Math and FUNDRAISING. Ex. 73, p


 Jerome Byrd
 2 years ago
 Views:
Transcription
1 Standards Preparation Connect 2.7 KEY VOCABULARY leading digit compatible numbers For an interactive example of multiplying decimals go to classzone.com. Multiplying and Dividing Decimals Gr. 5 NS 2.1 Add, subtract, multiply, and divide with decimals; add with negative integers; subtract positive integers from negative integers, and verify the reasonableness of the results. Before you multipled and divided fractions. Now you will multiply and divide decimals to prepare for Grade 6 Standard NS 1.4. You can represent 1 whole with a grid. The width of each row or column is 0.1. Each small square represents The area selected at the right represents seven tenths of 1.3, or There are 91 squares selected, so KEY CONCEPT Multiplying Decimals Words Multiplying Decimals 2 decimal places 12 decimal places 4 decimal places Multiply decimals as you would whole numbers. Then place the decimal point in the product. The number of decimal places in the product is equal to the sum of the number of decimal places in the factors. Numbers E XAMPLE 1 CHECK REASONABLENESS To check that the product in Example 1 is reasonable, round each factor to the place value of the leading digit, and then multiply. The leading digit of a number is the first nonzero digit Round to the nearest whole number Round to the nearest tenth. Because , the product in Example 1 is reasonable. Students should be familiar with the rules for multiplying and dividing whole numbers in order to multiply and divide decimals. Multiply decimals as you would whole numbers. Count the total number of decimal points in the factors. Place this number of decimal places in the product. When dividing decimals, the divisor must be a whole number. If necessary, multiply the divisor by a power of ten to make it a whole number. Multiply the dividend by the same power of ten. Line up the decimal point in the quotient with the one in the dividend and divide as you would with whole numbers. Math and FUNDRAISING Ex. 73, p. 111 For Your Notebook 2.7 Multiplying and Dividing Decimals Transparency Available Find the product or quotient ,500, , How much does Sam earn for mowing 5 lawns if he earns $18 for each lawn? $90 Transparency Available Promotes interactive learning and notetaking skills, pp Suggested Number of Days Basic Average Advanced 2 Days 2 Days 2 Days Block: 1 Block See Teaching Guide/Lesson Plan in Chapter 2 Resource Book, pp Big Idea 3, p. 66 How can you tell how many decimal places are in the product ? Tell students they will learn how to answer this question by finding the sum of the number of decimal places in the factors. Use decimal squares to model the product in the lesson opener. The digits and the number of decimal places in a decimal product are determined by the products of the numerators and denominators of corresponding fractions. For example, } 3 3 } 21 5 } }
2 E XAMPLE 2 Multiplying Decimals Find the product. Check that your answer is reasonable In checking the answer, why should you not round both factors to the nearest whole number? 0.41 would round to 0, giving an estimate of 0. An Animated Math activity in which students choose the appropriate operator tile to form an expression equal to a decimal is available online for Example 1. This activity is also available on the Power Presentations CDROM. Find the product. Check that your answer is reasonable. a. classzone.com Math b Why can you drop the ending zero in Part (a)? The cost of 18 tickets to attend a concert is $ What is the cost of each ticket? $30.25 Why is a zero placed in the dividend? You must divide to the thousandths place to round to the nearest cent. Multiple Representations In Example 3, students should realize that and are different representations of the same number. ANOTHER WAY You can also multiply decimals by rewriting them as fractions: } } } 100, About the Standards Note that Grade 6 Standard MR 2.6 expects you to round as specified. With money, round to the nearest hundredth to find the nearest cent. a decimal places 1 0 decimal places 2 decimal places After you place the decimal point, you can drop any zeros at the end of an answer. b decimal places 1 2 decimal places 5 decimal places c Answer c Answer GUIDED PRACTICE for Examples 1 and 2 Write a zero before the 7 as a placeholder so that the number has five decimal places. Find the product. Then check that your answer is reasonable DIVIDING DECIMALS To divide decimals by whole numbers, you can use long division. Line up the decimal points in the quotient and the dividend. E XAMPLE 3 Dividing a Decimal by a Whole Number TEAM PHOTOS Your baseball team is ordering photo trading cards of each player on your team. A set of 25 cards costs $ Find the price of each card. Round to the nearest cent. SOLUTION To find the cost per card, you need to divide. STEP 1 Divide $15.95 by 25. STEP Line up decimal point in 25q }}} quotient with decimal point in dividend Divide as you would with whole numbers. Round to the nearest cent. $.638 $ Chapter 2 Fraction and Decimal Operations Example 2 In this example, students apply Standard to multiply with decimals. They can also verify the reasonableness of the results. Use estimation to check reasonableness. In part(a), estimate using In part(b), estimate using c Answer The price of each card is about $.64. Catcher Catcher Kevin Baker Challenge advanced students to use decimal squares to create a model depicting the product
3 About the Standards Note that Grade 6 Standard MR 2.1 asks you to verify the reasonableness of results. AVOID ERRORS Don t forget to write zeros as placeholders and line up the decimal point in the quotient with the decimal point in the dividend. To check that the quotient in Example 3 is reasonable, you can use leading digits and compatible numbers. Compatible numbers are numbers that make a calculation easier. 25q } q } Because , the quotient in Example 3 is reasonable. DIVIDING BY A DECIMAL Notice the pattern in the equations below The quotient remains the same when the divisor and the dividend are multiplied by the same power of 10. This is because the quotients can be written as equivalent fractions multiplied by } 10, or 1. This fact can 10 help you to divide decimals. KEY CONCEPT Dividing by a Decimal Words E XAMPLE 4 a. 3.17q } b. 1.9q } Dividing Decimals q } q } GUIDED PRACTICE for Examples 3 and 4 For Your Notebook When you divide by a decimal, multiply both the divisor and the dividend by a power of ten that will make the divisor a whole number. 0.7 Numbers 12.5q } q } 87.5 Round divisor to place value of leading digit. Round dividend to a compatible number. Multiply the divisor and dividend by 100 by moving both decimal points two places to the right. Line up decimal points in dividend and quotient. Multiply the divisor and dividend by 10 by moving both decimal points one place to the right. Find the quotient. Round to the nearest hundredth if necessary Multiplying and Dividing Decimals 109 Find the quotient. a b If a decimal divisor has n decimal places, what power of ten must you multiply the divisor by to make it a whole number? n Encourage students to insert a zero as the leading digit in products that are less than 1. When doing long division, suggest that students place the decimal point in the correct location immediately after moving the decimal points in the divisor and dividend. This will help them avoid placing the decimal incorrectly in the quotient. As students include examples in their notebooks, encourage them to include a note for each example that they moved decimal points by multiplying the divisor and dividend by a power of ten. Students have learned to multiply and divide decimals. To bring closure, have students answer these questions: 1. Essential Question: How can you tell how many decimal places are in the product ? Find the sum of the number of decimal places in the factors. There are 3 decimal places in the product. 2. By what power of 10 do you multiply the divisor and dividend to divide 1.68 by 0.7? Find the quotient of ; 2.4 Encourage students to draw arrows as shown in Example 4 when they are dividing decimals.
