Numbers Large and Small. Chapter NUMBER. Big Idea. Learning Goals. Essential Question. Important Words

Transcription

1 NUMBER Numbers Large and Small Chapter Big Idea Understanding very large and very small numbers helps me describe and solve real-world problems. Learning Goals I can show my understanding of place value for numbers greater than one million. I can show my understanding of place value for numbers less than one thousandth. I can use technology to solve problems involving large numbers. Essential Question How can understanding large and small numbers help me understand the world around me? Important Words billion expanded form million millionth period standard form ten thousandth 3

2 Large Numbers Use your knowledge of large numbers to read and write numbers in standard and expanded form, and to compare and order large numbers. Example: Show the number in many ways. This number is one billion, three hundred five million, sixty-seven thousand, eight hundred ninety. I can write the number in a place value chart. Billions Millions Thousands Units Hundred Ten One Hundred Ten One Hundred Ten One Hundred Ten One I can write the number in expanded form as Or as (1 x ) + (3 x ) + (5 x ) + (6 x ) + (7 x 1000) + (8 x 100) + (9 x 10) 11. Write each number in a place value chart. a b c d List the numbers in question 1 from smallest to largest. Circle the largest number. Put a rectangle around the smallest number. How do you know those numbers are the largest and the smallest? 13. What is the value of the 5 digit in each number below? a b c d e f CHAPTER 3: Numbers Large and Small

3 Large Numbers (continued) 14. Put the numbers in question 3 in order from smallest to largest. Explain the strategies you used. 15. Use the place value chart below to answer the following questions. Billions Millions Thousands Units Hundred Ten One Hundred Ten One Hundred Ten One Hundred Ten One a. Describe any patterns you see in the place values. b. Each set of three place values is called a period. Describe any patterns you see in the periods. c. Model one of the numbers and explain how your model shows the pattern in the place values. d. Write each number in expanded form. e. Write each number in standard form. f. Read each number aloud and write it in words. A period in a number is a group of three place values: one, ten, hundred. g. One number has a 9 in the thousands period. Locate the digits 1, 2, 3, and 4 in the chart. Name the period where each digit is found. 16. The numbers below are written in expanded form. Write each number in standard form. Expanded form uses multiplication to show the value of each digit in a number. Standard form is the way numbers are usually written. The value of a digit is shown by its location. a b. ( ) + ( ) + ( ) + (4 100) c d. ( ) + ( ) + (2 100) + (4 10) CHAPTER 3: Numbers Large and Small 57

4 Large Numbers (continued) 17. The numbers below are written in words. Write each number in standard form. a. five million, four hundred twenty-seven thousand, one hundred twelve b. nine hundred seventy-eight million, six hundred thirty-four thousand c. one hundred eighty-five billion 18. Write the number that is a less than b less than c greater than 450 d greater than e less than f greater than A billion is a thousand millions, or Use your calculator to answer the questions below. a. Press each calculator key in order from 1 to 8. What number is displayed? b. What value does each digit have in the number displayed? c. What is the largest number that can be displayed in your calculator? 58 CHAPTER 3: Numbers Large and Small

5 Large Numbers (continued) 10. Write each of the following numbers in standard form. a. 15 billion b thousand c million d billion e thousand f million 11. Compare each pair of numbers by writing a statement using the greater than (>), less than (<), or equal (=) symbol. a and 3.4 million b. Eighty-four thousand and c. 2.5 million and 2500 thousand 12. Find the number described in each riddle. a. I am a number between 1 and I have six digits and the hundred digit is the same as the hundred thousands digit. There are six thousands. The digit in the tens is half the digit in the thousands. The tens digit is two more than the ones digit. If you add the digit in the thousands place to the number of tens and then subtract the number of ones you get the ten thousands digit. The hundreds digit is three less than the ten thousands digit. b. I am a number between 1 and I have eight digits, and no digits are repeated. There is one ten and three ten millions in the number. The digit in the thousands place is twice the digit in the tens place. The thousands digit is half the digit in the millions place. The digit in the ten thousands place is less than the digit in the tens place. The digit in the hundred thousands is twice the number of ten millions. The sum of the digits in the millions period is the digit in the hundreds place. The ones digit is two less than the hundreds digit. CHAPTER 3: Numbers Large and Small 59

