MATH NEWS Grade 5, Module 2, Topic A 5 th Grade Math Focus Area Topic A Math Parent Letter This document is created to give parents and students a better understanding of the math concepts found in Eureka Math ( 2013 Common Core, Inc.) that is also posted as the Engage New York material which is taught in the classroom. Grade 5 Module 2 of Eureka Math ( Engage New York) covers Multi-Digit Whole Number and Decimal Fraction Operations. This newsletter will discuss Module 2, Topic A. Topic A. Mental Strategies for Multi-Digit Whole Number Multiplication Words to know Find the product. Show your thinking 6 x 70 80 x 50 = 6 x 7 x 10 = (8 x 10) x (5 x 10) = 42 x 10 = (8 x 5) x (10 x 10) = 420 = 40 x 100 = 4,000 542 x 3 = (500 x 3) + (40 x 3) + (2 x 3) = 1,500 + 120 + 6 = 1,626 Distributive Property Associative Property Product Estimate Associative Property Factor Commutative Property Equation Distributive Property Things to Remember: Commutative Property The word "commutative" comes from "commute" or "move around", so the Commutative Property is the one that refers to moving stuff around. Example: 2 x 3 = 3 x 2 Associative Property - The word "associative" comes from "associate" or "group"; the Associative Property is the rule that refers to grouping. Example: 5 x 7 x 2 = (5 x 2) x 7 Distributive Property - The Distributive Property is easy to remember, if you recall that "multiplication distributes over addition". Example: 43 x 6 = (40 x 6) + (3 x 6) Symbol for meaning about - When multiplying whole numbers by multiples of 10 you cannot always count zeros in the factors and end up with the correct product. 5,000 x 60 30,000 5,000 x 60 (3 zeros) (1 zero) (4 zeros) = 5 x 1,000 x 6 x 10 = (5 x 6) x (1,000 x 10) = 30 x 10,000 = 300,000 OBJECTIVES OF TOPIC A Multiply multi-digit whole numbers and multiples of 10 using place value patterns and the distributive and associative properties. Round the factors to estimate the products. 867 x 46 900 x 50 7,231 x 25 7,000 x 30 = 45,000 = 210,000 Determine if these equations are true or false. Defend your answer using your knowledge of place value and the commutative, associative and/or distributive property. 850 x 6 x 10 = 85 x 6 x 100 -- these equations are TRUE (85 x 10) x 6 x 10 = 85 x 6 x (10 x 10) 85 x 6 x 10 x 10 = 85 x 6 x 10 x 10 77 x 30 x 10 = 770 x 3 -- these equations are FALSE (77 x 10) x 30 = 770 x 3 770 x 30 770 x 3 Estimate multi-digit products by rounding factors to a basic fact and using place value patterns.
Example Problems and Answers Laura wants to buy a new car. If the car payment each month is $367 for 5 years, about how much will the car cost her after the five year? $367 is about $400 --- there are 12 months in a year $400 x 12 = (4 x 100) x 12 = (4 x 12) x 100 = 48 x 100 = 4,800 For 5 years --- $4,800 x 5 = (48 x 100) x 5 = 48 x 5 x 100 = (40 x 5) + (8 x 5) x 100 = (200 + 40) x 100 = 240 x 100 = 24,000 The car will cost her about $24,000. Tickets to a baseball game are $23 for an adult and $12 for a student. If 37 adult tickets and 325 student tickets were bought, about how much money would it cost for everyone to attend the baseball game? $23 x 37 adults $20 x 40 = $800 $12 x 325 children $10 x 300 = $3,000 OR $12 x 300 $800 + $3,000 = $3,800 = 12 x (3 x 100) = (12 x 3) x 100 = 36 x 100 = 3,600 $800 + $3,600 = $4,200 It will cost about $3,800 for everyone to attend the game. Or It will cost about $4,200 for everyone to attend the game.
