# MATH NEWS. 5 th Grade Math. Focus Area Topic A. Grade 5, Module 2, Topic A. Words to know. Things to Remember:

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1 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 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, x 3 = (500 x 3) + (40 x 3) + (2 x 3) = 1, = 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 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 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 x 30 x 10 = 770 x 3 -- these equations are FALSE (77 x 10) x 30 = 770 x x x 3 Estimate multi-digit products by rounding factors to a basic fact and using place value patterns.

3 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 How many four hundred thirty-twos are we counting? (24) Decompose 24 ( ) 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 =1,728 =8,640 What are 24 groups of 432? 10,368 Problem 2: 532 x x ,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 x 300 = 150, x ,5 5 6

4 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 , ,000 1, ,000 5, = 2,313 = 5,140 = 25, x ,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 x ,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.

6 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 = x x Pat rides his bike a total of 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) x \$2.19 \$2.19 (x 100) 219 x 79 x 79 x 32 x = \$86.11 cost of protractor =\$70.08 cost of notebooks Courtney actually spent \$ \$86.11 cost of protractors +\$70.08 cost of notebooks \$ 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) ft 32 ft x 17 ft = x 544 x ft = \$4, 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

7 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 = fl oz e 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 = or 9540 mg

8 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 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) km 83,130m (total distance in one week of training) 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 (\$ 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 = 4.32 \$5.35 (cost for 2 lb) + \$4.32 (cost for 24 oz) \$9.67

9 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: Round 34 to is not a multiple of 3 but 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 Answer: 10 = 40 Divide. a. 640, 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) = = 60 Use basic facts to approximate quotients with two-digit divisors. c. 27, d. 350, =27, = 350, =(27,000 10) 9 = (350, ) 5 (shift one place to the right) (shift two places to the right) = 2,700 9 = 3,500 5 = 300 = 700

13 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 tens ones. tenths hundredths thousandths 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 = ( ) 9 = = = (84.2 2) 100 = = **************************************************** Estimate the quotients = (4.2 10) 6 = = = (54 9) 10 = 6 10 = = = (2.4 10) 6 = = = (2.4 6) 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 9) 10 = = = ( ) 2 = = rounds to is a divisible by 6, so, the dividend becomes rounds to is not a multiple of 9, but 54 is and it close to 53. so, the dividend becomes 54.

14 At times you may have to extend the dividend to tenths and hundredths. The weight of 35 identical toy cars is grams. What is the weight of each toy car? Strategy: 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 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 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 hundredths 40 = 2 hundredths (2 is placed in the hundredths place.) Now check to make certain quotient is correct same as hundredths x 3 5 x hundredths = (We can get another group of 35 with 39; so we can get 4 groups of 35 instead of 3 groups in 144 ones.) Each toy car weighs grams. A member of the cross country track team ran a total of 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: 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 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 Check: 5.1 same as 5 1 tenths x 5 9 x tenths = 300.9

16 Example 2: Mr. Smith has 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: kg of potatoes Stores in Lafayette... The tape diagram drawn to represent the total kilograms of potatoes ( 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: kg of potatoes The model is showing 18 units (equal sections) that equal We have to find the value of 1 unit or one section. Equation: = kg of potatoes delivered to each store Stores in Lafayette... Assess the reasonableness: Round the divisor: 18 rounds to is not a multiple of 2 but 14 is so our whole or dividend is = (1400 2) 10 = = 70 We can conclude that does make sense since it is close to 70. ********************************************* Step 3: kg of potatoes Now that we know the kilograms of potatoes delivered at each store, we need to multiply kg times 12 to determine how many kilograms of potatoes were delivered to the 12 stores in Lafayette Stores in Lafayette... Equation: 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.

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