Mathematical Explorers: Building Foundations · 2nd Class

Active learning ideas

Tens and Units , Building Numbers

Active learning works because place value is abstract until students physically group tens and count ones. Hands-on building makes the difference between 30 and 3 visible, turning confusion into clarity. Quick, repeated practice with manipulatives builds confidence before moving to symbols.

• 20–45 min
• Pairs → Whole Class
• 4 activities

Activity 01

• Experiential Learning
• 30 min · Small Groups

Manipulatives: Build the Number

Give each small group tens rods and unit cubes. Call out numbers like 28 or 53; students build them, record the standard form, and write the expanded form. Have groups swap builds to check accuracy.

What are the tens and units in a two-digit number?

Facilitation Tip

During Manipulatives: Build the Number, circulate with a question card that asks students to verbalize the value of each rod and cube before recording their number.

What to look for

Show students a number on the board, such as 63. Ask them to write down the tens digit and the units digit on a mini-whiteboard. Then, ask them to write the number in expanded form (60 + 3).

• Apply
• Analyze
• Evaluate
• Self-Awareness
• Self-Management
• Social Awareness

Activity 02

• Experiential Learning
• 20 min · Pairs

Pairs: Standard to Expanded Match

Prepare cards with standard numbers on one set and expanded forms on another. Pairs match them, such as 37 with 30 + 7, then build matches with manipulatives to verify. Discuss any mismatches as a class.

How can you build a number using tens rods and unit cubes?

Facilitation Tip

In Pairs: Standard to Expanded Match, provide one set of cards per pair and ask students to take turns explaining how the expanded form matches the standard form they built.

What to look for

Give each student a card with a number written on it (e.g., 81). Ask them to draw the number using tens rods and unit cubes, and then write the number in expanded form on the back of the card.

• Apply
• Analyze
• Evaluate
• Self-Awareness
• Self-Management
• Social Awareness

Activity 03

• Experiential Learning
• 35 min · Whole Class

Whole Class: Place Value Line-Up

Students hold number cards and line up to form a class number line from 10 to 99. Call changes like 'add 20' by inserting tens rods; everyone adjusts position and states the new number in expanded form.

Can you swap between the expanded form (e.g., 30 + 7) and the standard form (37) of a number?

Facilitation Tip

For Place Value Line-Up, have students hold digit cards and physically arrange themselves in order from least to greatest, reading the numbers aloud as they go.

What to look for

Present students with two numbers, for example, 45 and 54. Ask: 'What is the same about these numbers? What is different? How does the place of the digit 4 or 5 change its value?'

• Apply
• Analyze
• Evaluate
• Self-Awareness
• Self-Management
• Social Awareness

Activity 04

• Stations Rotation
• 45 min · Small Groups

Stations Rotation: Tens and Units Challenges

Set up three stations: build with blocks, draw expanded forms on mats, sort digit cards into tens/units columns. Groups rotate every 10 minutes, recording one fact per station.

What are the tens and units in a two-digit number?

Facilitation Tip

At Tens and Units Challenges stations, place answer keys in envelopes so early finishers can self-check their work before moving to the next challenge.

What to look for

Show students a number on the board, such as 63. Ask them to write down the tens digit and the units digit on a mini-whiteboard. Then, ask them to write the number in expanded form (60 + 3).

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

A few notes on teaching this unit

Experienced teachers introduce manipulatives immediately after a brief counting warm-up. Avoid rushing to symbols; let students describe their builds in their own words first. Research shows that students who verbalize while handling materials internalize place value more deeply. Always model the language you want students to use, such as ‘forty is four tens’ and ‘five is five ones’ during whole-class builds.

Students will confidently partition two-digit numbers into tens and units, switch between standard and expanded forms, and justify their choices using rods and cubes. Success looks like students explaining why 78 is 70 + 8 without hesitation and catching each other’s errors during partner work.

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Watch Out for These Misconceptions

• During Manipulatives: Build the Number, watch for students who count each cube individually as ones and ignore the value of the tens rod.

  Prompt students to trade ten unit cubes for one tens rod before counting again, then ask them to recount aloud, emphasizing the word ‘twenty’ instead of ‘two tens’ to reinforce the single group value.

• During Pairs: Standard to Expanded Match, watch for students who treat 30 + 4 and 34 as different values because the symbols look different.

  Ask partners to build both representations with rods and cubes, then compare the visual builds side by side while explaining how the total stays the same even though the written form changes.

• During Tens and Units Challenges, watch for students who reverse the order of tens and units when writing expanded form, such as writing 6 + 50 for 65.

  Have students read their expanded forms aloud while pointing to the corresponding rods and cubes, which helps them notice the mismatch and correct the order before recording.

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Methods used in this brief

• Experiential Learning
• Stations Rotation