Whole numbers

Karibu! Welcome to the World of Whole Numbers!

Habari mwanafunzi! Ever wondered how we count the number of cows in the shamba, the students in your class, or the shillings in your pocket? We use a special group of numbers that are the foundation of all mathematics. These are our friends, the Whole Numbers! They are simple, strong, and straightforward, just like the mighty baobab tree. Today, we will explore them together and see how they are part of our everyday life here in Kenya.

What Exactly Are Whole Numbers?

Think of it this way: whole numbers are the counting numbers you first learned, but we also include a very important hero: zero (0). They are complete numbers, with no fractions (like a half chapati) or decimals (like KSh 50.50). They are whole, just like a whole mandazi!

• They start from 0.
• They increase by one step at a time (0, 1, 2, 3, 4...).
• They do not have any fractions or decimal parts.
• They go on forever! There is no "last" whole number.

We can see them clearly on a number line:

A Simple Number Line (Mstari wa Nambari)

<----|----|----|----|----|----|----|----|----|---->
     0    1    2    3    4    5    6    7    8    ... and so on!

Place Value: Where a Number Gets its Power!

Imagine you have a large number, like the price of a prize-winning cow at the Nairobi International Trade Fair: KSh 245,789. Every digit in this number has a special position and value. This is called Place Value.

Mzee Kamau sold his coffee beans and received two hundred forty-five thousand, seven hundred and eighty-nine shillings. How do we write this down and understand its value? We use a place value chart!

+------------------+-----------------+-----------+----------+------+------+
| Hundred Thousands| Ten Thousands   | Thousands | Hundreds | Tens | Ones |
+------------------+-----------------+-----------+----------+------+------+
|         2        |        4        |     5     |     7    |   8  |   9  |
+------------------+-----------------+-----------+----------+------+------+

So, the number 245,789 is made of:
- 2 Hundred Thousands (200,000)
- 4 Ten Thousands (40,000)
- 5 Thousands (5,000)
- 7 Hundreds (700)
- 8 Tens (80)
- 9 Ones (9)

Understanding place value helps us read, write, and work with big numbers easily!

Operations: Putting Whole Numbers to Work!

This is where the fun begins! We can add, subtract, multiply, and divide whole numbers to solve real-life problems.

Addition (Kujumlisha - To Combine)

Addition is all about bringing things together. Imagine you have 30 goats, and you buy 15 more from the market.

**Image Suggestion:** A bright, sunny illustration of a Kenyan rural landscape. A smiling farmer is leading a small herd of 15 goats to join a larger herd of 30 goats near a homestead. The style should be warm and inviting, suitable for an educational textbook.

  30  (Goats you had)
+ 15  (Goats you bought)
----
  45  (Total goats)

Step 1 (Ones place): 0 + 5 = 5
Step 2 (Tens place):  3 + 1 = 4
You now have 45 goats! Hongera!

Subtraction (Kutoa - To Take Away)

Subtraction is for when we take a smaller number away from a bigger one. Let's say you go to the duka with KSh 200 to buy sugar for KSh 135.

  200  (Your money)
- 135  (Cost of sugar)
-----
   65  (Your change)

Step 1 (Ones): You can't take 5 from 0. You need to borrow.
Step 2 (Borrowing): Borrow from the tens place. It's also 0! So, borrow from the hundreds place. The 2 becomes 1. The middle 0 becomes 10, then you borrow from it, so it becomes 9. The last 0 becomes 10.
       1  9 10
       2  0  0
     - 1  3  5
     ---------
Step 3 (Calculate):
       Ones:   10 - 5 = 5
       Tens:    9 - 3 = 6
       Hundreds:1 - 1 = 0
Your change is KSh 65.

Multiplication (Kuzidisha - Repeated Addition)

Multiplication is a fast way of adding the same number over and over. If one crate holds 24 sodas, how many sodas are in 6 crates?

You could add 24 + 24 + 24 + 24 + 24 + 24, but that's too slow! Let's multiply.