4 Answer Transparencies available for all exercises Basic: Day 1: Exs. 1 14, 23, 40 Day 2: EP p. 693 Exs Exs , 72 80, Average: Day 1: MCP p. 65 Exs Exs. 1 6, 14 18, 23, 43 46, Day 2: MCP p. 65 Exs Exs , 41, 42, 51 54, 59, 64 70, 76, Advanced: Day 1: MRSPS p. 26 Exs. 4, 5 Exs. 1 5, 19 23, 47 50, Day 2: MRSPS p. 26 Exs. 6 8 Exs , 42, 55 59, 65 71, 76, 78, 80 88* Block: MCP p. 65 Exs Exs. 1 6, 14 18, 23, 32 35, 41 46, 51 54, 59 70, 76, For a quick check of student understanding of key concepts, go over the following exercises: Basic: 8, 12, 26, 28, 76 Average: 16, 18, 34, 76, 82 Advanced: 20, 22, 38, 82, 84 Student Edition, p. 693 Chapter 2 Resource Book: Practice Levels A, B, C, pp An easily readable reduced practice page (with answers) for this lesson can be found on pp. 66E 66F. 2.7 EXERCISES A SEE EXAMPLES 1 AND 2 on pp for Exs SEE EXAMPLES 3 AND 4 on pp for Exs The decimal point must move four places; The decimal point must move the same number of places in the divisor and the dividend; HOMEWORK KEY SKILLS PROBLEM SOLVING REASONING VOCABULARY Round to the place value of the leading digit. 5 MULTIPLE CHOICE PRACTICE Exs. 23, 42, 76, 78, HINTS AND HOMEWORK HELP for Exs. 7, 25, 79 at classzone.com VOCABULARY Using compatible numbers, what dividend and divisor would you use to estimate the quotient ? 56 and 7 6. WRITING Explain how you can use fractions to multiply decimals. Give an example. Write the decimals as fractions, and multiply. Sample answer: } 1 3 } 7 5 } 11 3 } 7 5 } } FINDING PRODUCTS Find the product. Check that it is reasonable MULTIPLE CHOICE What is the value of the expression ? B A B C D FINDING QUOTIENTS Find the quotient. Round your answer to the nearest hundredth if necessary ERROR ANALYSIS Describe and correct the error made in finding the product or quotient MULTIPLE CHOICE Which quotient is not equal to the others? q } q } A B C D ESTIMATING PRODUCTS Round to the place value of the leading digit to estimate the product Chapter 2 Fraction and Decimal Operations For Exercises 7 22, some students may need help when counting decimal places. Make sure that all students understand that they should count from the right when placing the decimal point in a product. Because students read numbers from the left, they may find this confusing. Remind them that the rightmost digit determines the place value of the decimal. A
5 B 69. Multiply the previous number by 5; 75, 375, Divide the previous number by 2; , , Multiply the previous number by 1.5; , , SEE EXAMPLE 3 on p. 108 for Exs pages; 36 min; pages in 1 hour pages left, more minutes. ESTIMATING QUOTIENTS Use compatible numbers to estimate the quotient MODELING Copy the number line below. Use your copy to show how to represent Use the fact that division is repeated subtraction. See margin xy ALGEBRA Evaluate the expression when p and q p p p q p p 5.08 p p 63. q p 1.12 p p q p p q q OPENENDED Describe the pattern Position n n used to relate the value of a term to its position n in the list. Create Value of term ? and describe your own pattern. Multiply n by 1.5; check students work. DESCRIBING PATTERNS Describe the pattern. Write the next three numbers , 0.6, 3, 15, , 0.5, 0.25, 0.125, , 3, 4.5, 6.75,... CONNECT SKILLS TO PROBLEM SOLVING Exercises will help you prepare for problem solving. Write the expression you would use to solve the problem. 72. Grapes are on sale for $1.25 per pound. You buy 1.8 pounds. How much do you pay for the grapes? Your class holds a car wash to raise money for a field trip. You charge $4.75 per car and earn $779. How many cars does your class wash? You have a wooden board that is 30 inches long. You cut it into pieces that are 3.75 inches long. How many pieces of wood do you have? Wanda buys 3 CDs. With tax, each CD costs $ How much does she spend? MULTIPLE CHOICE You knit a scarf using 4 balls of yarn. The yarn costs a total of $ How much does each ball of yarn cost? B A $.16 B $6.22 C $20.88 D $99.52 California for problem solving help at classzone.com 77. READING RATE Tyler can read about 1.25 pages per minute. Can he finish reading a 65page book in one hour? About how long would it take him to finish? How many pages would he have left after reading a 120page book for one hour? How much more time would he need? Explain. California for problem solving help at classzone.com Exercises 7 22 Students should realize that when using estimation to check for reasonableness, if they round one factor to 0, the estimate of the product will be 0. Thus, it is advisable to avoid rounding a factor to 0. Exercises Some students may multiply the divisor by a power of 10, but not the dividend. Remind students that they must multiply the divisor and the dividend by the same power of 10. Exercises Use compatible numbers to estimate the quotient means students should use numbers that will make it easy to estimate the quotient. You may wish to ask students to explain their answers to see if they used different compatible numbers and why Multiplying and Dividing Decimals 111 Exercise 68 In this exercise, students apply Standard to develop a generalization of the results to fi nd the value of the nth term. In positions 1, 2, 3, and 4, the value of each term is one and a half times the position number. Generalize to the value of the nth position. The value of the nth term is one and a half times n, or 1.5n.
