Explaining means telling someone else what you did and how you figured out the answer. When we explain our math thinking, we understand it better and help others learn too!

Builds Understanding

• When you explain, you think deeper
• Putting ideas into words helps you understand
• You remember better when you explain

Helps Others Learn

• Your explanation might help a friend
• Different ways of thinking help everyone
• Sharing ideas builds classroom community

Shows Your Thinking

• Teachers can see how you solved it
• You can get help if you're confused
• You feel proud of your thinking!

What You Did

• "I used blocks to show the problem"
• "I put these together"
• "I took some away"
• Describe your actions

How You Figured It Out

• "I counted them"
• "I used my fingers"
• "I made two groups"
• Share your strategy

What You Found Out

• "There are 5 altogether"
• "3 are left"
• "We need 2 more"
• State your answer

Beginning Words

• "First I..."
• "I started with..."
• "I had..."

Action Words

• "Then I..."
• "I put..."
• "I took away..."
• "I counted..."
• "I added..."

Ending Words

• "So the answer is..."
• "I found out that..."
• "There are..."
• "That makes..."

Step 1: Tell What You Started With

"I had 3 blocks."

Step 2: Tell What Happened

"My friend gave me 2 more blocks."

Step 3: Tell What You Did

"I put them all together and counted them."

Step 4: Tell the Answer

"I have 5 blocks now!"

Think-Pair-Share

1. Solve a problem with objects
2. Think about what you did
3. Turn to a partner
4. Explain how you solved it
5. Listen to your partner explain

Show and Tell

1. Solve a problem
2. Show the class your objects
3. Explain: "First I... Then I... So..."
4. Classmates can ask questions

Story Retell

1. Listen to a story problem
2. Solve it
3. Retell the story with your answer
   "There were 4 birds. 2 flew away. I took away 2. Now there are 2 birds."

Explain to Teacher

One-on-one:
1. Teacher asks how you solved it
2. You show and explain
3. Teacher asks questions to help you explain more

Addition Example

Problem: "You have 2 apples. You get 3 more. How many now?"

Child's Explanation:
"First I put out 2 blocks for my apples. Then I put out 3 more blocks for the new apples. Then I counted all of them: 1, 2, 3, 4, 5. So I have 5 apples!"

Subtraction Example

Problem: "You had 5 crackers. You ate 2. How many left?"

Child's Explanation:
"I started with 5 counters. Then I took 2 away because I ate them. Then I counted what was left: 1, 2, 3. So 3 crackers are left."

Taking Apart Example

Problem: "You have 6 toys. Some go in this box, some in that box. How many ways?"

Child's Explanation:
"I tried different ways. First I put 4 in this box and 2 in that box. Then I tried 3 and 3. Then I tried 5 and 1. I found lots of ways!"

Ask Good Questions

• "What did you do first?"
• "How did you figure that out?"
• "What happened next?"
• "How do you know that's the answer?"
• "Can you show me?"

Model Explaining

Teacher thinks aloud:
"Hmm, I have 3 blocks. I need to add 2 more. Let me put out 2 more blocks. Now let me count: 1, 2, 3, 4, 5. So 3 plus 2 equals 5!"

Encourage Showing

• "Show me with your hands"
• "Point to what you did"
• "Use the blocks to show me"
• Actions support words

Accept All Explanations

• There are many ways to explain
• Some children use simple words
• Some use lots of details
• All explanations are valuable!

Start Small

• Explain to one friend
• Explain to teacher
• Work up to whole class

Practice Often

• Explain every day
• Make it routine
• Gets easier with practice

Celebrate Explaining

• "Great explanation!"
• "You told us exactly what you did!"
• "That helps me understand!"

Challenge 1: "I Don't Know What to Say"

• Solution: Ask specific questions
• "What did you use?"
• "What did you do first?"
• Break it down into small steps

Challenge 2: Very Brief Explanation

Child says only: "I counted."
- Solution: Ask follow-up questions
- "What did you count?"
- "How many did you count?"
- "What was your answer?"

Challenge 3: Difficulty Putting It Into Words

• Solution: Let them show first
• "Show me what you did"
• Then help put actions into words

Challenge 4: Shy or Reluctant

• Solution: Start with partner sharing
• Build up confidence
• Never force public sharing

Deepens Understanding

• Explaining = thinking more deeply
• Connects actions to words
• Makes thinking visible

Develops Language Skills

• Math vocabulary grows
• Sentence structure improves
• Communication skills develop

Prepares for Future

• All of math requires explanation
• Problem solving needs communication
• Critical skill for school and life

Verbal

• Speaking your thinking
• Telling what you did
• Most common for Pre-K

Visual

• Showing with objects
• Demonstrating actions
• Acting it out
• Supports verbal explanation

Combined

Best for Pre-K:
- Show AND tell
- Act it out while explaining
- Objects + words = clear explanation

Listen for:
- Does child describe what they did?
- Do they mention the objects or strategy used?
- Do they state the answer?
- Does their explanation match their actions?
- Can they answer follow-up questions?
- Are they developing math vocabulary?

Make It Normal

• Everyone explains
• Every day
• Multiple times
• Not special or scary - just what we do!

Value Process Over Answer

• How you solved it matters
• Not just "what's the answer?"
• Celebrate thinking, not just correctness

Learn From Each Other

• Listen to classmates' explanations
• Try their strategies
• See multiple ways to solve

Once children can explain their thinking:
- They're ready for more complex problems
- They can compare different solution methods
- They're developing as mathematical thinkers
- They see themselves as capable problem solvers!

Explaining solutions helps us understand our own thinking and share it with others!