Whole Numbers Counting & Writing – JSS1 Mathematics Lesson Note (First Term)

Whole numbers are the counting numbers together with zero: 0, 1, 2, 3, 4 and so on without end.

Behavioural objectives

By the end of the lesson, students should be able to:

1. name the digits and the groups of whole numbers (units, tens, hundreds, thousands);
2. state the number of zeros in a million, a billion and a trillion;
3. give the place value of a digit using the place value chart;
4. write large numbers in figures and in words;
5. arrange whole numbers in ascending and descending order.

What are whole numbers?

Whole numbers are the numbers 0, 1, 2, 3, 4, 5 and so on, with no fractions, decimals or negative numbers.

• Smallest whole number: 0 is the smallest whole number.
• Largest whole number: there is none, because adding 1 always gives a bigger whole number.
• Counting numbers: 1, 2, 3 and so on start from 1, so they do not include 0.
• Next number: add 1 to a whole number to get the next one, for example 999 then 1,000.

How do we count in whole numbers?

We count by adding the same amount each time, starting from a chosen number.

• Counting in ones: 1, 2, 3, 4, 5, 6 and so on.
• Counting in tens: 10, 20, 30, 40, 50 and so on.
• Counting in hundreds: 100, 200, 300, 400 and so on.
• Counting in thousands: 1,000, 2,000, 3,000 and so on.

What are digits and how are numbers grouped?

Digits are the ten symbols used to write all numbers: 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9.

• Combining digits: digits can be combined in different ways to write any number, however large.
• Units (ones): single digits from 0 to 9.
• Tens: numbers from 10 to 99, such as 10, 25, 67 and 99.
• Hundreds: numbers from 100 to 999, such as 100, 456 and 999.
• Thousands: numbers from 1,000 upwards.

What is the place value system?

The place value system is the rule that the value of a digit depends on its position in the number.

• Grouping: large numbers are grouped in threes from the right.
• Group names: the groups are named thousands, millions, billions and trillions.
• Example: in 5,000, the digit 5 stands for five thousand. In 50, it stands for fifty.

Table of large numbers

Quick memory tip

• Million: 6 zeros.
• Billion: 9 zeros, which is 3 more than a million.
• Trillion: 12 zeros, which is 3 more than a billion.

What is the place value chart?

A place value chart is a table that gives each position in a number its own name.

Example: 75,800,074,890

• Read as: seventy-five billion, eight hundred million, seventy-four thousand, eight hundred and ninety.

What is the difference between face value and place value?

Face value is the digit itself, while place value is the value the digit has because of its position.

• Face value: the digit as it is written, whatever its position.
• Place value: the face value multiplied by the value of its position.

Example: the digit 7 in 37,456,891.

What are the rules for writing large numbers?

There are three main rules for writing large numbers: group in threes, use “and” correctly, and use zeros as placeholders.

1. Group numbers in threes from right to left, using commas or spaces.
   • Example: 1234567890 becomes 1,234,567,890 or 1 234 567 890.
2. Use “and” before the tens and units of each group of three.
   • Correct: five hundred and twenty-three.
   • Incorrect: five hundred and twenty and three.
3. Zeros act as placeholders. They show that a position has no value.
   • Example: 105 means 1 hundred, 0 tens and 5 units.

How do we write numbers in figures and in words?

To write a number in figures, change each named group to figures and add the groups together.

Example 1: Writing numbers in figures

• Question: write in figures: twenty-five trillion, three hundred and five billion, six hundred and sixty-nine million, one hundred thousand and forty-one.
• Method: break the number into parts, then add the parts.

Adding the parts:

• Answer: 25,305,669,100,041.

Example 2: Writing numbers in figures

• Question: write in figures: ninety billion, three hundred and nine million, ninety-one thousand, seven hundred and sixty-three.

Adding the parts:

• Answer: 90,309,091,763.

Example 3: Writing numbers in words

• Question: write in words: 456,789,012,345.

Identify each group, working from the left:

1. 456: four hundred and fifty-six (billions).
2. 789: seven hundred and eighty-nine (millions).
3. 012: twelve (thousands).
4. 345: three hundred and forty-five (units).

• Answer: four hundred and fifty-six billion, seven hundred and eighty-nine million, twelve thousand, three hundred and forty-five.

How do we arrange numbers in ascending and descending order?

Ascending order means arranging numbers from the smallest to the largest.

Descending order means arranging numbers from the largest to the smallest.

Steps for comparing whole numbers

1. Group each number in threes.
2. Count the digits. The number with fewer digits is smaller.
3. If the digits are equal in number, compare from the left. The larger first digit means the larger number.
4. If the first digits are the same, compare the next digit to the right, and continue.

Example 4: Arranging numbers in order

• Question: arrange in ascending order: 28,980,579 | 18,967,547 | 2,897,871 | 36,497,871 | 36,479,568 | 18,898,069 | 36,478,967.

1. The numbers are already grouped in threes.
2. Count the digits. 2,897,871 has 7 digits and the rest have 8, so 2,897,871 is the smallest.
3. Compare the first two digits of the 8-digit numbers: 18, 28 and 36. So the order of groups is 18, then 28, then 36.
4. Compare the two numbers starting with 18: 18,898,069 and 18,967,547. The hundred-thousands digits are 8 and 9, so 18,898,069 is smaller.
5. Compare the three numbers starting with 36: 36,478,967, 36,479,568 and 36,497,871. Look at the digits after 36,4: 78, 79 and 97. So the order is 36,478,967, then 36,479,568, then 36,497,871.

• Answer (ascending order): 2,897,871 | 18,898,069 | 18,967,547 | 28,980,579 | 36,478,967 | 36,479,568 | 36,497,871.

Evaluation

1. How many zeros are in one billion and in one trillion?
2. Write 5,000,000 in words.
3. Write in figures: forty-two million, five hundred and six thousand, three hundred and eight.
4. What is the place value of 8 in 18,967,547?
5. Arrange in descending order: 4,205,000 | 420,500 | 42,050,000.

Assignment

Exercise 1: Writing numbers in words

Write the following numbers in words:

1. 567,256,789
2. 18,000,901,234
3. 3,456,789,012
4. 125,000,000,000

Exercise 2: Writing numbers in figures

Write the following in figures:

1. Three hundred and twenty-nine billion, five hundred and sixty-two million, eight hundred and one thousand, four hundred and thirty-three.
2. Fifteen trillion, six hundred and seventy-one billion, three hundred and ninety-one million, eighty-eight thousand, five hundred and fifty-five.
3. Seven hundred and eight million, forty-five thousand, two hundred and one.
4. Ninety-nine trillion, nine hundred and ninety-nine billion, nine hundred and ninety-nine million, nine hundred and ninety-nine thousand, nine hundred and ninety-nine.

Exercise 3: Arranging numbers

Arrange the following numbers in ascending order (smallest to largest) and then in descending order (largest to smallest):

1,009,085,941 | 1,288,890,563 | 102,458,001 | 999,999,999 | 10,009,002 | 105,879,894,167

Exercise 4: Fill in the blanks

1. One million has _____ zeros.
2. 5,000,000 is read as _____.
3. The place value of 7 in 37,456,891 is _____.
4. The largest 3-digit number is _____.
5. One billion is _____ times larger than one million.