Mastering Skills & Concepts III Intermediate Mathematics. Print Activities

Transcription

1 Mastering Skills & Concepts III Intermediate ematics Print Activities

2 Riverdeep grants limited permission to classroom teachers to duplicate the reproducible portions of this publication for classroom use only and for no other purpose. In the interest of product improvement, information and specifications represented herein are subject to change without notice. ii Riverdeep Interactive Learning Limited. All rights reserved. MATH, Riverdeep, and the Riverdeep logo are trademarks of Riverdeep Interactive Learning Limited.

3 Table of Contents Mastering Skills & Concepts III NUMBERS AND NUMBER SENSE. Large and Small Numbers Whole Numbers to One Million Ordering and Rounding Whole Numbers Negative Whole Numbers. Numbers as Factors Finding Factors Prime and Composite Numbers Identifying Common Factors OPERATIONS WITH NUMBERS. Addition and Subtraction of Whole Numbers Whole Number Sums Differences Between Large Numbers. The Integers Integer Sums Differences Between Integers.3 Multiplication and Division of Whole Numbers Two-Digit Multipliers Introduction to Long Division Two-Digit Divisors 3 FRACTIONS 3. Proper and Improper Fractions Proper Fractions Improper Fractions Equivalent Fractions Ordering and Rounding Fractions 3. Addition and Subtraction Sums Involving Like Denominators Differences Involving Like Denominators Working with Unlike Denominators 3.3 Multiplication and Division Finding Products Quotients and Remainders iii

4 4 DECIMALS 4. Introduction Tenths, Hundredths, and Thousandths Ordering and Rounding Ratios, Decimals, and Percents 4. Addition and Subtraction Adding Decimals Subtracting Decimals 4.3 Multiplication and Division Multiplying Decimals Dividing Decimals by Whole Numbers 5 GEOMETRY 5. Measurement Lines, Angles, and Circles Rectangles and Squares Triangles Parallelograms and Trapezoids 5. Coordinate Geometry and Algebra The Coordinate Plane Symmetry and Transformations 6 DATA ANALYSIS AND PROBABILITY 6. Modeling and Displaying Events Displaying and Analyzing Data Looking at Chance iv

5 Notes to the Teacher Welcome to MATH. The student materials in this packet are designed to help students as they progress through the course. These materials, which remain consistent with the philosophy of MATH, are specifically intended to: keep students focused on the instruction. provide students with an opportunity to take notes, record information from the program, and reflect on the tutorials. allow students an opportunity for additional practice of the instruction in each session. provide a more open-ended assessment of the concepts in each session. use real-world examples and situations that students can identify with. There is a set of materials designed to support each session. Each set consists of: Student Logbook: This sheet is designed for students to use while viewing the tutorials. It consists of a one-page worksheet where students can record information from the tutorial, take notes, and reinforce their understanding. Your Turn: This is a one-page worksheet that provides additional practice for each session. It is designed for students to complete away from the computer to reinforce the concepts they have studied. It may also serve as a guide to what students need to review to complete their mastery of algebraic concepts. In addition, two sets of materials are provided to cover the concepts presented in each unit. Unit Review: The Unit Review problems are organized by session, with a fourth section integrating and extending the skills and concepts presented in the unit. Unit Assessment: Two pages of traditional practice covering all of the skills and concepts in the unit. v

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7 COURSE: MSC III MODULE : Numbers and Number Sense UNIT : Large and Small Numbers Whole Numbers to One Million As you work through the tutorial, complete the following.. What is your mission for this lesson?. Fill in the missing numbers from the list of the first ten whole numbers. 0,,, 3, 4, 5,, 7,, 9 3. When Dijit s height is unit, which expression represents the height of the dinosaur? Circle your answer If the dinosaur is 0 units tall, how tall is the skyscraper? is the same as , and its word name is. 7. To place commas in large numbers, we group the digits of the number in groups of starting at the right and moving to the is written in standard form as. 9. 0,000? Circle your answer The word name for 0,000 is. Key Words: Digit Place value Expanded form Standard form Thousand Ten thousand Hundred thousand Million Learning Objectives: Use 0 to generate the pattern of numbers, 0,00,,000, 0,000, 00,000, and,000,000 and to represent them in standard and word form. Expand the place value grid up to,000,000. Represent a number up to one million in expanded form and as the product of each digit times its place value. Write the word names of numbers up to a million.

8 . 0 0,000, and its word name is.. Write one million in standard form. 3. Fill in the missing numbers and labels on the place value grid. Millions Hundred Thousands Ten Thousands Thousands Hundreds Tens Ones , , , The number 756 contains hundreds tens and ones. 5. We can write 756 as 7 5 6, which is the product of each digit times its place value. 6. You can also write 756 as. This is called form. 7. The word name for,059 is.

9 COURSE: MSC III MODULE : Numbers and Number Sense UNIT : Large and Small Numbers Whole Numbers to One Million. Write the word name for 00,000.. Which of the following is equivalent to one million? a. Ten ten thousands b. Ten hundred thousands c. Ten one thousands 3. Complete each number sentence. a. 0 0,000 b. 0,000 c. 0, Write each number as the product of each digit times its place value. a. 395 b.,460 c. 870,0 5. Write each number in expanded form. a. 70,83 b.,05,65 c. 9,466 3

10 6. Write the word name for each number. a. 5 b. 7 c. 35,080 d. 69,000 e.,07, Mount McKinley, the highest peak in North America, is located in Alaska. The mountain is 0,30 feet tall and is also known by its native name, Denali, meaning The Great One. a. Write each digit of 0,30 in the place value grid above. b. The digit 3 represents the number of in 0,30. c. Write the word name for 0,30. d. Write 0,30 as the product of each digit times its place value. e. Write 0,30 in expanded form. 4

