Mathematics for Grade 4 Teachers

7/28/2019 Mathematics for Grade 4 Teachers

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Mathematics for Grade 4 Teachers

I. UNDERSTANDING NUMBERS BETTER

A. a. Read each of the following numbers. b. Give the place value and the value ofthe underlined digit. c. What place does 0 hold in each number?

1. 504 556 4. 473 025 7. 8 606 10. 263 087 674

2. 380 485 5. 672 348 033 8. 65 097 11. 650 947 562

3. 750 453 6. 460 345 364 9. 334 907 12. 67 034 658

B. Write each of the following numbers in figures.

1. eight hundred fifty-six 5. one thousand seventy-nine

2. ninety-seven 6. five thousand two hundred three

3. ten thousand eighty-seven 7. fifteen thousand one

4. nine hundred twenty-nine 8. fifty-six thousand eighty-five

9. five million, four hundred sixty thousand four hundred twenty-five

10. forty-two million, thirty-six thousand, nine hundred thirty-eight

C. Write the following Roman numerals in figures.

1. LXIV _______ 2. LXIX _______ 3. LXXII _______ 4. XLXIX _______

5. CXLXVI ______ 6. XCIII ______ 7. CLX _______ 8. CCLXXXV ______

D. Can you answer the following?

1. What is the smallest two-digit number in our system? ________

2. What is the largest two-digit number? ____________

3. Using any of the digits 0, 1, 3, 5, 7, and 9 only once for each,a. What is the smallest 3-digit number that you can make? ___________b. What is the smallest 4-digit number that you can make? ___________c. What is the largest 3-digit number that you can make? ___________d. What is the largest 4-digit number that you can make? ___________e. What is the largest 3-digit number less than 600? __________f. What is the smallest 4-digit number greater than 5000? ___________

4. In 34,540, how many times as great is the underlined 4 than the other 4?____________ What about in 467,824? __________

E. Find the pattern of the sequence. Fill in the missing numbers.

1. 18, 25, 32, 39, ____, ____, ____ 2. 101, 212, 323, ____, ____, ___

3. 12, 24, 48, 96, ____, ____, ____ 4. _____, _____, 37, 46, 55, 64

F. Find the number.

1. What is the largest nine-digit number without a digit repeated?

2. Counting my digits, you will find eight. All are zeros except one 8. What number amI?

3. Write the smallest number with the digit 6, 8, 9, 7, 5, 4.

4. Write the smallest even number with the digits 1, 1, 2, 9, 7?

5. What is the smallest odd /even number greater than 40,000 containing the digits5, 4, 4, 4, 1

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G. Round each number as indicated.Nearest 10 Nearest 100 Nearest 1 000 Nearest 10

000

1. 35 782 - __________ ___________ ___________________________

2. 42 938 - __________ ___________ _____________ ______________3. 26 899 - __________ ___________ _____________ ______________

4. 59 701 - __________ ___________ _____________ ______________

5. 798 846 - __________ ___________ _____________ ______________

H. Answer the following.

1. What number is halfway between the following?

a. 6 000 and 7 000 __________ c. 0 and 100 __________

b. 4 000 and 5 000 __________ d. 18 000 and 19 000 __________

2. What is the greatest and the least number that would produce the following whenrounded to the nearest hundred?

LEAST GREATEST LEAST GREATEST

a. 4 300 __________ ___________ b. 9 800 __________ ___________

27 368 = 20 000 + 7 000 + 300 + 60 + 8= (2 x 10 000) + (7 x 1 000) + (3 x 100) + (6 x 10) + (8 x 1)

= (2 x 104) + (7 x 103) + (3 x 102) + (6 x 101) + (8 x 100)I. Write the standard notation for each.

1. 4 x 104 = _______________ 3. 5 x 102 = _______________

2. 5 x 103 = _______________ 4. 9 x 108 = _______________

5. (9 x 105) + (5 x 104) + (2 x 102) + (10 x 101) + (4 x 100) = ______

6. (8 x 107) + (13 x 105) + (4 x 103) + (6 x 102) + (9 x 100) = ______

J. Find the answers.

1. About 6 x 103 babies are born every day in a city. How many babies are born each

day?

2. If there were 8 x 104 orange trees and 7 x 103 apple trees in an orchard, howmany fruit trees were there in all?

3. A supervisor of a supermarket took inventory of their canned goods. The store

was found to have 4 x 102 cans of sardines, 3 x 103 cans of tomato sauce and 5 x102 cans of milk. How many canned goods did the supermarket have?

