninsula, Argentina 131 Social Studies Link On the board, draw a unit box like the one in the margin. Write the names and heights of Everest and K-2, and underline the digit in the ten-thousands place in each numeral. Everest 29,028 K-2 28,250 Point out that this digit (2) is the same for both numbers, so it cannot be used to decide which mountain is higher. Now underline the second digit (thousands) in each numeral. Use a double underline, because these digits are different. Everest has one more thousand than K-2. So Everest is higher. Everest 29,028 K-2 28,250 The remaining 3 digits in each number can be ignored, because they are in the hundreds or smaller. Only the first 2 digits (the ten-thousands and thousands digits) are needed to determine that Everest is higher than K-2. Repeat this routine by comparing the heights of K-2 and Kanchenjunga and then the heights of Lhotse I and Makalu I. K-2 28,250 Lhotse I 27,923 Kanchenjunga 28,208 Makalu I 27,824 tens digit breaks the tie hundreds digit breaks the tie 374 Unit 5 Big Numbers, Estimation, and Computation
Finally, use the Oceans and Seas table shown on the same page of the Student Reference Book. Compare the depths of the Indian and Arctic Oceans. (You need to look only at the ten-thousands place.) Compare the depths of the Arctic Ocean and the South China Sea. (You need to look only at the thousands place.) Adjusting the Activity Refer students to Student Reference Book, page 294 for more information about how geographical measurements such as heights of mountains, depths of oceans, and lengths of rivers are obtained. A U D I T O R Y K I N E S T H E T I C T A C T I L E V I S U A L Looking Up and Comparing Data about the Countries in Europe (Math Journal 1, p. 134; Student Reference Book, pp. 279 281, 297, and 301; Math Masters, p. 426) PROBLEM SOLVING 5 11 Traveling to Europe It is time to leave Africa. Your destination is Region 2 the continent of Europe. You and your classmates will fly from Cairo, Egypt to Budapest, Hungary. Before exploring 280 297 301 Hungary, you will collect information about the countries in Region 2. You may even decide to visit another in Europe after your stay in Budapest. Use the World Tour section of your Student Reference Book to answer the questions. 1. Which in Region 2 has a. the largest population? France 60,424,000 population b. the smallest population? Iceland 294,000 population c. the largest area? France 211,200 sq mi. area d. the smallest area? Netherlands 16,000 sq mi. area Use the Climate and Elevation of Capital Cities table on page 297. 2. From December to February, which capital in Region 2 has a. the warmest weather? Athens Greece 56/45 F capital temperatures b. the coolest weather? Oslo Norway 32/20 F capital temperatures c. the greatest amount of rain? Rome Italy 3.3 capital inches rainfall d. the least amount of rain? Warsaw Poland 1.2 capital inches rainfall Use the Population Data table on page 301. 3. Which in Region 2 has a. the greatest percent of population ages 0 14? Iceland 23 percent b. the smallest percent of population ages 0 14? Italy 14 percent Math Journal 1, p. 134 Social Studies Link Students complete journal page 134 by looking up the information in the World Tour section of the Student Reference Book. Country population and area data are listed in the Country Profiles on pages 279 281. Temperature data are listed in the Climate and Elevation of Capital Cities table on page 297. Percent of a s population that is 0 14 years old is listed in the Population Data table on page 301. Adjusting the Activity ELL Have students shade 10-by-10 grids to interpret the Percent of Population Ages 0 14 data in the table on Student Reference Book, page 301. For example: The percent of population ages 0 14 for Ethiopia is 47. This means that 47 out of every 100 Ethiopians are 14 years old or younger. Have students shade 47 squares on a 10-by-10 grid (Math Masters, page 426). The shaded squares, 47_, represent the percent of the Ethiopian population that is 100 14 years old or younger. The percent of population ages 0 14 for the United States is 21. Have students shade 21 squares on a 10-by-10 grid (Math Masters, page 426). The shaded squares, 21_, represent the percent of the U.S. population that is 100 14 years old or younger. A U D I T O R Y K I N E S T H E T I C T A C T I L E V I S U A L Links to the Future In Unit 9 of Fourth Grade Everyday Mathematics, students will rename fourths, fifths, tenths, and hundredths as decimals and percents. Lesson 375
Water, Water Everywhere Solve each problem below. Record a number model for the problem using a letter for the unknown. You may want to use two number models for some of the problems. Then write a summary number model with your answer in place of the letter. 1. The world s largest lake is the Caspian Sea, with an area of about 143,200 square miles. The second largest lake, Lake Superior, has an area of about 31,320 square miles. What is the approximate total area of both lakes? Answer: About 174,520 square miles 143,200 + 31,320 = t 143,200 + 31,320 = 174,520 2. The Nile River in Egypt is about 4,132 miles long. The longest river in the United States, the Missouri River, stretches about 2,540 miles. How much longer is the Nile River than the Missouri River? Answer: About 1,592 miles 4,132 2,540 = m 4,132 2,540 = 1,592 3. To grow a single orange, it takes about 13.8 gallons of water. A tomato is made of 95% water, but takes only 3 gallons of water to grow it. How much more water is needed to grow an orange than a tomato? Answer: About Sample number models are given. 