Foundations of Mathematical Thinking · 2nd Year

Active learning ideas

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.

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

• 15–40 min
• Pairs → Whole Class
• 3 activities

Activity 01

• 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.

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'.

What to look for

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?'

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

Activity 02

• 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.

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.

What to look for

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.

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

Activity 03

• 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.

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.

What to look for

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.

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

A few notes on teaching this unit

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.

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.

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Watch Out for These Misconceptions

• 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.

  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.

• 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.

  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.

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Methods used in this brief

• Stations Rotation
• Inquiry Circle
• Peer Teaching