6 Exercise 78 Students should reason that the number of minutes it will take to complete the marathon is greater than The division in choices A and B will give numbers that are less than The subtraction in choice C would not make sense because you would be subtracting minutes from miles. Exercise 82 To complete this exercise, students must understand the meaning of rates. To find the cost per ounce of cereal means to find the cost of 1 ounce of cereal. 85. Sample answer : No, when dividing, the quotient times the divisor must equal the dividend, so if the quotient is a whole number and the divisor b is a whole number, whole number times whole number is always equal to a whole number, yes, ; yes, ; yes, Start at 1.5 and then move back 0.2 spaces until you reach 0. The quotient is the number of times you have to take away 0.2 from 1.5 to reach 0; Trade one dollar for 10 dimes. Separate the dimes into groups of 2. The quotient is the number of groups. 83. Yes; no; $27.75; $3.50 per gallon, $3.70 per gallon, 3.19 p $ a mm; mm; mm 78. MULTIPLE CHOICE A wheelchair racer takes about 5.95 minutes to travel 1 mile. Which expression shows how long it would take the racer to finish a 26.2mile marathon? D A B C D COMETS Encke s comet takes about 3.3 years to orbit the sun. Halley s comet takes about times as long. About how long does Halley s comet take to orbit the Sun? Round to the nearest tenth yr 8 0. SHORT RESPONSE Copy the division problem below. Explain how to use estimation to place the decimal point in the quotient q } WRITING Explain how to use a number line model to find Then explain how to use dollars and dimes to model $ MULTISTEP PROBLEM It costs $4.75 for a 25 ounce box of cereal and $3.45 for a 15 ounce box. a. What is the cost per ounce of each box of cereal? b. How many times the cost per ounce of the smaller box is the cost per ounce of the larger box? Explain. about 1.21 times; $.23 4 $.19 ø GASOLINE At one time, the price of gasoline ranged from $3.19 to $3.59 per gallon. A car needs 8.7 more gallons of gasoline to have a full tank. Is it possible that the cost to fill the tank is $30.45? What is the least possible cost to fill the tank? Explain how you solved the problem. 84. MEASUREMENT The objects below have been magnified. Their actual width w is much smaller. Measure each object in millimeters. Pollen w width shown Sample answer: 10 p 3 is 30, so the decimal should be placed between the 3 and the 2. Algae w width shown Athletes use racing chairs. $.19, $.23 Blood cell w width shown C a. Use your measurements to find the actual width w of each object. b. List the actual objects in order from least to greatest width. blood cell, pollen, algae 85. xy REASONING The quotient of a and b is a whole number. Can a be a decimal number if b is a whole number? Can b be a decimal number if a is a whole number? Can both a and b be decimal numbers? Can the quotient be greater than a? Justify your answers and give examples. See margin. 112 Chapter 2 Fraction 5 MULTIPLE and Decimal CHOICE Operations PRACTICE 5 HINTS AND HOMEWORK HELP at classzone.com
7 86. decimals less than 5.29; decimals greater than 5.29; 5.29; 5.29 divided by 2.3 is 2.3, so decimals smaller than 5.29 will be less than 2.3 when divided, and decimals greater than 5.29 will be greater than 2.3 when divided. NS 2.1 Gr. 5 NS 1.2 Gr. 4 NS REASONING Which decimal number(s) can you divide by 2.3 to make the quotient less than 2.3? greater than 2.3? equal to 2.3? Explain your reasoning. 87. CHALLENGE Runner A runs at a pace of 6.54 miles per hour for 1.3 hours. Runner B runs at a pace of 7.08 miles per hour for 1.1 hours. Who runs farther? How much longer must the other runner continue to run to match the distance of the first runner? Round to the nearest hundredth of an hour. Explain how you solved the problem. Runner A; 0.10 h; and , , then, CHALLENGE A store sells crafts. The first week it prices 5 baskets at $20 each. After each week, the price of each unsold basket drops to 0.9 times the previous week s price. All 5 baskets sell in the same week for a total of at least $53. In what week(s) could they have been sold? week 7 or before CALIFORNIA STANDARDS SPIRAL REVIEW 89. What is the value of } 5 1 } 7? (p. 75) C 6 10 A 3 } 4 B 6 } 5 C 23 } 15 D 49 } Which number is 6 } 1 wr itten as a decimal? (p. 40) A 8 A B 6.18 C 6.81 D During 4 days of basketball practice, you shoot a total of 140 free throws. You shoot the same number of free throws each day. How many free throws do you shoot per day? (p. 671) C A 25 B 30 C 35 D 40 QUIZ for Lessons Find the product or quotient. (p. 88, 94) 7 1. } } } 2. 2 } } 5 4 } } 15 7 } } } 2 5 } } } } 6. 5 } 5 4 } 1 81 } } } } 3 5 } 4 6 } Find the sum or difference. Then check your answer. (p. 102) Find the product or quotient. Round quotients to the nearest hundredth if necessary. Then check your answer. (p. 107) BOOKS Ryan had 180 books. He gave away } 1 of his books and sold } 3 of 3 4 the rest. How many books did he sell? Explain your reasoning. (p. 88) 90 books; } 1 ( 18 0 ) 5 120, } Find the product or quotient Estimate the product of by rounding each factor to the place value of the leading digit Jose bought 2.3 pounds of fish for $ Use compatible numbers to estimate the cost per pound. $9.50 Online Quiz classzone.com An alternate quiz for Lessons is available online in multiple choice format. Practice A, B, C in Chapter 2 Resource Book, pp Study Guide in Chapter 2 Resource Book, pp Practice Workbook, pp Additional challenge is available in the Chapter 2 Resource Book, p. 77. An easily readable reduced copy of the quiz on Lessons (with answers) from the Assessment Book can be found on pp. 66G 66H. EXTRA PRACTICE for Lesson 2.7, p Multiplying ONLINE and QUIZ Dividing at classzone.com Decimals 113 } 1 } D } } } } } D A
