UK K12 GCSE/A-Level: Year 4 KS2 Mathematics - Place Value, Numbers to 10000

Learning Objectives

By the end of this topic, students will be able to:

• Understand the concept of place value and its importance in representing numbers
• Identify and write numbers up to 10,000 using the correct place value notation
• Compare and order numbers up to 10,000
• Solve problems involving numbers up to 10,000, including addition and subtraction
• Explain the relationship between numbers and their place value

Core Concepts

Place value is a way of representing numbers using groups of digits, each with a specific value. The value of a digit depends on its position in the number. In the UK, we use the base-10 number system, which means that each digit has a value of 10 times the value of the digit to its right.

Understanding Place Value

Imagine a box of 10 boxes, each containing 10 pencils. If we have 100 pencils, we can represent this using the digit 100. The '1' represents 1 group of 100 pencils, the '0' represents 10 groups of 10 pencils, and the '0' represents 100 groups of 1 pencil.

Place Value Notation

To write numbers up to 10,000, we use the following place value notation:

• Thousands (10,000)
• Hundreds (1,000)
• Tens (100)
• Units (1)

For example, the number 4,567 can be written as:

• 4 thousands
• 5 hundreds
• 6 tens
• 7 units

Comparing and Ordering Numbers

To compare and order numbers up to 10,000, we need to compare the digits in each place value position. If the digits in the thousands place are the same, we compare the hundreds place, and so on.

Worked Examples

Example 1

Write the number 3,421 in place value notation.

To solve this problem, we need to break down the number into its place value components:

• 3 thousands
• 4 hundreds
• 2 tens
• 1 unit

So, the number 3,421 can be written as:

3 thousands 4 hundreds 2 tens 1 unit

Example 2

Compare the numbers 4,567 and 3,421.

To compare these numbers, we need to compare the digits in each place value position. Starting with the thousands place, we see that both numbers have 4 in the thousands place. Moving to the hundreds place, we see that 4,567 has 5 in the hundreds place, while 3,421 has 4 in the hundreds place. Therefore, 4,567 is greater than 3,421.

Common Misconceptions

• Students may confuse the place value notation with the actual value of the number. For example, they may think that the number 4,567 is equal to 4,000 + 500 + 60 + 7, rather than 4,000 + 500 + 60 + 7 = 4,567.
• Students may have difficulty comparing and ordering numbers, especially when the digits in the thousands place are the same.

Exam Tips

• Make sure to read the question carefully and understand what is being asked.
• Use the place value notation to represent numbers and solve problems.
• Compare and order numbers by comparing the digits in each place value position.
• Check your answers by using the place value notation to represent the numbers.

MCQs

MCQ 1 [F]

What is the place value of the digit 5 in the number 4,567?

A) Thousands B) Hundreds C) Tens D) Units

Answer: B) Hundreds Why the distractors fail: The distractors fail because they do not accurately represent the place value of the digit 5. Option A is incorrect because the digit 5 is not in the thousands place. Option C is incorrect because the digit 5 is not in the tens place. Option D is incorrect because the digit 5 is not in the units place.

MCQ 2 [H]

Compare the numbers 9,321 and 8,421.

A) 9,321 is greater than 8,421 B) 9,321 is less than 8,421 C) 9,321 is equal to 8,421 D) The numbers are not comparable

Answer: A) 9,321 is greater than 8,421 Why the distractors fail: The distractors fail because they do not accurately compare the numbers. Option B is incorrect because 9,321 is greater than 8,421. Option C is incorrect because 9,321 is not equal to 8,421. Option D is incorrect because the numbers are comparable.

MCQ 3 [F]

Write the number 2,100 in place value notation.

A) 2 thousands B) 1 thousand C) 2 tens D) 1 unit

Answer: A) 2 thousands Why the distractors fail: The distractors fail because they do not accurately represent the place value notation. Option B is incorrect because the number 2,100 is not equal to 1 thousand. Option C is incorrect because the number 2,100 is not equal to 2 tens. Option D is incorrect because the number 2,100 is not equal to 1 unit.

MCQ 4 [H]

Compare the numbers 5,432 and 4,321.

A) 5,432 is greater than 4,321 B) 5,432 is less than 4,321 C) 5,432 is equal to 4,321 D) The numbers are not comparable

Answer: A) 5,432 is greater than 4,321 Why the distractors fail: The distractors fail because they do not accurately compare the numbers. Option B is incorrect because 5,432 is greater than 4,321. Option C is incorrect because 5,432 is not equal to 4,321. Option D is incorrect because the numbers are comparable.

MCQ 5 [F]

What is the place value of the digit 1 in the number 3,421?

A) Thousands B) Hundreds C) Tens D) Units

Answer: C) Tens Why the distractors fail: The distractors fail because they do not accurately represent the place value of the digit 1. Option A is incorrect because the digit 1 is not in the thousands place. Option B is incorrect because the digit 1 is not in the hundreds place. Option D is incorrect because the digit 1 is not in the units place.

Short-answer Questions

Question 1

Write the number 6,543 in place value notation.

Question 2

Compare the numbers 7,654 and 6,543.

Question 3

Write the number 9,210 in place value notation.

Question 4

Compare the numbers 8,421 and 7,654.

Question 5

Write the number 4,567 in place value notation.

Note: Students should show their working and provide a clear explanation for their answers.