10.8 gallons 13.8 3 = m 13.8 3 = 10.8 Math Journal 1, p. 134A 178A 178B 134A 2 Ongoing Learning & Practice Updating the World Tour (Math Journal 1, pp. 171 173, 178, and 179; Student Reference Book, pp. 276, 277, 279 281, 297, and 302 305; Math Masters, pp. 419 421) Social Studies Link Students follow the established World Tour routine. They update the Route Map by drawing a line segment to connect Cairo, Egypt, and Budapest, Hungary. They use the World Tour section of the Student Reference Book to locate facts about Hungary and Budapest and fill in the Country Notes pages for this and capital. If students are using a Route Log, they update it. Solving Addition and Subtraction Number Stories (Math Journal 1, pp. 134A and 134B) Students solve addition and subtraction number stories about water. They find the answer, record a number model with an unknown, and then record a summary number model. Math Boxes (Math Journal 1, p. 135) Water, Water Everywhere continued 4. The average depth of the ocean is 4,267 meters. The deepest spot, Challenger Deep in the Mariana Trench near Guam, is about 11,030 meters below the surface. How much deeper is Challenger Deep than the average depth of the ocean? Sample number Answer: About 6,763 meters models are given. 11,030-4,267 = d 11,030-4,267 = 6,763 5. The total annual rainfall for the three wettest inhabited places in the world is 1,416 inches. In the wettest place, Cherrapunji, India, it rains about 498 inches per year. In the second wettest place, Mawsynram, India, it rains about 467 inches per year. About how many inches per year does it rain in the third wettest place, Waialeale, Hawaii? Answer: About 451 in. 1416 498 467 = r (number model(s) with unknown) 1416 498 467 = 451 (number model(s) with answer) 6. Alaska, the biggest state in the United States, has more miles of rivers and streams than any other state. The next four highest ranked states are California with 211,513 miles; Texas with 191,228 miles; Montana with 176,750 miles; and Nevada with 143,750 miles. The top five states have 1,088,241 miles of rivers and streams. How many miles of rivers and streams does Alaska have? Answer: About 365,000 miles 211,513 + 191,228 + 176,750 + 143,750 = 723,241; 1,088,241-723,241 = m (number model(s) with unknown) 211,513 + 191,228 + 176,750 + 143,750 = 723,241; 1,088,241-723,241 = 365,000 (number model(s) with answer) Mixed Practice Math Boxes in this lesson are paired with Math Boxes in Lesson 5-9. The skill in Problem 6 previews Unit 6 content. Ongoing Assessment: Recognizing Student Achievement Math Boxes Problems 2a 2d Use Math Boxes, Problems 2a 2d to assess students ability to compare numbers up to 1 billion. Students are making adequate progress if they can insert > and < symbols to make true number sentences. Some students may be able to solve Problem 2e, which involves exponential notation for powers of 10. Study Link (Math Masters, p. 172) Home Connection Students compare numerical data. They practice reading numbers in the billions. Math Journal, p. 134B 376 Unit 5 Big Numbers, Estimation, and Computation
3 Differentiation Options READINESS Playing Number Top-It (Student Reference Book, p. 255; Math Masters, pp. 492, 493, and 506) 5 15 Min To explore comparing large numbers, have students play Number Top-It. Players make a place-value mat by taping together Math Masters, pages 492 and 493. Students compare two numbers by seeing them, one under the other, with the same-place digits aligned. Students compare the values of the aligned pairs of digits, starting on the left. For example: Math Boxes 1. Estimate the sum. Write a number model to show how you estimated. a. 799 + 11,304 + 48,609 Number model: b. 4,382 + 6,911 + 7,035 Sample answers: 800 + 11,000 + 49,000 = 60,800 Number model: 4,000 + 7,000 + 7,000 = 18,000 3. a. Draw a pair of parallel line segments. Sample answer: b. Draw a pair of perpendicular line segments. Sample answer: 5. Multiply. Use a paper-and-pencil algorithm. 7 208 = 1,456 181 2. Write <, >, or = to make each number sentence true. a. 356,789 > 354,999 b. 670,000 < 67,000,000 c. 62 million > 9,700,000 d. 105,000,000 > 15,500,000 e. 10 4 > 1,000 4. Complete. +0.12 Rule: in out 6.46 6.58 3.08 11.34 25.25 100.1 63.09 63.21 3.20 11.22 25.37 99.98 5 6 94 95 162 166 6. Which of the angles below has a measure less than 90 degrees? Circle it. 5,274,906 The millions digits are the same; their value is 5,000,000 each. 18 19 93 5,293,881 The hundred-thousands digits are the same; their value is 200,000 each. The ten-thousands digits are not the same; 90,000 is greater than 70,000, so 5,293,881 is greater than 5,274,906. Math Journal 1, p. 135 Have students record a few rounds of play on Math Masters, page 506 and then choose one of the rounds to explain how they knew which number was greater. EXTRA PRACTICE Playing High-Number Toss (Student Reference Book, p. 252; Math Masters, p. 487) 5 15 Min To practice comparing numbers, have students play High-Number Toss. See Lesson 2-7 for additional information. STUDY LINK Comparing Data This table shows the number of pounds of fruit produced by the top 10 fruit-producing countries in 2001. Read each of these numbers to a friend or a family member. 1. Which produced the most fruit? China 2. Which produced the least fruit? France Study Link Master Country Pounds of Fruit Brazil 77,268,294,000 China 167,046,420,000 France 26,823,740,000 India 118,036,194,000 Iran 28,599,912,000 Italy 44,410,538,000 Mexico 34,549,912,000 Philippines 27,028,556,000 Spain 36,260,392,000 United States 73,148,598,000 4 3. For each pair, circle the that produced more fruit. a. India Mexico b. United States Iran c. Brazil Philippines d. Spain Italy 4. Which two countries together produced about as much fruit as India? Italy and the United States Practice Estimate the sum. Write a number model. Sample answers: 5. 687 + 935 700 + 900 = 1,600 6. 2,409 + 1,196 + 1,327 2,400 + 1,200 + 1,300 = 4,900 7. 11,899 + 35,201 12,000 + 35,000 = 47,000 Math Masters, p. 172 Lesson 377