8 MIXED REVIEW of Skills and Problem Solving California classzone.com Students who need more review and practice should see the following lessons in the Exercise 1: Lesson 2.5 Exercise 2: Lesson 2.7 Exercise 3: Lesson 2.7 Exercise 4: Lesson 2.7 Exercise 5: Lesson 2.6 Exercise 6: Lesson 2.7 Exercise 7: Lesson 2.4 Exercise 8: Lesson 2.5 Multiple Choice Practice for Lessons You have a piece of wood that is 51 inches long. For a craft project, you need pieces that are each 4 1 } 2 inches long. 51 in. How many pieces that are 4 1 } 2 inches long can you cut from the wood? NS 2.1 A A 11 B 12 C 229 D What is the value of the expression x p when x ? Gr. 5 NS 2.1 B A B C D What is rounded to the nearest hundredth? Gr. 5 NS 2.1 D A B 0.03 C D The table shows the amount of money raised by 3 homerooms at a school fair. How much more was the total raised by homerooms 6A and 6C than by homeroom 6B? Gr. 5 NS 2.1 B Homeroom 6A 6B 6C Money raised $ $ $ A $14.71 B $ C $ D $ What is the value of ? Gr. 5 NS 2.1 B A B C D The recipe shown makes enough garlic mashed potatoes for 5 servings. You want to make 150 servings for a garlic festival. How many cups of water and cups of milk do you need? NS 2.1, MR 3.1 B Garlic Mashed Potatoes 4. In the table below, which description relates a position n to its value? NS 2.2, MR 1.2 C Position n Value 1 2} Garlic Mashed Potatoes 1 box garlic mashed potato mix 1 tbsp butter 2 1/3 c water 1/3 c milk 3 7} n? A Multiplyn by 1 } 1. 2 B Dividen by 1 } 1. 2 A 67} 2 cups water and 9 } 2 cups milk 3 3 B 70 cups water and 10 cups milk C 116} 2 cups water and 16 } 2 cups milk 3 3 D 350 cups water and 50 cups milk C Multiplyn by 2 1 } 2. D Dividen by 2 1 } What is the value of 2 3 } } 12? NS 2.2 A 192 } 875 B 20 } 21 C C 1 1 } 20 D 52 1 } Chapter 2 Fraction and Decimal Operations Exercise 4 In this exercise, students formulate and justify mathematical conjectures based on a general description, as called for in Standard. Formulate a conjecture. Justify the conjecture using reasoning. The values are greater than the position numbers, so n is multiplied to obtain the value of position n. Each value is more than double its position number. The only reasonable choice is C. The value of each number is 2 1 } 2 times its position. Exercise 7 In this exercise, students evaluate the reasonableness of the solution in the context of the original situation, as called for in Standard. You want to make , or 30 times the given recipe amounts. Calculate } 3 c u p s w a t e r a n d } 3 c u p milk. Check the reasonableness of the answer using estimation: cups water and } cups milk is needed.
Evaluate and Simplify Algebraic Expressions
1.2 Evaluate and Simplify Algebraic Expressions Before You studied properties of real numbers. Now You will evaluate and simplify expressions involving real numbers. Why? So you can estimate calorie use,
More informationReteaching. Properties of Operations
 Properties of Operations The commutative properties state that changing the order of addends or factors in a multiplication or addition expression does not change the sum or the product. Examples: 5
More informationUnit 4 Number and Operations in Base Ten: Multiplying and Dividing Decimals
Unit 4 Number and Operations in Base Ten: Multiplying and Dividing Decimals Introduction In this unit, students will learn how to multiply and divide decimals, and learn the algorithm for dividing whole
More informationDATE PERIOD. Estimate the product of a decimal and a whole number by rounding the Estimation
A Multiplying Decimals by Whole Numbers (pages 135 138) When you multiply a decimal by a whole number, you can estimate to find where to put the decimal point in the product. You can also place the decimal
More information2. Perform the division as if the numbers were whole numbers. You may need to add zeros to the back of the dividend to complete the division
Math Section 5. Dividing Decimals 5. Dividing Decimals Review from Section.: Quotients, Dividends, and Divisors. In the expression,, the number is called the dividend, is called the divisor, and is called
More informationDIAMOND PROBLEMS 1.1.1
DIAMOND PROBLEMS 1.1.1 In every Diamond Problem, the product of the two side numbers (left and right) is the top number and their sum is the bottom number. Diamond Problems are an excellent way of practicing
More informationPAYCHEX, INC. BASIC BUSINESS MATH TRAINING MODULE
PAYCHEX, INC. BASIC BUSINESS MATH TRAINING MODULE 1 Property of Paychex, Inc. Basic Business Math Table of Contents Overview...3 Objectives...3 Calculator...4 Basic Calculations...6 Order of Operation...9
More informationUnit 5 Ratios and Proportional Relationships: Real World Ratio and Percent Problems
Unit 5 Ratios and Proportional Relationships: Real World Ratio and Percent Problems The material in this unit crosses three strands The Number System (NS), Expressions and Equations (EE), and Ratios and
More informationChapter 4  Decimals
Chapter 4  Decimals $34.99 decimal notation ex. The cost of an object. ex. The balance of your bank account ex The amount owed ex. The tax on a purchase. Just like Whole Numbers Place Value  1.23456789
More informationOperations on Decimals
Operations on Decimals Addition and subtraction of decimals To add decimals, write the numbers so that the decimal points are on a vertical line. Add as you would with whole numbers. Then write the decimal
More information5 th Grade CCGPS Math Unit 2: Numbers and Operations in Base Ten Student Study Guide
5 th Grade CCGPS Math Unit 2: Numbers and Operations in Base Ten Student Study Guide Dear Student: Please review the Math standards below to prepare for the Georgia Milestones test. This will require that
More informationDividing Decimals 4.5
4.5 Dividing Decimals 4.5 OBJECTIVES 1. Divide a decimal by a whole number 2. Divide a decimal by a decimal 3. Divide a decimal by a power of ten 4. Apply division to the solution of an application problem
More informationSTUDENT NAME: GRADE 8 MATHEMATICS
STUDENT NAME: GRADE 8 MATHEMATICS Administered October 2009 Name: Cla ss: 8th Grade TAKS Practice Test 1 1 A librarian arranged some books on the shelf using the Dewey decimal system. Choose the group
More informationDividing Decimal Numbers
Section 2.4 PREACTIVITY PREPARATION Dividing Decimal Numbers The cost of your homeowner s insurance for one year is $856.2. If you opt for equal monthly payments to be automatically withdrawn from your
More informationUnit 1 Number Sense. In this unit, students will study repeating decimals, percents, fractions, decimals, and proportions.
