11-Plus Mathematics: Number and Place Value

Understanding Number and Place Value

The topic of Number and Place Value is fundamental in the 11-plus Mathematics curriculum. It encompasses reading, writing, and ordering numbers up to millions, as well as understanding the place value of digits in both whole numbers and decimals.

Reading and Writing Numbers

Students should be able to read and write numbers accurately, including large numbers in the millions. This skill is essential for performing calculations and understanding numerical data.

Understanding Place Value

Place value refers to the value of a digit depending on its position in a number. For example, in the number 5,432, the digit 5 is in the thousands place, which means it represents 5,000. Understanding place value helps students grasp the significance of each digit in a number.

Ordering Numbers

Students learn to compare and order numbers, which is crucial for understanding their relative sizes. This includes both positive and negative numbers. For instance, when comparing -3 and 2, students should recognize that -3 is less than 2.

Rounding Numbers

Rounding is another important skill. Students should be able to round numbers to the nearest 10, 100, or 1,000. For example, when rounding 267 to the nearest hundred, it becomes 300. This skill is useful in estimating calculations and understanding the size of numbers.

Working with Negative Numbers

Understanding negative numbers is essential in various mathematical contexts. Students should be able to compare and order negative numbers on a number line, recognizing that numbers further to the left are smaller. For example, -5 is less than -2.

Using Number Lines

Number lines are a valuable tool for visualizing the relationships between numbers, including whole numbers and decimals. Students can use number lines to help with ordering, rounding, and understanding the position of negative numbers.

Worked Example

Problem: Round the number 4,678 to the nearest hundred.

Solution:

• Identify the hundreds place, which is 6 in this case.
• Look at the digit to the right (the tens place), which is 7.
• Since 7 is 5 or greater, round up the hundreds place from 6 to 7.
• The rounded number is 4,700.

By mastering these concepts, students will build a strong foundation in mathematics, which is essential for success in the 11-plus examinations.