    24
 x   6
------
   144

Step 1: 6 x 4 = 24. Write down the 4 and carry over the 2.
Step 2: 6 x 2 = 12. Add the 2 you carried over: 12 + 2 = 14.
There are 144 sodas in total. Perfect for a party!

Division (Kugawa - To Share Equally)

Division helps us share things equally. A teacher has 120 sweets to share among 40 students after a successful sports day.

     __3_
 40 | 120
    - 120
    -----
        0

Step 1: Ask, "How many times can 40 go into 120?"
Step 2: Let's try multiplying 40 by simple numbers:
        40 x 1 = 40
        40 x 2 = 80
        40 x 3 = 120  (Aha! It fits perfectly!)
Step 3: So, 120 divided by 40 is 3.
Each student gets 3 sweets.

Let's Try a Real-World Challenge!

You are helping to organise a school trip to the Nairobi National Park. The school bus can carry 52 students. If there are 312 students in your stream who want to go, how many bus trips will be needed to take everyone?

What operation should we use? We are grouping 312 students into groups of 52. That's division!

Solution:

We need to calculate 312 ÷ 52.

Let's estimate. 50 goes into 300 about 6 times. Let's try multiplying 52 by 6.

     52
   x  6
  -----
   312  (50x6=300, 2x6=12. 300+12=312)

It's a perfect fit!

     __6_
 52 | 312
    - 312
    -----
        0

Answer: The bus will need to make 6 trips.

You are a Whole Number Champion!

Today, you have learned what whole numbers are and how to use them in ways that matter every single day. From counting livestock to sharing sweets and planning trips, whole numbers are your tools for understanding the world. Keep practicing, stay curious, and you will become a true master of mathematics. Kazi nzuri!

Karibu! Let's Conquer Whole Numbers Together!

Habari mwanafunzi! Have you ever counted the number of people in a matatu? Or maybe the amount of shillings you need to buy a nice new exercise book? The numbers you used for counting - 0, 1, 2, 3, 10, 50, 100 - are the heroes of our story today. They are called Whole Numbers! They are the building blocks of mathematics, and by the end of this lesson, you'll be a master at using them. Let's begin!

1. What Exactly Are Whole Numbers?

Think of it this way: whole numbers are numbers for counting complete things. You can have 3 mangoes, but you can't have half a live chicken! Whole numbers are all the positive counting numbers, plus zero.

• They start from 0 and go on forever (0, 1, 2, 3, 4, ...).
• They do not have fractions (like ½).
• They do not have decimals (like 2.5).
• They are not negative (like -5).

Here is a simple number line to show you where they live:

<---(Negative Numbers)---[ 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | ... ]--->
                         ^
                         |
                       Whole Numbers Start Here!

2. The Power of Place Value

Imagine the number 5,842. It's not just a 5, an 8, a 4, and a 2. Each number has a special job based on its position, or 'place'. This is called Place Value. It's like a family where everyone has a different role!

Let's break down Ksh. 5,842, maybe the price of a new school uniform and shoes.

+-----------+-----------+----------+--------+
| Thousands | Hundreds  |   Tens   |  Ones  |
+-----------+-----------+----------+--------+
|     5     |     8     |     4    |    2   |
+-----------+-----------+----------+--------+
|  5 x 1000 |   8 x 100 |  4 x 10  |  2 x 1 |
|   5000    |    800    |    40    |    2   |
+-----------+-----------+----------+--------+

So, 5,842 is really Five thousand, eight hundred and forty-two. See? Each digit's value depends on where it is sitting. Vizuri sana!

Example from the Shamba: A farmer in Molo harvested 1,273 bags of potatoes. The '1' represents 1 thousand bags, the '2' represents 2 hundred bags, the '7' represents 70 (7 tens) bags, and the '3' represents 3 single bags. Every number has its power!