6 Large Numbers (continued) c. I am a number between 1 million and 1 billion. I have nine digits. The millions digit and the hundreds digit are the same. There is one ten thousand. The digit in the ten millions place is double the digit in the tens place. The ten millions digit is half of the digit in the hundred millions place. There is a two in the tens place. The hundred thousands digit is three more than the ones digit. The digit in the ones is four more than the digit in the tens. The millions is the difference between the hundred thousands and the ones. The digits in the ten thousands place and the thousands place are consecutive. 13. Write your own riddle for a number between 1 million and 100 billion. Exchange with a partner and try to find each other s number. Compare the strategies you each used to find the number. 14. Explain how the patterns in place values could be important in knowing about numbers. 15. Our number system is sometimes called a base ten system. Use what you know about place value to explain why that is a good name for our number system. I can show my understanding of place value for numbers greater than one million. 60 CHAPTER 3: Numbers Large and Small

7 Numbers Around Us Use your knowledge of large numbers to work with numbers from contexts such as sky science, populations, money, and technology. Example: In 1998, the music industry sold seven hundred eleven million CDs. Of these, they sold approximately: one hundred sixty million, nine thousand R & B albums. three hundred eighty-one million, thirty thousand rap albums. one hundred million, four hundred thousand alternative albums. two hundred seventeen million country albums. a. Write each number in standard form. R & B Rap A lt Country b. Order the numbers from smallest to largest. A lt R & B These both have 1 hundred million, but R & B has 6 ten millions so it sold more than A l ternative. Country Rap Rap is the highest because it has 3 hundred millions. c. Explain when you might choose to write numbers in each of these forms. I would always write the digits. I think numbers are easier to compare when they re written in standard form. The numbers might need to be written in words if they were starting a sentence. CHAPTER 3: Numbers Large and Small 61

8 Numbers Around Us (continued) 11. The following headlines include large numbers. City of Edmonton plans to spend more than $1.5 million to fix roads Walk-a-thon raises almost a quarter-million for cancer research Wednesday lottery draw an estimated $50 million China s population passes 1.3 billion Crowd of over 56K attends Stampede game a. Write each number in standard form. b. Explain why headlines might write numbers in this way. 12. Write a headline using each of the following numbers. a b c d Estimate or research to gather the following data: the number of legs on a dog the number of students in our class the number of students in the school the number of books in the library the cost of a new car the cost of a house the amount you could win in the lottery the number of people who live in Canada the distance from Mars to the Sun the number of people who live in India a. What sorts of numbers did you find? b. In which period is each number? c. Which number is largest? smallest? 62 CHAPTER 3: Numbers Large and Small

9 Numbers Around Us (continued) 14. The population for each of the ten most populous countries is given in the table below. Country Population (2010) China India United States Indonesia Brazil Pakistan Bangladesh Nigeria Russia Japan a. Write each population in a place value chart. A million is a thousand thousands, or b. Japan s population is about million. Write each population in millions. 15. The number of transistors used in a computer chip in each decade since their invention in the 1950s is shown in the table below. Decade 1950s Number of transistors one 1960s s s 1990s 2000s 275 thousand 3.1 million billion a. Write each number in standard form. b. What observations can you make about the number of transistors used in a computer chip in each decade? c. Predict how many transistors there might be in one computer chip in the 2010s. CHAPTER 3: Numbers Large and Small 63

10 Numbers Around Us (continued) 16. The diameter of each of the first four planets in our solar system is shown below. Planet Diameter (millions of metres) Mercury 4.88 Venus Earth Mars a. Write each number in standard form. b. Write each number in expanded form. c. List the planets in order from the one having the smallest diameter to the one having the largest diameter. 17. The largest bill still printed in Canada is the $100 bill. In the last century, some countries have printed bills with large numbers on them. Country Angola Argentina Bolivia Bosnia-Herzegovina China Germany Hungary Zimbabwe Bill kwanzas readjustos pesos 10 million pesos bolivianos dinara yuan marks 100 quintillion pengo 100 trillion dollars a. Write the number on the bill from Bolivia in standard form. b. A quintillion is a 1 with 18 zeros after it. Write the number for the bill from Hungary. c. A trillion is a 1 with 12 zeros after it. Write the number for the bill from Zimbabwe. d. Name the country that had the bill with the highest number. e. Explain whether you can tell from the numbers which bill is worth the most. 64 CHAPTER 3: Numbers Large and Small

