Number and Place Value

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Overview

In Year 6 Maths, you are about to embark on an exciting journey exploring the fascinating world of numbers and place value. This topic is crucial as it forms the foundation for more advanced mathematical concepts you’ll encounter in the coming years. Understanding numbers and their place value unlocks the door to solving complex problems and lays the groundwork for your mathematical prowess. So, let’s dive in and discover the magic of numbers together!

Learning Outcomes

By the end of this article, you will:

• Master the concept of expanded notations using place values.
• Learn how to round numbers to the nearest hundred, thousand, ten thousand, and so on.
• Be able to add and subtract numbers with positive and negative outcomes.
• Differentiate between prime and composite numbers.
• Understand the Highest Common Factor (HCF).
• Grasp the concept of the Lowest Common Multiple (LCM).

Expanded Notation

Let’s start by exploring expanded notation, a powerful tool that helps us understand how numbers are built from their place values. Take the number 7,189,624, for example. Breaking it down using place values, we can write it as:

(7 x 1,000,000) + (1 x 100,000) + (8 x 10,000) + (9 x 1,000) + (6 x 100) + (2 x 10) + (4 x 1)

Isn’t it amazing how each digit’s place value contributes to the overall value of the number? This method allows us to comprehend numbers on a deeper level and perform operations more efficiently.

Rounding

Rounding numbers is a handy technique when you want to approximate values quickly. Let’s consider the number 16,487. To round it to the nearest hundred, we focus on the tens place. Since the digit in the tens place, 8, is greater than or equal to 5, we round the number up to 16,500.

Now, let’s round it to the nearest thousand. Looking at the hundreds place, which is 4, we keep the thousands place intact and round down to 16,000.

Lastly, rounding to the nearest ten thousand, we examine the thousands place, which is 6. As it is greater than or equal to 5, we round up to 20,000.

Question: Can you try rounding the number 34,925 to the nearest hundred, thousand, and ten thousand? Take a moment to give it a shot.

Positive and Negative Numbers

Understanding positive and negative numbers is like having a compass to navigate through mathematical operations. Remember, 0 is right in the centre of the number line. The positives are to the right of it, and the negatives are to its left.

On a number line, adding a number means hopping to the right, while subtracting involves hopping to the left. Let’s explore a few examples:

-5 + 3 = -2

In this case, we start at -5 and hop three units to the right, landing at -2.

-1 – 8 = -9

Starting at -1, we hop eight units to the left, reaching -9.

3 – 7 = -4

Beginning at 3, we move seven units to the left, ending up at -4.