Adding Two-Digit Numbers (With Regrouping)

Active learning helps students grasp regrouping because adding two-digit numbers is more than calculation. It requires visualizing how ten ones become a ten, which blocks and written records make concrete. When students manipulate materials and talk through steps, they connect the abstract rule to a physical action they can see and feel.

• 1st Grade
• Mathematics
• 3 activities
• 15 min–30 min

Learning Objectives

1. Calculate the sum of two two-digit numbers involving regrouping, accurately recording the result.
2. Explain the process of regrouping when adding two two-digit numbers, using base-ten block language.
3. Construct a visual representation using base-ten blocks to demonstrate the composition of 10 ones into 1 ten during addition.
4. Compare and contrast the steps for adding two-digit numbers with and without regrouping.
5. Critique a provided incorrect solution for a two-digit addition problem with regrouping, identifying the specific error related to place value.

Inquiry Circle

⏱ 25 min·Small Groups

Inquiry Circle: The Trading Post

Small groups use base-ten unit cubes to model problems. When the ones pile reaches 10 or more, one student physically takes 10 units to the trading post (a separate bin) and exchanges them for a rod. The group records the trade in their equation by writing a small 1 above the tens column and explains what the 1 represents.

Prepare & details

Justify why we 'carry over' a ten when the sum of the ones is 10 or more.

Facilitation Tip: During The Trading Post, circulate and ask each group to explain aloud why they must trade before moving the new ten to the tens column.

Setup: Groups at tables with access to source materials

Materials: Source material collection, Inquiry cycle worksheet, Question generation protocol, Findings presentation template

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

Think-Pair-Share

⏱ 15 min·Pairs

Think-Pair-Share: What Did We Get Wrong?

Show a worked example of a regrouping problem with a common error: the student wrote both digits of the ones sum without making a trade (e.g., wrote 17 in the ones column). Partners identify the error, explain what should have happened, and show the correction with blocks.

Prepare & details

Construct a model to show how 10 ones become 1 ten during addition.

Setup: Standard classroom seating; students turn to a neighbor

Materials: Discussion prompt (projected or printed), Optional: recording sheet for pairs

• Understand
• Apply
• Analyze
• Self-Awareness
• Relationship Skills

Stations Rotation

⏱ 30 min·Small Groups

Stations Rotation: Concrete, Pictorial, Abstract

At station one, students use base-ten blocks to model and solve with a trade. At station two, they draw the model and cross out 10 ones to draw one rod. At station three, they write the equation using standard notation with a carried digit. Groups rotate through all three stations.

Prepare & details

Critique a common error made when regrouping in addition.

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

Start with base-ten blocks to build the problem, then connect the blocks to written recording. Avoid rushing to the algorithm; instead, insist on verbalizing each step. Research shows that students who articulate why the trade happens develop stronger retention than those who only memorize the procedure.

What to Expect

Successful learning looks like students solving two-digit addition problems with regrouping, explaining why they traded ten ones for a ten, and using accurate place value language. They should demonstrate understanding both on paper and when using manipulatives without prompting.

Watch Out for These Misconceptions

Common Misconception

During The Trading Post, watch for students who write the full two-digit ones sum below the column without trading. Prompt them to count the units and see that 10 or more cannot fit in the ones place, then model the trade by exchanging 10 units for 1 rod and moving it to the tens side.

What to Teach Instead

During The Trading Post, watch for students who treat the carried digit as a single one rather than one ten. Have them label the carried mark on their paper as ‘1 ten’ and read their solution aloud using the correct place value language before recording the final answer.

Assessment Ideas

Exit Ticket

After The Trading Post, provide students with the problem: 'Sarah has 36 stickers and John gives her 28 more. How many stickers does Sarah have now?' Ask students to solve the problem on paper and write one sentence explaining why they had to regroup.

Quick Check

During Station Rotation, display a problem like 47 + 15. Ask students to use base-ten blocks to model the addition. Circulate and observe if students correctly trade 10 ones for 1 ten and place the new ten in the tens column before recording the sum.

Discussion Prompt

After Think-Pair-Share, present students with a common error: 'Someone added 24 + 38 and got 512. What mistake did they make? How should they have solved it?' Facilitate a brief class discussion where students explain the error and the correct procedure using their own words.

Extensions & Scaffolding

• Challenge: Provide problems with three addends (e.g., 28 + 35 + 17) and require students to model and solve using blocks before recording.
• Scaffolding: Give students a template with pre-labeled tens and ones columns and allow them to use only blocks without writing until they are confident.
• Deeper exploration: Ask students to create their own two-digit addition problem with regrouping and write a short paragraph explaining why regrouping is necessary in their example.

Key Vocabulary

Ones Place	The position in a number that represents the count of individual units. When adding, if the total ones are 10 or more, we regroup.
Tens Place	The position in a number that represents groups of ten. After regrouping, additional tens are added here.
Regrouping	The process of exchanging 10 ones for 1 ten when the sum of the ones column is 10 or more. This is also called 'carrying over'.
Base-Ten Blocks	Manipulatives used to represent numbers. Small cubes represent ones, and rods represent tens. They help visualize regrouping.
Composition	The act of combining smaller units to form a larger unit. In this topic, 10 ones are composed to make 1 ten.