11 COURSE: MSC III MODULE : Numbers and Number Sense UNIT : Large and Small Numbers Ordering and Rounding Whole Numbers As you work through the tutorial, complete the following.. What is your mission for this lesson?. Write the word name for 4,056, The digit 4 in each of the numbers 4,056,33 and 4,778,33 is in the place. 4. To compare 4,056,33 and 4,778,33, since the digits in the millions place are the same, look next at the digits in the place. 5. Insert one of these signs,,, or to compare these numbers. Key Words: Number line Place value Scale Plotting a point Order, ordering a number Rounding a number Symbols:,,, Learning Objectives: Compare and order large numbers using place value grids and/or number lines. 4,778,33 4,056,33 6. An inequality sign points to the number. So, Which number is greater? Circle your answer.,9,836,739, The units used to identify the marked spaces along a number line make up the. Use equality or inequality signs to express the relationship between two whole numbers. Round whole numbers down to specified place values. Round whole numbers up to specified place values. 5

12 9. Approximating a number to a particular place value is called. 0. Which number represents 4,778,33 rounded to the nearest thousand? Circle your answer. 4,778,000 4,778,300 4,778,400 4,779,000. If a number being rounded lies less than halfway between two numbers, round it to the (lesser, greater) of the two numbers. Circle one.. To show that two numbers are approximately equal, use the symbol. 3. If a number is halfway between two numbers or more than halfway between them, round it to the (lesser, greater) of the two numbers. Circle one. 4. The number halfway between 5,000 and 6,000 has the digit 5 in the place. 5. When rounding a number to a particular place, look at the digit to the of that place. a. If that digit is less than 5, round to the number. b. If that digit is 5 or greater, round to the number. 6

13 COURSE: MSC III MODULE : Numbers and Number Sense UNIT : Large and Small Numbers Ordering and Rounding Whole Numbers. According to the U.S. Census, the population of Maine in 999 was,53,040. The population of Idaho was,5,700. Maine Idaho Millions a. Write the numbers for the populations of Maine and Idaho in the place value grid above. b. Which place would you look at to compare these two numbers? Hundred Thousands Ten Thousands Thousands c. Which state has the greater population?. Use,, or to compare each pair of numbers. Tell which place value you compared. Hundreds a. 5,49 5,073 b. 37,40 37,495 c. 8,006 8,06 d. 77,65 77,700 Tens Ones 3. Which place would you look at in order to round a number to each of the following place values? a. hundreds place b. ten thousands place c. millions place d. thousands place 7

14 4. Round the following numbers to the nearest hundred. a. 3,470 b. 09,557 c. 7,85,9 d Round the following numbers to the nearest thousand, and then plot the rounded numbers on the number line. a. 67,80 b. 63,507 c. 6,39 d. 69,97 60,000 70, The surface of the Sun has a temperature of 6,394 o F. a. Round this temperature to the nearest hundred. b. Round this temperature to the nearest thousand. 8

15 COURSE: MSC III MODULE : Numbers and Number Sense UNIT : Large and Small Numbers Negative Whole Numbers As you work through the tutorial, complete the following.. What is your mission for this lesson?. On a number line, the numbers to the of zero are greater than zero. 3. On a number line, the distance between one whole number and the next whole number is always unit. 4. The value of a number tells us how far it is from. 5. A number is a number greater than zero. A number is a number less than zero. 6. What sign used in front of a number tells us that a number is positive? negative? 7. Complete the scale on the number line below. Key Words: Negative number Positive number Number line Integers Zero Signed number Opposite numbers Symbols:,,,, Learning Objectives: Graph positive and negative whole numbers on a number line. Compare two or more integers using statements involving,, and. Round negative integers to specified place values numbers lie the same distance from zero on a number line, but on sides of zero. 9

16 9. The number that is halfway between two opposite numbers is. 0. Zero is a whole number that is neither nor.. A signed number is a or number.. The number is neither positive nor negative. 3. Negative numbers are used to measure which of the following? Circle your answer. Area Temperature Speed 4. On a vertical number line, numbers lie below zero, and numbers lie zero. 5. To report a temperature that is above zero, use a number. To report a temperature that is below zero, use a number. 6. The number 0 represents sea level. Positive numbers represent the height sea level, and negative numbers represent the depth sea level. 0

17 COURSE: MSC III MODULE : Numbers and Number Sense UNIT : Large and Small Numbers Negative Whole Numbers. The table below shows the average monthly temperatures in degrees Celsius during five months in a Wisconsin city. Month Nov. Dec. Jan. Feb. Mar. Temperature (C) a. Plot and label a point on the number line below to show each temperature b. During which month was the average temperature the highest? c. During which month was the average temperature the lowest?. Use,, or to compare each of the following pairs of numbers. a. 3,03 3,005 b c d. 0 0 e f. 5,560 5, Round each of the following numbers to the nearest ten. a. 68 b. 34 c.,975 d. 4

18 4. Round each of the following numbers to the nearest hundred. a. 4,33 < b. 89 < c.,057 < d. 65 < 5. Write the opposite number for each of the following numbers. a. 7 b. 45 c. 9 d Which number is its own opposite? Explain. 7. Wanda is scuba diving at a depth of 9 feet below sea level. Her brother Mark who is also scuba diving is 6 feet below sea level. a. What integer represents Wanda s position? b. What integer represents Mark s position? c. Plot and label points that represent Wanda s and Mark s positions. Sea Level ft. d. Who is closer to the surface of the water, Wanda or Mark? Explain.