Image Suggestion: A vibrant, colourful Kenyan open-air market. A vendor is selling sukuma wiki, tomatoes, and carrots. A large, clear price tag in front of a pile of potatoes reads "Ksh. 1,273 per bag" with the place values (Thousands, Hundreds, Tens, Ones) lightly annotated above each digit. The style should be cheerful and illustrative.

3. The Four Big Operations: Your Mathematical Tools!

Now for the fun part - using whole numbers! These are the four main operations you'll use every single day.

A. Addition (+) - Combining Things

Addition is simply putting groups of things together. If your friend gives you 15 marbles and you already had 23, you add them to find the total.

Problem: A class has 42 boys and 39 girls. How many students are there in total?

  Step 1: Arrange the numbers vertically, aligning the Ones and Tens.

      42
    + 39
    ----

  Step 2: Add the Ones column (2 + 9 = 11).
          Write down the 1 in the Ones place and carry over the other 1 to the Tens column.
      1
      42
    + 39
    ----
       1

  Step 3: Add the Tens column, including the carried-over 1 (1 + 4 + 3 = 8).
          Write down the 8.
      1
      42
    + 39
    ----
      81

  Answer: There are 81 students in total.

B. Subtraction (-) - Taking Away

Subtraction is what you do when you give something away or use something up. If you have Ksh. 100 and you buy a soda for Ksh. 35, you subtract to find your change.

Problem: You had 54 mangoes, but you sold 28 at the market. How many are left?

  Step 1: Arrange the numbers vertically.

      54
    - 28
    ----

  Step 2: Subtract the Ones column (4 - 8).
          You can't take 8 from 4! So, we 'borrow' 1 from the Tens column (the 5 becomes a 4).
          The borrowed 1 is a Ten, so the Ones column becomes 10 + 4 = 14.

      4  14
      5  4
    - 2  8
    ------

  Step 3: Now subtract the Ones (14 - 8 = 6).
          Then subtract the Tens (4 - 2 = 2).

      4  14
      5  4
    - 2  8
    ------
      2  6

  Answer: You have 26 mangoes left.

C. Multiplication (x) - Repeated Addition

Multiplication is a fast way of adding the same number over and over. If 1 crate holds 24 sodas, 3 crates hold 24 + 24 + 24, or simply 24 x 3.

Problem: If a bus ticket from Nairobi to Nakuru costs Ksh. 450, how much will it cost for a family of 5?

     450
   x   5
   -----

  Step 1: Multiply the Ones digit (5 x 0 = 0). Write 0.
     450
   x   5
   -----
       0

  Step 2: Multiply the Tens digit (5 x 5 = 25). Write 5, carry over 2.
     2
     450
   x   5
   -----
      50

  Step 3: Multiply the Hundreds digit (5 x 4 = 20). Add the carried-over 2 (20 + 2 = 22). Write 22.
     2
     450
   x   5
   -----
    2250

  Answer: It will cost the family Ksh. 2,250.

D. Division (÷) - Sharing Equally

Division is all about sharing. If you have a big bag of sweets and want to share it equally among your friends, you use division.

Problem: A teacher has 96 new exercise books to share equally among 4 students. How many books does each student get?

        2  4
      ____
    4 | 96
      - 8  (4 goes into 9 two times, 2x4=8)
      ---
        16 (Bring down the 6)
      - 16 (4 goes into 16 four times, 4x4=16)
      ----
         0 (No remainder)

  Answer: Each student gets 24 books.

Image Suggestion: An overhead shot of a group of four smiling Kenyan children sitting in a circle on a woven mat. In the center is a pile of 96 colourful exercise books, and each child has a neat stack of 24 books in front of them, showing the result of equal sharing. The style is bright and heartwarming.

4. Rounding Off - Making Numbers Simpler!

Sometimes you don't need the exact number. You just need a close idea. This is called rounding. For example, if something costs Ksh. 99, you might just say, "It costs about 100 shillings."

The Rule: Look at the digit to the right of the place you are rounding to.

