Name Period Date UNIT 1: INTEGERS WEEK 2: Student Packet 2.1 Integers: Introduction Represent integers on a number line. Explore integer addition and subtraction using a number line model. Write equations and inequalities using integers. Solve problems involving integers. Understand the meaning of absolute value. 2.2 Whole Numbers: Division with Remainder Learn strategies for finding quotients of whole numbers. Estimate and round numbers. Use division vocabulary. Use a variation of the standard division algorithm. Interpret the meaning of remainders. 2.3 Whole Numbers: Expanded Form and Divisibility Write whole numbers in expanded form. Use rules of divisibility. Review math concepts from prior lessons. Demonstrate competency in addition, subtraction, and properties of addition (highlighted review). 1 8 12 Week 2 SP
FOCUS ON VOCABULARY 2 Unscramble the words to reveal words from the word bank. Then, choose five words and write their definitions or give examples. Example: getinres integers: (Definition) Whole numbers and their opposites. (Examples) 4, -6, 100 1. galhimort 2. vidisebli 3. dedexpan morf 4. redrenami 5. endviddi 6. tamitsee 7. tansradd fmor 8. rosidvi 9. eqtinaou 10. bastuleo velua Word Bank remainder divisible expanded form integers algorithm absolute value estimate divisor dividend quotient standard form Week 2 SP0
2.1 Integers: Introduction INTEGERS: INTRODUCTION Ready (Summary) We will place integers on a number line. We will write equations and inequalities using integers. Set (Goals) Represent integers on a number line. Explore integer addition and subtraction using a number line model. Write equations and inequalities using integers. Solve problems involving integers. Understand the meaning of absolute value. Go (Warmup) Here are some average temperatures in Fahrenheit from various locations around the world in July. Label the vertical number line at right, showing temperatures from 100 degrees below zero (-100 ) to 100 degrees above zero (+100 ). Indicate the temperature for each location with a point on the number line. 1. Point C: Cape Denison (a region in Antarctica) at 0. 2. Point M: Moscow (a city in Russia) at 60. 0 3. Point N: North Pole (a city in Alaska) at 40. 4. Point S: The South Pole (a location in Antarctica) at -70. 5. Point D: Death Valley (a region in California) at 100. 6. Point E: Ellsworth Land (a region in Antarctica) at -35. Week 2 SP1
2.1 Integers: Introduction COMPARING TEMPERATURES Compare the temperatures using your number line. Complete the word sentences. Write a number sentence using <, =, or > for each word sentence. Fold along the dotted line to view your number line from the previous page 1. 2. 3. 4. Word sentence The temperature in Death Valley is greater than the temperature at the Pole. The temperature in Ellsworth Land is less than the temperature in Cape Denison. The temperature in Ellsworth Land is the temperature at the South Pole. The temperature in Moscow is the temperature at the South Pole. Number Sentence 100 > 40 Use your number line to complete each number sentence with <, =, or >. Then, write a word sentence for each number sentence. Number Word Sentence Sentence 5. Forty degrees is greater than zero degrees. - 40 0 6. -45 60 7. -60-35 8. -95-55 Week 2 SP2
2.1 Integers: Introduction TEMPERATURE CHANGES 1 Find each afternoon temperature. Then, write a number sentence to describe the temperature change. Use the number line as needed. Morning Temperature Change Afternoon Temperature Number Sentence(s) 1. 0 rises 10 10 0 + 10 = 10 2. 60 rises 30 3. 40 rises 5 4. -70 rises 85 5. -15 rises 10 6. -35 rises 35 7. 0 falls 10-10 or 0 + (-10) = -10 0 10 = -10 0 8. 40 falls 70 9. -20 falls 20 10. 15 falls 15 11. 3 falls 5 12. -20 falls 5 Week 2 SP3