Challenge!1. Rounding me to the nearest hundred makes me 500. Rounding me to the nearest

ten makes me 540. The sum of my digits is 12. What number am I?

2. Rounding me to the nearest thousand makes me 6000. The sum of my digits is14. If you read me forward or backward, I am still the same. What number am I?

3. Eric is helping his grandmother in their store. A girl came to buy a sandwich worth12.75 and gave Eric 13.00. Eric can use 5 , 10 and 25 to give the change.

One way is to give her one 25 . What are the other ways Eric can give thechange?

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4. During a trip to Tagaytay, the driver made a 90-mile trip averaging 45 km perhour. On the return trip, he averaged 30 km per hour. What was his average forthe whole trip?

5. If we count by 4s starting with 1, the following sequence is formed: 1, 5, 9, 13,17, ... What is the 50th number of the sequence?

II. UNDERSTANDING MORE ABOUT THE BASIC OPERATIONS

A. Find each sum. How many can you do mentally?

a b c d e f g h i j k l

1. 34 56 25 43 56 64 25 36 46 97 68 78+ 54 + 42 + 27 + 39 + 27 + 45 + 74 + 89 + 68 + 76 + 57+69

2. 78 45 59 72 67 93 84 95 61 72 86 75- 36 - 23 - 37 - 45 - 28 - 67 - 39 - 68 - 39 - 37 - 59 - 36

3. 25 34 62 46 28 64 68 58 95 57 63 48x 6 x 6 x 7 x 5 x 7 x 8 x 9 x 5 x 4 x 7 x 7 x8

___ ____ ____ ____ ____ ____ ____ ____ ____ ____4. 3)66 6)96 5)95 7)91 7)125 5)168 8)248 8)396 6)455

9)405

B. How fast can you complete the pattern?

C. Find the numbers asked for.

1. What is 17 more than the sum of 19 and 15?

2. What is 10 more than the product of 6 and 22?

3. Subtract 25 from the sum of 113 and 38.

4. Fifty more than the quotient of 155 divided by 5 is _______.

5. Divide the result of #4 by 9.

6. How many even numbers are there from 11 to 89?

7. What is the largest 2-digit prime number less than 100?

8. How many prime numbers are there between 20 and 100?

9. What is the smallest/largest 3-digit odd number?10. What is the sum of the smallest 5 prime numbers?

11. What is the remainder when 3456 is divided by 27?

12. 5 more than the sum of twice 12 and 17 is equal to what number?

13. Thrice 16 plus 200 minus 80 equals what number?

3

38 26 29

14

21 24 37

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14. 1724 deducted from the product of 4200 and 60 will give what number?

15. 123 added to the quotient of 294 divided by 7 will result in what number?

D. Find the answer to each problem.

1. Two of the highest mountains in the Philippines are Mt. Apo in Mindanao which is

2 953 meters high and Mt. Pulog in Luzon which is 2 930 meters high. How manymeters higher is Mt. Apo than Mt. Pulog?2. The distance around the earth is 39,844 km. Records show that one Arctic tern

flew half this distance in one year. How far did it fly?

3. The library has 4 893 books. As of last week, 2 863 books were borrowed. Thisweek, 1791 books were returned, while 2 035 books were borrowed. How manybooks are now in the shelves?

4. During the year, 10,000,000 computers were manufactured in the United States.If factory workers worked for 52 weeks, 5 days a week, and 8 hours a day, abouthow many computers were produced in a week, in a day, in an hour?

5. The length of a spread of a newspaper is about 70 cm. If 25 spreads were placedend to end, how far would they reach?

6. A piece of candy costs 65 centavos. How many pieces of candy can Francis buywith his 15? How much will he have left?

E. Find the two numbers satisfying the given conditions.

1. product is 44 and sum is 15 6. product is 42 and sum is 132. product is 20 and sum is 12 7. product is 30 and sum is 133. product is 63 and sum is 16 8. product is 56 and sum is 184. product is 48 and sum is 26 9. product is 0 and sum is 235. product of 24 and sum is 25 10. product is 1 and sum is 2

F. Who am I? Write the number.

1. No matter what number you multiply me by, I will always be the product.

2. When you multiply me by any number, the product will be that number?

3. When you multiply me by myself, you will see me again when you add the twodigits of the product.

4. When you multiply me by 7, you will see me again when you add the two digits ofthe product.

5. The sum of my 6 digits is 28. Three of them are the same. Rounding me to thenearest ten, hundred, and thousand will give you the same number.

