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.

• 2nd Class
• Mathematical Explorers: Building Foundations
• 4 activities
• 20 min–45 min

Learning Objectives

1. Identify the tens and units digits in numbers up to 199.
2. Construct numbers by combining tens rods and unit cubes, and represent them in expanded form.
3. Convert numbers between standard form (e.g., 57) and expanded form (e.g., 50 + 7).
4. Explain the value of each digit in a two-digit number based on its position.

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.

Prepare & details

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.

Setup: Varies; may include outdoor space, lab, or community setting

Materials: Experience setup materials, Reflection journal with prompts, Observation worksheet, Connection-to-content framework

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

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.

Prepare & details

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.

Setup: Varies; may include outdoor space, lab, or community setting

Materials: Experience setup materials, Reflection journal with prompts, Observation worksheet, Connection-to-content framework

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

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.

Prepare & details

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.

Setup: Varies; may include outdoor space, lab, or community setting

Materials: Experience setup materials, Reflection journal with prompts, Observation worksheet, Connection-to-content framework

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

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.

Prepare & details

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.

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

Teaching This Topic

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.

What to Expect

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.

Watch Out for These Misconceptions

Common Misconception

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

What to Teach Instead

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.

Common Misconception

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

What to Teach Instead

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.

Common Misconception

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.

What to Teach Instead

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.

Assessment Ideas

Quick Check

After Manipulatives: Build the Number, 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 write the number in expanded form (60 + 3).

Exit Ticket

During Pairs: Standard to Expanded Match, 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 on one side of the card, and then write the number in expanded form on the back before turning it in.

Discussion Prompt

After Place Value Line-Up, 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?' Have students turn and talk, then share their reasoning with the class.

Extensions & Scaffolding

• Challenge: Ask students to create the largest and smallest possible numbers using three digit cards, then write both in expanded form.

Key Vocabulary

Tens	Groups of ten. In a two-digit number, the tens digit tells us how many groups of ten there are.
Units	Singles or ones. In a two-digit number, the units digit tells us how many ones are left over after making groups of ten.
Place Value	The value of a digit based on its position in a number. For example, in 37, the 3 has a value of 30 because it is in the tens place.
Expanded Form	Writing a number as the sum of the value of its digits. For example, 42 in expanded form is 40 + 2.