Addition and Subtraction Strategies within 100

Active learning helps students move beyond memorized procedures by letting them test strategies in real time. This topic requires flexibility, not just speed, so students need repeated chances to compare methods and see why one might work better for certain numbers. Student-to-student talk and hands-on tools turn abstract ideas like place value and compensation into something they can manipulate and discuss.

• 2nd Grade
• Mathematics
• 3 activities
• 20 min–45 min

Learning Objectives

1. Compare the efficiency of at least two different strategies (e.g., breaking apart, compensation, open number line) for solving addition and subtraction problems within 100.
2. Explain how the commutative property of addition can simplify the calculation of a two-digit addition problem.
3. Calculate the sum or difference of two-digit numbers within 100 using at least three distinct strategies.
4. Justify the choice of a specific strategy for solving a subtraction problem within 100, referencing the numbers involved.
5. Demonstrate the relationship between addition and subtraction by solving a subtraction problem using an addition strategy.

Think-Pair-Share

⏱ 20 min·Pairs

Think-Pair-Share: Strategy Showdown

Present one two-digit addition problem to the class (e.g., 38 + 47). Students solve it individually using any strategy. Partners compare strategies side by side, name each strategy, and decide which was more efficient for these specific numbers. Three pairs share to build a class list of strategy names and when each works best.

Prepare & details

Compare different strategies for adding two-digit numbers, such as breaking apart and compensation.

Facilitation Tip: During Strategy Showdown, ask each pair to prepare a 15-second explanation of their chosen method before sharing with the group.

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

Inquiry Circle

⏱ 35 min·Small Groups

Inquiry Circle: 100 Ways to Get There

Groups are given a target sum (e.g., 75). They must find at least four different addition equations that reach that target, using four different strategies. Groups post their equations and strategies on chart paper. The class identifies which strategy appeared most across groups.

Prepare & details

Explain how the commutative property of addition can make problems easier to solve.

Facilitation Tip: During 100 Ways to Get There, circulate and ask guiding questions like, 'What would happen if you adjusted the larger number instead?' to push flexible thinking.

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

Stations Rotation

⏱ 45 min·Small Groups

Stations Rotation: Strategy Stations

Four stations each feature one strategy: place value decomposition, compensation, counting up on a number line, and using fact families. Students solve two problems at each station using that station's assigned strategy, then rate how efficient they found it for those specific numbers on a 1-3 scale.

Prepare & details

Assess the efficiency of various subtraction strategies for different types of problems.

Facilitation Tip: During Strategy Stations, set a timer so students rotate every 6 minutes, forcing them to adapt their approach quickly to new constraints.

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

Teach this topic by contrasting strategies side by side so students notice efficiency differences. Avoid rushing to the algorithm; anchor every new method to concrete tools like base-ten blocks or number lines first. Research shows that students who explain their reasoning to peers develop deeper understanding and retain strategies longer.

What to Expect

Successful learning looks like students choosing strategies that match the numbers, explaining their choices clearly, and catching their own mistakes as they go. You’ll see them move from counting one by one to using place value, properties, and adjustments with purpose. By the end of these activities, they should be able to justify why they used a particular strategy.

Watch Out for These Misconceptions

Common Misconception

During Strategy Showdown, watch for students who decompose 53 + 28 into 50 + 20 = 70 and 3 + 8 = 11, then write 81 without regrouping the extra ten.

What to Teach Instead

Ask them to model the problem with base-ten blocks and recount the tens column after combining the ones. Have them record each step in a T-chart labeled Tens and Ones to make the regrouping visible before they share their answer.

Common Misconception

During 100 Ways to Get There, watch for students who subtract the smaller digit from the larger in 73 - 28, writing 55 or 45 without regrouping.

What to Teach Instead

Have them build both numbers with blocks and physically remove 28 from 73 to show the difference. Then prompt them to compare 73 - 28 with 28 - 73 on the same mat to highlight the mismatch in results.

Common Misconception

During Strategy Stations, watch for students who adjust both addends in a compensation problem, such as changing 45 + 32 to 50 + 37 by adding 5 to each, then forgetting to subtract the 5 at the end.

What to Teach Instead

Give them a whiteboard to record each adjustment step and the corresponding change to the sum. Ask a partner to check their final compensation move before they move to the next station.

Assessment Ideas

Exit Ticket

After Strategy Showdown, present the problem 53 + 28 and ask students to solve it using two different strategies on the same sheet. Collect responses and look for clear evidence of regrouping or compensation and a written sentence explaining which strategy felt more efficient for these numbers.

Discussion Prompt

After 100 Ways to Get There, pose the subtraction problem 72 - 35 and ask students to share their strategies. Listen for mentions of open number lines, place value decomposition, or compensation. Facilitate a brief discussion on which strategy felt easiest for these numbers and why some methods are better fits for certain subtractions.

Quick Check

During Strategy Stations, write the problem 45 + 32 on the board and ask students to show their answer with a thumbs signal: up for place value decomposition, sideways for compensation, down for another strategy. Circulate to note which signals are most common and ask two or three students to explain their method aloud before rotating.

Extensions & Scaffolding

• Challenge students who finish early to create a new problem where compensation is the most efficient strategy and solve it twice—once correctly and once with a common mistake—for a partner to identify.
• Scaffolding: Provide sentence frames for Strategy Showdown so students practice articulating each step, especially the regrouping or adjustment parts.
• Deeper exploration: Have students write a reflection comparing two strategies they tried for the same problem, including which felt more reliable and why.

Key Vocabulary

Place Value	The value of a digit based on its position in a number, such as the tens place or the ones place.
Decomposing	Breaking a number apart into smaller parts, often by place value (e.g., breaking 47 into 40 and 7).
Compensation	Adjusting one number in a problem to make it easier to solve, then adjusting the other number or the answer to account for the change.
Commutative Property of Addition	The property that states that the order of addends does not change the sum (e.g., 25 + 30 is the same as 30 + 25).
Open Number Line	A visual representation of a number line where students can make jumps to show addition or subtraction steps.