Mathematics · 1st Grade · The Power of Ten and Place Value · Quarter 2

Adding Two-Digit Numbers (With Regrouping)

Students add two two-digit numbers with regrouping, understanding the concept of composing a new ten.

• Common Core State Standards
• CCSS.Math.Content.1.NBT.C.4

About This Topic

Adding two two-digit numbers with regrouping is one of the most conceptually demanding topics in first grade arithmetic. CCSS.Math.Content.1.NBT.C.4 asks students not just to compute correctly but to understand why regrouping works: when the ones column produces a sum of 10 or more, those 10 ones are composed into a single ten, which is added to the tens column. This is the inverse of decomposing a ten during subtraction.

Physical models are essential here. Students who skip the concrete stage and learn regrouping as a rote procedure frequently make errors because they have no conceptual anchor. Base-ten blocks make the composition of a new ten visible: students trade 10 unit cubes for one rod, see that the quantity has not changed, and understand why a 1 appears above the tens column in the written work.

Active learning accelerates this topic because students who explain the trade to a partner must articulate each step in the composition process. Hearing peers explain the reasoning reinforces the meaning behind the procedure for the entire group, reducing errors that arise from following steps mechanically without understanding.

Key Questions

1. Justify why we 'carry over' a ten when the sum of the ones is 10 or more.
2. Construct a model to show how 10 ones become 1 ten during addition.
3. Critique a common error made when regrouping in addition.

Learning Objectives

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

Before You Start

Adding Two-Digit Numbers (Without Regrouping)

Why: Students must first master adding two-digit numbers where the sum of the ones is less than 10.

Understanding Place Value (Tens and Ones)

Why: A strong grasp of what tens and ones represent is fundamental to understanding the regrouping process.

Counting to 100

Why: Students need to be comfortable with numbers up to 100 to perform the addition and understand the sums.

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.

Watch Out for These Misconceptions

Common Misconception

Write both digits of the ones sum below the ones column.

What to Teach Instead

Students frequently write the full two-digit ones sum (e.g., 13) below the ones column. Using base-ten blocks during collaborative modeling, where students physically cannot fit more than 9 units in the ones section without overflowing, makes the need for the trade a concrete reality rather than an arbitrary rule.

Common Misconception

The carried 1 is the number one, not one ten.

What to Teach Instead

Students often add the carried digit as a one rather than a ten. Labeling the carried mark explicitly as one ten during small-group work and requiring students to read it aloud as one ten in their explanation builds the correct place value interpretation.

Active Learning Ideas

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.

25 min·Small Groups

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.

15 min·Pairs

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.

30 min·Small Groups

Real-World Connections

• When shopping, a cashier might add the cost of two items, like a $15 shirt and a $27 pair of pants. They need to regroup to find the total cost, $42.
• Construction workers might measure two pieces of wood. If one is 18 inches and the other is 25 inches, they use regrouping to determine the combined length of 43 inches.

Assessment Ideas

Exit Ticket

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 and then write one sentence explaining why they had to regroup.

Quick Check

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.

Discussion Prompt

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.

Frequently Asked Questions

Why do we say 'carry the 1' when regrouping?

The 1 represents one group of ten, not the number one. When the ones in both numbers add up to 10 or more, those 10 ones are exchanged for 1 ten. Writing a small 1 above the tens column records that trade. The shortcut phrase is much more meaningful after students have first made the physical exchange with blocks.

How do I model regrouping for a first grader who is confused?

Start with just the ones. Build 8 ones and 6 ones separately with unit cubes, push them together, count the total, and ask: can we make a ten? Bundle 10 cubes and label them a ten. Students can now see one ten and 4 ones remaining. Connect this physical result to each step of the written equation.

Does first grade require the standard algorithm for addition?

The Common Core expectation at grade 1 is strategies and models, not the full standard algorithm, which is formalized in grade 4. First graders should understand the reasoning behind regrouping using concrete and pictorial representations. Written notation with a carried digit may be introduced as a shorthand once students have solid conceptual understanding.

How can active learning help students understand composing a new ten?

The trading-post activity and peer explanation strategies require students to physically act out and then verbalize the composition process. When a student explains to a partner that they had 14 ones so they sent 10 to the trading post and got a rod back, they consolidate procedural and conceptual knowledge simultaneously. This embodied, social learning is far more durable than being shown the carry notation on a board.