Unit 1 Number Sense In this unit, students will study repeating decimals, percents, fractions, decimals, and proportions. BLM Three Types of Percent Problems (p L34) is a summary BLM for the material
More information5th Grade. Division.
1 5th Grade Division 2015 11 25 www.njctl.org 2 Division Unit Topics Click on the topic to go to that section Divisibility Rules Patterns in Multiplication and Division Division of Whole Numbers Division
More informationAdd Decimal Numbers LESSON 4
LESSON 4 Add Decimal Numbers In this lesson, we will begin using the algebradecimal inserts to represent decimals. Turn a red hundred square upside down so the hollow side is showing, and snap the flat
More informationSection R.2. Fractions
Section R.2 Fractions Learning objectives Fraction properties of 0 and 1 Writing equivalent fractions Writing fractions in simplest form Multiplying and dividing fractions Adding and subtracting fractions
More informationDECIMALS are special fractions whose denominators are powers of 10.
DECIMALS DECIMALS are special fractions whose denominators are powers of 10. Since decimals are special fractions, then all the rules we have already learned for fractions should work for decimals. The
More informationSECTION 5.1 CONSTRUCTING DECIMALS
D E C I M A L R E P R E S E N T A T I O N S 5 SECTION 5.1 CONSTRUCTING DECIMALS We have all been concerned about the cost of an item when we shop or go out to eat. For example, a cheeseburger might cost
More information100 which when written as a decimal is 0.06.
Solve the following problem. Session 28 Decimal Multiplication and Division Find the electric bill for 370 kwh s of electricity from Red River Region Coop, which charges 0.094 dollars per kilowatthour
More informationMath Help and Additional Practice Websites
Name: Math Help and Additional Practice Websites http://www.coolmath.com www.aplusmath.com/ http://www.mathplayground.com/games.html http://www.ixl.com/math/grade7 http://www.softschools.com/grades/6th_and_7th.jsp
More informationHundreds Chart. Vocabulary. Place Value
Addition plus, sum, addend Subtraction minus, difference Multiplication times, product, factor Division quotient, divisor, dividend Hundreds Chart SYMBOLS Addition: + Subtraction: Multiplication: x * Division:
More informationChapter 5. Decimals. Use the calculator.
Chapter 5. Decimals 5.1 An Introduction to the Decimals 5.2 Adding and Subtracting Decimals 5.3 Multiplying Decimals 5.4 Dividing Decimals 5.5 Fractions and Decimals 5.6 Square Roots 5.7 Solving Equations
More information6 th Grade Intensive Math
6 th Grade Intensive Math 21 Practice A Properties and Mental Math Choose the letter of the equation that shows the given property. 1. Associative Property 2. Distributive Property A 2 + 3 = 3 + 2 F 3
More informationActivity 21. Extending the place value system
2. DECIMAL NUMBERS 21 Extending the place value system 2 22 Is it a decimal point? 5 23 The size of decimal numbers 6 24 Scales with decimal numbers 7 25 Decimal accuracy 8 26 Rounding decimal numbers
More informationMonomial. 5 1 x A sum is not a monomial. 2 A monomial cannot have a. x 21. degree. 2x 3 1 x 2 2 5x Rewrite a polynomial
9.1 Add and Subtract Polynomials Before You added and subtracted integers. Now You will add and subtract polynomials. Why? So you can model trends in recreation, as in Ex. 37. Key Vocabulary monomial degree
More informationeday Lessons Mathematics Grade 8 Student Name:
eday Lessons Mathematics Grade 8 Student Name: Common Core State Standards Expressions and Equations Work with radicals and integer exponents. 3. Use numbers expressed in the form of a single digit times
More informationSolve Quadratic Equations by the Quadratic Formula. The solutions of the quadratic equation ax 2 1 bx 1 c 5 0 are. Standardized Test Practice
10.6 Solve Quadratic Equations by the Quadratic Formula Before You solved quadratic equations by completing the square. Now You will solve quadratic equations using the quadratic formula. Why? So you can
More informationDear Teachers, Many Thanks, The Eureka Math Team Great Minds. All rights reserved. greatminds.net
Dear Teachers, During the listening tour, the Eureka Math Team enjoyed the opportunity to witness our curriculum being implemented in St. Charles classrooms. We listened carefully to the feedback you provided
More informationWSMA Decimal Numbers Lesson 5
To multiply and divide decimal numbers, you multiply as if they were whole numbers. After that, the only question is: Where do you put the decimal point?! Decimal Numbers Multiplication: Whole Number and
More informationexpression undefined is called an excluded value. For example, } is x 2 3 undefined when x 5 3. So, 3 is an excluded value. Find excluded values
1.4 Simplify Rational Expressions Before You simplified polynomials. Now You will simplify rational expressions. Why So you can model a cost over time, as in Example. Key Vocabulary rational expression
More informationLesson 1 Order of Operations
Lesson 1 Order of Operations "Operations" means things like add, subtract, multiply, divide Student A solved the following problem: 177 x 2 = 20. Is he correct? Why or why not? Lesson 1 Order of Operations
More informationSummer Math Packet. Review of Number Sense Skills for Students Entering Math 7. No Calculators!
Name Summer Math Packet Review of Number Sense Skills for Students Entering Math 7 No Calculators! The purpose of this summer math packet is to provide you with notes and practice problems to help you
More informationIn 5th grade, you learned how to divide using models and partial quotients. Take a look at this problem.