11 Numbers Around Us (continued) 18. The average distance from the sun to each of the eight planets is given in the table below. Planet Average distance from the sun (kilometres) Earth Jupiter Mars Mercury Neptune Saturn Uranus Venus a. Write four of the distances in another form, such as in millions of kilometres. b. List the planets in order from the one closest to the Sun to the one farthest from the Sun. 19. Explain whether one ten million is the same as ten millions. 10. Explain the strategies you used to order large numbers. 11. Why might there be many ways to write the same number? I can show my understanding of place value for numbers greater than one million. CHAPTER 3: Numbers Large and Small 65

12 Small Numbers Use your knowledge of small numbers to read and write numbers in standard and expanded form and to compare and order small numbers. Example: Show the number in many ways. This number is zero and three hundred seventy-five ten thousandths. I can write it in a place value chart Ones Tenths Hundredths Thousandths Ten Thousandths 7 5 Hundred Thousandths Millionths Ten Millionths Hundred Millionths I can write the number in expanded form as Or as (3 x 0. 01) + (7 x ) + (5 x ) Or as + + I can write this number as a fraction What is the value of the 5 digit in each number? a b c d e f The numbers below are written in expanded form. Write each number in standard form. a b. (8 0.1) + (6 0.01) + ( ) + ( ) c d CHAPTER 3: Numbers Large and Small

13 Small Numbers (continued) 13. Use the place value chart to answer the following questions.. Tenths Ones Ten Hundred Hundredths Thousandths Thousandths Thousandths Millionths Ten Millionths Hundred Millionths a. Describe any patterns you see in the place values. b. Model one of the numbers and explain how your model shows the pattern in the place values. c. Write each number in expanded form. d. Write each number in standard form. e. Read each number aloud and write each number using words. 14. Write each number in a place value chart. a b c d List the numbers in question 4 from smallest to largest. Circle the largest number. Put a rectangle around the smallest number. How do you know the numbers are the largest and the smallest? 16. Write each of the following numbers in words. a b c d e Order the numbers from question 6 from smallest to largest. CHAPTER 3: Numbers Large and Small 67

14 Small Numbers (continued) 18. Write each of the following as numbers in standard form. a. two and three hundred sixty eight thousandths b. four hundred and ninety-three ten thousandths c. four hundred ninety-three ten thousandths One millionth is one part when a whole is divided into one million parts. d. sixteen and seven hundred four thousand, nine hundred twenty-five millionths 19. You have been given the digits 2, 5, and 8, a decimal point, and four 0 digits. Use all of these digits to make a number: One ten thousandth is one part when a whole is divided into ten thousand parts. a. less than one b. close to one c. close to 0.5 d. less than one thousandth e. close to f. close to one ten thousandth g. close to one quarter 10. Arrange the numbers you made in question 9 from smallest to largest. 68 CHAPTER 3: Numbers Large and Small

15 Small Numbers (continued) 11. Compare each pair of numbers by writing a statement using the greater than (>), less than (<), or equal (=) symbol. a and b. 3 millionths and c and 8 hundred thousandths 12. Solve each riddle to discover the mystery number. a. My number has four digits. My number is greater than one. The digit in the hundredths is the same as the number of toes on one foot. The ones digit is two greater that the hundredths digit. The digit in the tenths place is three less than the digit in the ones place. The thousandths digit is half the tenths digit. b. My number has five digits. My number is less than 10. The first two digits are consecutive numbers. The ones digit is the same as the number of legs on a dog. The digit in the ten thousandths place is the same as the number of tails on a dog. The hundredths digit is seven more than the ten thousandths digit. The thousandths is five less than the sum of the ten thousandths and the hundredth. 13. Write the number that is: a less than b greater than c less than d greater than 450. e. 0.1 less than f greater than CHAPTER 3: Numbers Large and Small 69

16 Small Numbers (continued) 14. Numbers can be expressed as decimals or fractions. a. Copy and complete the table below. Place value Decimal Fraction Ones 1 1 Tenths 0.1 Hundredths 0.01 Thousandths Ten thousandths Hundred thousandths Millionths What fraction might be used to represent: b ? c ? d ? 15. How could you use fractions to write a decimal number in expanded form? 16. Write your own mystery number riddle using a number between one millionth and one. Exchange with a partner and try to find each other s number. Compare the strategies you each used to find the number. 17. Explain how the patterns in place values could be important in knowing about numbers. 18. Our number system is sometimes called a base ten system. Use what you know about place value to explain why that is a good name for our number system. I can show my understanding of place value for numbers less than one thousandth. 70 CHAPTER 3: Numbers Large and Small

