Adding Two-Digit Numbers With Renaming

Active learning transforms abstract renaming into concrete understanding. When students physically manipulate base-10 materials or move through stations, they see why 15 units become one ten and five, making the algorithm meaningful. Movement and collaboration also reduce anxiety about carrying, a common barrier for learners transitioning from simple addition.

• 2nd Class
• Mathematical Explorers: Building Foundations
• 4 activities
• 20 min–35 min

Learning Objectives

1. Calculate the sum of two-digit numbers that require renaming, accurately carrying over tens.
2. Explain the process of renaming units as tens when the sum of the units column is 10 or more.
3. Identify the steps involved in adding two-digit numbers with renaming, including adding units and then tens.
4. Solve addition problems involving two-digit numbers with renaming, demonstrating understanding of place value.

Experiential Learning

⏱ 30 min·Pairs

Manipulative Match-Up: Base-10 Addition

Provide base-10 blocks, place value mats, and number cards like 47 + 38. Students build each number, add units, trade 10 ones for a ten rod if needed, then add tens. Record the final sum and explain the trade to a partner.

Prepare & details

What happens when the units digits add up to 10 or more?

Facilitation Tip: During Manipulative Match-Up, circulate to ensure pairs trade ten unit blocks for one ten rod only when the units total 10 or more.

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

⏱ 25 min·Small Groups

Relay Race: Renaming Sprints

Divide class into teams. Each student solves one two-digit addition with renaming on a whiteboard, passes to next teammate. First team to finish correctly wins. Review errors as a class.

Prepare & details

How do you carry a ten into the tens column when adding?

Facilitation Tip: For Relay Race: Renaming Sprints, place a visible timer and a ‘carry flag’ at each station so students physically move the flag when they rename a ten.

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·Small Groups

Story Problem Stations: Shopkeeper Adds

Set up stations with scenarios like adding prices: 28c + 47c. Students draw base-10 models, solve with renaming, and create their own problems. Rotate stations.

Prepare & details

Can you solve addition problems like 47 + 38 using renaming?

Facilitation Tip: In Story Problem Stations, provide play money with fixed denominations so students must trade ten 1c coins for a 10c coin before calculating totals.

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·Whole Class

Whole Class Challenge: Number Line Climb

Project problems on board. Students take turns adding jumps on a giant number line, showing renaming with counters. Class votes on correct steps.

Prepare & details

What happens when the units digits add up to 10 or more?

Facilitation Tip: Use the Number Line Climb to model renaming as ‘jumps’: one jump of 7 units to 54, then a 3-unit jump plus a 4-unit carry jump to land at 91.

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

Teaching This Topic

Experienced teachers begin with hands-on materials to build the concept of renaming before introducing symbols. They explicitly connect the physical trade of blocks to the written arrow notation (e.g., 15 → 5 with a small 1 above the tens column). Teachers avoid rushing to the abstract algorithm and instead ask students to narrate each step aloud. Research shows that verbalizing the process, especially naming the carried ten, strengthens memory and transfer to new problems.

What to Expect

Students will confidently add two-digit numbers requiring renaming by explaining each step aloud and justifying their carries. They will model the process with manipulatives, catch errors through peer checking, and articulate why the units column must be addressed first. Success looks like accurate totals paired with clear reasoning about place value.

Watch Out for These Misconceptions

Common Misconception

During Manipulative Match-Up, watch for students adding tens first and ignoring the units trade. Redirect by asking them to count the loose unit blocks and physically group ten into a ten rod before touching the tens column.

What to Teach Instead

Prompt them to explain how many units they have, how many rods they can make, and where the extra units remain before adding the tens.

Common Misconception

During Relay Race: Renaming Sprints, watch for students treating the carried ten as an extra addend rather than a renamed ten. Halt the race and have partners swap mats to verify that the carried rod replaces ten units in the units column.

What to Teach Instead

Ask each pair to count aloud the units left in the column after the trade and confirm the new tens total matches the written sum.

Common Misconception

During Story Problem Stations, watch for students skipping renaming when the units sum to 11 or more. Stop the station rotation and provide a self-check card with the correct total; ask students to trace the error using their play money to see the missing trade.

What to Teach Instead

Require them to recount the coins, trade ten for a note, and recalculate the total before moving to the next station.

Assessment Ideas

Quick Check

After Manipulative Match-Up, present 56 + 27. Ask students to write the units sum, draw the trade, and show the final total on their base-10 mats before moving to the next station.

Exit Ticket

After Relay Race: Renaming Sprints, give each student a card with 38 + 45. Ask them to solve it and write one sentence explaining why the units needed renaming, leaving the sentence starter ‘I had to rename because…’.

Discussion Prompt

During Number Line Climb, ask pairs to explain to another group how they modeled 47 + 38. Listen for mention of adding units first, trading ten units for one ten, and then adding the tens column plus the carried ten.

Extensions & Scaffolding

• Challenge early finishers to create their own two-digit addition problems with renaming and trade roles to become the ‘shopkeeper’ who checks another student’s work.
• Scaffolding: Provide a place-value mat with pre-labeled columns and sticky notes for students to physically move digits when renaming.
• Deeper exploration: Ask students to generate a three-digit problem that also requires renaming in the hundreds place and predict how the renaming rule extends to larger numbers.

Key Vocabulary

Renaming	Exchanging 10 units for 1 ten, or 10 tens for 1 hundred, to make addition easier. This is also called carrying.
Units Column	The column on the right side of a two-digit number, representing the ones place.
Tens Column	The column to the left of the units column, representing the tens place.
Carry Over	Writing the extra ten from the units column sum above the tens column to be added with the other tens.