Challenge!

1. A grandfather clock strikes once at 1:00, twice at 2:00, and so on for every hour.How many times does the clock strike in (a) 12 hours? (b) 24 hours?

2. Roda left the book she is reading open at a certain page such that the sum of thefacing page numbers is a. 157 b. 421. c. 703.To which pages will she resume reading?

3. The houses of Ogie and Steve are 60 km apart. The house of Mar is betweenthem. If the distance from Ogie's to Mar's is four times the distance from Mars'sto Steve's, how far is it from Ogie's house to Mar's house? and from Mar'shouse to Steve's house?

4. When 267 is added to 122, no regrouping is needed. How many different three-digit numbers can you add to 122 without having to regroup?

5. The sum of two numbers is 87. Their difference is 13. What is their product?

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6. Forty-two students took a final exam on which the passing score was 72 to thenearest whole number. The mean score of those who passed was 76 and thosewho failed was 66. How many students passed? failed?

7. I have twenty 1 coins, twelve 25 coins and six 5 coins.a. What is the smallest cost of an item that I can pay for?b. What is the largest cost of an item that I can pay for?

c. What other costs of items can I pay for?III UNDERSTANDING DIVISIBILITY, PRIMES, GCF & LCM BETTER

A. Divisibility

Use divisibility tests to determine if each number in the table is divisible by eachof the numbers at the top row. Put a check in the appropriate column and row.

B. Prime and composite numbers

From the 100-table, 1 and all multiples of 2 and 5 have been removed. If allmultiples of 3 and 7 are removed, why are the remaining numbers all primes?

2 3 5 7 11 13 17 19 21 23 27 29

31 33 37 39 41 43 47 49 51 53 57 59

61 63 67 69 71 73 77 79 81 83 87 89

91 93 97 99

C. Express each number as a product of prime factors

1. 46 3. 56 5. 369 7. 572 9. 1450

2. 84 4. 78 6. 144 8. 1360 10. 6425D. Find the smallest positive numbers whose factors are:

1. 2, 11, 3, 5 3. 13, 5, 2, 3 5. 23, 33, 7

2. 5, 5, 3, 3 4. 17, 2, 7, 3 6. 52, 32, 2

E. Find the GCF and LCM of each set of numbers.

1. 15, 36 2. 10, 6, 12 3. 16, 24, 12 4. 12, 15, 205. 36, 42, 84 6. 42, 84 7. 72, 96 8. 84, 124

F. 1. Give three fractions equal to:

a. 3/5 b. 5/9 c. 8/13 d. 7/11

2. Reduce each to its lowest terms.

a. 16/20 b. 18/27 c. 24/32 d. 56/84 e. 60/90

3. Change the following to improper fractions.

5

2 3 4 5 6 7 8 9 10

1. 4320

2. 25203. 5040

4. 3960

5. 4860


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a. 4 1/3 b. 8 3/4 c. 9 2/3 d. 8 5/7 e. 6 7/13

f. 3 3/5 g. 7 3/5 h. 8 2/5 i. 7 3/4 j. 8 4/7

4. Reduce to integers or mixed numbers.

a. 9/4 b. 12/3 c. 22/5 d. 28/8 e. 24/5 f. 25/4

g. 47/7 h. 52/4 i. 67/8 j. 52/25 k. 91/18 l. 735/57

G. Write or = on the space provided for.

1. 18/23 ____ 15/23 3. 7/9 ____ 9/11 5. 12/17 ____ 17/23

2. 16/21 ____ 17/21 4. 7/8 ____ 13/15 6. 14/19 ____ 18/25

H. Write the answer as a mixed number with the fraction in lowest terms.

1. Darwin cut some oranges in half. After eating some pieces, he had 15 halves on

the table. How many oranges were left?

2. Joy cut some apples in fourths and thirds. She has 12 pieces of thirds and 12pieces of fourths on the table. How many apples did she cut in all?

3. Mother cut pizzas into sixths. After serving 28 pieces, she had 12 left. How manypizzas did she cut?

4. Melissa bought oranges and apples. One half of the fruits were oranges. If shegave two-thirds of the oranges to her brother what part of the fruits bought byMelissa did she give her brother?

5. A farmer sold 3/5 of his land, and then he had 15 3/4 hectares left. How muchland had he at first?

6. How many pieces of ribbon 3 1/5 dm long can be cut from a piece 12 meterslong.

Challenge!