Lesson 38 Part 1: Introduction Equivalent Divide MultiDigit Ratios Numbers Develop Skills and Strategies MAFS 6.NS.2.2 In 5th grade, you learned how to divide using models and partial quotients. Take
More informationMultiply and Divide Decimals
Lesson 10 Part 1: Introduction Multiply and Divide Decimals Develop Skills and Strategies MAFS 6.NS.2.3 You ve learned about place value. You ve also learned how to multiply and divide decimals to the
More informationIntroduce Decimals with an Art Project Criteria Charts, Rubrics, Standards By Susan Ferdman
Introduce Decimals with an Art Project Criteria Charts, Rubrics, Standards By Susan Ferdman hundredths tenths ones tens Decimal Art An Introduction to Decimals Directions: Part 1: Coloring Have children
More informationMath Questions & Answers
What five coins add up to a nickel? five pennies (1 + 1 + 1 + 1 + 1 = 5) Which is longest: a foot, a yard or an inch? a yard (3 feet = 1 yard; 12 inches = 1 foot) What do you call the answer to a multiplication
More informationDIVISION OF DECIMALS. 1503 9. We then we multiply by the
Tallahassee Community College 0 DIVISION OF DECIMALS To divide 9, we write these fractions: reciprocal of the divisor 0 9. We then we multiply by the 0 67 67 = = 9 67 67 The decimal equivalent of is. 67.
More informationParamedic Program PreAdmission Mathematics Test Study Guide
Paramedic Program PreAdmission Mathematics Test Study Guide 05/13 1 Table of Contents Page 1 Page 2 Page 3 Page 4 Page 5 Page 6 Page 7 Page 8 Page 9 Page 10 Page 11 Page 12 Page 13 Page 14 Page 15 Page
More informationRelationships Between Quantities
Relationships Between Quantities MODULE 1? ESSENTIAL QUESTION How do you calculate when the numbers are measurements? CALIFORNIA COMMON CORE LESSON 1.1 Precision and Significant Digits N.Q.3 LESSON 1.2
More information2. In , 90 is the? and 5 is the?.
Vocabulary Choose the best term from the box. divisor remainder thousandths quotient tenths 1. The? is the number that is left over after the division is complete. 3 How much money would a fifthgrader
More informationUNIT 5 VOCABULARY: DECIMAL NUMBERS
º ESO Bilingüe Página UNIT 5 VOCABULARY: DECIMAL NUMBERS.. Decimal numbers Decimal numbers are used in situations in which we look for more precision than whole numbers provide. In order to do that, we
More informationMultiplying and Dividing Decimals
Name: Date: Chapter Multiplying and Dividing Decimals Practice 1 Multiplying Decimals Multiply. Write the product as a decimal. Example 2 0.3 2 3 tenths 6 tenths 0.6 So, 2 0.3 0.6. 1. 5 0.6 5 tenths tenths
More informationThis lesson plan is from the Council for Economic Education's publication:
This lesson plan is from the Council for Economic Education's publication: Mathematics and Economics: Grades 35 To purchase Mathematics and Economics: Grades 35, visit: http://store.councilforeconed.org/mathandecon35.html
More informationMath Refresher. Book #2. Workers Opportunities Resources Knowledge
Math Refresher Book #2 Workers Opportunities Resources Knowledge Contents Introduction...1 Basic Math Concepts...2 1. Fractions...2 2. Decimals...11 3. Percentages...15 4. Ratios...17 Sample Questions...18
More informationDECIMALS. The student will be able to:
DECIMALS The student will be able to: 1. Perform basic operations using decimal numbers: addition, subtraction multiplication, and division. Demonstrate an understanding of place value Locate decimal numbers
More informationScholastic Fraction Nation
Scholastic correlated to the ematics: Grades 48 2010 TM & Scholastic Inc. All rights reserved. SCHOLASTIC,, and associated logos are trademarks and/or registered trademarks of Scholastic Inc. Scholastic
More informationPreAlgebra Lecture 6
PreAlgebra Lecture 6 Today we will discuss Decimals and Percentages. Outline: 1. Decimals 2. Ordering Decimals 3. Rounding Decimals 4. Adding and subtracting Decimals 5. Multiplying and Dividing Decimals
More informationScore 4.0. The student: Score 3.0
Strand: 5.NS.1 (Decimal Place Value) Topic: Use a number line to compare and order decimals In addition to, indepth inferences and applications that go beyond what was taught. 3.5 In addition to score
More informationMathematical Reasoning. Lesson 2: Division with Decimals. LESSON 2: Division with Decimals. Weekly Focus: Decimals Weekly Skill: Division
LESSON 2: Division with Decimals Weekly Focus: Decimals Weekly Skill: Division Lesson Summary: For the warm up, students will solve a word problem. In Activity 1, they will practice dividing whole numbers
More informationLesson Plan  Percent of a Number/Increase and Decrease
Lesson Plan  Percent of a Number/Increase and Decrease Chapter Resources  Lesson 411 Find a Percent of a Number  Lesson 411 Find a Percent of a Number Answers  Lesson 412 Percent of Increase and
More informationMM 61 MM What is the largest number you can make using 8, 4, 6 and 2? (8,642) 1. Divide 810 by 9. (90) 2. What is ?
MM 61 1. What is the largest number you can make using 8, 4, 6 and 2? (8,642) 2. What is 500 20? (480) 3. 6,000 2,000 400 = (3,600). 4. Start with 6 and follow me; add 7, add 2, add 4, add 3. (22) 5.
More informationGrade 5 Module 2 Lessons 1 29
Eureka Math Grade 5 Module 2 Lessons 29 Eureka Math, Published by the nonprofit Great Minds. Copyright Great Minds. No part of this work may be reproduced, distributed, modified, sold, or commercialized,
More informationDr Brian Beaudrie pg. 1
Multiplication of Decimals Name: Multiplication of a decimal by a whole number can be represented by the repeated addition model. For example, 3 0.14 means add 0.14 three times, regroup, and simplify,
More informationThe gas can has a capacity of 4.17 gallons and weighs 3.4 pounds.
hundred million$ ten million$ million$ 00,000,000 0,000,000,000,000 00,000 0,000,000 00 0 0 0 0 0 0 0 0 0 Session 26 Decimal Fractions Explain the meaning of the values stated in the following sentence.
