Foundations of Mathematical Thinking · 2nd Year · The Power of Place Value · Autumn Term

Understanding Hundreds, Tens, and Units

Students use concrete materials to represent and rename numbers within 200, focusing on the value of each digit.

• NCCA Curriculum Specifications
• NCCA: Primary - Number
• NCCA: Primary - Understanding and recalling facts

About This Topic

This topic focuses on the foundational structure of our base-ten number system, specifically looking at numbers up to 200. In the NCCA Primary Mathematics Curriculum, developing a deep sense of place value is essential for mental computation and future work with larger numbers. Students move beyond rote counting to understand that the position of a digit determines its value. They learn to compose and decompose numbers, recognizing that 124 is not just a sequence of digits but a collection of one hundred, two tens, and four units.

By exploring renaming, students discover that 124 can also be represented as 12 tens and 4 units or 11 tens and 14 units. This flexibility is a prerequisite for understanding regrouping in addition and subtraction. This topic comes alive when students can physically model the patterns using base-ten blocks, lollipop sticks, or money.

Key Questions

1. What is the value of the digit 1 in the number 15?
2. Can you show the number 124 using hundreds, tens, and units?
3. How does knowing place value help you read bigger numbers?

Learning Objectives

• Represent numbers up to 200 using concrete materials like base-ten blocks, demonstrating an understanding of place value.
• Rename numbers within 200 in multiple ways, for example, showing 124 as 1 hundred, 2 tens, and 4 units, or as 12 tens and 4 units.
• Explain the value of each digit in a number up to 200 based on its position.
• Compare the value of digits in different positions within a number up to 200, such as identifying the value of the digit 1 in 15 versus 105.

Before You Start

Counting and Cardinality to 100

Why: Students need a solid foundation in counting and understanding quantities up to 100 before extending this to numbers within 200.

Introduction to Place Value (Tens and Units)

Why: Prior experience with identifying tens and units in numbers up to 100 is essential for understanding hundreds.

Key Vocabulary

Hundreds	Represents a quantity of 100. In a three-digit number, the digit in the leftmost position signifies the number of hundreds.
Tens	Represents a quantity of 10. The digit in the middle position of a three-digit number indicates the number of tens.
Units	Represents a quantity of 1. Also known as ones, this is the digit in the rightmost position of a number.
Place Value	The value of a digit determined by its position within a number. For example, in 150, the '1' has a value of one hundred, the '5' has a value of fifty, and the '0' has a value of zero.
Rename	To express a number in a different form using place value. For example, 1 hundred and 2 tens can be renamed as 12 tens.

Watch Out for These Misconceptions

Common Misconception

Students may read 105 as 'fifteen' or 'one hundred five' but write it as 1005.

What to Teach Instead

This happens when students write exactly what they hear without considering place value columns. Use a three-column place value mat and physical blocks to show that the hundred belongs in a single column, preventing the 'extra' zeros from appearing.

Common Misconception

Believing that 12 tens is the same as 12 units.

What to Teach Instead

Students often focus on the digits rather than the unit of measure. Use bundles of ten lollipop sticks to show that 12 bundles is a much larger quantity than 12 single sticks, helping them visualize the magnitude of the tens column.

Active Learning Ideas

Stations Rotation: The Renaming Challenge

Set up three stations where students must represent the same number (e.g., 142) in different ways. At station one, they use hundreds, tens, and units; at station two, they use only tens and units; at station three, they use a 'bank' of coins to show the value.

40 min·Small Groups

Inquiry Circle: The Zero Mystery

Give pairs a set of number cards (0-9) and a place value mat. Ask them to create the largest and smallest numbers possible using three cards, then discuss what happens to the value when the 0 moves from the units to the tens place.

20 min·Pairs

Peer Teaching: Place Value Architects

One student acts as the 'Architect' and describes a secret number using place value clues (e.g., 'My number has 14 tens and 3 units'). The 'Builder' must use concrete materials to construct the number and name it correctly.

15 min·Pairs

Real-World Connections

• Bank tellers count money, needing to quickly identify the value of bills and coins (units, tens, hundreds) to make accurate transactions and provide correct change.
• Librarians organize books by Dewey Decimal Classification, which uses a hierarchical system based on hundreds, tens, and units to categorize and locate specific subjects.
• Construction workers use measurements that often involve hundreds, tens, and units when calculating materials needed for building projects, such as lengths of wood or quantities of bricks.

Assessment Ideas

Quick Check

Present students with base-ten blocks representing a number up to 200. Ask: 'How many hundreds, tens, and units do you see?' Then, ask them to write the number on a whiteboard. Follow up with: 'Can you show me this number using only tens and units?'

Exit Ticket

Give each student a card with a number (e.g., 135). Ask them to: 1. Write the number showing its hundreds, tens, and units. 2. Write the number showing only tens and units. 3. Explain in one sentence why the digit '3' in 135 has a different value than the digit '3' in 35.

Discussion Prompt

Pose the question: 'Imagine you have 15 tens. How many hundreds and tens do you have?' Facilitate a class discussion where students use concrete materials or drawings to explain their reasoning, focusing on the process of regrouping tens into hundreds.

Frequently Asked Questions

Why is renaming numbers emphasized so much in 2nd Year?

Renaming is the secret to successful addition and subtraction with regrouping. If a child understands that 1 ten can be swapped for 10 units, they will find 'borrowing' much more intuitive later on. It builds the flexibility needed for mental math.

How can active learning help students understand place value?

Active learning allows students to physically manipulate the numbers. Instead of just looking at a worksheet, they are grouping, swapping, and building. Using materials like Dienes blocks or ten-frames in a collaborative setting forces students to verbalize their reasoning, which clarifies their internal understanding of how digits shift in value.

What is the best way to explain the role of zero as a placeholder?

Think of zero as a 'space keeper.' Use a place value pocket chart. If we have 1 hundred and 5 units, we must show that the 'tens' room is empty so the 'hundred' stays in its correct spot. Without the zero, the 1 would slide into the tens place and become 15.

Should I use money to teach place value at this stage?

Yes, Euro coins are excellent. A €1 coin, 10c coins, and 1c coins perfectly mirror the hundreds, tens, and units system. It provides a real-world context that Irish students encounter daily, making the abstract concept of place value more concrete.