Mathematical Explorers: Building Foundations · 2nd Class

Active learning ideas

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.

• NCCA Curriculum Specifications
• NCCA: Junior Cycle - Number - N.1.3

• 20–35 min
• Pairs → Whole Class
• 4 activities

Activity 01

• 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.

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.

What to look for

Present students with the problem 56 + 27. Ask them to write down the sum of the units column, then show how they rename it and carry over the ten. Finally, have them calculate the total sum.

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

Activity 02

• 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.

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.

What to look for

Give each student a card with a two-digit addition problem requiring renaming, such as 38 + 45. Ask them to solve the problem and then write one sentence explaining why they needed to rename the units.

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

Activity 03

• 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.

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.

What to look for

Ask students: 'Imagine you are explaining to a friend how to add 47 and 38. What is the first step you would tell them to do, and why? What happens next?' Listen for explanations of adding units first and then renaming.

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

Activity 04

• 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.

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.

What to look for

Present students with the problem 56 + 27. Ask them to write down the sum of the units column, then show how they rename it and carry over the ten. Finally, have them calculate the total sum.

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

A few notes on teaching this unit

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.

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.

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Watch Out for These Misconceptions

• 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.

  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.

• 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.

  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.

• 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.

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

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Methods used in this brief

• Experiential Learning