2.1 Integers: Introduction TEMPERATURE CHANGES 2 Find each morning temperature, change in temperature, or afternoon temperature. Then write a number sentence to describe the situation. Use the number line as needed. Morning Temperature Change Afternoon Temperature 1. rises 10-20 Number Sentence(s) + 10 = -20 2. 60-10 3. 40 45 Or 60 + = -10 60 = -10 4. -70 rises 85 5. rises 10-5 6. -35 rises 35 0 7. 0-10 8. falls 70-30 9. -20 falls 20 10. falls 15 0 11. 3-2 12. -20 falls 5 Week 2 SP4
2.1 Integers: Introduction INTEGER PROBLEMS Use a number line to answer each question. Write an addition statement and a subtraction statement for each problem. 1. At 7:00 AM, the temperature in Los Angeles was 55 F. At noon the temperature was 85 F. What was the temperature change from 7:00 AM to noon? Answer: 2. The temperature in a freezer is -5 F. The temperature in a refrigerator is 40 F. What is the difference in these temperatures? Answer: Addition: Addition: Subtraction: Subtraction: 3. In Anchorage, Alaska, the temperature rose 15 F during the day. The high temperature was -10 F. What was the low temperature? Answer: 4. A shark is at an elevation of -25 meters. It swims down 50 meters. What is its new elevation? Answer: 0 Addition: Addition: Subtraction: Subtraction: Week 2 SP5
2.1 Integers: Introduction ELEVATION Label the vertical number line, showing elevations from 100 meters below sea level (-100 m) to 100 meters above sea level (+100 m). Locate the following animals on the number line. 1. (Point S) swimmer at sea level 2. (Point D) dolphin at 20 m below sea level 3. (Point C) crow at 55 m above sea level 4. (Point W) whale at 60 m below sea level 5. (Point P) pigeon at 10 m above sea level Fill in the blanks with words from the answer bank. Answer Bank positive absolute value zero 10 20 6. Distance is always. On a number line, the of a number is its distance from zero. Since an absolute value 0 m represents a distance, it is always. 7. Sea level is located at on the number line. Therefore, the absolute value of 0 (written 0 ) is. 8. On the number line, the pigeon is meters from zero. Therefore, the absolute value of 10 (written 10 ) is. 9. On the number line, the dolphin is meters from zero. Therefore -20 =. Week 2 SP6
2.1 Integers: Introduction DISTANCE Use the vertical number lines on the precise page to find the distance between each pair of animals. Write absolute value statements. Animals Distance Between Them Absolute Value Statements 1. crow and pigeon 45 m 55 10 = 45 = 45 10 55 = -45 = 45 2. pigeon and swimmer 10 m 3. swimmer and dolphin 4. dolphin and whale 5. pigeon and dolphin 6. crow and whale Week 2 SP7
2.2 Whole Numbers: Division with Remainder WHOLE NUMBERS: DIVISION WITH REMAINDER Ready (Summary) We will learn some procedures for finding quotients of whole numbers. Set (Goals) Learn strategies for finding quotients of whole numbers. Estimate and round numbers. Use division vocabulary. Use a variation of the standard division algorithm. Interpret the meaning of remainders. Go (Warmup) Highlighters come in packages that hold 3 highlighters each. How many packages are needed to hold 727 highlighters? Week 2 SP8
2.2 Whole Numbers: Division with Remainder A DIVISION ALGORITHM VARIATION Highlighters come in packages that hold 3 highlighters each. How many packages are needed to hold 727 highlighters? This variation of the division algorithm will allow you to use known facts and estimation to close in on the quotient in a sense-making way. Step 1: Write the problem with a line drawn down the right side and write down some multiples of 3 for reference. Without going over, estimate how many groups of 3 are in 727. (Think about easy multiples of 3. Since 3 100 = 300, and 300 < 727, this is a good place to start.) Write some multiples of 3 for reference 3 1 = 3 3 10 = 3 2 = 37 2 7 Write the number of groups (100) on the right side. Subtract the number of highlighters used (300) from the total (727) to get the remainder (427). 