19 COURSE: MSC III MODULE : Numbers and Number Sense UNIT : Large and Small Numbers Whole Numbers to One Million. Draw lines to match each number to its word name. 00,000 ten thousand 0,000 one thousand,000 one hundred thousand. Mount Everest, the highest peak in the world, is part of the Himalayan mountain range. Located in Asia, near the border of Tibet and Nepal, Mount Everest is 9,035 feet above sea level. a. The digit in the number 9,035 represents the number of. b. Write 9,035 in expanded form. c. Write 9,035 as the product of each digit times its place value. d. What is the word name for 9,035? Ordering and Rounding Whole Numbers 3. The height of the Sears Tower in Chicago, Illinois, is,454 feet. The height of the CN Tower in Toronto, Canada, is,85 feet. a. Use,, or to compare the heights of the two towers.,454,85 b. Which place value did you look at to compare the heights? c. Round each height to the nearest hundred feet. Sears Tower ft CN Tower ft 3

20 Negative Whole Numbers 4. A student picked four numbers out of a box and recorded them in the chart below. Round each number to the nearest ten, and name the opposite of each number. Number 3, Rounded to the Nearest T en Opposite of the Number Putting It All Together This table shows the change in the population of four states from 998 to 999. State New Jersey South Carolina North Dakota West Virginia Population Change 47,870 46,58 4,4 4, Write the number showing the change in the population of South Carolina in expanded form. a. Which state had a population that changed the least? b. Which state had the greatest change in population? 6. Use,, or to compare each pair of numbers. 4 a. 47,870 46,58 b. 4,4 4,760

21 COURSE: MSC III MODULE : Numbers and Number Sense UNIT : Large and Small Numbers. In 990, the population of Houston, Texas, was,63,000. The population of Detroit, Michigan, was,08,000, and the population of Philadelphia, Pennsylvania, was,586,000. Plot points that represent the population of each ciy. Label each point with the name of the city.,000,000,000,000. In 990, the city of Houston had the fourth-largest population in the United States. Use the information in question to determine if the following statements are possible or not possible. Then, explain your reasoning. a. In 990, the city of Detroit had the second-largest population in the United States. b. In 990, the city of Philadelphia had the fifth-largest population in the United States. 3. Use,, or to compare the populations of Houston and Philadelphia. 5

22 The table shows the lowest points below sea level on four continents. Continent Africa Europe North America South America Lowest Point Below Sea Level 56 m 8 m 86 m 40 m 4. What is the lowest point below sea level in North America written as signed number? 5. Use a number sentence and signed number to compare the lowest point in North America and the lowest point in Europe. 6. In which continent is the lowest point closest to sea level? 7. Which continent has the lowest point? 8. The top of a cliff is 80 feet above the the surface of the ocean. A scuba diver is swimming at a depth of 80 feet below sea level. 6 a. What integer represents each location? Height of cliff ft. Depth of diver ft. b. What can you say about the distance from the top of the cliff to the surface of the water, and the distance from the surface of the water to the diver?

23 COURSE: MSC III MODULE : Numbers and Number Sense UNIT : Numbers as Factors Finding Factors As you work through the tutorial, complete the following.. What is your mission for this lesson?. In the number sentence 3 4 a. Which number is the product? b. Which number is the factor? 3. A factor is a number that is by another number to give a. 4. Three ways to represent are: 5. Area is the number of in a surface. Key Words: Factor Area of a rectangle Unit square Commutative Property of Multiplication Multiplication Property of Learning Objectives: Use an area model to represent multiplication. Demonstrate that multiplication is commutative. Find the pairs of factors of a whole number. Recognize that any number has and itself as factors. 6. The area of a rectangle is equal to its times its. 7. We can use 3 groups of unit squares to show. 8. The Commutative Property of Multiplication states that if the positions of two or more are changed, their remains the same. 7

24 9. Three different pairs of factors for are and, and, and and. 0. Complete the table to show four different factor pairs of 4. Factor Factor Product Neither 4 nor 5 is a factor of 4 because.. The number 4 has different pairs of factors. 3. The factors common to both and 4 are,,, and.. The least common factor of and 4 is. 4. The Multiplication Property of states that times any number equals that. 5. The factor pairs of 4 are: 3 and, and 6, and, and and 6. The factors of a number are always either less than or the number. 8

25 COURSE: MSC III MODULE : Numbers and Number Sense UNIT : Numbers as Factors Finding Factors. Show three expressions that equal 8.. Each square inside this rectangle represents square unit. What is the length L, width W, and area A of the rectangle? L units W L W units A square units 3. Explain how you know can tell these two rectangles have the same area. 4. Complete each number sentence. Then tell what property each number sentence represents. a b

26 5. Two friends are planting flowers in a garden shaped like a rectangle. Its area is 8 square feet. Use what you know about factor pairs to draw the possible shapes of the garden. Label the length and width of each rectangle. 6. Write all the pairs of factors for each whole number in any order. Then tell how many different factor pairs there are. Number Factor Pairs Number of Pairs

27 COURSE: MSC III MODULE : Numbers and Number Sense UNIT : Numbers as Factors Prime and Composite Numbers As you work through the tutorial, complete the following.. What is your mission for this lesson?. The Multiplication Property of states that times any number equals that number. 3. The number has and as a factor pair. Therefore, has only factor. 4. The number 4 has factors and two pairs of factors: and. 5. All whole numbers greater than have at least different factors. Key Words: Prime number Composite number Divisible Factor Factor pairs Factor tree Learning Objectives: Identify the prime numbers less than 50. Determine the prime factors in a number. 6. A prime number is a number that has exactly different factors, and. 7. What are the prime numbers between and?,,,, and. 8. Draw a circle around each number that has as a factor. Draw a square around each number that has 3 as a factor. Draw a triangle around each prime number

28 9. List the numbers from to 30 that have both and 3 as factors. 0. What are the prime numbers between 30 and 50?. A number is a counting number greater than that is not prime.. The number is neither nor. It is the only counting number with just factor. 3. Every composite number is the product of two or more. 4. Complete these factor trees to show the prime factors of Rewrite 00 as a product of its prime factors. 6. True or False: By looking at the factors of a number, you can tell whether it is a prime or a composite number.

