U n d e r s t a n d i n g I n s t r u c t i o n s U n d e r s t a n d i n g I n s t r u c t i o n s U n d e r s t a n d i n g I n s t r u c t i o n s
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MATHEMATICS 4
Content Standards The learner…
1. demonstrates
understanding of whole numbers up to 100,000.
2. demonstrates understanding of
multiplication and division of whole numbers including money.
Performance Standards The learner…
1. demonstrates
understanding of whole numbers up to 100,000.
2. demonstrates understanding of
UNIT 1
UNIT 1 UNIT 1 UNIT 1
A number is a mathematical object used to count, measure, and label. The original examples are the natural numbers 1, 2, 3, 4, and so forth.
Numbers can be represented in language with number words. More universally, individual numbers can be represented by symbols, called numerals; for example, "5" is a numeral that represents the number five. As only a relatively small number of symbols can be memorized, basic numerals are commonly organized in a numeral system, which is an organized way to represent any number. The most common numeral system is the Hindu–Arabic numeral system, which allows for the representation of any number using a combination of ten fundamental numeric symbols, called digits.
In addition to their use in counting and measuring, numerals are often used for labels (as with telephone numbers), for ordering (as with serial numbers), and for codes (as with ISBNs). In common usage, a numeral is not clearly distinguished from the number that it represents.
VISUALIZING VISUALIZING VISUALIZING
NUMBERS NUMBERS NUMBERS
LESSON 1 LESSON 1 LESSON 1
Our number system is called a place value system because the value of a digit depends on its position, or place, in a number. The number 537
has a different value than the number 735
Even though they use the same digits, their value is different because of the different placement of the 3 and the 7 and the 5 .Money gives us a familiar model of place value. Suppose a wallet contains three $100 bills, seven $10 bills, and four $1 bills. The amounts are summarized in the image below. How much money is in the wallet?
Base-10 blocks provide another way to model place value, as shown in the image below. The blocks can be used to represent hundreds, tens, and ones. Notice that the tens rod is made up of 10
ones, and the hundreds square is made of 10 tens, or 100
ones.
Find the total value of each kind of bill, and then add to find the total. The wallet contains $374.
The image below shows the number 138
modeled with base-10 blocks.
We use place value notation to show the value of the number 138
.
There are 2
hundreds squares, which is 200
. There is
1
tens rod, which is 10
. There are
5
ones blocks, which is 5
.
Use place value notation to find the value of the number modeled by the base-10 blocks shown.
An image consisting of three items. The first item is two squares of 100 blocks each, 10 blocks wide and 10 blocks tall.
The second item is one horizontal rod containing 10 blocks. The third item is 5 individual blocks.
LEARNING ACTIVITIES WORKSHEET 1.1
Number: 123 = flats= ___+ rods= _____+ units= ____
Use the Base-10 blocks to represent the number below by dragging the correct tiles into the shaded area. Then identify the number of flats, rods, and units used to represent the number.
Note: To remove a tile, drag it out of the shaded area
Legend 100 10 1
LEARNING ACTIVITIES WORKSHEET 1.1
Use the Base-10 blocks to represent the number below by dragging the correct tiles into the shaded area. Then identify the number of flats, rods, and units used to represent the number and put your anwer at the box.
Legend 100 10 1
PLACE VALUE PLACE VALUE PLACE VALUE
LESSON 2 LESSON 2 LESSON 2
By looking at money and base-10 blocks, we saw that each place in a number has a different value. A place value chart is a useful way to summarize this information. The place values are separated into groups of three, called periods. The periods are ones, thousands, millions, billions, trillions, and so on. In a written number, commas separate the periods.
Just as with the base - 10
blocks, where the value of the tens rod is ten times the value of the ones block and the value of the hundreds square is ten times the tens rod, the value of each place in the place-value chart is
ten times the value of the place to the right of it.
The chart below shows how the number 5
, 278
, 194
is written in a place value chart.
The digit 5 is in the millions place. Its value is 5 000, 00
The digit 2 is in the hundred thousands place. Its value is 200,000.
The digit 7 is in the ten thousands place. Its value is 70,000.
The digit 8 is in the thousands place. Its value is 8,000.
The digit 1is in the hundreds place. Its value is 100.
The digit 9 is in the tens place. Its value is 90.
The digit 4 is in the ones place. Its value is 4 In the number 63,407,218
; find the place value of each of the following digits:
7 0 1 6 3 1.
2.
3.
4.
5.
The 7 is in the thousands place.
The 0 is in the ten thousands place.
The 1 is in the tens place.
The 6 is in the ten millions place.
The 3 is in the millions place.
2 1 4 7 6
For each number, find the place value of digits listed:
27,493,615 1.
2.
3.
4.
5.
LEARNING ACTIVITIES WORKSHEET 2.1
For each number, find the place value of digits listed:
519,711,641,328
For each number, find the place value of digits listed:
1,813,497,628 9
4 2 6 7 1.
2.
3.
4.
5.
9 4 2 6 7 1.
2.
3.
4.
5.
What is "Rounding" ?
Rounding means making a number simpler but keeping its value close to what it was.
The result is less accurate, but easier to use.
ROUNDING ROUNDING ROUNDING
NUMBERS NUMBERS NUMBERS
LESSON 3 LESSON 3LESSON 3
Example: 73 rounded to the nearest ten is 70, because 73 is closer to 70 than to 80. But 76 goes up to 80.
Common Method
There are several different methods for rounding. Here we look at the common method, the one used by most people.
