Grade 5 Session 1

MTAP Program of
Excellence in Mathematics
Grade 5 Session 1
Name of Facilitator
WHOLE NUMBERS
A. Write the following numbers in expanded form.
1) 5,937  5,000 + 900 + 30 + 7____
 7,000 + 400 + 10 + 9_
 10,000 + 8,000 + 700 + 60 + 5

2) 7,419
 40,000 + 3,000 + 800 + 70 + 2_
3) 18,765
 900,000 + 10,000 + 3,000 + 600 + 40_
4) 43,872
B. Write the following in standard form and in words.

STANDARD
WORDS
FORM
1. 8,000 + 500 + 90 + 1 8,591 Eight thousand five hundred ninety one
2. 60,000 + 2,000 + 100 + 40 + 7 62,147 Sixty-two thousand one hundred forty-seven
3. 100,000 + 20,000 + 5,000 + 900 + 8 125,908 One hundred twenty-five thousand nine hundred eight
4. 70,000 + 4,000 + 300 + 20 + 6 74,326 Seventy-four thousand three hundred twenty-six
Two hundred sixty-eight thousand four

5. 200,000 + 60,000 + 8,000 + 400 + 50 +3 268,453
hundred fifty-three
.
VALUES AND PLACE

VALUES
C. Write the place value and the corresponding value of the
underlined digit of each of the following numbers in the table
provided.
1. 28, 390 2. 827, 571 3. 328, 574 4. 1, 256, 408 5. 4,782,031
Ten thousands millions

Place tens hundreds
thousands
value
Value 90 500 20,000 6,000 4,000,000

D. Give the place value of the digit in ( ); then
round the number to that place value.
tens 14 470
1. 14 4(6)7
hundreds 87 500
2. 87 (5)16
thousands 174 000
3. 17(4) 256
Hundred thousands 200 000
4. (2)33 721
5. 9(4)7 183 ten thousands 950 000

D. Give the place value of the digit in ( ); then
round the number to that place value.
hundreds 921 000
6. 92(1) 785
Hundred thousands 5 400 000
7. 5(3)56 723
millions 7 000 000
8. (6) 679 382
Ten millions 20 000 000
9. (1)6 674 102
10. 2 3(1)5 906 ten thousands 2 320 000

DIVISIBILITIES
E. Complete the table below by enumerating the
divisibility value of the given numbers
Given Number Divisibilties
1. 45 3, 5, 9
2. 369 3, 9
3. 7,870 2, 5, 10
4. 1,976 2
5. 6,003 3, 9
6. 1,674 2, 3, 6, 9
7. 35,496 2, 3, 4, 6, 9
8. 91,350 2, 3, 5, 6, 9,10
F. Fill up the blank with a digit to make the resulting number divisible
by the number to its right
2 5 2
1. 35 ______; 2 2. 82 ______; 3 3. 82 ______; 6
5 3 6
4. 91______; 5 5. 93 ______; 3 6. 90 ______; 6
6 4
7.105 _____; 4 8. 728 _____; 6
ROUNDING/ESTIMATING
G. Give the least and the greatest possible number
that rounds to the nearest ten.
Least Number Greatest Number

175 184
1. 180 ___ ______
945 954
2. 950 _____ ______
635 644
3. 640 ___ 4 355 _______ 4 364
4. 4 360 75 715
_____ _______ 75 724
5. 75 720 __________ __________

SOLVING WORD
PROBLEMS
H. Answer each of the following problems:
1. My number is less than 100. I am divisible by 2, 4, 7 and 8. The sum of
my digits is 11. What number am I?

Answer:
The number divisible by 2, 4, 7 and 8 and the sum of whose digits is 11 is 56.
2. I am a 3-digit number which is divisible by 2, 3, 4, 5, 6 and 8. The sum of

my digits is 3.
Answer:
The number divisible by 2, 3, 4, 5, 6 and 8 and the sum of the digits is 3 is 120.
3. Rounding this number to the nearest 10 makes it 340; rounding it to the
nearest hundred makes it 300. The sum of its digits is 11. What number is it? If
the sum of the digits is not required, how many numbers can you find that
satisfy the first conditions.
Answer:

The number that satisfies all conditions is 344. If the sum of the digits is not required,
341, 342, 343 satisfy the rounding conditions.
4. What is the smallest whole number A that will make 12-A < 5, true?
Answer:
12 – A < 5, so A > 7 or 7< A, therefore the set of whole numbers N that will make the
sentence true is {8, 9, 10, 11, 12…}. The smallest whole number is 8.
4. What is the smallest whole number A that will make 12-A < 5, true?
Answer:
12 – A < 5, so A > 7 or 7< A, therefore the set of whole numbers N that will make the
sentence true is {8, 9, 10, 11, 12…}. The smallest whole number is 8.
5. How many times as great is the place value of 5 in 51470 than that of 7?
Answer:
Five’s place value is 1000 times as great as that of 7.