A. 1. Tom had between 10 and 28 marbles. One half of his marbles were green. Therest were red or blue. Julius traded 3 of his red marbles for 3 of Toms greenones. Now only 1/3 of Tom's marbles are green. How many marbles did Tomhave?

2. A school bus can carry 55 children. The bus picks up 1 child at the first stop. Atthe second stop it picks up 2 children. At the third stop it picks up 3 children, andso forth. After how many stops will the bus be full?

3. Archie gave Betty 1/2 of his peanuts. Betty gave Jughead 1/2 of the peanuts shegot from Archie. Jughead gave Ronnie 1/2 of the peanuts he got from Betty.Ronnie got only 6 peanuts. How many peanuts did Archie have at first?

4. What different digits can you place in the blank so that:

a. 345____6 b. 345____5 c. 345____4 is divisible by 3?

5. Can you give other numbers that can be completed by each of the patterns in a,b and c?

B. 1. Rita can put her stamps either 12 or 15 to a page without any left over. What isthe least number of stamps that she can have?

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2. The product of 4 consecutive whole numbers is 1 less than (991)2. What are thefour numbers?

3. In a classroom, chairs are arranged so that each row has the same number ofchairs. If Rose sits 3rd from the front, 5th from the back; 4th from the left and3rd from the right, how many chairs are there?

4. Find the ones digit of each of the following. a. 234 b. 287 c. 345 d. 388e. 755 f. 797

IV. UNDERSTANDING ABOUT FRACTIONS BETTER

A. Find the missing terms to get fractions equal to the given.

1. 3/4 = /16 4. 2/3 = 50/ 7. 8/12 = /3 10. 7/8 = 28/

2. 7/9 = 21/ 5. 24/18 = 4/ 8. 7/10 = /70 11. 36/60 = 3/

3. 5/6 = /18 6. 12/17 = 36/ 9. 25/100 = /300 12. 40/25 = /10

B. Write each fraction in lowest terms.1. 16/18 = 4. 35/70 = 7. 9/30 = 10. 10/40 =

2. 15/60 = 5. 12/15 = 8. 72/100 = 11. 6/21 =

3. 14/32 = 6. 36/40 = 9. 30/45 = 12. 24/36 =

C. Change each to an improper fraction.

1. 3 2/3 2. 4 3/4 3. 2 5/6 4. 5 5/6 5. 6 4/5 6. 7 3/6

D. Change each to a mixed number.

1. 15/6 2. 18/7 3. 17/7 4. 19/6 5. 24/5 6. 45/7

E. Compare the fractions by writing >,


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3. There are 24 cookies in a box. Allan has 35 cookies. How many boxes of cookiesdoes he have?

4. Jan had a board that is 50 cm long. He cut it into 8 pieces of the same length.How long is each piece?

5. Jolie knocked down 3/5 of the bowling pins on his first try. Ernie knocked down

4/10 of the bowling pins on his first try. Who knocked down more bowling pins?Why?6. Fifty votes were cast in a class election. Mercy got 1/5 of the votes. Flor got as

many votes as Julia and Meredith put together. Meredith got 1/3 as many votesas Julia. How many votes did each candidate receive?

7. Martin left his house at 4:15 P.M. He walked for 2/3 of an hour, ran for 1/2 thattime, and then jogged for 1/4 of an hour. What time was it when he finished?

8. There are 42 students in Miss Clare's class. Two-sevenths of the students aregirls. Three-fourths of the boys wear glasses. How many boys do not wear

glasses?

9. Elmer ran a certain distance in 5 1/2 minutes. A horse ran the same distance in1/2 the time. How many minutes did it take the horse to run the same distance?

10. Mike is 1 1/2 years old. Alex is 1 1/3 times Mike's age. Sarah is 2 times Mike'sage, and Rosie is 1 1/6 times Sarah's age. How old is each person?

11. Jerry can walk to the municipal hall in 1/4 hour. If he walks back and forth forone hour, how many round trips would he make?

12. Linda has 2 1/2 sheets of red paper. She uses 1/4 sheet to make a triangle. Howmany triangles can she make?

13. A volleyball team practiced for 3 1/2 hours. After each 1/2 hour, the playersrested. How many times did the players rest?

14. A shelf is 32 2/3 cm long. How many books 2 1/3 cm thick will fit in the shelf?

15. A piece of rope, 14 1/3 m long, is cut into 5 equal parts. How long is each piece?

16. If Ethel answered 13/15 of every quiz correctly, how many points did she get if

the total points of the quizzes is 75?

