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

Adding Two-Digit Numbers (No Regrouping)

Students add two two-digit numbers without regrouping, focusing on adding tens to tens and ones to ones.

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

About This Topic

Adding two two-digit numbers without regrouping is the first full-column addition experience most first graders encounter. Under CCSS.Math.Content.1.NBT.C.4, students develop conceptual understanding by connecting physical models to written procedures. The essential understanding is that tens are added to tens and ones are added to ones, each place value treated as its own addition within the same problem.

This topic is structured around place value logic rather than a memorized algorithm. Students learn to add the ones column first, verify the sum is less than 10, then add the tens. Working with base-ten blocks or drawn models before written equations ensures the place value reasoning stays visible and the procedure has a conceptual anchor.

Peer collaboration adds significant value here because students can compare place value sketches, discuss which column they added first, and notice that the order (ones before tens or tens before ones) does not affect the final sum. These conversations push students toward flexible thinking and build a solid foundation for the regrouping work that follows in the next topic.

Key Questions

1. Explain why adding the ones first is a helpful strategy.
2. Compare adding two-digit numbers to adding one-digit numbers.
3. Design a step-by-step process for adding two-digit numbers without regrouping.

Learning Objectives

• Calculate the sum of two two-digit numbers without regrouping by adding tens to tens and ones to ones.
• Compare the process of adding two-digit numbers to adding one-digit numbers, identifying similarities and differences.
• Explain the strategy of adding the ones column before the tens column and why it is effective for sums less than 10.
• Design a visual representation, such as a place value chart or base-ten blocks drawing, to model the addition of two two-digit numbers.
• Identify the correct sum when adding two two-digit numbers without regrouping, demonstrating accuracy in calculation.

Before You Start

Adding and Subtracting within 20

Why: Students need a foundational understanding of addition facts and the concept of combining quantities.

Understanding Place Value (Tens and Ones)

Why: This topic relies heavily on students' ability to identify and work with the tens and ones digits separately.

Key Vocabulary

Place Value	The value of a digit based on its position in a number, such as the ones place or the tens place.
Tens	Groups of ten. In a two-digit number, the digit in the tens place tells how many groups of ten there are.
Ones	Individual units. In a two-digit number, the digit in the ones place tells how many individual units there are.
Sum	The answer when two or more numbers are added together.

Watch Out for These Misconceptions

Common Misconception

Add all the digits together without regard to place value.

What to Teach Instead

Students may add 2 + 3 + 4 + 1 for 23 + 41 without separating tens and ones. Using a place value mat that visually separates the two columns during group work prevents this error by making the column structure a physical boundary rather than an abstract concept.

Common Misconception

The sum changes if you add tens before ones.

What to Teach Instead

Some students worry that order matters and feel anxious choosing where to start. Demonstrating with blocks that combining rods first and then units gives the same result as reversing the order builds flexibility and removes the pressure of choosing the one correct sequence.

Active Learning Ideas

Think-Pair-Share: Ones First or Tens First?

Present the same problem solved two ways on the board: ones added first, then tens added first. Partners discuss whether both approaches give the same answer and which order they find more intuitive. The class shares out and establishes a useful default strategy with reasons.

15 min·Pairs

Inquiry Circle: Base-Ten Blueprint

Groups model three different two-digit plus two-digit problems using base-ten blocks. After building each, they draw a quick sketch and write the equation, making sure the tens and ones in their drawing match the written digits. Groups share models and check each other's work for accuracy.

25 min·Small Groups

Gallery Walk: Matching Models

Post pairs of images around the room (a base-ten block model and a corresponding equation). Half the pairs are correctly matched; half are mismatched. Students circulate, identify the errors, and explain the correction in writing on a sticky note.

20 min·Pairs

Real-World Connections

• A cashier at a grocery store adds the cost of items, like two loaves of bread costing $3.25 each, by adding the dollars ($3 + $3 = $6) and the cents ($0.25 + $0.25 = $0.50) separately to find the total cost of $6.50.
• When planning a party, a parent might add the number of guests invited on two different days, such as 12 guests on Monday and 15 guests on Tuesday, by adding the tens (10 + 10 = 20) and the ones (2 + 5 = 7) to find a total of 27 guests.

Assessment Ideas

Exit Ticket

Provide students with two problems: 23 + 14 and 41 + 26. Ask them to solve each problem and then write one sentence explaining how they added the numbers.

Quick Check

Write the problem 35 + 22 on the board. Ask students to use base-ten blocks or draw a picture to show their work. Circulate and ask students to explain which parts they added first and why.

Discussion Prompt

Pose the question: 'Imagine you are teaching a younger student how to add 42 + 35. What steps would you tell them to follow, and why is it important to add the ones first?'

Frequently Asked Questions

What is the best strategy for adding two-digit numbers without regrouping?

The place value strategy works reliably: add the ones, then add the tens. Write each partial sum in the appropriate column. Base-ten blocks make this concrete because students physically combine the units first, then the rods, and no trade is needed.

How do I know if a problem needs regrouping before solving it?

Check the ones digits first. Add them mentally or on fingers; if the total is 9 or less, no regrouping is needed. If it is 10 or more, regrouping will be required. Teaching this preview habit prepares students well for the regrouping topics that follow.

Why do we add ones before tens in the standard approach?

Adding ones first is a convention that scales cleanly into regrouping problems. When tens need to carry over, starting from the ones is necessary. Building the habit in no-regrouping problems makes the transition smoother because the procedural sequence is already established.

How does active learning support students learning to add two-digit numbers?

When students build the same problem with blocks and compare their models with a partner, they verify their own understanding and often catch errors before the teacher does. Explaining a base-ten drawing to a peer requires students to use place value language precisely, which accelerates both procedural fluency and conceptual understanding simultaneously.