2.NBT.9: Explaining Addition and Subtraction Strategies

Visual Models to Use

• Place Value Blocks - Physical or virtual blocks that show how regrouping works when adding or subtracting with place value, helping children explain why these strategies work.
• Number Line - A visual tool that helps children explain why counting on or counting back strategies work for addition and subtraction.
• Expanded Form - Writing numbers in expanded form (e.g., 245 = 200 + 40 + 5) to explain why breaking apart numbers by place value works for addition and subtraction.
• Arrow Cards - Cards showing place value that can be overlapped to demonstrate why regrouping works when adding or subtracting.

Everyday Activities

1. Math Teacher Game

Have your child pretend to be a math teacher and explain to you (or a stuffed animal) why a particular addition or subtraction strategy works.

2. Strategy Journal

Keep a journal where your child solves problems and writes explanations of why their strategies work, using drawings and words.

3. Family Math Night

Have each family member solve the same problem using different strategies, then take turns explaining why your strategy works.

4. Math Vlogger

Have your child create short videos explaining different addition and subtraction strategies and why they work, like a math YouTube channel.

Strategies When Your Child Struggles

1. Use "Why" Questions

When your child solves a problem, ask "Why does that work?" or "How do you know that's true?" to encourage explanation of their thinking.

2. Provide Sentence Starters

Give your child phrases like "This strategy works because..." or "I know this is true because..." to help them structure their explanations.

3. Draw It Out

Have your child draw pictures or diagrams to help them explain why their addition or subtraction strategy works.

4. Connect to Place Value

Remind your child to use place value language (ones, tens, hundreds) when explaining why their strategy works.

5-Minute Practice Activities

1. Math Talk

Solve a simple addition or subtraction problem together, then take turns explaining why the strategy you used works. Focus on using math vocabulary.

2. Strategy Comparison

Solve the same problem using two different strategies (e.g., counting on vs. making ten), then discuss why both strategies work.

3. Explain Your Thinking

Have your child solve a problem, then record a short video of them explaining why their strategy works.

4. Spot the Error

Show your child an incorrect solution and ask them to explain why it doesn't work, then fix it and explain why the correct strategy works.

Mid-Year Expectations

By the middle of second grade, your child should be able to:

• Explain why addition strategies like counting on or making ten work
• Explain why subtraction strategies like counting back or using related addition facts work
• Use place value language when explaining strategies for single-digit addition and subtraction
• Draw pictures to support their explanations

End-of-Year Expectations

By the end of second grade, your child should be able to:

• Explain why addition strategies work for two-digit and three-digit numbers
• Explain why subtraction strategies work for two-digit and three-digit numbers
• Use place value understanding to explain regrouping in addition and subtraction
• Compare different strategies and explain why they all work

Mastery Signs

Your child has mastered this standard when they can:

• Clearly explain their mathematical thinking using place value language
• Justify why a strategy works, not just how to use it
• Identify when a strategy would or wouldn't work and explain why
• Connect their explanations to visual models or drawings
• Teach someone else why a strategy works

Below Grade Level

Practice problems focusing on explaining simple addition and subtraction strategies with single-digit numbers, building the foundation for explaining more complex strategies.

Download Practice Worksheet

At Grade Level

Standard practice with explaining why addition and subtraction strategies work for two-digit numbers, using place value understanding.

Download Grade Level Worksheet

Above Grade Level

Challenging problems requiring explanations of multiple strategies for three-digit addition and subtraction, including comparing and contrasting different approaches.

Download Challenge Worksheet