17. Which two numbers give a difference of exactly 1?3/5 3/11 3/2 3/6 3/4 3/8

Challenge!1. Dexter had written down two mixed numbers. If he subtracts the smaller from the

larger, the difference is 4 1/9. If he adds the two mixed numbers, the answer is13. What are the two mixed numbers?

2. Five boys are running in a race. Ricky is ahead of Roy by 20 m. Harry is behind

Ricky by 10 m. Roy is behind Dennis by 5 m. Edward is ahead of Harry by 5 m. Ifthe boys finish the race in this order, find out the position where each boyfinished.

3. Five people ordered 13 small pizzas. Each pizza was cut into 8 slices. Liza atetwice as much as Roda. May ate two pieces less than Danny. Eric ate 2 slices ofeach pie. If Danny ate 2 3/4 pies, how many pies did each person eat?

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4. Two thirds of Mrs. Mateo's Grade IV class were boys. There were between 2 and14 boys. One day twin girls joined the class. Now 3/5 of the students are boys.How many students are in Mrs. Mateo's class now?

5. There are bicycles and tricycles in a parking lot. If there are 29 wheels, how manybicycles are there if there are 26 pedals?

6. Five boys are each thinking of a different number. Mike's number is 3,000 morethan Gerry's which is 500 more than Barry's. Larry's number is 2,600 more thanSam's which is 663. Sam's number is 90 less than Barry's. What is each boy'snumber?

V. UNDERSTANDING DECIMALS BETTER

A. 1. Write in figures.a. three and three tenths ________

b. four and thirty-six hundredths ________

c. ninety-seven and seventy-eight hundredths __________d. ten thousand five hundred six and forty-one hundredths ________

e. three hundred eighty-seven and twenty-six hundredths _______

2. Make each equality true. Write each decimal as a fraction in lowest terms or amixed number with the fraction part in lowest terms.

DECIMAL FRACTION DECIMAL FRACTION DECIMAL FRACTION

a. 0.5 = _____ b. 0.68 = _____ c. _____ = 87/100

d. _____ = 17/10 e. _____ = 3/10 f. 0.375 = _____

g. _____ = 36/100 h. 6.8 = _____ i. _____ = 567/100

j. 0.325 = _____ k. _____ = 374/100 l. 2.625 = _____

m. _____ = 3055/1000 n. 1.25 = _____ o. _____ = 345/1000

3. a. 3.7 is equal to how many tenths? _________b. 5.21 is equal to how many hundredths? __________________

c. Write (a) and (b) as fractions. _________ _________

4. What is the place value of the underlined digit? Give the answer orally.

a. 3.69 b. 68.2 c. 576.91 d. 153.25 e. 5.24 f. 4.368

g. 1.309 h. 2.417 i. 65.23 j. 84.26 k. 7.567 l. 4.404

5. Perform the indicated operations. How many can you do orally?

a. 3.6 b. 8.05 c. 9.23 d. 89.3 e. 45.7+ 2.7 + 5.68 + 2.59 + 6.8 + 35.8

f. 9.85 g. 8.80 h. 62.4 i. 78.5 j. 94.8- 4.37 - 3.45 - 38.5 - 48.9 - 27.5

B. Mystery numbers: how many can you find?1. I am a number between 5 and 10. My decimal is in tenths. The sum of my digits is

10. What numbers can I be?

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2. I have both a ones digit and a tenths digit. I am less than 7. One of my digits is 3greater than the other. What numbers can I be?

3.I am greater than 4 and less than 6. I'm closer to 4 than 6. The sum of my 2 digitsis 8. What number am I?

4. I am a number expressed in ones, tenths, and hundredths. The sum of my digits

is 15. No digit is greater than 6. What numbers can I be?5. Rounded to tenths I'm 3.2. Rounded to ones I'm 3. Write three numbers I can be.

6. Rounded up to tenths I'm 4.5. Rounded to ones I'm 4. Write three numbers I couldbe.

7. Rounded to tenths I'm 6.4. Rounded to ones I'm 6. Write three numbers I couldbe.

C. Write the numbers in order from least to greatest.

1. a. I am 0.3 greater than 2.17. b. I am twice 1.5.

c. I am halfway between 2.3 and 2.4.

2. a. I am 0.8 greater than 3.26. b. I am 0.2 less than 5.78.c. I am 0.7 greater than 4.33.

