Welcome to Year 4 Number and Place Value!

In this chapter, we are going to become number experts! Numbers are all around us, from the score in a football match to the price of a chocolate bar. We are going to learn how to handle much bigger numbers (up to 4 digits!), how to round them to make them easier to work with, and even how to count backwards past zero. Don't worry if some of this feels big at first—we will take it one step at a time!

1. Understanding 4-Digit Numbers

So far, you’ve worked with hundreds, tens, and ones. In Year 4, we introduce a new "room" in our place value house: the Thousands column.

Every digit in a number has a "value" depending on where it sits. Let’s look at the number 4,321:

  • The 4 is in the Thousands place, so it is worth \(4,000\).
  • The 3 is in the Hundreds place, so it is worth \(300\).
  • The 2 is in the Tens place, so it is worth \(20\).
  • The 1 is in the Ones place, so it is worth \(1\).

If we add them all together: \(4,000 + 300 + 20 + 1 = 4,321\). This is called partitioning!

Quick Review:

Question: In the number 7,852, what is the 8 worth?
Answer: It is in the hundreds column, so it is worth 800.

Key Takeaway: The position of a digit tells you how much it is worth. As you move to the left, the value gets 10 times bigger!

2. Counting in Steps

In Year 4, we practice counting in specific "jumps." This helps with our times tables and spotting patterns.

You need to be able to count in steps of 6, 7, 9, 25, and 1,000.

  • Counting in 1,000s: This is the easiest one! Only the thousands digit changes: 1,000, 2,000, 3,000, 4,000...
  • Counting in 25s: Think of this like quarters of a hundred. The pattern always goes: 0, 25, 50, 75, 100, 125, 150, 175, 200...
  • Counting in 6s, 7s, and 9s: These can be tricky. Try using your fingers or a number line to help you until you feel confident.
Did you know?

If you are counting in 9s, the digits of each number often add up to 9 or a multiple of 9! For example: \(1 + 8 = 9\), \(2 + 7 = 9\), and \(3 + 6 = 9\).

3. Comparing and Ordering Numbers

When we compare numbers, we want to see which one is bigger or smaller. We use these symbols to help us:

  • > means Greater Than (Bigger)
  • < means Less Than (Smaller)
  • = means Equal To (The same)

The Hungry Alligator Trick: Imagine the symbol is an alligator’s mouth. The alligator is very hungry, so it always wants to eat the biggest number!
Example: \(4,500 > 2,100\) (The mouth opens toward 4,500).

How to compare big numbers:

1. Always look at the Thousands column first. The number with more thousands is bigger.
2. If the thousands are the same, look at the Hundreds column.
3. If those are the same, look at the Tens, and finally the Ones.

Key Takeaway: Start comparing from the left side (the biggest value) and move right until you find a difference.

4. Rounding Numbers

Rounding is like giving a number a "rough estimate." It makes numbers easier to use in our heads. In Year 4, we round to the nearest 10, 100, or 1,000.

The Golden Rule of Rounding:

Look at the digit to the right of the one you are rounding to:

  • If it is 5 or more, we Round Up (The number grows).
  • If it is 4 or less, we Round Down (The number stays the same, and the rest become zeros).

Example: Round 436 to the nearest 100.
1. We are rounding to the hundreds, so look at the 4.
2. Look at the neighbor to the right: it’s a 3.
3. 3 is "4 or less," so we Round Down.
4. 436 rounded to the nearest 100 is 400.

Common Mistake:

When people hear "round down," they sometimes think the number should get smaller (like 4 becoming 3). It actually means the digit stays the same and everything after it becomes a zero!

5. Negative Numbers

Negative numbers are numbers less than zero. Think of them like being underground in a lift or a very cold temperature.

When we count backwards from zero, we use a minus sign (-):

\(3, 2, 1, 0, -1, -2, -3...\)

Analogy: The Thermometer

Imagine a thermometer. As it gets colder, the red line drops. When it goes below 0, we start using "minus" degrees. -5 is colder than -1 because it is further away from the warmth of the sun (the positive numbers).

Key Takeaway: The "bigger" a negative number looks (like -10), the smaller its actual value is because it is further below zero!

6. Roman Numerals

Long ago, the Romans used letters instead of numbers. You might see these on old clocks or at the end of movie credits. In Year 4, we learn the symbols for numbers up to 100 (C).

  • I = 1
  • V = 5
  • X = 10
  • L = 50
  • C = 100
A Simple Trick:

To remember the order, use this sentence: I Value Xylophones Like Candy!

How to read them:
- If a smaller letter is after a bigger one, add them: \(VI = 5 + 1 = 6\).
- If a smaller letter is before a bigger one, subtract it: \(IV = 5 - 1 = 4\).

Quick Review:

Question: What is LXV in our numbers?
Answer: L (50) + X (10) + V (5) = 65.

Key Takeaway: Roman Numerals don't have a zero! They just combine these 5 letters in different ways to make all their numbers.

Final Summary Checklist

Check off these skills as you master them!

  • [ ] I can name the value of any digit in a 4-digit number.
  • [ ] I can count in 6s, 7s, 9s, 25s, and 1,000s.
  • [ ] I can use < and > symbols to compare numbers.
  • [ ] I can round numbers to the nearest 10, 100, or 1,000.
  • [ ] I can count backwards past zero into negative numbers.
  • [ ] I can read Roman Numerals up to 100 (C).

Great job! Number and Place Value is the foundation for all of maths. Keep practicing, and soon these big numbers will feel small!