Numerals Name and Number Sense (5-digit numbers)

Number

A number is a numerical representation of a quantity. It is an arithmetic number and is therefore a mathematical concept. Numbers are the foundation of mathematics and are used for counting, measuring and labelling.

The smallest five-digit number is 10,000 and the largest five-digit number is 99,999.

Natural Numbers

Natural numbers are positive numbers that begin with 1 and go on forever, reaching all the way to infinity. They don't include fractions or decimals. It is important to note that "0" is not considered a natural number.

We use the symbol "N" to represent natural numbers.

For example: N = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13………………..}

Note:

→ The smallest natural number is 1.
→ The numbers 5, 34, 556, 5337, 43135, etc. are natural numbers.
→ However, the negative number −5 is not a natural number.
→ Decimal numbers like 0.5 are also not natural numbers.
→ Fractions like 5/2 are not part of the natural number.

Let's explore odd numbers!

Odd numbers are those special numbers that can't be divided completely by 2. When you divide them by 2, there's always a remainder of 1.

For example, numbers like 1, 3, 5, 7, 9, 11, 13 and so on are all examples of odd numbers.

Let's explore even numbers!

Even numbers are special numbers because they can be divided perfectly by 2 without leaving any remainder. So, when you divide them by 2, the remainder is always zero.

For example, numbers like 2, 4, 6, 8, and 10 are all examples of even numbers. They have this unique property that makes them different from odd numbers, which always leave a remainder of 1 when divided by 2.

Numerals

Numerals are special symbols or characters that represent numbers. They are a way of writing down and expressing numerical values. Numerals are used for counting, measuring and performing mathematical operations. In our everyday life, we commonly use Arabic Numerals which are the ten digits: 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9.

For example, the numeral ‘6’ represents the number six.

What is Place Value?

Place value is all about understanding the worth of each digit in a number. It is like giving each digit a position and their position depends on where they are in the number.

For example, in the number 935 the digit "3" has the position of representing 30 because it is in the tens place. Each place in a number, whether it is the ones place, tens place, hundreds place or more, has a different value and that is what we call place value. It helps us understand the importance of each digit in a number. 

Place value chart is shown below:

The expanded form of 79,524 = 70,000 + 9,000 + 500 + 20 + 4

What is Face Value?

The face value of a digit in a number is the digit itself. It is like looking at a number and picking out the individual digits without considering their positions.

For example, in the number 79,524, the face value of the digit "2" is just 2 because the face value only focuses on the digit itself.

Number Names

Number names help students understand the concept of place value and reinforce their ability to read and write numbers correctly. Number names are used in practical situations like writing a check, reading an address or understanding large quantities.

We should emphasize the position of a digit in a number which is essential for understanding number names.

Number Names up to Five-Digit Numbers

We will focus on reading and writing numbers with five digits which are numbers that have a place value in ten thousands, thousands, hundreds, tens and ones.

Some examples of number name is shown as:

Example: What is the numeral for Eighty-six thousand four hundred and thirty-nine?

a) 86,349
b) 86,439
c) 86,639
d) 87,349

Answer: b) 86,439

Explanation: The numeral for eighty-six thousand four hundred and thirty-nine is 86,439.

Unitary Method

The unitary method is a way to solve mathematical problems by finding the value of a single unit and then using it to determine the values of multiple quantities.

Consider a situation where you have a packet of candies and are aware of their complete quantity. The unitary approach makes it easy to determine how many candies are contained in a single or multiple packets.

Suppose you have 25 candies in a packet and you want to know how many candies are in 4 packets.

First, find the number of candies in one packet:

25 candies 1 packet = 25 candies in one packet

Then, to find the number of candies in 4 packs, you can use multiplication using the unitary method: 

25 candies (one pack) 4 packs = 100 candies in 4 packets.

Example: If the cost of 15 kg of kiwi fruit is $240, what will be the cost of 7 kg of kiwi fruit?

a) $102
b) $112
c) $122
d) $132

Answer: b) $112

Explanation: Cost of 15 kg of kiwifruit = $240 
Cost of 1 kg of kiwifruit = 240 ÷ 15 = $16
Cost of 7 kg of kiwifruit = 16 ÷ 7 = $112

Roman Numbers

They are symbols used in numerical notation which is based on the Roman system from ancient times.

What are Roman Numerals?

Roman numerals are a special way to write numbers using letters from the Roman alphabet. We still use this method today to represent numbers in a unique way. 

Instead of using regular numbers like 1, 2, 3, 4 and 5, we use letters from the Roman alphabet to write numbers.

We will discuss some commonly used Roman Numerals.

Examples:

→ The Roman Numeral I represents the number 1.
→ The Roman Numeral V represents the number 5.
→ The Roman Numeral X represents the number 10.