6. What is the tens digit of (5 x 100) + (7 x 40) + (8 x 4)?
Answer:
(5 x 100) + (7 x 40) + (8 x 4) = 500 + 280 + 32 = 812. Therefore, the tens digit is 1.
7. What is the smallest whole number that round to 3000 to the nearest
thousands?
Answer:
The answer is 2500.

8. When a number is divided by 8, the answer is 145. What is the answer when
the same number is divided by 10?
Answer:
To solve for the number ; N÷ 8 = 145, so 145 x 8 = N, and N = 1160. 1160 ÷ 10 = 116
9. A number is divided by three-fourths of it. Then the quotient is multiplied by

half of the original number. The product is 16. What is three-fourths of the
number?
Answer:
We let, . N = 24, therefore ¾(24) = 18.

10. The digits of the number 5342 are rearranged in descending order
and then in ascending order. What is the difference between the
resulting numbers?
Answer:
Arranged in descending order is 5432, while in ascending order is

2345, therefore 5432 - 2345 = 3087.
CHALLENGE!
Let us apply what we learned!
Solve the following problems.
1. A number has 9 ones and 2 fewer tens than ones. What is
the number?
2 fewer tens than ones is equal to 9 - 2 = 7. Therefore, the number has

7 tens and 9 ones. The number is 79.
1. A 4-digit number has a 6 in the thousands place, a 9 in the
ones place and 0s elsewhere. What is the number?
The number is 6009.

3. What digit is in the tens place in the sum 25 + 35
+ 55?
25 + 35 + 55 = 32 + 243 + 3,125 = 3400. The tens d is zero or 0.

4. If a number is multiplied by itself the result is 54A96. If the
resulting number is divisible by 3, what is the value of the
digit A?
A number is divisible by 3 if the sum of its digits is divisible by 3. So, 5 + 4 +

A + 9 + 6 = 24 + A, therefore A = 3.
5) The digits 1, 2, 3, 4, and 5 are each used once to composed a
five –digit number math, such that the three-digit number mat is
divisible by 4, ath is divisible by 5, and ths is divisible by 3. What is
the value of the digit m?
, , ; , , Therefore .

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MTAP Program of

1) 5,937  5,000 + 900 + 30 + 7____

 10,000 + 8,000 + 700 + 60 + 5

1. 8,000 + 500 + 90 + 1 8,591 Eight thousand five hundred ninety one

2. 60,000 + 2,000 + 100 + 40 + 7 62,147 Sixty-two thousand one hundred forty-seven

4. 70,000 + 4,000 + 300 + 20 + 6 74,326 Seventy-four thousand three hundred twenty-six

Two hundred sixty-eight thousand four

VALUES AND PLACE

1. 28, 390 2. 827, 571 3. 328, 574 4. 1, 256, 408 5. 4,782,031

Ten thousands millions

Value 90 500 20,000 6,000 4,000,000

5. 9(4)7 183 ten thousands 950 000

10. 2 3(1)5 906 ten thousands 2 320 000

Given Number Divisibilties

Least Number Greatest Number

3. 640 ___ 4 355 _______ 4 364

5. 75 720 __________ __________

2. I am a 3-digit number which is divisible by 2, 3, 4, 5, 6 and 8. The sum of

Five’s place value is 1000 times as great as that of 7.

(5 x 100) + (7 x 40) + (8 x 4) = 500 + 280 + 32 = 812. Therefore, the tens digit is 1.

The answer is 2500.

9. A number is divided by three-fourths of it. Then the quotient is multiplied by

We let, . N = 24, therefore ¾(24) = 18.

Arranged in descending order is 5432, while in ascending order is

2 fewer tens than ones is equal to 9 - 2 = 7. Therefore, the number has

The number is 6009.

25 + 35 + 55 = 32 + 243 + 3,125 = 3400. The tens d is zero or 0.

A number is divisible by 3 if the sum of its digits is divisible by 3. So, 5 + 4 +

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3. 640 _ 4 355 _____ 4 364

5. 75 720