UK K12 GCSE/A-Level: Year 1 KS1 Mathematics - Number, Counting to 100 Place Value

Learning Objectives

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

• Count and write numbers up to 100 in numerals and words
• Understand the concept of place value, including hundreds, tens, and ones
• Recognize and write numbers in expanded form (e.g., 456 = 400 + 50 + 6)
• Compare and order numbers up to 100 using place value
• Use number lines and hundreds charts to support counting and place value understanding

Core Concepts

Counting to 100

Counting is the process of listing numbers in order. We can count objects, numbers, or even the days of the week. To count to 100, we start with 0 and add 1 each time. For example, 0, 1, 2, 3, and so on. We can also use number lines to help us count. A number line is a line with numbers marked on it, like a ruler. We can start at 0 and move our finger along the line, counting each number as we go.

Place Value

Place value is the value of a digit in a number based on its position. The position of a digit tells us how much it is worth. In the number 456, the 4 is in the hundreds place, the 5 is in the tens place, and the 6 is in the ones place. We can write numbers in expanded form to show their place value. For example, 456 = 400 + 50 + 6.

Expanded Form

Expanded form is a way of writing numbers by breaking them down into their place value parts. For example, 456 = 400 + 50 + 6. This shows that the 4 is in the hundreds place, the 5 is in the tens place, and the 6 is in the ones place.

Worked Examples

Example 1: Counting to 100

Sarah has 5 groups of 20 pencils. How many pencils does Sarah have in total?

Let's use counting to find the answer. We can start with 0 and add 20 each time, until we reach 100. 0, 20, 40, 60, 80, 100. Sarah has 100 pencils.

Example 2: Place Value

What is the value of the digit 5 in the number 456?

To find the value of the digit 5, we need to look at its position. The 5 is in the tens place, so it is worth 50.

Example 3: Expanded Form

Write the number 456 in expanded form.

We can write the number 456 in expanded form by breaking it down into its place value parts. 456 = 400 + 50 + 6.

Common Misconceptions

• Students may confuse the concept of place value with the concept of position value. Position value refers to the value of a digit based on its position in a number, whereas place value refers to the value of a digit based on its position in a number and its relationship to other digits.
• Students may struggle to understand that the value of a digit can change depending on its position in a number.
• Students may have difficulty recognizing and writing numbers in expanded form.

Exam Tips

• Make sure to read the question carefully and understand what is being asked.
• Use number lines and hundreds charts to support counting and place value understanding.
• Break down numbers into their place value parts to make them easier to understand.
• Use expanded form to show the place value of a number.

MCQs

MCQ 1: [F]

What is the value of the digit 4 in the number 456?

A) 40 B) 400 C) 4 D) 0

Correct answer: B) 400 Why the distractors fail: A) 40 is the value of the digit 4 in the number 40, not 456. C) 4 is the value of the digit 4 in the number 4, not 456. D) 0 is not the value of any digit in the number 456.

MCQ 2: [H]

Write the number 456 in expanded form.

A) 400 + 50 + 6 B) 400 + 60 + 5 C) 450 + 6 D) 460 + 5

Correct answer: A) 400 + 50 + 6 Why the distractors fail: B) The digit 6 is in the ones place, not the tens place. C) The digit 5 is in the tens place, not the hundreds place. D) The digit 6 is in the ones place, not the tens place.

MCQ 3: [F]

What is the value of the digit 5 in the number 456?

A) 50 B) 500 C) 5 D) 0

Correct answer: A) 50 Why the distractors fail: B) The digit 5 is in the tens place, not the hundreds place. C) The digit 5 is in the tens place, not the ones place. D) The digit 5 is in the tens place, not the hundreds place.

MCQ 4: [H]

What is the value of the digit 4 in the number 456?

A) 40 B) 400 C) 4 D) 0

Correct answer: B) 400 Why the distractors fail: A) 40 is the value of the digit 4 in the number 40, not 456. C) 4 is the value of the digit 4 in the number 4, not 456. D) 0 is not the value of any digit in the number 456.

MCQ 5: [F]

Write the number 456 in words.

A) Four hundred and fifty-six B) Four hundred and fifty C) Four hundred and six D) Four hundred and fifty-nine

Correct answer: A) Four hundred and fifty-six Why the distractors fail: B) The number is 456, not 450. C) The number is 456, not 406. D) The number is 456, not 459.

Short-answer Questions

Question 1

Explain the concept of place value.

Question 2

Write the number 456 in expanded form.

Question 3

Compare and order the numbers 456, 457, and 458.

Question 4

Use a number line to count from 0 to 100.

Question 5

Write the number 456 in words.