D. Analyze each problem and then solve it.

1. Linda filled 2.5 boxes with oranges. She filled another 3.25 boxes with apples.How many boxes did she fill?

2. Elmer weighs 50.45 kilos and his friend Michael weighs 48.85 kilos. How muchmore does Elmer weigh than his friend? How much do they weigh together?

3. How many 0.25 kg bags of sugar can be filled from a sack containing 50kilograms?

4. How many pieces of ribbon each 2.5 dm long can be cut from a spool of ribbon 15m long?

5. The perimeter of a triangle is 18 cm, and the lengths of two of its sides are 5.47cm and 6.68 cm. Find the third side?

6. Liza bought 6.5 meters of tetoron at 46.50 a meter, 5 meters of Indian head at

44.75 a meter and three zippers at 10.55 each. How much did she spend?7. Suppose your step is 0.45 m and you make 75 steps a minute, how far is your

house from your school if you take 8 minutes to reach school?

8. The three sides of a triangle measure 5.4 dm, 6.65 dm and 8.85 dm respectively.What is its perimeter?

9. Ricky ran 6.75 km the first week, 8.2 km the second week and 9.45 km the thirdweek. About how many km did Ricky run in 3 weeks?

Challenge!!!

1. What is the smallest number that gives a remainder of 1 when it is divided byeach of the following? a. 2 and 3 b. 3 and 5 c. 5 and 7 d. 2, 3,and 5e. 2, 3, 5, and 7What is the pattern in the answers?

2. Round each of the following to the nearest 10.a. 762 b. 976 c. 1257 d. 5344

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3. How many whole numbers, round to 200 to the nearest 100?

4. Jolina forgot her locker number at school. She remembers that the sum of thedigits of the number is 11 and that the digits are odd numbers. She also knowsthat there are 120 lockers. Use this information to find Jolina's locker number.

5. Twin primes are prime numbers that differ by 2. Here are the first two twinprimes. 3 and 5; 5 and 7(a) Find the next five twin primes.(b) How many twin primes are there between 1 and 100?(c) What are the smallest 3-digit twin primes?

________6. If you triple both 23 and 1,495 in this problem, 2 3)1 4 9 5

how is the answer changed?VI. UNDERSTANDING RATIO AND PROPORTION BETTER

A. Express each ratio in simplest form. How many can you do orally?

1. 3:6 2. 9:45 3. 6:9 4. 9:12

5. 6:30 6. 26:39 7. 16:24 8. 12:32

9. 36:42 10. 4:24 11. 5:15 12. 20:80

13. 12:24 14. 5:10 15. 15:40 16. 24:36

B. Find the ratio of each of the following.

1. 3 days to 2 weeks 6. 240 meters to 1 kilometer

2. 35 minutes to 1 hour 7. 25 cm to 8 dm

3. 75 cm to 3 meters 8. 30 red balls to 65 green balls

4. 9 months to 2 years 9. 90 seconds to 3 minutes

5. 25 girls to 35 boys 10. 36 hours to 3 days

C. Write the ratios for each of the following.

1. Silas has a collection of 50 toys. He has 24 toy cars but eight are bigger in size.He, also, has 10 toy soldiers.

Find the:a. ratio of toy cars to all the toys.

b. ratio of the bigger toy cars to the smaller cars.c. ratio of toy cars to the other toys.d. ratio of toy soldiers to the other toys.e. ratio of toy soldiers to all the toys.

2. Jolie bought a bag of candy of 3 different colors. In a bag, there are 12 redcandies, 16 green candies and 18 blue candies.

Find the ratio of: a. red candies to green candies.b. green candies to blue candies. d. red candies to all candies.c. red candies to blue candies. e. blue candies to all candies.

D. Express the following as unit rates or the price of one unit.

1. 27 for 3 notebooks 2. 150 students for 3 buses3. 500 books for 100 students 4. 48 cookies for 6 children5. 6 tickets for 2 families 6. 90 rotations in 2 minutes7. 200 centimeters in 2 meters 8. 50 meters in 10 seconds9. 180 kilometers in 3 minutes 10. 726 words in 3 minutes

E. Solve for the missing term in the proportion.

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1. 1. 7:4 = 28:n 2. n:15 = 8:3 3. 15:n = 5:12 4. 14:3 =n:48

5. 9:n = 13:26 6. 4:5 = 32:n 7. 4:9 = n:21 8. n:8 = 9:18

F. Solve each problem.

1. If a sandwich sells at 12.25 a piece, milk shake at 7.25 a piece, and an apple

at 8.50 a piece, how much will Tess pay if she will buy a sandwich, 2 milkshakes, and an apple?