Grade 5, Module 2, Topic B MATH NEWS 5 th Grade Math Math Parent Letter This document is created to give parents and students a better understanding of the math concepts found in Eureka Math ( 2013 Common Core, Inc.) that is also posted as the Engage New York material which is taught in the classroom. Grade 5 Module 2 of Eureka Math ( Engage New York) covers Multi- Digit Whole Number and Decimal Fraction Operations. This newsletter will discuss Module 2, Topic B. Topic B. The Standard Algorithm for Multi-Digit Whole Number Multiplication Words to Know Area Model Product Standard Algorithm Factor Numerical Expression Decompose Estimate Things to Remember!!! Standard Algorithm Step-by-step procedure to solve a problem OBJECTIVES OF TOPIC B Numerical Expression A mathematical phrase involving only numbers and one or more operational symbol Example: 11 x (6+13) Symbol for about Product The answer when two or more numbers are multiplied together. 7 x 3 = 21 Factor Factor Product Connect visual models and the distributive property to partial products of the standard algorithm without renaming. Fluently multiply multi-digit whole numbers using the standard algorithm to solve multi-step word problems. Connect area diagrams and the distributive property to partial products of the standard algorithm with and without renaming. Fluently multiply multi-digit whole numbers using the standard algorithm to solve multi-step word problems and using estimation to check for reasonableness of the product. Focus Area Topic B Problem 1: 432 x 24 Draw using area model and then solve using the standard algorithm. Use arrows to match the partial products from the area model to the partial products of the algorithm. To find the answer to this problem, first we represent units of 432. Decompose 432 to make finding the partial product easier. 400 + 30 + 2 How many four hundred thirty-twos are we counting? (24) Decompose 24 ( 20 + 4) Multiply: What is the product of 4 and 2? 8 What is the product of 4 and 30? 120 Continue recording the product in the area model. Now add each row of partial products. Solve using the standard algorithm. Compare the partial products in the area model to the partial products in the algorithm. 4 + 20 400 + 30 + 2 1600 120 8 8000 600 40 =1,728 =8,640 What are 24 groups of 432? 10,368 Problem 2: 532 x 283 1 4 3 2 x 2 4 1 1 7 2 8 +8 6 4 0 1 0,3 6 8 Estimate the product. Solve using standard algorithm. Use your estimate to check the reasonableness of the product. To estimate the product round each factor. 532 closer to 5 hundreds than 6 hundreds on the number line 283 closer to 3 hundreds than 2 hundreds on the number line Multiply the rounded factors to estimate the product. Multiply the rounded factors to estimate the product. 532 x 283 500 x 300 = 150,000 5 3 2 x 2 8 3 1 1 1 1 5 9 6 4 2 5 6 0 +1 0 6 4 0 0 1 5 0,5 5 6
Problems and Answers The Grand Theatre purchased 257 new theatre seats for their auditorium at $129 each. What s the total cost of the new theatre seats? To find the answer to this problem, first we draw an area model. 9 We represent the number of seats in the + area model by decomposing 257 to 20 make finding the partial 5, product easier. + Next, decompose 129 which is the cost of 100 each seat. Record the products. 200 + 50 + 7 1,800 450 63 4,000 1,000 140 20,000 5,000 700 = 2,313 = 5,140 = 25,700 2 5 7 x 1 2 9 1 2 3 1 3 1 5 1 4 0 +2 5 7 0 0 3 3,1 5 3 The total cost of the theatre seats is $33,153. Peter has collected 15 boxes of football cards. Each box has 312 cards in it. Peter estimates he has about 6,000 cards, so he buys 10 albums that hold 600 cards each. A. Did Peter purchase too many, not enough, or just the right amount of albums to hold his football cards? Explain your answer? Step 1: To solve this problem, first estimate the number of cards in each box. 312 closer to 300 than 400 Multiply the number of boxes times estimated number of cards in each box. 312 x 15 Note: You may round 15 to 20 and then multiply 300 x 20 which equals 6,000. Therefore you could say that Peter has about 6,000 cards. Since both factors were rounded up, the actual number of cards is less than 6,000. Step 2: Find the total number of cards the 10 albums hold altogether. 600 x 10 = 6,000 The 10 albums can hold 6,000 cards. 300 x 15 = (3 x 100) x 15 = (3 x 15) x 100 = 45 x 100 = 4500 Peter has about 4,500 cards. Step 3: Peter purchased too many albums to hold his football cards. He has about 4,500 cards and ten albums would hold 6,000 cards. (Explanation could be justified by statement written in the note above.) B. How many cards does Peter have? Use the standard algorithm to solve the problem. 1 3 2 x 1 5 1 5 6 0 + 3 1 2 0 4,6 8 0 Peter has a total of 4,680 cards. C. How many albums will he need for all his cards? 1 album 600 cards 2 albums 1,200 cards 3 albums 1,800 cards 4 albums 2,400 cards 5 albums 3,000 cards 6 albums 3,600 cards 7 albums 4,200 cards 8 albums 4,800 cards Peter will need 8 albums for all his cards.
Grade 5, Module 2, Topic C MATH NEWS 5 th Grade Math Math Parent Letter This document is created to give parents and students a better understanding of the math concepts found in Eureka Math ( 2013 Common Core, Inc.) that is also posted as the Engage New York material which is taught in the classroom. Grade 5 Module 2 of Eureka Math ( Engage New York) covers Multi-Digit Whole Number and Decimal Fraction Operations. This newsletter will address decimal multi-digit multiplication. Topic C. Words to know Decimal Multi-Digit Multiplication Product Factor Estimate Standard Algorithm Decimal Fraction Things to Remember: A decimal fraction uses a point to separate the whole number part from the fractional part of a number. Example: in the number 36.9 the point separates the 36 (the whole number part) from the 9 (the fractional part, which really means 9 tenths). So 36.9 is 36 and nine tenths. When multiplying by a decimal fraction, you convert the decimal fraction to a whole number by multiplying it by a power of 10 (10 or 100) depending on the number of places after the decimal point. The problem now resembles a whole number multiplication problem. Once you finish multiplying, you then have to divide the answer by the same power of 10 you multiplied by. If the decimal fraction has one place after the decimal, you multiply by 10. The digits will then shift one place to the left. The result is a number that is 10 times greater than the original number. If the decimal has two places after the decimal, you multiply by 100. The digits will shift two places to the left. The result is a number that is 100 times greater than the original number. When a number is divided by 10, the digits shift one place to the right. The result is a number that is as large as the original number. When a number is divided by 100, the digits shift two places to the right. The result is a number that is as large as the original number. OBJECTIVES OF TOPIC C Multiply decimal fractions with tenths by multi-digit whole numbers using place value understanding to record partial products. Multiply decimal fractions by multi-digit whole numbers through conversion to a whole number problem and reasoning about the placement of the decimal. Focus Area Topic C Problem 1 Solve using standard algorithm. 54 x 3.5 3.5 x 10 35 x 54 x 54 140 + 1750 1890 1890 10 = 189.0 Problem 2 Round the factors to estimate the products. (Symbol means about) Solve 7.5 x 52 17.6 x 22 95 x 3.3 8 x 50 18 x 20 100 x 3 = 400 = 360 = 300 Problem 3 Estimate the product. Solve using an area model and the standard algorithm. Solve: 4.7 x 24 Standard Algorithm 4.7 x 2 4 4.7 x 24 5 x 20 x 10 47 x 24 188 + 940 1128 1128 10 = 112.8 x 10 10 54 x 3.5 1890 189.0 4 + 20 Estimation Area Model When we compare our answer (112.8) to our estimate (100), we can conclude that our answer is reasonable. 40 160 28 800 140 + 7 tenths = 188 = 940 1128 tenths = 112.8 Reason about the product of a whole number and a decimal with hundredths using place value understanding and estimation.