29 COURSE: MSC III MODULE : Numbers and Number Sense UNIT : Numbers as Factors Prime and Composite Numbers. List all the factor pairs for each of the numbers in the table. Then give the number of different factors for each number, and tell if the number is prime (P) or composite (C) Factor Pairs Number of Prime or Factors Composite. Complete the factor tree Start with a factor pair other than 5 and 9 and make a different factor tree for

30 4. Why is the set of prime factors of the number 45 the same in both factor trees? 5. a. Complete these two factor trees for b. Write 48 as the product of its prime factors. 6. List the factors of 36. Then sort the factors into prime and composite numbers. Factors of 36: Prime Factors Composite Factors 4

31 COURSE: MSC III MODULE : Numbers and Number Sense UNIT : Numbers as Factors Identifying Common Factors As you work through the tutorial, complete the following.. What is your mission for this lesson?. Is a prime factor of 4? Why or why not? 3. is a way to write a number as the product of its prime factors. 4. The prime factorization of 4 is. 5. A diagram is a way to display objects that have certain properties in common. 6. The prime factorization of 40 is. Key Words: Prime number Composite number Venn diagram Common factor Greatest Common Factor Learning Objectives: Find the common factors of two whole numbers. Use factor trees and a Venn diagram to identify the Greatest Common Factor of two - digit numbers. Find the Greatest Common Factor of two 3-digit numbers. 7. The greatest factor that 4 and 40 have in common is. 8. What do you know about the numbers that appear in the overlapping region of a Venn diagram? 9. In this Venn diagram, the overlapping region shows the factors common to and

32 0. The GCF, or, is the greatest factor that two or more numbers have in common.. The GCF of 4 and 40 is, or.. a. Complete these factor trees to find the prime factors of 400 and b. Write the prime factorization of each number Draw a Venn diagram showing the prime factors of 5 and The GCF of 400 and 5 is. 6

33 COURSE: MSC III MODULE : Numbers and Number Sense UNIT : Numbers as Factors Identifying Common Factors. Use these factor trees to find the prime factorizations of 36 and Prime factorization of 36: Prime factorization of 48:. Use this Venn diagram to show the prime factors of 36 and The Greatest Common Factor of 36 and 48 is. Explain how you found your answer. 7

34 4. What is the Greatest Common Factor of 54 and 7?. Draw a Venn diagram or two factor trees to explain your answer. 5. Use the space below and create factor trees to find the prime factorization of 0 and What prime factors are common to 0 and 60? 7. What is the GCF of 0 and 660? Explain: 8. a. The GCF of two numbers is not always a prime number. Give an example of two numbers whose GCF is prime.,, and two numbers whose GCF is not prime.,. b. Give an example of two -digit composite numbers that have no common factor. and 8

35 COURSE: MSC III MODULE : Numbers and Number Sense UNIT : Numbers as Factors Finding Factors. What are the factor pairs of 3? a. How many different factor pairs are there? b. Why do the factor pairs and 6 and 6 and count as one pair of factors? Prime and Composite Numbers. Use the space on the right to make a factor tree for 60. Circle the prime factors Sort the following numbers into two groups, prime numbers and composite numbers. Explain how you sorted the numbers. 3, 8, 5, 7, 3, 7, 3, 39, 43, 49 Prime Numbers Composite Numbers Explain: 9

36 Identifying Common Factors 4. What is the prime factorization of each numbers? a b. Complete the Venn diagram to show the factors of 30 and c. Which prime factors are common to both 30 and 4? d. The GCF of 30 and 4 is. Explain: Putting It All Together 5. Terri is making bracelets from blue, red, and gold beads. She has a lot of blue beads, but she has only 4 red beads and 48 gold beads. Terri wants all the bracelets to have an equal number of red beads and an equal number of gold beads. a. If Terri uses all of the red and gold beads, what is the greatest number of bracelets she can make? b. Each bracelet will have red beads and gold beads. 30 c. Explain.

37 COURSE: MSC III MODULE : Numbers and Number Sense UNIT : Numbers as Factors. Clint is a bird-watcher. One weekend, he spots the following numbers of birds: Friday: 4 Saturday: 64 Sunday: 48 Clint makes a chart to record the number of birds he saw. He uses a bird symbol to stand for a certain number of birds. For example, could equal birds. a. What is the greatest number of birds that one symbol can represent to show his data? Explain. b. If Clint wants to make a picture graph, how many symbols will represent the number of birds seen on Friday? Saturday? Sunday?. What property does each number sentence represent? a b. 3. Use these three clues below to identify a mystery number. : It is greater than 0 and less than 5. : It is 3 less than a prime number. 3: It has six factors. The mystery number is. Explain. 3