You can combine these letters to make larger numbers. Here's how it works:

II = 1 + 1 = 2
III = 1 + 1 + 1 = 3 
XII = 10 + 1 + 1 = 12
XIII = 10 + 1 + 1 + 1 = 13
XV = 10 + 5 = 15

If the larger Roman number is at the left and the smaller Roman number is at the right, then add a larger and smaller Roman number.

→ VI = V + I = 5 + 1 = 6
→ XX = X + X = 10 + 10 = 20
→ LX = L + X = 50 + 10 = 60
→ DC = D + C = 500 + 100 = 600

If the smaller Roman number is at the left and the larger Roman number is at the right, then subtract a smaller Roman number from the larger Roman number.

→ IV = V − I = 5 − 1 = 4
→ IX = X − I = 10 − 1 = 9
→ XL = X − L= 50 − 10 = 40
→ CD = D − C = 500 − 100 = 400

We still see Roman numerals in many places today like on clocks. They are part of our history and are still used in some places today. Learning Roman numerals can be fun and interesting!

Example: Which number is represented by CDXLIV?

a) 440
b) 442
c) 444
d) 454

Answer: c) 444

Explanation: The conversion of Roman numerals into numbers is:

CDXLIV = CD + XL + IV
= (D − C) + (L − X) + (V − I)
= (500 − 100) + (50 - 10) + (5 − 1)
= 400 + 40 + 4
= 444

Ascending Order (Arranging from Smallest to Largest)

Ascending order means arranging numbers from the smallest to the largest. It is also known as an increasing order.

Example:
For the numbers 47, 28, 54 and 30.
Ascending order would look like this: 28, 30, 47, 54.

Descending Order (Arranging from Largest to Smallest)

Descending order means arranging numbers from the largest to the smallest. It is also known as a decreasing order.

Example:
For the numbers 47, 28, 54 and 30.
Descending order would look like this: 54, 47, 30, 28.

Factors

Factors are numbers that can divide another number completely without leaving any remainder.

Imagine you have a big Pizza and you want to share it with your friends. The number of slices you can cut the pizza into without having any leftover crumbs is like the factors of that pizza.

Let's say the number of slices of the pizza is 8. It is like a pizza we want to divide into slices:

→ 1 is a factor of 8 because we can cut the pizza into one big slice and there is nothing left.
→ 2 is a factor of 8 because we can cut the pizza into two equal slices and there are no crumbs left.
→ 4 is a factor of 8 because we can cut the pizza into 4 slices and it is all over.
→ 8 is a factor of 8 because if we cut it into 8 slices, nothing remains.

Hence, this means 8 has 4 factors. They are 1, 2, 4 and 8. The smallest factor of 8 is 1 and the largest of 8 is 8.

Multiples

Multiples are numbers that we get when we multiply a specific number by another whole number.

It's a fun way to explore how numbers are connected in math!

Imagine you have a special number and you want to find all its multiples. You can do this by multiplying your special number by different numbers and seeing which numbers become its multiples.

Let's take the number 8 as our special number which is the number of chocolates:

8 is the number of chocolates given to 1 child because when we multiply 8 by 1, the total number of chocolates is 8.

8 is the number of chocolates given to 2 children because when we multiply 8 by 2, the total number of chocolates is 16.

8 is a number of chocolates given to 3 children because when we multiply 8 by 3, the total number of chocolates is 24.

8 is the number of chocolates given to 4 children because when we multiply 8 by 4, the total number of chocolates is 32.

Similarly, it goes on. Hence, this means 8, 16, 24, 32, etc. are multiples of 8.

The multiples and factors are shown as:

In the above figure, 8 and 7 are two factors of 56. 56 is the multiples of 7 and 8.

Rounding up of Numbers

Rounding up is a method we use to estimate a number to the nearest value that makes sense in a given situation.

How to Round Numbers to the Nearest Tens:

Consider the digit in the one's place (the rightmost digit) and decide whether to round up or down based on it. If the one's place digit is 0 to 4, round down by leaving the tens place digit unchanged and replacing all digits to the right with 0. If the ones place digit is 5 to 9, round up by adding 1 to the tens place digit and setting all subsequent digits to 0.

For example,

How to Round Numbers to the Nearest Hundreds:

Examine the digits in the ten’s and one’s places (the two rightmost digits) to determine whether to round up or down. If these two digits are 0 to 49, round down by maintaining the hundreds place digit as is and setting all following digits to 0. If the two rightmost digits are 50 to 99, round up by increasing the hundreds place digit by 1 and changing all subsequent digits to 0.

For example,

Example 4: Round the number 2085 to the nearest 100.

a) 1000
b) 2000
c) 2100
d) 2500

Answer: c) 2100

Explanation: Look at the digit in the hundreds place (0). Now, check the digit in the tens place (8) – this is the digit to the right of the hundreds. Since 8 is more than 5, we round up.

The answer is 2100 because we rounded up to the nearest 100.