2. Romulo has 112.25 in his piggy bank. He also has 327.75 in the bank. IfRomulo has lent 93.65 to Anthony, how much does Romulo have in all?

3. For an hour of TV shows, 8 TV commercials are shown which last about 0.2minute each. How long are the commercials for a 3-hour show?

4. Eloy got 96, 93, 94, 92, 88, and 91 on his six arithmetic tests. What was hisaverage score on the six tests?

5. Dolores's mother baked 8 cakes. Each cake is divided into 12 equal parts. If all

the pieces are to be divided equally between her 4 cousins' families, how manypieces will each family receive?

6. Michael Jagger, a basketball player averages 18 points per game. At this rate,how many points can he make in 9 games?

7. If Theresa reads 320 words per minute, how many words can she read in 15minutes? 20 minutes?

8. In a Metro Manila barangay, there are 2 children for every adult. How manychildren are there if there are 578 adults.

9. Miss Passion, an efficient secretary can type 80 words per minute. At this rate,how long will it take her to type 5,400 words?

10. My grandfather walks at an average rate of 4440 meters per hour. Thedistance from our home to our church is about 740 meters. How long will it takemy grandfather to travel this distance?

11. A vendor pays 19.40 for each pineapple and sells each one for 25. If oneweek he was able to sell 380 pineapples, how much did he earn?

12. Five friends ordered three pizzas. Each pizza was cut into 8 slices. What isthe greatest number of slices each person can have?

13. Julia has 2- 5 coins, and 2 1-peso coins, while Sophia has 2-25 and 3- 1 coin.Do the they have enough money to buy their teacher a rose which costs 15.50?

14. There are 80 fish in an aquarium. There are 5 aquariums in a pet shop. If 125of the fishes are goldfish, how many are not goldfish?

15. There are 85 rows of cabbages in a field. Each row has 25 cabbages. If 1 546 ofthe cabbages are already harvested, how many cabbages still remain?

Challenge!!!

1. Remove 4 sticks and move 1 so that only 4 squaresof the same size remain.

2. A snail is trying to cross the road. Each day it travels 3.5 m in the right direction.At night, it gets confused and goes 1.5 m in the opposite direction. If the road is20 m wide, how long will it take him to cross the road?

3. Express a. 68 b. 36 c. 24 d. 28 e. 34 as the sum of two primes in twodifferent ways.

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4. The product of three whole numbers is 1,100. The three numbers have nocommon factors in pairs. What are the numbers?

5. A 3-men crew can do a certain job in 3 weeks and 2 days. If we are to hire a 4-men crew instead, with the same rate as the first crew, how long would it takethe 4-men crew to do the same job? Note: a week contains 6 work days.

6. I have 30 coins consisting of 5 and 25 coins. The total value of the coins is4.10. How many of each coin do I have?

7. The digits of a 2-digit number are interchanged to form a new 2-digit number.If the difference of the original number and the new number is 36, find allnumbers that satisfy the conditions.

8. A jar filled with water weighs 10 kg. When one-half of the water is poured out, thejar and remaining water weigh 5 1/4 kg. How much does the jar weigh?

VII. UNDERSTANDING MEASUREMENT BETTER

A. Choose the more reasonable measurement; give the answer orally.

1. length of a pencil 20 dm 20 cm2. length of a flashlight battery 4 dm 4 cm3. width of a sidewalk 1 m 1 dm4. height of a building 20 m 20 dm5. thickness of a book 2 km 2 m 2 cm6. width of a classroom 15 km 15 m 15 cm7. distance from one city to another 150 km 150 m 150 cm

B. Complete, fill in the missing measurements.

1. 4 km = _______ m 6. 18 km = _______ m 11. 900 cm =_____ m

2. 45 m = _______ cm 7. 12 m = _______ cm 12. 2 cm = _____mm

3. 7 900 m = ____ km 8. 0.4 L = _____ mL 13. 6.4 kg =_____ g

4. 0.09 km = _____ m 9. 82 945 mL = _____ L 14. 780 g = _____ kg

5. 5,000 m = _____ km 10. 2,000 m = ______ km 25. 60 cm = ______mm

C. What unit of measurement will you use to measure the following.1. a glass of juice? 11. a drop of water?

2. distance between cities 12. height of a person

3. length of a safety pin 13. length of a car

4. water in a swimming pool? 14. lemonade in pitcher?