• If it's 5 or more (5, 6, 7, 8, 9), you round up (increase the digit).
• If it's 4 or less (4, 3, 2, 1, 0), you round down (the digit stays the same).

Example: Round 3,862 to the nearest hundred.

  1. Identify the Hundreds digit: It's 8. (3,`8`62)

  2. Look at the digit to its right: It's 6. (`6`2)

  3. Use the rule: 6 is '5 or more', so we round the Hundreds digit (8) UP to 9.

  4. All digits after the rounded digit become zero.

  ASCII Art Number Line:

       <----|---------------[3,862]---------|---->
         3,800                            3,900

  As you can see, 3,862 is much closer to 3,900.

  Answer: 3,862 rounded to the nearest hundred is 3,900.

A Day at the Market:

Mama Biko goes to the market. She buys sukuma wiki for Ksh. 75, tomatoes for Ksh. 120, and onions for Ksh. 55. To quickly check if she has enough money, she rounds in her head: "75 is about 100. 120 is close to 100. 55 is about 50. So, 100 + 100 + 50 = 250. I need about Ksh. 250." This quick calculation helps her manage her money easily!

You've Done It!

Wow! Look at everything you've learned. From understanding what whole numbers are, to their place values, and using all four major operations to solve real-life Kenyan problems. Maths is not just in your book; it's in the market, on the farm, and in every shilling you spend. Keep practicing, stay curious, and you will become a true maths champion. Kazi nzuri!

Karibu! Let's Explore the Amazing World of Whole Numbers!

Habari Mwanafunzi! Welcome to our mathematics adventure. Think about this: How many players are in the Harambee Stars football team? How many shillings did you use for lunch? How many counties are there in Kenya? The answers to all these are Whole Numbers! They are the building blocks of mathematics, and today, we are going to master them together. Get your thinking cap on, because this is going to be fun!

Image Suggestion: A vibrant, colourful illustration of Kenyan children of different genders and backgrounds, happily counting a pile of shiny shillings, with a backdrop of a bustling Gikomba market scene. The style should be cheerful and cartoonish.

What Exactly Are Whole Numbers?

This sounds like a big question, but the answer is very simple. Whole numbers are all the counting numbers you already know, starting from zero.

• They are complete, or 'whole' - no fractions!
• They are not negative.
• They have no decimals.

So, the set of whole numbers is: 0, 1, 2, 3, 4, 5, ... and it goes on forever!

Let's draw a number line to see them clearly:

  <--- The numbers go on forever! --->
  |----|----|----|----|----|----|----|----|----
  0    1    2    3    4    5    6    7    8 ...

Place Value: The Power of Position!

Have you ever looked at a big number like KSh 5,842 and wondered what each digit means? That's where Place Value comes in. It's the idea that a digit's value depends on its position in the number. It's like having a specific seat in a matatu; your position matters!

Let's break down the number 5,842:

+-----------+-----------+----------+--------+
| Thousands | Hundreds  |   Tens   |  Ones  |
+-----------+-----------+----------+--------+
|     5     |     8     |     4    |    2   |
+-----------+-----------+----------+--------+

• The 2 is in the Ones place, so its value is 2 x 1 = 2.
• The 4 is in the Tens place, so its value is 4 x 10 = 40.
• The 8 is in the Hundreds place, so its value is 8 x 100 = 800.
• The 5 is in the Thousands place, so its value is 5 x 1000 = 5,000.

When you add them up: 5000 + 800 + 40 + 2, you get back to 5,842! See? Every digit has its own important job.

Writing Numbers in Words and Figures

Being able to switch between numbers written as figures (like 123) and in words (like "one hundred and twenty-three") is a very important skill, especially when writing cheques or filling out official forms.

Real-Life Example: Imagine your school sends a fee reminder via M-Pesa. It says: "Please pay KSh 25,650." You need to know that this is "Twenty-five thousand, six hundred and fifty shillings."

From Figures to Words:

Let's take 43,871.