First some examples (explanations follow):
Decide which is the last digit to keep
Leave it the same if the next digit is less than 5 (this is called rounding down)
But increase it by 1 if the next digit is 5 or more (this is called rounding up)
Example: Round 74 to the nearest 10
We want to keep the "7" (it is in the 10s position)
The next digit is "4" which is less than 5, so no change is needed to "7"
Answer: 70
(74 gets "rounded down")
Example: Round 86 to the nearest 10 We want to keep the "8"
The next digit is "6" which is 5 or more, so increase the "8" by 1 to "9"
Answer: 90
(86 gets "rounded up")
So: when the first digit removed is 5 or more, increase the last digit remaining by 1.
Why does 5 go up ?
5 is in the middle ... so we could go up or down. But we need a method that everyone agrees to.
So think about sport: we should have the same number of players on each team, right?
0,1,2,3 and 4 are on team
"down"
5,6,7,8 and 9 are on team
"up"
And that is the "common" method of rounding. Read about other methods of rounding.
A farmer counted 87 cows in the field, but when he rounded them up he had 90.
Rounding Decimals
First work out which number will be left when we finish.
Rounding to tenths means to leave one number after the decimal point.
Rounding to hundredths means to leave two numbers after the decimal point.
etc.
3.1416 rounded to hundredths is 3.14 as the next digit (1) is less than 5
3.1416 rounded to thousandths is 3.142 as the next digit (6) is more than 5
1.2735 rounded to tenths is 1.3 as the next digit (7) is 5 or more
To round to "so many decimal places" count that many digits from the decimal point:
1.2735 rounded to 3 decimal places is 1.274 as the next digit (5) is 5 or more
Rounding Whole Numbers
We may want to round to tens, hundreds, etc, In this case we replace the removed digits with zero.
134.9 rounded to tens is 130 as the next digit (4) is less than 5
12,690 rounded to thousands is 13,000 as the next digit (6) is 5 or more
15.239 rounded to ones is 15 as the next digit (2) is less than 5
Round to the nearest ten thousand.
LEARNING ACTIVITIES WORKSHEET 3.1
LEARNING ACTIVITIES WORKSHEET 3.2
The term denomination is used to describe a currency. Every country has its own currency as well as denominations. For
example, the Philippines has currency Peso and it can further be divided into different smaller currencies like ₱1, ₱2, ₱5, ₱10, ₱20,
₱50, and ₱100. In this lesson, we will learn to identify denominations using charts and examples.
IDENTIFYING IDENTIFYING IDENTIFYING
DENOMINATIONS DENOMINATIONS DENOMINATIONS
LESSON 4 LESSON 4 LESSON 4
Meaning of Denominations
Money is a common term used for currency. It is exchanged between various people, used in trade, and deposited in banks.
Money, be it a printed currency note or a coin, as such does not have any value. Its value is decided by the government or
economists of a country who give it a particular value. We buy goods or avail of a service based on the numerical value
denoted by money. Thus there is a currency specific to every country, for example, Indian Currency is Rupees, US currency is Dollars, and so on.
Splitting up a given number into various smaller numbers is called denomination. Denomination meaning in the context of money can be well understood by thinking of place values. Let us take Philippines currency Peso into our consideration to understand more about denominations.
Identification of Denominations
The place values are ones, tens, hundreds, thousands, and so on.
₱1, ₱10, ₱100 are similar to place values of units, tens, and hundreds. There can be any number of one peso, ten peso, hundred peso in a given amount. For example, we can say a hundred peso comprise a hundred ₱1 or ten ₱10 or one ₱100.
These are the currency notes used in the United States. The paper notes come in the following denominations:
As we can see, we can compare money in different denomination.
4 centavo 1 Peso
88 centavo 20 Peso Bill
What operation we can use here?
There is a lot of way to solve this. We can use the addition, multiplication or other way to do this.
But here, We have 20 PESO BILL AND 1 CENTAVO COIN.
So we can use here the Multiplication How does it happen?
• First identify, how many 25 centavo in 1 PESO coin.
1PESO COIN = 4 (25 centavo) 20 PESO COIN = ____ (25 centavo)
What we gonna do here? We have to multiple the 4 and the 20.
So that,
20 PESO COIN = _80_ (25 centavo)
For 100 Peso bill, How many 5 peso coin you need to have?
How does it happen?
• First identify, how many 5 Peso coin in 100 peso bill?
100 PESO BILL=____ (5 PESO COIN)
5+5+5+5+5+5+5+5+5+5+5+5+5+5+5+5+5+5+5+5=100 5X20=100
There is addition and multiplication way...
For 100 Peso bill, How many 10 peso coin you need to have?
How does it happen?
• First identify what operation you can use and answer how many 10 Peso coin in 100 peso bill?
100 PESO BILL=____ (10 PESO COIN)
10X10=100
We can use different ways to visualize the value of money. We can use the addition, multiplication, division, multiples, skip counting or what ever way we may do. But we must use the fastest way.
What do we do if we receive a change? Of course, we count the value of every money. But what if the change have a lot of
different money value, so this topic will be use in this situation.
Fill the blank to make it equal.
LEARNING ACTIVITIES WORKSHEET 4.1
1.
2.
3.
4.
1 50 Peso Bill
1 100 Peso Bill
1 5 Peso coin
1 200 Peso Bill _____ 5 Peso coin
____ 25 centavo coin
____ 10 Peso coin
____ 1Peso coin
Get the Value.
LEARNING ACTIVITIES WORKSHEET 4.2
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