1. This step shows: 727 = 3 ( ) + 427 2. Why do you need to continue to divide? Step 2: Without going over, estimate how many groups of 3 are in 427. Since 3 100 = 300, and 300 < 427, we can use this estimate again. Write the number of groups (100) on the right side. Subtract the number of highlighters used (300) from the remainder (427) to get a new remainder (127). 3. This shows 727 = 3 ( ) + 127. 4. Why do you need to continue to divide? Week 2 SP9
2.2 Whole Numbers: Division with Remainder A DIVISION ALGORITHM VARIATION (continued) Step 3: Without going over, estimate how many groups of 3 are in 127. Since 3 40 = 120, and 120 < 127, we can use this estimate. Write the number of groups (40) on the right side. Subtract the number of highlighters used (120) from the remainder (127) to get a new remainder (7). 5. This step shows 727 = 3 ( ) + 7. 6. Why do you need to continue to divide? Step 4: Without going over, estimate how many groups of 3 are in 7. Since 3 2 = 6, and 6 < 7, we can use this estimate. Write the number of groups (2) on the right side. Subtract the total number of highlighters used (6) from the remainder (7) to get a new remainder (1). 7. Why is the division process finished at this point? 8. These 4 steps show that 727 = (3) ( ) +. 9. These 4 steps also show that 3 7 2 7 R 10. How many packages are needed to hold 727 highlighters? 11. Show another way to arrive at this answer. Week 2 SP10
2.2 Whole Numbers: Division with Remainder MORE DIVISION PROBLEMS Solve each problem using a division algorithm. Be sure to interpret any remainders using the context of the problem. 1. How many miles per gallon did Mr. Garcia get while driving his car if he drove 594 miles and used 27 gallons of gas? 2. A backyard has an area of 672 square meters. Find the length of the backyard if it is 7 meters wide. Solution: Solution: 3. A bus holds 63 students. If 2,442 students are going on a field trip, how many buses will be needed? 4. A softball team earns $1,200 to purchase uniforms. If a uniform costs $38, how many uniforms can the team purchase? Solution: Solution: Week 2 SP11
2.3 Whole Numbers: Expanded Form and Divisibility SKILL BUILDER 1 1. A number is divisible by 2 if the digit in the ones place is a(n) number. 2. A number is divisible by 5 if the number ends in or. 3. If the sum of the digits of a number is divisible by 3, the number is divisible by. 4. Circle all the numbers divisible by 5. 36 335 2,061 7,030 5,253 5. Circle all the numbers divisible by 3. 35 42 117 40 313 6. Circle all the numbers divisible by 2. 45 439 200 210 458 7. Circle the numbers that are divisible by both 2 and 3. 102 36 416 2,000 86 8. Circle the numbers that are divisible by both 2 and 5. 76 40 35 60 44 Write each number in place value expanded form. Standard Form Place Value Expanded Form Ex. 764 700 + 60 + 4 9. 25 10. 320 11. 618 12. 3,482 13. Rudy used an area model to multiply 204 by 45. Find and explain his error. 200 + 40 204 45 = 10,800 40 + 5 8,000 1,600 1,000 200 Rectangle is not drawn to scale. Week 2 SP12
2.3 Whole Numbers: Expanded Form and Divisibility SKILL BUILDER 2 Write each number in place value expanded form. Standard Form Place Value Expanded Form 1. 4,592 4,000 + 500 + + 2. 2,340 3. 4,009 4. All even numbers are divisible by. 5. A number is divisible by 5 if the number ends in or. 6. Circle all the numbers divisible by 2. 16 87 149 2,067 111 50 7. Circle all the numbers divisible by 5. 135 57 20 216 42 5,000 Compute. 8. 2,659 158 + 586 9. 2,659 (158 + 586) Multiply using an area model. 10. 465 25 11. 245 89 Rectangles are not drawn to scale. Week 2 SP13