5. height of a bus 15. width of a piece of paper

6. glue in a small bottle? 16. coffee in a cup?

D. Solve each problem mentally.

1. Sheldon ran a 7500 m race. Ferdinand ran an 8 km race. Who ran the longerrace?

How much longer?

2. Eugene uses an almanac to find the world temperatures. The page is smudged,and he cannot tell whether the temperature at the North Pole is 40O C or -40O C.Which is the more likely temperature? Why?

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3. Mr. Lorenzo's lot is 9 m by 11 m. His scale drawing showed dimensions of 18 cmby 22 cm. What scale did Mr. Lorenzo use?

4. Architect Lupin used a scale of 2 cm: 3 m to make a drawing of the schoolcafeteria. The dimensions of the drawing are 20 cm by 16 cm. What are theactual dimensions of the cafeteria?

E. Answer the following. Use = 3.14 where needed.1. One side of a flower bed is 25 m long. If the flower bed is shaped like a square,

what is its area? Its perimeter?

3. What is the distance around a circular lagoon which is 12 meters across? 24meters across?

4. Genny wants to sew lace on the edges of her blanket. If the blanket is 3 meterslong and 2 meters wide, how many meters of lace does she need?

6. Jose wants to make a rectangular garden with a perimeter of 32.8 m. If thelength is 8.9 m, what should be the width?

8. How many rectangles can have perimeters of 36 cm if dimensions are wholenumbers. Which rectangle has the biggest area?

9. Edgar has a triangular lot in Quezon City. It has a base of 195.5 m and its heightis 125.2 m. What is the area of the lot?

10. A square tile whose sides measure 25 cm costs 29.00 each. If Jayvee is taskedto buy the tiles for a floor that is 2.75 m by 3.5 m, a. how many tiles are needed?b. how much would all cost?

12. How much milk can be contained in a can with a radius of 3 cm and height of 8cm?

14. One cylinder has a radius of 10 cm and a height of 8 cm. Another has a radiusof 8 cm and a height of 10 cm. Which has the greater volume? By how much?

15. The school's library is 15 m long, 8 m wide, and 4 m high. If the air is changedcompletely every 3 minutes, how many cubic meters of the air would movethrough the room in one hour?

Challenge!!!A. 1. Christina needs pieces of ribbon that are 7 cm long. How many can she cut

from a piece of ribbon 7.2 m long?

2. Sheila had to put 14 L of water into a bucket. She used an 8 L bottle and a 3 Lbottle to measure the water. How did she do it?

3. A piece of cloth is rectangular. Its perimeter is 10 m. The length is 4 m. What isthe width? What is the area?

4. How many bags of cement are needed to cover a path 12 m long and 2 m wide ifone bag of cement covers 6 sq. m?

5. Mr. Garcia bought a lot 20 m long and 18 m wide. Mr. Bacani bought another lot25 m wide and 15 m long. Whose lot is a bigger and by how much?

6. The area of a rectangle is 42 square meters. One side is 6 meters long. How longare the other 3 sides?

B. 1. How many rectangles of different shapes can you find that have an area of 64square units? What are the dimensions of each if the length and width are wholenumbers? the length and width can be any numbers?

2. Chester fenced his rectangular garden. The length is 24 m and the width is 15 m.He used bamboo posts which he placed 1.5 m apart. How many posts did heuse?

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3. Fifteen 1 peso coins are put into 4 piles so that each pile has a different numberof coins. In how many ways can this be done?

4. Justin has 36 meters of fencing material. How many different rectangular gardenscould he have fencing for?

C. 1. Three containers have capacities of three, five, and nine liters. How can you

use these containers to measure exactly seven liters of water? How about 11liters of water?

2. To fence the side of his property facing the street, Mr. Flor had planned to usefence posts placed 2 meters apart. Because of the increase in price of the posts,he decided to buy 4 fewer posts than planned and to place the posts 3 metersapart. How many posts did he buy?

3. The squares of a 13 by 13 grid are colored alternately red and white. If thecentermost square is colored white, how many red and white squares are there?

4. Cross out one or more numbers in each row so that the remaining numbers will

have a product equal to the product on the right.product product

3 5 6 7 8 336 2 5 6 8 9 2403 5 6 7 8 210 2 5 6 8 9 3603 5 6 7 8 144 2 5 6 8 9 7203 5 6 7 8 168 2 5 6 8 9 480

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Mathematics for Grade 4 Teachers