Example Problems and Answers Pat rides his bike a total of 6.83 miles to and from school every day. How many miles does he ride in 25 days? 6.83 miles x 25 days 6.83 (x 100) 683 x 25 x 25 3415 + 13660 17075 17075 100 = 170.75 x 100 100 25 x 6.83 17075 170.75 Pat rides his bike a total of 170.75 miles in 25 days. A. Courtney buys 79 protractors at $1.09 each and 32 composition notebooks at $2.19 each. About how much money did she spend? $1.09 per protractor x 79 protractors $1 x 80 = $80 $2.19 per notebook x 32 notebooks $2 x 30 = $60 $80 + $60 = $140 Courtney spent about $140 on protractors and notebooks. B. How much money did she actually spend? 79 x $1.09 $1.09 (x 100) 109 32 x $2.19 $2.19 (x 100) 219 x 79 x 79 x 32 x 32 1 981 1 438 + 7630 + 6570 8611 7008 8611 100 = $86.11 cost of protractor 7008 100 =$70.08 cost of notebooks Courtney actually spent $156.19. $86.11 cost of protractors +$70.08 cost of notebooks $156.19 total cost of supplies A kitchen measures 32 feet by 17 feet. If tile cost $7.98 per square foot, what is the total cost of putting tile in the kitchen? w i d t h length $7.98 (x 100) 798 32 ft 32 ft x 17 ft = x 544 x 544 3192 31920 + 399000 17 ft 434112 434112 100 = $4,341.12 544 sq. ft A Note: Area refers to the number of square units needed to cover the inside of a shape. To determine the area of this rectangle you multiply the length times the width. The formula for area is Area =length x width. The total cost of putting tile in the kitchen is $4,341.12
Grade 5, Module 2, Topic D MATH NEWS 5 th Grade Math Math Parent Letter This document is created to give parents and students a better understanding of the math concepts found in Eureka Math ( 2013 Common Core, Inc.) that is also posted as the Engage New York material which is taught in the classroom. Grade 5 Module 2 of Eureka Math ( Engage New York) covers Multi- Digit Whole Number and Decimal Fraction Operations. This newsletter will discuss Module 2, Topic D. Topic D. Words to know OBJECTIVES OF TOPIC D Measurement Word Problems with Whole Number and Decimal Multiplication millimeter (mm) milligram (mg) centimeter (cm) gram (g) kilometer (km) kilogram (kg) inch (in) ounce (oz) foot/feet (ft) pound (lb) yard (yd) ton mile (mi) fluid ounce (fl oz) cup (c) liter (L) pint (pt) milliliter (ml) quart (qt) kiloliter (kl) gallon (gal) unit Things to Remember!!! When converting bigger unit to smaller unit, you multiply by the bigger unit by whole number of smaller units. Use whole number multiplication to express equivalent measurements. Use decimal multiplication to express equivalent measurements. Solve two-step word problems involving measurement and multi-digit multiplication. Focus Area Topic D Measurement Conversions through multiplication Knowing the unit conversions 1 foot = 12 inches 1 yard = 3 feet = 36 inches 1 mile = 5,280 feet 1 mile = 1,760 yards 1 centimeter = 10 millimeter 1 meter = 100 centimeters = 1,000 millimeters 1 kilometer = 1,000 meters 1 pound = 16 pound 1 ton = 2,000 pounds 1 gram= 1,000 milligrams 1 kilogram = 1,000 grams 1 cup= 8 fluid ounces 1 pint = 2 cups 1 quart = 2 pints 1 gallon = 4 quarts 1 liter = 1,000 milliliters 1 kiloliter = 1,000 liters Convert. a. 15 yd = ft yards to feet: big unit to small unit - multiply 3 ft = 1 yd 15 yd x 3 ft per yd = 45 ft b. g = 18 kg kilograms to gram: big unit to small unit - multiply 1,000 g =1 kg 18 kg x 1,000 g per kg =18,000 g c. 16 gal= qt = pt gallons to quarts to pints: big unit to small unit to smaller unit multiply twice 4 qt = 1 gal 1 qt =2 pt 16 gal x 4 qt per gal = 64 qt 64 qt x 2 pt per qt =128 pt d. fl oz = 6.32 c cups to fluid ounces: big unit to small unit -multiply 8 fl oz =1 cup 6.32 c x 8 fl oz per c = 632 hundredths c x 8 fl oz per c = 5056 hundredths fl oz = 50.56 fl oz e. 9.54 g = mg grams to milligrams: big unit to small unit - multiply 1,000 mg = 1 g 9.54 g x 1000 mg per g = 954 hundredths g x 1000 mg per g = 954,000 hundredths mg = 9540.00 or 9540 mg
John s dog had 5 puppies! When John and his sister Peggy weigh all the puppies together, they weigh 4 pounds 1 ounce. Since all the puppies are about the same size, how many ounces does each puppy weigh? Answer: First, we need to put all of the puppies weight in the same units. We are looking for a final answer of ounces. So, we are converting from pounds to ounces: big unit to small unit - multiply. 16 ounces = 1pound 4 pounds x 16 ounces per pound = 64 ounces 64 ounces + 1 ounce = 65ounces 65 ounces = 5 puppies weight in ounces 65ounces? oz (weight of puppy)? oz (weight of puppy)? oz (weight of puppy)? oz (weight of puppy)? oz (weight of puppy) 65ounces 5 puppies = 13 ounces Each puppy weighs 13 ounces. 