17 Numbers in the World Use your knowledge of small numbers to read and write numbers in standard and expanded form. The numbers are taken from contexts such as statistics, body science, and measurement. Example: The anthrax bacteria causes a disease that can affect humans and livestock. The bacteria are between and metres long. Show this number in many ways. I can read these numbers as one millionth of a metre and nine millionths of a metre. I can show these numbers in a place value chart. Ones Tenths Hundredths Thousandths Ten Thousandths Hundred Thousandths Millionths Ten Millionths Hundred Millionths I can write metres as 9 x metres. I can think of m as mm. 11. Coach Nichols collected the statistics below about the kids on his baseball team. He wants to calculate the batting average of each player. The batting average is the number of hits divided by the number of times at bat. Name Number of hits Number of times at bat Amal Curtis Erica Jared Krista Nina Thomas a. Use a calculator to find the batting average of each player. b. Arrange the players in order from highest to lowest batting average. CHAPTER 3: Numbers Large and Small 71

18 Numbers in the World (continued) 12. Environment Canada, a department of the Government of Canada, tracks the precipitation in cities across Canada. The average precipitation (in metres) in each city in four specific months is shown in the table below. City January (m) April (m) July (m) October (m) Victoria, BC Edmonton, AB Winnipeg, MB Ottawa, ON Fredericton, NB St. John s, NL Whitehorse, YK a. Which city gets the most precipitation in January? the least? b. Which city gets the most precipitation in April? the least? c. Which city gets the most precipitation in July? the least? d. Which city gets the most precipitation in October? the least? e. In which city would you like to live? Why? 13. The dimensions of different parts of the average human body are shown in the table below. Body part Hair Front tooth Red blood cells Liver cell Ovum Fingernail Dimension m wide m wide m wide m long m long 0.01 m wide a. Write each number in a place value chart. b. Write each number in expanded form. c. Compare expanded form and place value charts for showing numbers. d. Arrange the body parts from smallest to largest. 72 CHAPTER 3: Numbers Large and Small

19 Numbers in the World (continued) 14. One of the longest bugs is a stick bug which can grow to 36 cm, or 0.36 m. The length of some of the smallest bugs is shown in the table below. Bug Dust mite Red ant Fairy fly Feather-winged beetle Nanosellini beetle Flea Length m m m m m m a. Write each number in expanded form. b. Compare expanded form and standard form for showing numbers. c. Name the shortest insect whose length is shown in this table. 15. Silk, cotton, and wool have been used for clothing for thousands of years. The width of four fibers is shown in the table below. Fiber Spider web silk Cotton fiber Silk fiber Wool fiber Width m m m m a. Write each number in words. b. Explain whether you can tell from the numbers which fiber will be the smoothest. 16. Explain whether one ten thousandth is the same as ten thousandths. 17. Explain the strategies you used to compare small numbers. 18. Why might there be many ways to write the same number? I can show my understanding of place value for numbers less than one thousandth. CHAPTER 3: Numbers Large and Small 73

20 Numbers Large and Small Use your knowledge of small and large numbers to compare and order numbers. You will need to work with numbers in standard and expanded form. Example: million 985 millionths Explain how you know which number is bigger. Ada s strategy: Millions are much larger than millionths so million must be more that 985 millionths. Bianka s strategy: I put both numbers into the same place value chart to compare them. Hundred Million Ten Million One Million Hundred Thousands Ten Thousands One Thousand Hundreds Tens Ones Tenths Hundredths One Thousandths Ten Thousandths Hundred Thousandths One Millionths Ten Millionths Dakota s strategy: I used a calculator to multiply x to get I multiplied 985 x to get Then I compared the numbers is much bigger than Cailyn s strategy: I wrote each number in expanded form to help me tell which was bigger CHAPTER 3: Numbers Large and Small

21 Numbers Large and Small (continued) 11. Write a number between: a. 1 and c and e and b. 0 and 1. d and f. 0 and Use your calculator to find the operation that can be used to find the next number in the table. a. When moving from the millions place value down to the smaller number. b. When moving from the millionths place value up to the larger number. Place value Value Millions Hundred thousands Ten thousands Thousands 1000 Hundreds 100 Tens 10 Ones 1 Tenths 0.1 Hundredths 0.01 Thousandths Ten thousandths Hundred thousandths Millionths CHAPTER 3: Numbers Large and Small 75