38 4. A spinner is divided into 6 equal sections, and each section contains one of the 0 numbers 0, 8,, 5, 4, or 7. If the spinner lands on a number with the greatest or least number of prime factors, a player earns 0 points. What numbers 5 must a player spin to earn 0 points? Explain. 5. a. Create a Venn diagram to show the prime factors of 4 and b. What is the GCF of 4 and 4? 6. Sonya draws these three numbers from a stack of number cards: 350, 480, and 630. To win a round in a math game, she needs to identify which pair of numbers has the greatest common factor. Find the GCF of each pair of numbers and identify which numbers Sonya should choose. Use factor trees or Venn diagrams to find your answer. a. GCF of 350 and 480: b. GCF of 350 and 630: c. GCF of 480 and 630: d. Sonya should choose and. 3

39 COURSE: MSC III MODULE : Operations with Numbers UNIT : Addition and Subtraction of Whole Numbers Whole Number Sums As you work through the tutorial, complete the following.. What is your mission for this lesson?. The lengths of four of the Great Lakes are given in this chart. Great Lake Length (miles) Superior 350 Huron 06 Erie 4 Ontario 93 Rounded Values (miles) a. Round each length to the nearest hundred, and write the values in the chart. b. What is the estimated length in miles of the journey from Lake Superior to Lake Ontario? Key Words: Sum Estimate Plus sign (+) Commutative Property of Addition Learning Objectives: Estimate the sum of two or more 3-, 4-, and 5-digit numbers. Find the sum of two or more 3-, 4-, and 5-digit numbers. Check an addition by using the Commutative Property of Addition. 3. When you add the actual lengths of the lakes, the sum of the numbers in the ones place before regrouping is. 4. You can represent ten ones with the digit in the ones place and the digit in the tens place. 5. The sum of the numbers in the tens place before regrouping is. 6. You can regroup 9 tens by writing the digit in the tens place and the digit in the hundreds place. 7. The sum of the numbers in the place is 9. 33

40 8. The actual length of the journey,, is reasonably close to the estimated length,. 9. The Commutative Property of Addition states that when two or more numbers are, if the position of the numbers is changed, the remains the same. 0. To check an addition problem, you can change the of the addends and see if you get the same.. Use the place value grid on the right to find the sum of these numbers. Use the top row in the grid to show any regroupings. 3 Ten Thousands,, 3, Thousands Hundreds Tens Ones 9, 9 0 7, To find the sum of large numbers: start by adding the digits in the place. if the sum in the ones place is greater than, regroup it as a number of ones and. continue to the numbers in each place. 34

41 COURSE: MSC III MODULE : Operations with Numbers UNIT : Addition and Subtraction of Whole Numbers Whole Number Sums. The chart below shows distances a person drove during five days. Day Distance Rounded Distance (miles) (miles) Monday 5 Tuesday 07 Wednesday 35 Thursday 80 Friday a. Round each distance to the nearest hundred, and write the values in the chart. b. What is the estimated total distance driven during these five days? c. What is the actual distance driven over five days?. Explain the regrouping you had to use to find the sum in part (c). 35

42 3. Find each sum. Use the Commutative Property of Addition to check your answer. a. 3,580 b.,60 4,035 3, ,700 8,3 4. The chart below shows the distances by air between four U.S. cities. From To Distance Rounded Distance (miles) (miles) Seattle, WA Denver, CO,06 Denver, CO Dallas, TX 660 Dallas, TX Miami, FL,08 a. Round each distance to the nearest thousand, and write the values in the chart. b. Use the rounded values and estimate the distance by air from Seattle to Miami, flying by way of Denver and Dallas. c. Find the actual distance in part (b). d. What is the difference between the estimated distance and the actual distance? 36

43 COURSE: MSC III MODULE : Operations with Numbers UNIT : Addition and Subtraction of Whole Numbers Differences Between Large Numbers As you work through the tutorial, complete the following.. What is your mission for this lesson?. a. Use the place value grid to show b. To subtract, the (greater, lesser) number is written above the (greater, lesser) number. Circle the answers. Thousands,, Hundreds Tens Ones Key Words: Difference Minus sign () Learning Objectives: Use regrouping to subtract two 4-digit numbers. Use regrouping to subtract two 5-digit numbers. Check the difference by addition. c. What is the difference? 3. When subtracting two whole numbers, in what place do you begin? 4. How can you check that 3 is the correct difference between 953 and 9? 5. To check any subtraction problem, the sum of the difference and the number (the subtrahead) should equal the number (the minuend). 6. Use the numbers in the place value grid and complete this problem. a. To subtract 3 from 0 in the ones place, first, 8 tens. Thousands Hundreds Tens, 9 8 0, Ones b. Eight tens can be regrouped as tens and ones. 37

44 c. You can regroup in the tens place because 8 tens 0 80, and 7 tens and 0 ones d. What is the difference between 980 and 953? e. How would you check the answer? 7. Use this place-value grid to complete this problem. Use the upper row in the grid to show any regroupings. a. What is the difference in the ones place? b. You cant t subtract the digits in the tens place or the digits in the hundreds place yet because is less than, and is less than. c. To regroup in the tens place and hundreds place, you need to regroup in the place. Ten Thousands Thousands 9, 8, 0 Hundreds 3 5 Tens 5 0 Ones d. Regroup thousands as thousands and hundreds. e. Then regroup hundreds as hundreds and tens. f. Next, add tens to the in the tens place to get tens. g. The difference between 9,035 and 8,50 is. 38

45 COURSE: MSC III MODULE : Operations with Numbers UNIT : Addition and Subtraction of Whole Numbers Differences Between Large Numbers. Regroup each of the following number. a. 5 hundreds 4 hundreds and tens b. 8 ten thousands ten thousands and 0 thousands c. ten 0 tens and ones. Use this place value grid to complete this problem. Thousands Hundreds Tens 6, , 8 Ones a. Why do you need to regroup in the tens and hundreds places? b. Circle the place value grid that shows a number equal to 6,304. Thousands Hundreds Tens Ones Thousands Hundreds Thousands Hundreds Tens Ones Tens Ones c. Find the difference between 6,304 and 5,8. d. Use addition and check your answer. 39