1. Start from the left. The first group is '43' in the thousands place. So, that's "Forty-three thousand".
2. Look at the next three digits, '871'. That's "eight hundred and seventy-one".
3. Combine them: "Forty-three thousand, eight hundred and seventy-one."

From Words to Figures:

Let's take "Six hundred two thousand, four hundred and five."

1. "Six hundred two thousand" tells you to write 602 and put a comma.
2. "four hundred and five" tells you to write 405.
3. Combine them: 602,405. Easy!

Operations: The Fun Part!

This is where we get to do the real work - adding, subtracting, multiplying, and dividing. Let's solve some everyday Kenyan problems!

1. Addition (Kujumlisha - To Add)

Addition is simply combining things together. Imagine a farmer in Makueni harvested 1,258 mangoes on Monday and 975 mangoes on Tuesday. How many mangoes did he harvest in total?

  1258   (Mangoes from Monday)
+  975   (Mangoes from Tuesday)
------
  2233   (Total mangoes)

Step-by-step:
- Ones place: 8 + 5 = 13. Write down 3, carry over 1 to the tens place.
- Tens place: 5 + 7 + 1 (carry-over) = 13. Write down 3, carry over 1.
- Hundreds place: 2 + 9 + 1 (carry-over) = 12. Write down 2, carry over 1.
- Thousands place: 1 + 1 (carry-over) = 2. Write down 2.

The farmer harvested a total of 2,233 mangoes!

2. Subtraction (Kutoa - To Subtract)

Subtraction is taking away. You have 500 shillings and go to the duka. You buy sugar for 150 shillings and bread for 65 shillings. How much change should you get? First, let's find the total cost: 150 + 65 = 215 shillings.

   500   (The money you had)
-  215   (The cost of items)
------
   285   (Your change)

Step-by-step (with borrowing):
- Ones place: 0 - 5. Can't do. Borrow from tens. But tens is 0! So, borrow from hundreds.
- The 5 in hundreds becomes 4. The 0 in tens becomes 10.
- Now borrow from the tens. The 10 becomes 9, and the 0 in ones becomes 10.
- Ones place: 10 - 5 = 5.
- Tens place: 9 - 1 = 8.
- Hundreds place: 4 - 2 = 2.

You should receive 285 shillings in change. Always count your change!

Image Suggestion: A close-up, friendly illustration of a hand receiving Kenyan shillings as change from a shopkeeper over a counter. The shop (duka) should have familiar Kenyan products like bread and sugar on the shelves behind.

3. Multiplication (Kuzidisha - To Multiply)

Multiplication is like a shortcut for repeated addition. A matatu on the Nairobi-Nakuru route makes 4 trips a day. If it carries 14 passengers on each trip, how many passengers does it carry in total in one day?

   14   (Passengers per trip)
x   4   (Number of trips)
----
   56   (Total passengers)

Let's try a bigger one!
If a school has 18 classrooms and each classroom needs 35 desks, how many desks does the school need in total?

    35
x   18
------
   280  (This is 35 x 8)
+  350  (This is 35 x 10, notice the placeholder 0)
------
   630

The school needs a total of 630 desks.

4. Division (Kugawa - To Divide)

Division is all about sharing equally. A community group receives a donation of 5,480 books to be shared equally among 8 local primary schools. How many books will each school receive?

      685
    _______
8 | 5480
    -48     (6 x 8 = 48)
    ---
      68    (Bring down the 8)
     -64    (8 x 8 = 64)
     ---
       40   (Bring down the 0)
      -40   (5 x 8 = 40)
      ---
        0   (No remainder)

Each school will receive exactly 685 books. That's fantastic!

You are a Whole Number Champion!

Congratulations! You have journeyed through the world of whole numbers. From understanding what they are and the power of place value, to performing all four major operations using real-life Kenyan examples. Remember, mathematics is everywhere around you - in the market, on the road, and at home.

Keep practicing, stay curious, and you will find that numbers are not just for class, they are your tools to understand and build the world. Hongera sana!