2.3 Whole Numbers: Expanded Form and Divisibility SKILL BUILDER 3A Write each number in place value expanded form. Standard Form Place Value Expanded Form 1. 53,145 2. 4,015 3. Circle all the numbers divisible by 2. 23 222 432 11 97 105 Compute. 4. 1, 700 25 5. 802 14 6. 1,760 + 171 515 7. 143 22 8. Michael added the following way: 515 + 182 + 18 = 515 + (182 + 18) = 515 + 200 = 715 What addition property did Michael use? 9. True or False? Explain. 642 is not divisible by 3 because the digit in the ones place is not divisible by 3. Week 2 SP14
2.3 Whole Numbers: Expanded Form and Divisibility SKILL BUILDER 3B Show answers clearly as asked. 10. A trained dolphin started at the bottom of a 25-foot pool and then jumped 10 feet out of the water to grab a ring. How far did the dolphin travel from the bottom of the pool to get the ring? Answer: 11. A pelican is flying at 37 meters above the surface of the ocean. It dives for a fish that is 3 meters below the surface of the ocean. How far did the pelican travel to get the fish? Answer: Addition: Addition: 0 Subtraction: Subtraction: Write each number in place value expanded form. Standard Form Place Value Expanded Form 12. 415 13. 2,004 14. 5,200 15. Compute 43,865 + 1,420 12,809. 16. What property is illustrated by 3(4 + 5) = 3(5 + 4)? Week 2 SP15
2.3 Whole Numbers: Expanded Form and Divisibility TEST PREPARATION 2 Show your work on a separate sheet of paper and choose the best answer. 1. 741 489 A. 368 B. 386 C. 362 D. 252 2. Which statement is not true? E. -3 is greater than -5 G. -3 is less than 5 F. 8 is less than -10 H. 8 is greater than -10 3. Compute 9,288 36. A. 252 B. 258 C. 233 D. 263 4. What is the correct standard form for 200 + 50 + 5? E. 255 F. 250 G. 2,550 H. 205 5. Which number is missing from 3,000 + + 60 + 7 = 3,567? A. 5,000 B. 500 C. 50 D. 5 6. 759 E. 8 F. 8 r3 G. 9 H. 9 r3 Week 2 SP16
2.3 Whole Numbers: Expanded Form and Divisibility KNOWLEDGE CHECK 2 Show your work on a separate sheet of paper and write your answers on this page. 2.1 Integers: Introduction 1. Locate these integers on the vertical number line to the right. Then, write the numbers from least to greatest. -3, 6, 2, -5 2. What is the distance between -7 and 1 on a number line? 3. Complete the number sentence with >, <, or =. -15 0 0 2.2 Whole Numbers: Division with Remainder Find each quotient using a division algorithm or procedure. 4. 270 15 5. 2,220 15 2.3 Whole Numbers: Expanded Form and Divisibility 6. Write three different mathematical expressions for 6 times 7. 7. A number is divisible by 5 if the digit in the ones place is or. 8. Write 4,329 in expanded form. Highlighted Review: Whole Numbers: Addition and Subtraction, Properties of Addition Compute. 9. 566 784 + 79 10. 1,222 + 3,426 1,572 Week 2 SP17
2.3 Whole Numbers: Expanded Form and Divisibility Home-School Connection 2 Here are some questions from this week s lessons to review with your young mathematician. 1. Locate these integers on the horizontal number line below. Then, write the integers from least to greatest. -2, 4, -7, 1 0 2. Use a division algorithm or procedure to compute 2,088 29 3. Write three numbers that are divisible by both 3 and 5. Parent (or Guardian) signature Selected California Mathematics Content Standards NS 2.3.2 Use repeated subtraction, equal sharing, and forming equal groups with remainders to do division. NS 3.1.5 Use expanded notation to represent numbers (e.g., 3,206 = 3,000 + 200 + 6). NS 4.1.4 Decide when a rounded solution is called for and explain why such a solution may be appropriate. NS 4.1.8 Use concepts of negative numbers (e.g., on a number line, in counting, in temperature, in "owing"). NS 6.2.3 Solve addition, subtraction, multiplication, and division problems, including those arising in concrete situations, that use positive and negative integers and combinations of these operations. Week 2 SP18