46 3. The Nile River in Egypt is the longest river in the world. It is 6,693 kilometers long. The second longest river is the Amazon River in South America. It is 6,436 kilometers long. a. What is the difference between the lengths of the two rivers? b. Use addition to check your answer. 4. The time line below shows the years in which three states joined the Union. Delaware 787 California 850 Hawaii year a. How many years passed from the time Delaware joined the Union to the time Hawaii joined the Union? Check your answer. b. How many years passed from the time Delaware joined the Union to the time California joined the Union? Check your answer. 40

47 COURSE: MSC III MODULE : Operations with Numbers UNIT : Addition and Subtraction of Whole Numbers Whole Number Sums. Find each sum. a. 53 b.,50 c. 53, ,43,45 6,05,353. a. Round each number in problem (c) to the nearest hundred, and find the sum. b. What is the difference between the estimate and the actual sum? 3. Explain how you can check your answer to the sum of two or more numbers using the Commutative Property of Addition. Differences Between Large Numbers 4. Use the numbers in the place value Thousands Hundreds Tens Ones grid and complete this problem. a. Use the top row in the grid to show how you can regroup 9,560 in order to subtract. 9, 4, b. What is the difference between 9,560 and 4,77? 4

48 5. a. Find the difference between 0,84 and 9,73. b. Show how to check your answer. Putting It All Together 6. The chart below shows the distances by air between four cities. From To Distance Rounded Distance (miles) (miles) Honolulu, HI Los Angeles, CA,55 Los Angeles, CA St. Louis, MO,595 St. Louis, MO Boston, MA,04 a. Round each distance to the nearest thousand, and write the values in the chart. b. Use the rounded values and estimate the distance by air from Honolulu to Boston, flying through Los Angeles and St. Louis. Then find the actual distance. Estimated Distance: Actual Distance: c. Find the difference between the distance from Los Angeles and Honolulu and the distance from Los Angeles to St. Louis. 4

49 COURSE: MSC III MODULE : Operations with Numbers UNIT : Addition and Subtraction of Whole Numbers. The chart below shows the areas in sqare miles of four states. State Area Rounded Area (square miles) (square miles) Ohio 40,953 West Virginia 4,087 Kentucky 39,73 Michigan 56,809 a. Round each area to the nearest thousand square miles, and write the values in the chart. b. Use the rounded values and estimate the total area covered by the four states? c. What is the actual total area covered by the four states? d. What is the difference between the estimate and the actual distance?. Use the data in the chart and find the actual difference between the areas of Michigan and Ohio. 3. a. One student found the difference between the areas of Kentucky and West Virginia to be 5,755 square miles. Describe the errors that the student made. b. What is the difference in the areas of these two states? 43

50 4. The distance by air from Phoenix, Arizona, to Atlanta, Georgia, is,589 miles. The distance by air from Atlanta, Georgia, to London, England, is 4,8 miles. Circle True or False for each of the following statements, and rewrite each false statement to make it true. a. If each distance is rounded to the nearest hundred, the estimated distance by air from Phoenix to London by way of Atlanta is 5,800 miles. (True, False) b. The actual distance by air from Phoenix to London by way of Atlanta is 5,797 miles. (True, False) c. The actual distance by air between Phoenix and Atlanta is,739 miles less than the distance by air between Atlanta and London. (True, False) 44

51 COURSE: MSC III MODULE : Operations with Numbers UNIT : The Integers Integer Sums As you work through the tutorial, complete the following.. What is your mission for this lesson?. Which of the following is not a signed number? Circle your answer The integers are the positive and negative, and. 4. a. Draw lines above the number line to show the sum of 3 and Key Words: Whole number Signed number Zero Opposite numbers Learning Objectives: Find the sum of two positive whole numbers using a number line. Find the sum of two negative whole numbers. Find the sum of a positive and negative whole number. b. The number 3 is units to the of zero on the number line. To add 5, start at and move units to the. c. What is the sum of the two integers. 5. The integer 3 is read as. 6. The minus signs in the expression 3 (5) represent the of the numbers and the plus sign between the numbers represents the of 3 and 5. 45

52 8. a. Draw arrows above the number line to represent the expression 3 (5) b. To add 5 to 3, move units to the of 3. c. What is the sum of the integers. 9. The sum of two positive numbers is always. The sum of two negative numbers is always. 0. When adding numbers with like signs, the sum has the same as the numbers being added.. a. Draw arrows above the number line to represent the expression 3 (5) b. To add 5 to 3, you need to move units to the of 3. c. What is the sum of the integers?. a. The sum of two numbers that are different distances from 0 and have unlike signs is either or. b. The sign of the non-zero sum of two numbers with unlike signs is the sign of the (greater, lesser) number. Circle one. 46

53 COURSE: MSC III MODULE : Operations with Numbers UNIT : The Integers Integer Sums. Without actually adding the numbers, classify the sum of each pair of numbers as positive or negative. a. 5 ( 39) b. 7 ( 6) c. 4 (8) d Complete the number sentence shown by the set of arrows above each number line. a b a. Draw a set of arrows above the number line to represent (6) b. What is the sum? 47

54 4. Use the number line to help you find each sum a. 4 (9) b. (7) c. 6 (3) d. 7 () e. (4) f. 8 (5) 5. The entrance to the Goodwater hiking trail is 0 feet below sea level. After hiking up 65 feet, a group of hikers stops to rest. a. On the number line below represent the location of the hikers when they stop to rest. Sea level feet b. Complete the number sentence (65). c. When the hikers stop to rest, are they above or below sea level? Explain. 48