More informationGrade 7  Chapter 1 Recall Prior Knowledge
MATH IN FOCUS Grade 7  Chapter 1 Recall Prior Knowledge REFRESH YOUR MEMORY! CHAPTER 1 Recall Prior Knowledge In order to be successful with the new information in Chapter 1, it is necessary to remember
More informationDecimals Worksheets. The decimal point separates the whole numbers from the fractional part of a number.
Decimal Place Values The decimal point separates the whole numbers from the fractional part of a number. 8.09 In a whole number the decimal point is all the way to the right, even if it is not shown in
More informationTYPES OF NUMBERS. Example 2. Example 1. Problems. Answers
TYPES OF NUMBERS When two or more integers are multiplied together, each number is a factor of the product. Nonnegative integers that have exactly two factors, namely, one and itself, are called prime
More informationRoselle Math Curriculum Unit Title: 7 Multiplying and Dividing Decimals Grade: _5_. Common Core Standards, 2010
Essential Question(s) How do decimal numbers impact multiplication and division? Enduring Understanding(s) Decimals can be multiplied and divided in the same way as whole numbers. What strategies can be
More informationSaxon Math Home School Edition. September 2008
Saxon Math Home School Edition September 2008 Saxon Math Home School Edition Lesson 4: Comparing Whole Lesson 5: Naming Whole Through Hundreds, Dollars and Cent Lesson 7: Writing and Comparing Through
More informationExtending Division Patterns
Lesson 5.1 Extending Division Patterns Use patterns to find the quotients. 1. 8,500 4 100 5 8,500 4 1,000 5 8,500 4 10,000 5 8,500 4 100,000 5 8,500 4 1,000,000 5 3. 5,000 4 2 5 5,000 4 20 5 5,000 4 200
More informationThe PartialQuotients Division Algorithm, Part 1
The PartialQuotients Division Algorithm, Part 1 Objectives To introduce and provide practice with a lowstress division algorithm for 1digit divisors. www.everydaymathonline.com epresentations etoolkit
More informationSBI Lesson Objectives Common Core Standards MN State standards Lesson 1: Ratios
The Project MARS curriculum consists of 21 lessons designed to be implemented over a 6 week instructional period. The following chart outlines each lesson and how it aligns with Minnesota state standards
More informationImproper Fractions and Mixed Numbers
This assignment includes practice problems covering a variety of mathematical concepts. Do NOT use a calculator in this assignment. The assignment will be collected on the first full day of class. All
More informationCanceling Before Multiplying Fractions
Mastery Drill Canceling Before Multiplying Fractions In the following problem, we multiply, then rewrite the answer in simplest form. We can save work when multiplying fractions if we cancel first. Canceling
More informationSolve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem.
Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem. Solve word problems that call for addition of three whole numbers
More information115 Dividing Polynomials. Find each quotient. 1. (8a a) 4a ANSWER: 2a (4z 3 + 1) 2z ANSWER: 3. (12n 3 6n ) 6n ANSWER:
Find each quotient. 1. (8a 2 + 20a) 4a 2a + 5 9. (4y 2 + 8y + 3) (y + 2) 2. (4z 3 + 1) 2z 10. (4h 3 + 6h 2 3) (2h + 3) 3. (12n 3 6n 2 + 15) 6n 11. (9n 3 13n + 8) (3n 1) 4. (t 2 + 5t + 4) (t + 4) t + 1
More informationCompass Math Study Guide
Compass Math Study Guide The only purpose of this study guide is to give you an overview of the type of math skills needed to successfully complete the Compass math assessment. The Study Guide is not intended
More informationIntroduction to Decimals
Introduction to Decimals Reading and Writing Decimals: Note: There is a relationship between fractions and numbers written in decimal notation. Threetenths 10 0. 1 zero 1 decimal place Three 0. 0 100
More informationSolve Absolute Value Equations and Inequalities
1.7 Solve Absolute Value Equations and Inequalities Before You solved linear equations and inequalities. Now You will solve absolute value equations and inequalities. Why? So you can describe hearing ranges
More informationInterpreting Graphs. Interpreting a Bar Graph
1.1 Interpreting Graphs Before You compared quantities. Now You ll use graphs to analyze data. Why? So you can make conclusions about data, as in Example 1. KEY VOCABULARY bar graph, p. 3 data, p. 3 frequency
More informationSQUARES AND SQUARE ROOTS
1. Squares and Square Roots SQUARES AND SQUARE ROOTS In this lesson, students link the geometric concepts of side length and area of a square to the algebra concepts of squares and square roots of numbers.
More informationEureka Lessons for 7th Grade Unit ONE ~ ADD/SUBTRACT Rational Numbers Concept 11
Eureka Lessons for 7th Grade Unit ONE ~ ADD/SUBTRACT Rational Numbers Concept 11 LESSONS 7, 8, & 9 are the FOURTH set of Eureka Lessons for Unit 1. Also Includes four fluency drills, 2 in lesson 8 and
More informationUnit 7 The Number System: Multiplying and Dividing Integers
Unit 7 The Number System: Multiplying and Dividing Integers Introduction In this unit, students will multiply and divide integers, and multiply positive and negative fractions by integers. Students will
More informationYear Five Maths Notes
Year Five Maths Notes NUMBER AND PLACE VALUE I can count forwards in steps of powers of 10 for any given number up to 1,000,000. I can count backwards insteps of powers of 10 for any given number up to
More informationDECIMAL REVIEW. 2. Change to a fraction Notice that =.791 The zero in front of the decimal place is not needed.
