Mathematics · 2nd Grade · Algebraic Thinking: Patterns and Equations · Weeks 19-27

Using Models for Addition within 100

Students use concrete models or drawings and strategies based on place value to add within 100, including composing a ten.

• Common Core State Standards
• CCSS.Math.Content.2.NBT.B.5

About This Topic

In the US K-12 curriculum aligned to CCSS 2.NBT.B.5, second graders learn to add within 100 using concrete representations before moving to abstract algorithms. Base-ten blocks are central to this work: students physically group ten ones into a ten-rod, experience the act of composing a ten, and see that the total quantity remains the same. This hands-on work makes the regrouping process visible rather than mysterious. Open number lines are another key model, allowing students to hop by tens and ones while tracking their total.

The transition from concrete to pictorial is deliberate. Students draw base-ten diagrams or jumps on a number line before writing purely symbolic equations. This sequence matches how the US curriculum builds procedural fluency on a foundation of conceptual understanding. Students who can explain why they regroup using a model have internalized place value in a way that supports long-term mathematical flexibility.

Active learning deepens this topic because students who discuss their strategies with a partner, compare methods at a gallery walk, or defend their model to the class must articulate their reasoning, which strengthens both understanding and retention.

Key Questions

1. Design a model using base-ten blocks to demonstrate regrouping when adding two-digit numbers.
2. Explain how bundling ten ones into a ten rod simplifies the addition process.
3. Analyze how an open number line can be used to visualize adding two-digit numbers.

Learning Objectives

• Design a base-ten block model to demonstrate composing a ten when adding two-digit numbers.
• Explain how bundling ten ones into a ten rod simplifies the addition process.
• Calculate the sum of two-digit numbers using an open number line model.
• Compare the efficiency of using base-ten blocks versus an open number line for adding two-digit numbers.
• Analyze the relationship between place value and regrouping in addition problems.

Before You Start

Addition and Subtraction within 20

Why: Students need a solid foundation in basic addition facts to build upon when working with larger numbers and regrouping.

Understanding Place Value to 100

Why: Students must be able to identify the tens and ones digits in two-digit numbers to effectively use base-ten models and number lines.

Key Vocabulary

Base-ten blocks	Manipulatives representing ones (units), tens (rods), hundreds (flats), and thousands (cubes) to model numbers and operations.
Composing a ten	The process of combining ten ones to make one ten, often called regrouping or carrying over in addition.
Place value	The value of a digit based on its position within a number (e.g., the '2' in 25 represents 2 tens).
Open number line	A number line without pre-marked numbers, used to visually represent jumps for addition and subtraction.
Regrouping	Exchanging units of one place value for an equivalent number of units in the next higher place value, such as exchanging 10 ones for 1 ten.

Watch Out for These Misconceptions

Common Misconception

Students may regroup whenever they see two two-digit numbers, even when the ones digits total less than 10.

What to Teach Instead

Have students count the ones cubes aloud before deciding to trade. A 'do I have ten or more ones?' check step, practiced in pairs, helps them develop the habit of verifying before regrouping rather than applying it automatically.

Common Misconception

Students may record the composed ten in the wrong column when transitioning to written notation.

What to Teach Instead

Use a clearly labeled place value mat when writing equations. When students narrate aloud where the new ten goes as they work with a partner, peer correction catches placement errors before they become habitual.

Common Misconception

Students may confuse the quantity shown in their block model with the symbolic notation.

What to Teach Instead

Have students match blocks to written numerals side by side. Paired explanation prompts like 'show me where the 3 in 37 lives in your blocks' build the connection between concrete model and symbolic representation.

Active Learning Ideas

Gallery Walk: Model Museum

Pairs create a poster showing at least two different models for adding two two-digit numbers (base-ten block drawing and open number line). The class walks through the museum and writes sticky notes identifying the strategy used on each poster.

30 min·Pairs

Think-Pair-Share: Regroup or Not?

Teacher poses a set of addition problems, some requiring composing a ten and some not. Partners predict whether regrouping will be needed before solving, then discuss their reasoning before computing the answer together.

20 min·Pairs

Inquiry Circle: Build It Three Ways

Small groups receive a two-digit addition problem and represent it with physical blocks, a drawing, and a number line. They compare representations and explain which model helped them most and why.

35 min·Small Groups

Stations Rotation: Add and Explain

Students rotate through three stations: physical base-ten blocks, drawn models, and open number lines. At each station they solve the same problem and record what the specific model makes visible about the regrouping process.

45 min·Small Groups

Real-World Connections

• Cashiers at a grocery store use place value and regrouping when counting out change for customers, such as combining coins to make dollars or bills to make larger amounts.
• Construction workers use base-ten concepts when measuring and cutting materials, like bundling small units of measurement into larger ones to simplify calculations for building projects.
• Bank tellers organize money into stacks of tens and hundreds, using the concept of composing larger units to efficiently count large sums of money.

Assessment Ideas

Exit Ticket

Provide students with two-digit addition problems, such as 37 + 25. Ask them to solve it using base-ten blocks (drawing or physical) and then solve it again using an open number line. Collect their work to check for accurate use of both models.

Quick Check

Present a problem like 48 + 14. Ask students to hold up fingers to show how many tens they would 'carry over' or 'compose' after adding the ones. Then, ask them to draw one jump on an imaginary number line representing adding the tens.

Discussion Prompt

Pose the question: 'When adding 56 + 38, why is it helpful to think about the ones first? How does this help us find the total sum more easily?' Listen for student explanations that connect to composing a ten and place value.

Frequently Asked Questions

What active learning strategies work best for teaching addition with regrouping in 2nd grade?

Partner work where students narrate their steps aloud is highly effective. When one student explains 'I have 15 ones, so I bundle 10 into a ten-rod and have 5 left,' they reinforce their own understanding while the partner checks the reasoning. Gallery walks comparing different models also build flexibility across strategies.

How do base ten blocks help with addition in 2nd grade?

Base-ten blocks make the abstract idea of place value tangible. When students physically trade ten unit cubes for one ten-rod, they experience composing a ten rather than memorizing a rule. This concrete manipulation directly supports understanding of regrouping, making the written algorithm meaningful rather than a series of steps to follow.

What is an open number line and how is it used for addition?

An open number line is a blank line where students mark their own starting point and jumps. For addition, a student might start at 46, jump +20, then +7, landing at 73. It shows the decomposition strategy visually and helps students track partial sums, particularly for students who think in chunks rather than ones.

When should second graders move from models to the standard algorithm?

Models should remain available even after students show proficiency with notation. The US curriculum emphasizes that conceptual understanding precedes and supports procedural fluency. If a student can explain why they regroup using a model, they are ready to write the algorithm alongside it, not instead of it.