55 COURSE: MSC III MODULE : Operations with Numbers UNIT : The Integers Differences Between Integers As you work through the tutorial, complete the following.. What is your mission for this lesson?. The opposite of 4 is. 3. If red chip represents, then 4 red chips represent. If blue chip represents, then 4 blue chips represent. Write the sum of all the chips as. 4. The sum of opposite numbers is. 5. The sum 3 (4) (4) 3 can be written as The Addition Property of Zero states that. 7. These chips represent 7 and (4). Key Words: Integer Positive integer Negative integer Signed number Zero Opposite numbers Addition Property of Zero Learning Objectives: Recognize that the sum of two opposites is 0. Represent the sum of two integers using colored chips. Find the difference between a negative integer and a positive integer. Check a difference using addition. a. Cross out all opposite pairs of chips. b. Write an addition sentence that represents the sum of 7 and 4. 49

56 8. These positive chips represent 7. a. Cross out chips to show 7 (3). b. Complete the number sentence: 7 (3) c. Write an addition sentence to check your answer. 9. These negative chips represent 7. a. Add more chips so you can subtract (take away) 3. b. What is the value represented by the chips you added to the 7 negative chips? c. Cross out chips to show 7 (3). d. Complete the number sentence: 7 (3) e. Write an addition sentence to check your answer. 0. This positive chip represents. a. Add the fewest number of positive and negative chips to the chip above to subtract (take away) 6. b. What is the value represented by the chips you added to the positive chip above? c. Cross out chips to show (6). d. Complete the number sentence: (6) e. Write an addition sentence to check your answer. 50

57 COURSE: MSC III MODULE : Operations with Numbers UNIT : The Integers Differences Between Integers For questions through 7, let red chip +, and let blue chip -.. Write the integer that each group of chips represents. a. 3 blue chips b. red chips c. 8 red chips d. blue chip. Draw lines to match each set of chips to its sum. 9 red chips 4 blue chips 4 blue chips 5 red chips 9 blue chips 0 chips 6 red chips 6 blue chips 4 red chips 7 red chips 3 blue chips 5 red chips 3. Write an expression to represent each set of chips. Then find each sum. a. 3 red chips 0 blue chips b. blue chip 4 red chips c. 7 red chips 7 blue chips d. 9 blue chips 8 red chips 4. Suppose you want to use chips to show 8 (3). a. Start with 8 chips. b. To subtract 3, you can add red chips and blue chips. c. Complete the number sentence: 8 (3) 5

58 5. Suppose you have 5 blue chips and you want to show 5 (). a. Do you need to add more chips? Explain, b. What is 5 ()? c. Write an addition sentence to check your answer. 6. Write a number sentence that represents each expression and its answer. a. 5 subtracted from 6 b. added to 4 c. 3 minus 7 d. 0 plus 8 7. Complete each subtraction. Add to check each answer. Subtract Add to Check a. 8 (7) 7 ( ) b. 5 (6) 6 ( ) c. 3 (4) 4 ( ) 5

59 COURSE: MSC III MODULE : Operations with Numbers UNIT : The Integers Integer Sums. Write an addition sentence shown by the set of arrows above the number line Use the number line to help you find each sum a. (6) b. 7 (8) c. (5) d. 3 (4) Differences Between Integers For questions 3 and 4, let red chip +, and let blue chip. 3. Write a number sentence represented by each set of chips and its sum. a. 8 red chips and 4 blue chips b. 5 blue chips and 5 red chips c. 7 red chips and 9 blue chips 4. Write a number sentence that represents each expression and its answer. a. 5 subtracted from b. minus 3 c. 6 subtracted from 4 53

60 5. Complete each subtraction, and then complete each check. Subtract Add to Check a. 7 (5) 5 ( ) b. (7) 7 ( ) c. 4 (0) 0 ( ) Putting It All Together 6. Early one morning a thermometer read 3 C. By 0 A.M. the temperature had risen by 7 C. a. Draw an arrow to show this temperature change on the number line. b. Write a number sentence that represents the change in temperature. c. Write a number sentence to check your answer. C 0 7. The next morning the temperature was 3 C. However, by noon, it was 7 C colder. a. Circle the expression that represents the change in temperature 3 (7) 3 (7) b. What was the change in temperature? the difference as an integer. c. Write an addition sentence to check your answer. 54

61 COURSE: MSC III MODULE : Operations with Numbers UNIT : The Integers Unit Assessment. A helicopter took off from an airport that was at sea level. It climbed to an altitude of 50 feet above sea level, and then dropped 400 feet to land on the floor of a canyon. a. Use the number line and arrows below to write a number sentence that represents the change in altitude and position of the helicopter feet b. The helicopter then takes off from the floor of the canyon and climbs 75 feet. Draw an arrow above the number line to show this change in altitude. c. What integer represents the altitude of the helicopter now?. A scuba diver descends to a depth of 5 feet below sea level, where he sees a sea turtle. He dives 8 feet deeper, and then rises 8 feet, where he sees a second turtle. a. Draw arrows above the number line, starting at 0 (sea level) to represent the movement of the diver during these dives feet b. How many feet below the surface of the water is the diver when he sees the second turtle? 55