5 1 3 6 5-5 1 5-1 5 0 Susan is training to be in the Mrs. Fitness contest. She ran 3.75 km, swam 0.76 km, and biked for 23.2 km. Susan completed this routine three times a week. How far did Susan travel in one week while training? Express your answer in meters. Answer: First, we will convert from km to m: big unit to small unit - multiply. 1,000 m = 1km 3.75km x 1000 m per km =3,750 m 0.76 km x 1000 m per km =760 m 23.2km x 1000m per km = 23,200m (Susan ran) (Susan swam) (Susan biked) 3,750m 760m 27,710 m + 23,200m x 3 (trainings in a week) 27,710m (Susan s travel for 1time) 83,130 m Susan traveled a total of 83,130 meters in one week of training. Another Approach: 3.75 km 27,710m 0.76 km x 3 (trainings in a week) 23.20 km 83,130m (total distance in one week of training) 27.71 km x 1000 m per km = 27,710 m Fast Mail charges $5.35 to ship a 2 lb-package. For each ounce over 2 lb, they charge an additional $0.18 per ounce. How much would it cost to ship a package weighing 3 lb 8 oz? Answer: First we need to see how many 2 pounds can be taken out of the total weight of the package. 3 lb 8 oz (weight of package) - 2 lb 0 oz ($5.35 - cost for shipping 2 lb) Now we need to convert our packages left over weight into the same unit of ounces. 1 lb 8 oz (left over weight) Convert pounds to ounces: big unit to small unit (multiply) 16 oz = 1 lb 16 oz + 8 oz 24 oz ($0.18 per oz) 0.18 x 100 = 18 It will cost $9.67 to ship a package weighing 3 lb 8 oz. 24 oz x 18 1 9 2 + 2 4 0 4 3 2 432 100 = 4.32 $5.35 (cost for 2 lb) + $4.32 (cost for 24 oz) $9.67
Grade 5, Module 2, Topic E MATH NEWS 5 th Grade Math Math Parent Letter This document is created to give parents and students a better understanding of the math concepts found in Eureka Math ( 2013 Common Core, Inc.) that is also posted as the Engage New York material which is taught in the classroom. Grade 5 Module 2 of Eureka Math (Engage New York) covers Multi- Digit Whole Number and Decimal Fraction Operations. This newsletter will discuss Module 2, Topic E. Topic E. Words to know OBJECTIVES OF TOPIC E Mental Strategies for Multi-Digit Whole Number Division multiples dividend (whole) quotient divide divisor division round estimation approximate ( ) basic facts Things to Remember!!! When estimating quotients, round the divisor only. Once the divisor is rounded, find a multiple of the first digit of the divisor that would create a number that is close to the dividend. Example: 835 34 Round 34 to 30. 8 is not a multiple of 3 but 9 900 30 is, so our dividend becomes 900. = 30 The dividend is referred to as the whole. When dividing by a power of 10 (10, 100, 1000) the digits in the whole (dividend), shift to the right. When dividing by 10, the digits shift 1 place to the right. When dividing by 100, the digits shift 2 places to the right and when dividing by 1,000, the digits shift 3 places to the right. Use divide by 10 patterns for multi-digit whole number division. Focus Area Topic E Mental Multi-digit whole number division Knowing the multiples of a number 2 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 3 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 4 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 5 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 6 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, 7 7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84, 8 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96, 9 9, 18, 27, 36, 45, 54, 63, 72, 81, 90, 99, 108, 10-10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 11-11, 22, 33, 44, 55, 66, 77, 88, 99, 110, 121, 132, 12-12, 24, 36, 48, 60, 72, 84, 96, 108, 120, 132, 144, Divide. Below number disks are used to show what happens when 400 is divided by 10. 400 10 Answer: 10 = 40 Divide. a. 640,000 100 b. 420,000 7,000 (shift two places to the right) = 420,000 1,000 7 = 6,400 =( 420,000 1,000) 7 (shift three places to the right) = 420 7 = 60 Use basic facts to approximate quotients with two-digit divisors. c. 27,000 90 d. 350,000 500 =27,000 10 9 = 350,000 100 5 =(27,000 10) 9 = (350,000 100) 5 (shift one place to the right) (shift two places to the right) = 2,700 9 = 3,500 5 = 300 = 700
