Understanding Hundreds, Tens, and Units

Active learning works because place value is a spatial concept. Students need to see, touch, and move numbers to understand that digits represent quantities in specific positions. When students manipulate physical materials and talk through their reasoning, they build mental models that prevent common errors like misplacing zeros or ignoring the value of tens.

• 2nd Year
• Foundations of Mathematical Thinking
• 3 activities
• 15 min–40 min

Learning Objectives

1. Represent numbers up to 200 using concrete materials like base-ten blocks, demonstrating an understanding of place value.
2. 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.
3. Explain the value of each digit in a number up to 200 based on its position.
4. 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.

Stations Rotation

⏱ 40 min·Small Groups

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.

Prepare & details

What is the value of the digit 1 in the number 15?

Facilitation Tip: During The Renaming Challenge, circulate and ask each group to explain their renaming using the place value mat and blocks, focusing on the language of 'hundreds, tens, and units'.

Setup: Tables/desks arranged in 4-6 distinct stations around room

Materials: Station instruction cards, Different materials per station, Rotation timer

• Remember
• Understand
• Apply
• Analyze
• Self-Management
• Relationship Skills

Inquiry Circle

⏱ 20 min·Pairs

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.

Prepare & details

Can you show the number 124 using hundreds, tens, and units?

Facilitation Tip: During The Zero Mystery, encourage students to explain why a zero is necessary in numbers like 105 by physically covering the hundred block and asking what remains.

Setup: Groups at tables with access to source materials

Materials: Source material collection, Inquiry cycle worksheet, Question generation protocol, Findings presentation template

• Analyze
• Evaluate
• Create
• Self-Management
• Self-Awareness

Peer Teaching

⏱ 15 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.

Prepare & details

How does knowing place value help you read bigger numbers?

Facilitation Tip: During Place Value Architects, listen for students to use precise vocabulary like 'regroup' or 'compose' when explaining their building to peers.

Setup: Presentation area at front, or multiple teaching stations

Materials: Topic assignment cards, Lesson planning template, Peer feedback form, Visual aid supplies

• Understand
• Apply
• Analyze
• Create
• Self-Management
• Relationship Skills

Teaching This Topic

Teach place value by starting with quantities students can visualize, like bundles of sticks or stacks of blocks, before moving to symbols. Avoid rushing to abstract notation, as students need time to internalize that the position of a digit changes its value. Research shows that students benefit from frequent opportunities to compose and decompose numbers in multiple ways, which strengthens their mental flexibility with place value.

What to Expect

Successful learning looks like students confidently explaining that 148 means 1 hundred, 4 tens, and 8 units, and that 148 is not the same as 148 units. They should use proper vocabulary, regroup quantities smoothly, and justify their answers with concrete materials or drawings. Students should also recognize when a number can be expressed differently, such as 100 units as 10 tens or 1 hundred.

Watch Out for These Misconceptions

Common Misconception

During The Renaming Challenge, watch for students writing 105 as 1005 because they hear 'one hundred five' but write what they hear without considering place value columns.

What to Teach Instead

Have students place the hundred block in the 'H' column of the place value mat first, then add five units in the 'U' column, and ask them to count the total aloud to see why 105 cannot be 1005.

Common Misconception

During The Zero Mystery, watch for students believing that 12 tens is the same as 12 units because they focus on the digits rather than the unit of measure.

What to Teach Instead

Use bundles of ten lollipop sticks to show that 12 bundles is much larger than 12 single sticks, then have students count the total in both representations to see the difference in quantity.

Assessment Ideas

Quick Check

After The Renaming Challenge, 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

After The Zero Mystery, 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

During Place Value Architects, 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.

Extensions & Scaffolding

• Challenge: Provide a number like 175 and ask students to find all the ways to represent it using only hundreds, tens, and units (e.g., 1 hundred 7 tens 5 units, 17 tens 5 units, 1 hundred 6 tens 15 units).
• Scaffolding: For students struggling with The Renaming Challenge, provide pre-made place value mats with columns labeled 'H', 'T', and 'U' and restrict numbers to multiples of 10 or 100.
• Deeper exploration: Ask students to research and present on how place value is used in other cultures, such as the Mayan vigesimal system, and compare it to the base-ten system.

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.