22 Numbers Large and Small (continued) 13. Compare each pair of numbers by writing a statement using the greater than (>), less than (<), or equal (=) symbol. a. ten thousand and ten thousandths b and c. 2.4 and 2.4 million d. 324 millionths and Use a calculator to find the pattern in each set of expressions. Predict the next term in the pattern. b. 2 3 a In your own words, explain standard form and expanded form. I can show my understanding of place value for numbers greater than one million. I can show my understanding of place value for numbers less than one thousandth. I can use technology to solve problems involving large numbers. 76 CHAPTER 3: Numbers Large and Small

23 Numbers at Large Use your knowledge of small and large numbers to estimate and calculate answers to problems in contexts such as science, geography, technology, money, and measurement. Example: Mary reads for 25 minutes each night. For how many minutes does she read in two years? For how many hours does she read for in two years? For how many seconds does she read in two years? 25 minutes x 365 nights x 2 years = minutes Mary reads for minutes in two years m 60 m/hour = hours Mary reads for hours in two years m x 60 seconds/m = seconds Mary reads for seconds in two years. 11. The diameter of each of the first four planets in our solar system is shown below. Planet Diameter (millions of metres) Mercury 4.88 Venus Earth Mars a. Write each number in standard form. b. Determine how much larger the diameter of Venus is than the diameter of Mercury. c. Calculate how many times larger the diameter of Venus is than the diameter of Mercury. d. Explain whether you think the number from b or the number from c tells you more about the size of Venus and Mercury. e. Find the planet with a diameter that will fit about twice into the diameter of another planet. CHAPTER 3: Numbers Large and Small 77

24 Numbers at Large (continued) 12. Two different boxes of balloons are available at the local party store. a. Find the cost of one balloon from each box. b. Explain which box is the better buy. 13. Statistics Canada tracks the population of every region in the country. The populations are shown in the table below: Province or Territory 2008 population (millions) Alberta British Columbia Manitoba New Brunswick Newfoundland and Labrador Northwest Territories Nova Scotia Nunavut Ontario Prince Edward Island Québec Saskatchewan Yukon a. Calculate the total population of Canada in millions. b. Write the population of Canada in standard form. c. Write the population of Canada in expanded form. d. Calculate how many more people there are in Alberta than in Saskatchewan. e. Calculate how many times larger Alberta s population is than Saskatchewan s population. f. Explain whether the number from d or the number from e tells you more about the populations of Alberta and Saskatchewan. g. Write two questions that can be answered using the numbers in this table. 78 CHAPTER 3: Numbers Large and Small

25 Numbers at Large (continued) 14. Environment Canada tracks the precipitation in cities across Canada. The average precipitation (in metres) in each city in four specific months is shown in the table below. City January (m) April (m) July (m) October (m) Victoria, BC Edmonton, AB Winnipeg, MB Ottawa, ON Fredericton, NB St. John s, NL Whitehorse, YK a. Calculate the total precipitation in each city for the months shown. b. Which city gets the most total precipitation? c. Which city gets the least total precipitation? d. What is the difference in precipitation between the two cities in b and c? e. In which city would you prefer to live? Why? 15. A million dollars sounds like a lot of money. a. How many five cent candies can you buy for a million dollars? b. How many eighty-five cent candy bars can you buy for a million dollars? c. How many $ cars can you buy for a million dollars? d. How many $ houses can you buy for a million dollars? e. What would you buy with a million dollars? 16. Susannah sleeps eight hours each night. a. How many hours does she sleep in one year? b. Susannah is 12 years old. How many hours has she slept in her life? c. How many minutes has Susannah slept in her life? d. How many seconds has Susannah slept in her life? e. How many years has Susannah slept in her life? CHAPTER 3: Numbers Large and Small 79

26 Numbers at Large (continued) Use a calculator to help you answer the following questions. Explain the steps you followed to answer each question. 17. Explain whether you think one million tennis balls would fit into your classroom. 18. Calculate how many times your heart has beat in your life. 19. Determine which is taller, you or a million-dollar stack of ten-dollar bills. 10. Use a dictionary to estimate the number of words in the English language. 11. How did using a calculator help you answer these questions? 12. Write your own question using large or small numbers. Exchange questions with a partner and solve each other s problem. Compare the solution strategies you used. I can show my understanding of place value for numbers greater than one million. I can show my understanding of place value for numbers less than one thousandth. I can use technology to solve problems involving large numbers. 80 CHAPTER 3: Numbers Large and Small