Estimate the quotient for the following problems. a. 243 56 56 rounds to 60 b. 633 92 92 rounds to 90 c. 483 64 64 rounds to 60 240 60 24 is a multiple of 6, = (240 10) 6 so the dividend = 24 6 becomes 240 = 4 d. 3,924 64 64 rounds to 60 630 90_ 63 is a multiple of 9, = (630 10) 9 so the dividend = 63 9 becomes 630 = 7 e. 5,567 94 94 rounds to 90 480 60 48 is a multiple of =(480 10) 6 6, so the dividend = 48 6 becomes 480 = 8 f. 2,749 47 47 rounds to 50 3,600 60 39 is not a multiple = (3,600 10) 6 of 6, but 36 is and it is = 360 6 close to 39, so the = 60 dividend becomes 3,600 g. 8,391 38 38 rounds to 40 5,400 90 55 is not a multiple = (5,400 10) 9 of 9, but 54 is and it is = 540 9 close to 55, so the = 60 dividend becomes 5,400 h. 6,438 73 73 rounds to 70 2,500 50 27 is not a multiple = (2,500 10) 5 of 5, but 25 is and it is = 250 5 close to 27, so the = 50 dividend becomes 2,500 i. 6,205 27 27 rounds to 30 8,000 40 8 is a multiple of 4, so = (8,000 10) 4 the dividend becomes = 800 4 8,000 = 200 6,300 70 64 is not a multiple = (6,300 10) 7 of 7, but 63 is and it = 630 7 close to 64, so the = 90 dividend becomes 6,300 6,000 30 6 is a multiple of 3, = (6,000 10) 3 so the dividend = 600 3 becomes 6,000 = 200 Mrs. Henry spent $513 buying Christmas gifts for her 21 grandchildren. If all of the gifts were the same cost, about how much did she spend on each gift? Problem Solving Approach: $513 (amount spent on gifts) 21 (number of grandchildren) 21 rounds to 20 $600 20 5 is not a multiple of 2, but 6 is and it is close to 5, = (600 10) 2 so the dividend becomes 600 = 60 2 = $30 Mrs. Henry spent about $30 on each gift for her 21 grandchildren. Marcus has saved $3,345 working about 42 different home repair jobs. If he was paid about the same amount per job, about how much did Marcus make at each different job? Problem Solving Approach: $3,345 (Marcus s savings) 42 (number of Marcus jobs) 42 rounds to 40 $3,200 40 33 is not a multiple of 4, but 32 is and it is close to 33, = (3,200 10) 4 so the dividend becomes 3,200 = 320 4 = $80 Marcus made about $80 at each of his different home repair jobs.
Grade 5, Module 2, Topic F MATH NEWS 5 th Grade Math Module 2: Multi-Digit Whole Number and Decimal Fraction Operations Math Parent Letter This document is created to give parents and students a better understanding of the math concepts found in Eureka Math ( 2013 Common Core, Inc.) that is also posted as the Engage New York material which is taught in the classroom. Grade 5 Module 2 of Eureka Math (Engage New York) covers Multi- Digit Whole Number and Decimal Fraction Operations. This newsletter will discuss Module 2, Topic F. Topic F. Partial Quotients and Multi-Digit Whole Number Division Words to know dividend (whole) estimate divisor about ( ) quotient multiple remainder decompose division algorithm Things to Remember!!! Before dividing, estimate to get an idea of about how many groups of the divisor can be made. Example: 84 23 80 20 = 4 (4 is placed in the ones place of the quotient.) 4 23 8 4-92 The remainder has to be smaller than the divisor. A division problem is not complete unless there is a digit above the last digit in the dividend. OBJECTIVES OF TOPIC F 3 R 15 23 8 4-69 15 Divide two- and three-digit dividends by multiples of 10 with single-digit quotients and make connections to a written method. Divide two- and three-digit dividends by two-digit divisors with single-digit quotients and make connections to a written method. Divide three- and four-digit dividends by two-digit divisors resulting in two- and three-digit quotients, reasoning about the decomposition of successive remainders in each place value. Focus Area Topic F Multi-digit Whole Number Division Knowing division with the standard algorithm Can we divide 6 hundreds by 80? (No) Since there are 10 tens in 1 hundred, we can decompose 6 hundreds to 60 tens. There are already 4 tens, so there is a total of 64 tens. Can we make a group of 80 with 64 tens? (No) 644 80 Since there are 10 ones in 1 ten, we can decompose 64 tens to 640 ones. There are already 4 ones, so there is a total of 644 ones. Can we make a group of 80 with 644 ones? (Yes) So we are dividing 644 ones by 80. Step 1: Estimate quotient to know where to begin. 64 is a multiple of 8 64 8 = 8 so 644 becomes 640. 640 80 = 8 Step 2: Set up the division algorithm and use the estimation to find the actual quotient. Step 3: Check by multiplying the divisor of 80 by the quotient of 8, and then add the remainder of 4. If the quotient is correct, the answer will equal the dividend. ************************************************************* Application Problem and Answer: A shipment of 288 brochures was sent to the main rest areas in the state of Louisiana. Each of the 30 rest areas in the state received the same amount. After the brochures were distributed, were there any extras? If so how many extra brochures were there? (Cannot make a group of 30 with 2 hundred, so decompose 2 hundreds to 20 tens and combine with the 8 tens you already have. Now there is a total of 28 tens. Cannot make a group of 30 with 28 tens, so 28 tens is decompose to 288 ones.) Step 1: Estimate 288 30 270 30 = 9 9 R 18 Step 2: Solve 30 2 8 8-2 7 0 1 8 Step 3: Check 30 x 9 = 270 270 + 18 = 288 80 8 R 4 6 4 4-6 4 0 4 8 0 x 8 6 4 0 640 + 4= 644 28 is not a multiple of 3 but 27 is and it is close to 28. Answer: There will be 18 extra brochures.