62 3. A student wants to find the value of 4 (3). On the number line, draw arrows to represent the addends and label the sum If red chip represents, and blue chip represents, explain how to use colored chips to find the sum in problem These negative chips represent 5. a. Add positive and negative chips to the 5 negative chips above so that you can subtract 8 from 5. b. Complete the number sentence: 5(8) 5. These positive chips represent +5. a. Show how many positive and negative chips you need to add to the 5 positive chips above to subtract 8 from 5. b. Cross out chips to subtract (take away) 8. c. Complete the number sentence: 5(8) 56

63 COURSE: MSC III MODULE : Operations with Numbers UNIT 3: Multiplication and Division of Whole Numbers Two-Digit Multipliers As you work through the tutorial, complete the following.. What is your mission for this lesson?. We can express the height of the Statue of Liberty as either or. 3. Why did Dijit group the first 0 columns of the 9 by 7 rectangle as a 9 by 0 red rectangle? 4. The area of the rectangle the area of the rectangle the area of the large rectangle. 5. The expression 9 7 can also be represented as the sum of ( ) ( ). 6. We represented the width of the large rectangle,7, as the sum of and, so we can write the area of the large rectangle as 9 ( ). 7. The Distributive Property states that multiplying a sum by a number is equal to multiplying each in the by that number. Key Words: Factor Product Partial product Distributive Property Area Rectangle Commutative Property of Multiplication Learning Objectives: Model the productof a -digit number and a - digit number using the areas of rectangles. Apply the Distributive Property to multiply two numbers. Use the multiplication algorithm to find the product of two -digit numbers. Check a product using the Commutative Property of Multiplication. 57

64 8. Use the place value grid to multiply 3 and 48. As you work, fill in the four partial products and their sum. Thousands Hundreds 4 Tens 8 Ones 3, 9. You can check the value of 48 3 by changing the order of the factors to. We can do this because multiplication is. 0. Use this place value grid and check your answers in problem 8. Show the two partial products and their sum. Thousands Hundreds 4 Tens 3 8 Ones, 58

65 COURSE: MSC III MODULE : Operations with Numbers UNIT 3: Multiplication and Division of Whole Numbers Two-Digit Multipliers. This large rectangle has been separated into two smaller rectangles, X and Y. a. Complete the information 8 X Y in the table for rectangles X and Y. 3 Rectangle Length Width Length x Width X Y X Y b. Use the values in the table to find the product of 8 and ( ) c. The formula for the area A of a rectangle is A l x w, where l and w are the length and width of the rectangle. Use the formula to find the area of each rectangle. Rectangle X Y X + Y Area d. Complete this multiplication to check the product of 8 x 3 in part (b). Show the two partial products and their sum. Hundreds Tens 3 8 Ones e. What does each partial product in the multiplication in part (d) represent? 59

66 3. Use the place value grid to find the product of 4 and 65. Show the four partial products and their sum. Hundreds Tens 4 Ones Use Dijit s quicker way to find each pair of products. Show all partial products. Then, check your answers using the Commutative Property of Multiplication. a. 9 check: 43 b. check: a. 3 check: b. 68 check:

67 COURSE: MSC III MODULE : Operations with Numbers UNIT 3: Multiplication and Division of Whole Numbers Introduction to Long Division As you work through the tutorial, complete the following.. What is your mission for this lesson?. Write an expression to find the number of 6-inch lengths in 08 inches. 3. To find the width of a rectangle, rewrite the formula for its area as width. 4. Complete these expressions to see which product is closer to 08, the area of the rectangle Because 08 is than 6 0 and than 6 0, the width of the rectangle is 0 and Dividing 08 by 6 shows that the grasshopper can jump times its own length. 7. Identify the parts of a division problem as shown below. a b. c. Key Words: Factor Division Divisor Dividend Quotient Learning Objectives: Model the quotient of a 3-digit number and a -digit number using areas of rectangles. Estimate a quotient by locating it between consecutive multiples of 0. Check the division by multiplying the quotient and the divisor. Use the division algorithm to divide a 3-digit number by a -digit number without a remainder. 6

68 8. If , then Use the place value grid to find the value of Hundreds Tens Ones If 84 8, then 8.. When you divide, the whole number that is the quotient is a of the dividend. 6

69 COURSE: MSC III MODULE : Operations with Numbers UNIT 3: Multiplication and Division of Whole Numbers Introduction to Long Division. Use the place value grid and find the quotient of Hundreds Tens Ones 7 divided by Find each quotient. Check your division by multiplying the quotient and the divisor. a. 5 I45 Check: b. 9 I6 Check: c. 7 I3 Check: 63

70 3. Three students spend a total of 38 minutes working on a history project. If each student works the same amount of time, how many minutes does each student work? Show your work and check your answer. 4. A total of 54 fifth-graders are visiting a local museum. There are 7 museum guides. If each guide is responsible for the same number of students, how many students are in each group? Show your work and check your answer. 64

71 COURSE: MSC III MODULE : Operations with Numbers UNIT 3: Multiplication and Division of Whole Numbers Two-Digit Divisors As you work through the tutorial, complete the following.. What is your mission for this lesson?. Rewrite this division problem as a multiplication problem. Distance Speed Time 3. The quotient (Time) and the divisor (Speed) are of the dividend (Distance). 4 To find how many hours it took to travel by train from New York City to San Francisco in 869, complete this division, using a place value grid. Key Words: Division Divisor Dividend Quotient Remainder Learning Objectives: Divide a 4-digit number by a -digit number. Identify the remainder in a division problem. Thousands Hundreds Tens Ones 5 3,

72 5. Complete this division to find the quotient of 40 and 4. Hundreds Tens Ones a. The quotient of 40 divided by 4 is, with a remainder of. b. The 40 hours represents days and hours. 6. A is a whole number less than the divisor that is left over when dividing. 7. In division, the quotient the divisor the the dividend. 66