DECIMAL REVIEW A. INTRODUCTION TO THE DECIMAL SYSTEM The Decimal System is another way of expressing a part of a whole number. A decimal is simply a fraction with a denominator of 10, 100, 1 000 or 10
More informationMultiplying Decimal Numbers by 10, by 100, and by 1000
Multiplying Decimal Numbers by 10, by 100, and by 1000 Lesson 111 111 To multiply by 10, shift the decimal to the right one place. To multiply by 100, shift the decimal to the right two places. To multiply
More informationSolving and Graphing Linear Inequalities 66.1 Solve Inequalities Using Addition and Subtraction
Solving and Graphing Linear Inequalities 66.1 Solve Inequalities Using Addition and Subtraction 6.2 Solve Inequalities Using Multiplication and Division 6.3 Solve MultiStep Inequalities 6.4 Solve Compound
More informationMultiplying and Dividing Signed Numbers. Finding the Product of Two Signed Numbers. (a) (3)( 4) ( 4) ( 4) ( 4) 12 (b) (4)( 5) ( 5) ( 5) ( 5) ( 5) 20
SECTION.4 Multiplying and Dividing Signed Numbers.4 OBJECTIVES 1. Multiply signed numbers 2. Use the commutative property of multiplication 3. Use the associative property of multiplication 4. Divide signed
More informationMATH 65 NOTEBOOK CERTIFICATIONS
MATH 65 NOTEBOOK CERTIFICATIONS Review Material from Math 60 2.5 4.3 4.4a Chapter #8: Systems of Linear Equations 8.1 8.2 8.3 Chapter #5: Exponents and Polynomials 5.1 5.2a 5.2b 5.3 5.4 5.5 5.6a 5.7a 1
More informationLesson Plan  Rational Number Operations
Lesson Plan  Rational Number Operations Chapter Resources  Lesson 312 Rational Number Operations  Lesson 312 Rational Number Operations Answers  Lesson 313 Take Rational Numbers to WholeNumber
More informationTo Multiply Decimals
4.3 Multiplying Decimals 4.3 OBJECTIVES 1. Multiply two or more decimals 2. Use multiplication of decimals to solve application problems 3. Multiply a decimal by a power of ten 4. Use multiplication by
More informationSixth Grade Problem Solving Tasks Weekly Enrichments Teacher Materials. Summer Dreamers 2013
Sixth Grade Problem Solving Tasks Weekly Enrichments Teacher Materials Summer Dreamers 2013 SOLVING MATH PROBLEMS KEY QUESTIONS WEEK 1 By the end of this lesson, students should be able to answer these
More informationRP623 Ratios and Rates with Fractional Terms Pages 41 43
RP62 Ratios and Rates with Fractional Terms Pages 4 4 STANDARDS 6.RP.A.2, 6.RP.A. Vocabulary equivalent ratio rate ratio table Goals Students will understand that ratios with fractional terms can turn
More informationUse Square Roots to Solve Quadratic Equations
10.4 Use Square Roots to Solve Quadratic Equations Before You solved a quadratic equation by graphing. Now You will solve a quadratic equation by finding square roots. Why? So you can solve a problem about
More informationUse Measures of Central Tendency and Dispersion. Measures of Central Tendency
13.6 Use Measures of Central Tendency and Dispersion Before You analyzed surveys and samples. Now You will compare measures of central tendency and dispersion. Why? So you can analyze and compare data,
More informationGrade 5 Math Curriculum Guide
Grade 5 Math Curriculum Guide Lesson 1 1 st Nine Weeks Unit 1: Number and Operations in Base Ten Understand Place Value 5.NBT.1. Recognize that in a multidigit number, a digit in one place represents
More information4.3 Notes Ratios and unit rates(part I)
Name Period 4.3 Notes Ratios and unit rates(part I) I CAN Identify unit rates. Compute unit rates. Compute unit rates involving complex fractions. Apply unit rates to real world applications Rate: A
More informationUsing Proportions to Solve Percent Problems I
RP71 Using Proportions to Solve Percent Problems I Pages 46 48 Standards: 7.RP.A. Goals: Students will write equivalent statements for proportions by keeping track of the part and the whole, and by solving
More informationMath, Grades 35 TEKS and TAKS Alignment
111.15. Mathematics, Grade 3. 111.16. Mathematics, Grade 4. 111.17. Mathematics, Grade 5. (a) Introduction. (1) Within a wellbalanced mathematics curriculum, the primary focal points are multiplying and
More information1.6 Division of Whole Numbers
1.6 Division of Whole Numbers 1.6 OBJECTIVES 1. Use repeated subtraction to divide whole numbers 2. Check the results of a division problem 3. Divide whole numbers using long division 4. Estimate a quotient
More information4.2 Dividing Decimals
LESSON 4.2 Dividing Decimals Number and operations Multiply and divide positive rational numbers fluently.? ESSENTIAL QUESTION How do you divide decimals? EXPLORE ACTIVITY Modeling Decimal Division Use
More informationNumber and Operations in Base Ten
Lesson 1 Number and Operations in Base Ten Name Use Base Ten Blocks to model each number as a fraction of 1,000. Write the decimal. Tell the number in each placevalue position. 1. 2. tenths hundredths
More informationDecimals. Understanding Thousandths Write the decimal shown in each placevalue chart. Example. Ones Tenths Hundredths Thousandths
Name: Date: Chapter Practice 1 Understanding Thousandths Write the decimal shown in each placevalue chart. Example Ones Tenths Hundredths Thousandths 1. 0.237 Ones Tenths Hundredths Thousandths 2. Ones
More informationPlace value chart for comparing decimals using <, >, = What Comes After this Module:
Tips for Parents Place Value and Decimal Fractions In this first module of Grade 5, we will extend 4 th grade place value work to multidigit numbers with decimals to the thousandths place. Students will
More informationHow do you compare numbers? On a number line, larger numbers are to the right and smaller numbers are to the left.
The verbal answers to all of the following questions should be memorized before completion of prealgebra. Answers that are not memorized will hinder your ability to succeed in algebra 1. Number Basics
More informationPreAlgebra Interactive Chalkboard Copyright by The McGrawHill Companies, Inc. Send all inquiries to:
PreAlgebra Interactive Chalkboard Copyright by The McGrawHill Companies, Inc. Send all inquiries to: GLENCOE DIVISION Glencoe/McGrawHill 8787 Orion Place Columbus, Ohio 43240 Lesson 51 Lesson 52
More informationPrerequisite Skills Workbook: Remediation and Intervention
ALGEBRA Prerequisite Skills Workbook: Remediation and Intervention For use with Glencoe PreAlgebra Glencoe Algebra 1 Glencoe Algebra: Concepts and Applications Glencoe/McGrawHill Copyright by The McGrawHill
More information