There were 192 students at 4-H camp. The camp has 32 cabins. An equal number of students sleep in each cabin. How many students slept in each cabin? Strategy: 192 32 Can we make a group of 32 with 1 hundred? (No) We decompose 1 hundred to 10 tens. There are already 9 tens, so there is a total of 19 tens. Can we make a group of 32 with 19 tens? (No) We decompose 19 tens to 190 ones. There are already 2 ones, so there is a total of 192 ones. Can we make a group of 32 with 192 ones? (Yes) Step 1: Estimate Round 32 to 30. 192 32 19 is not a multiple of 3 but 18 is and it is close to 19. 180 30 = 6 Step 2: Solve 32 6 1 9 2-1 9 2 Step 3: Check 32 x 6 = 192 Answer: 6 students slept in each cabin. Bart was arranging his 823 baseball cards in a book that holds 24 cards per page. Bart divided 823 by 24 and got a quotient of 34 with a remainder 7. Explain what the quotient and remainder represent. 24 3 4 R 7 8 2 3-7 2 1 0 3-9 6 7 Answer: 823 is the total number of baseball cards, and the divisor, 24, is the amount of cards a page holds. Therefore 34, the quotient, is the amount of pages that will be full in his book. The remainder of 7 will be the amount of cards on the last page. Erin made 1,695 chocolate fudge candies for her Christmas gifts. She put them in bags of 36 candies per bag. How many candy bags did Erin give out? Did she have any candies left over? If so, how many candies were left over? Strategy: 1,695 36 Can we make a group of 36 with 1 thousand? (No) Decompose 1 thousand to 10 hundreds. There are already 6 hundreds, so there is a total of 16 hundreds. Can we make a group of 36 with 16 hundreds? (No) Since there are 10 tens in 1 hundred, we decompose 16 hundreds to 160 tens. There are already 9 tens, so there is a total of 169 tens. Can we make a group of 36 with 169 tens? (Yes) First division step 169 tens 36 Estimate: 160 tens 4 tens = 40 (4 is placed in the tens place of the quotient) After subtracting, there are 25 tens left. Can we make a group of 36 with 25 tens? (No) Since there are 10 ones in 1 ten, we compose 25 tens to 250 ones. There are already 5 ones, so there is a total of 255 ones. Can we make a group of 36 with 255 ones? (Yes) Next division step 255 ones 36 240 ones 40 = 6 (6 is placed in the ones place of the quotient) After subtracting, there are 39 ones left. Can we make a group of 36 with 39? (Yes) So there are 7 groups of 36 in 255 and not 6. Answer: Erin gave out 47 bags of candy. She had 3 candies left over. 36 36 4 1, 6 9 5-1 4 4 2 5 4 6 1, 6 9 5-1 4 4 2 5 5-2 1 6 3 9 36 Check: 4 7 x 3 6 2 8 2 1,692 +1 4 1 0 + 3 1,6 9 2 1,695 4 7 R 3 1, 6 9 5-1 4 4 2 5 5-2 5 2 3
Grade 5, Module 2, Topic G MATH NEWS 5 th Grade Math Math Parent Letter This document is created to give parents and students a better understanding of the math concepts found in Eureka Math ( 2013 Common Core, Inc.) that is also posted as the Engage New York material which is taught in the classroom. Grade 5 Module 2 of Eureka Math (Engage New York) covers Multi- Digit Whole Number and Decimal Fraction Operations. This newsletter will discuss Module 2, Topic G. Topic G. Words to know OBJECTIVES OF TOPIC G Partial Quotients and Multi-Digit Decimal Division multiple dividend (whole) factor quotient divisor approximate/estimate ( ) round decompose Things to Remember!!! The dividend is referred to as the whole. When dividing by a power of 10 (10, 100, 1000) the digits in the whole (dividend), shift to the right. When dividing by 10, the digits shift 1 place to the right. When dividing by 100, the digits shift 2 places to the right and when dividing by 1,000, the digits shift 3 places to the right. This is how it would look on a place value chart. 10 36 3.6 10.36 10.036 tens ones. tenths hundredths thousandths 3 6. 3. 6. 3 6. 0 3 6 Divide decimal dividends by multiples of 10, reasoning about the placement of the decimal point and making connections to a written method. Use basic facts to approximate decimal quotients with two-digit divisors, reasoning about the placement of the decimal point. Divide decimal dividends by two-digit divisors, estimating quotients, reasoning about the placement of the decimal point, and making connections to a written method. Focus Area Topic G Multi-Digit Whole Number and Decimal Fraction Operations Divide. Show division in two steps. Let s decompose 60 with 10 as a factor. 10 x 6 = 60 Would the quotient be affected if we divided by 6 first then by 10? **************************************************** Divide. Show division in two steps. 0.36 90 = (0.36 10) 9 = 0.036 9 = 0.004 84.2 200 = (84.2 2) 100 = 42.1 100 = 0.421 **************************************************** Estimate the quotients. 1. 4.23 62 4.2 60 = (4.2 10) 6 = 0.42 6 = 0.07 2. 53.9 91 54 90 = (54 9) 10 = 6 10 = 0.6 2.4 60 = 2.4 10 6 = (2.4 10) 6 = 0.24 6 = 0.04 2.4 6 10 = (2.4 6) 10 = 0.4 10 = 0.04 OR OR Step 1: Divide 2.4 by 10 Step 2: Divide 0.24 by 6 The divisor didn t change so the quotient didn t change. 0.36 90 = (0.36 9) 10 = 0.04 10 = 0.004 84.2 200 = (84.2 100) 2 = 0.841 2 = 0.421 62 rounds to 60. 4.2 is a divisible by 6, so, the dividend becomes 4.2. 91 rounds to 90. 53 is not a multiple of 9, but 54 is and it close to 53. so, the dividend becomes 54.
At times you may have to extend the dividend to tenths and hundredths. The weight of 35 identical toy cars is 844.2 grams. What is the weight of each toy car? Strategy: 844.2 35 Can we make a group of 35 with 8 hundreds? (No) Since there are 10 tens in 1 hundred, decompose 8 hundreds to 80 tens. There are already 4 tens, so there is a total of 84 tens. Can we make a group of 35 with 84 tens? (Yes) First division step 84 tens 35 Estimate 80 tens 40 = 2 tens or 20 (2 is placed in the tens place of the quotient.) After subtracting, there are 14 tens left. Can we make a group of 35 with 14 tens? (No) Since there are 10 ones in 1 ten, we decompose 14 tens to 140 ones. There are already 4 ones, so there is a total of 144 ones. Can we make a group of 35 with 144 ones? (Yes) Next division step 144 ones 35 120 ones 40 = 3 (3 is placed in the ones place.) After subtracting, there are 4 ones left. Can we make a group of 35 with 4 ones? (No) Since there are 10 tenths in 1 one, we decompose 4 ones to 40 tenths. There are already 2 tenths, so there is a total of 42 tenths. Can we make a group of 35 with 42 tenths? (Yes) Next division step 42 tenths 35 40 tenths 40 = 1 tenth (1 is placed in the tenths place.) After subtracting, there are 7 tenths left. Can we make a group of 35 with 7 tenths? (No) Since there are 10 hundredths in 1 tenth, we decompose 7 tenths to 70 hundredths. A zero is added to dividend to show hundredths. Next division step 70 hundredths 35 80 hundredths 40 = 2 hundredths (2 is placed in the hundredths place.) Now check to make certain quotient is correct. 2 4. 1 2 same as 2 4 1 2 hundredths x 3 5 x 3 5 1 2 0 6 0 7 2 3 6 0 8 4 4 2 0 hundredths = 844.20 2 35 8 4 4. 2 7 0 1 4 2 3 35 8 4 4. 2 7 0 1 4 4 1 0 5 39 (We can get another group of 35 with 39; so we can get 4 groups of 35 instead of 3 groups in 144 ones.) 2 4. 1 35 8 4 4. 2 7 0 1 4 4 1 4 0 4 2 3 5 7 2 4. 1 2 35 8 4 4. 2 0 7 0 1 4 4 1 4 0 4 2 3 5 7 0 7 0 2 4 35 8 4 4. 2 7 0 1 4 4 1 4 0 4 Each toy car weighs 24.12 grams. A member of the cross country track team ran a total of 300.9 miles in practice over 59 days. If the member ran the same number of miles each day, how many miles did the member run per day? Strategy: 300.9 59 Can we make a group of 59 with 3 hundreds? (No) There are 10 tens in 1 hundred, so decompose 3 hundreds to 30 tens. Can we make a group of 59 with 30 tens? (No) There are 10 ones in 1 ten, so decompose 30 tens to 300 ones. Can we make a group of 59 with 300 ones? (Yes) First division step 300 ones 59 300 ones 60 = 5 (5 is placed in the ones place.) After subtracting, there are 5 ones left. Can we make a group of 59 with 5 ones? (No) There are 10 tenths in 1 one, so decompose 5 ones to 50 tenths. There are already 9 tenths, so there is a total of 59 tenths. Can we make a group of 59 with 59 tenths? (Yes) Next division step 59 tenths 59 = 1 tenth (1 is placed in the tenths place.) The member ran 5.1 miles each day. 5 5 9 3 0 0. 9 2 9 5 5 5. 1 5 9 3 0 0. 9 2 9 5 5 9 5 9 Check: 5.1 same as 5 1 tenths x 5 9 x 5 9 4 5 9 2 5 5 0 3 0 0 9 tenths = 300.9
Grade 5, Module 2, Topic H MATH NEWS 5 th Grade Math Module 2: Multi-Digit Whole Number and Decimal Fraction Operations Math Parent Letter This document is created to give parents and students a better understanding of the math concepts found in Eureka Math ( 2013 Common Core, Inc.) that is also posted as the Engage New York material which is taught in the classroom. Grade 5 Module 2 of Eureka Math (Engage New York) covers Multi- Digit Whole Number and Decimal Fraction Operations. This newsletter will discuss Module 2, Topic H. In this topic, students apply the work of Module 2 to solve multi-step word problems using multi-division. Topic H. Measurement Word Problems with Multi-Digit Division Words to know: Model/Tape Diagram Reasonableness Equation/Number Sentence Solution/Answer Units/Sections Things to remember: Tape Diagram Drawing that looks like a segment of tape, used to illustrate number relationships. Example: There are 452 heart pamphlets that must be delivered to 4 hospitals. If each hospital receives the same amount, how many pamphlets are delivered to each hospital? 452 The whole diagram represents the 452 pamphlets. Since there are 4 hospitals, the diagram is divided into 4 units/sections. To find the value of 1unit/ section you would 1 hospital divide 452 by 4. OBJECTIVE OF TOPIC H Approach to solving a problem: Draw a model, write an equation/number sentence, compute, and assess the reasonableness of answer/solution. Solve division word problems involving multi-digit division with group size unknown and the number of groups unknown. Focus Area Topic H Example 1: Measurement Word Problems with Multi-Digit Division Billy is saving for a 52 inch flat screen TV that costs $1,218. He already saved half of the money. Billy earns $14.00 per hour. How many hours must he work in order to save the rest of the money? Strategy Approach: Step 1: Step 2: Step 3: Saved? Saved $609.00 $1218 Draw a tape diagram to represent $1,218 which is amount he needs to buy the TV. It is divided into 2 equal units since the problem states that he already saved half of the money. $1218 $1218 $609.00 $609.00 How many hours does he need to work? To find out how much he already saved, we divide 1218 by 2. Equation: 1218 2 = 609 If half is equal to $609.00, then the other half is equal to $609.00. Since he makes $14.00 per hour, we want to find out how many 14s are contained in 609. Number sentence: 609 14 = 43.5 Solution/Answer: Billy needs to work 43.5 more hours. Reasonableness: 609 14 Student could round 14 to 10 and 60 is a 600 10 multiple of 10. Since 14 is rounded down to 10, = 60 the answer will be less than the estimate. OR 609 14 600 15 = 40 Student knows that 15 is a factor of 60 and 15 is very close to 14.
Example 2: Mr. Smith has 1354.5 kilograms of potatoes to deliver in equal amounts to 18 stores. 12 of the stores are in Lafayette. How many kilograms of potatoes will be delivered to stores in Lafayette? Strategy Approach: Step 1: 1354.5 kg of potatoes 1 2 3 4 5 6 7 8 9 10 11 12 18 Stores in Lafayette... The tape diagram drawn to represent the total kilograms of potatoes (1354.5 kg) that needs to be deliver to 18 stores. The three dots in the rectangle between 12 and 18 represent stores 13 to 17. ***************************************** Step 2: 1354.5 kg of potatoes The model is showing 18 units (equal sections) that equal 1354.5. We have to find the value of 1 unit or one section. Equation: 1354.5 18 = 75.25 75.25 kg of potatoes delivered to each store. 1 2 3 4 5 6 7 8 9 10 11 12 18 Stores in Lafayette... Assess the reasonableness: Round the divisor: 18 rounds to 20 13 is not a multiple of 2 but 14 is so our whole or dividend is 1400. 1400 20 = (1400 2) 10 = 700 10 = 70 We can conclude that 75.25 does make sense since it is close to 70. ********************************************* Step 3: 1354.5 kg of potatoes Now that we know the kilograms of potatoes delivered at each store, we need to multiply 75.25 kg times 12 to determine how many kilograms of potatoes were delivered to the 12 stores in Lafayette. 1 2 3 4 5 6 7 8 9 10 11 12 18 Stores in Lafayette... Equation: 75.25 x 12 = 903 kg 903 kg of potatoes were delivered to 12 stores in Lafayette. Assess the reasonableness: When studying the model it is easy to see that more than half of the total amount of potatoes is being delivered to stores in Lafayette. 903 kg is more than half.