Explaining in math: Communicating mathematical thinking by clearly stating the problem, describing the strategy used, showing the steps taken, justifying the approach, and verifying the solution.
I am adding 34 and 27 because the problem asks for the total when combining two amounts.
34 + 27 = 61. I used addition because I needed to find the total of both numbers.
• Addition: Used when combining quantities or finding totals
• Place value: Add ones with ones and tens with tens
• Regrouping: Carry over when a place value exceeds 9
Mathematical communication: The ability to clearly express mathematical thinking using precise language, appropriate vocabulary, and logical organization of ideas.
I am subtracting 28 from 52 because the problem involves taking away or finding the difference between amounts.
52 - 28 = 24. I used subtraction because I needed to find what remained after taking away.
• Subtraction: Used when removing quantities or finding differences
• Borrowing: Regroup when a digit in the minuend is smaller than the subtrahend
• Verification: Check by adding the difference back to the subtrahend
Spatial reasoning explanation: Describing geometric concepts by identifying properties, explaining measurement processes, and justifying the use of formulas or methods.
To find the perimeter of a rectangle, I need to measure the distance around the outside of the shape.
The perimeter is 20 units. I found this by adding all four sides of the rectangle.
• Perimeter: The total distance around the outside of a shape
• Rectangle properties: Opposite sides are equal in length
• Formula: Perimeter = 2 × (length + width)
- Clear statement of the answer
- Reason for choosing a particular strategy
- Step-by-step description of the process
- Justification of why the method works
- Verification that the answer makes sense
- State your answer clearly
- Explain your strategy choice
- Describe each step in order
- Justify your mathematical decisions
- Verify your solution
- Connect to the original problem
- Always explain WHY you chose a particular operation or strategy
- Use precise mathematical vocabulary consistently
- Show your work step by step in order
- Justify your mathematical decisions
- Verify that your answer makes sense in context
- Read and understand the problem completely
- Decide on an appropriate strategy or operation
- Solve the problem showing all work clearly
- Explain your thinking using sentence starters
- Justify your approach and verify your answer
- Connect your solution back to the original problem
- Simple: "I added because the problem asked for the total"
- Intermediate: "I used subtraction because items were taken away"
- Advanced: "I multiplied because I needed to find groups of equal size"
- Always use "because" to justify your mathematical decisions
- Don't skip steps in your explanation
- Make sure your explanation matches your actual work
- Practice using mathematical vocabulary regularly
- Check that someone else could follow your reasoning
- Use sentence starters: "I know this because..."
- Follow the sequence: first, then, next, finally
- Always verify your answer makes sense
- Explain your strategy choice clearly
- Show all work and thinking steps
Student Questions
Question: Why do I need to explain my math if I already know the answer?
Answer: Great question Sam! Explaining your math is important for several reasons:
- It shows you truly understand the concept, not just getting lucky with the answer
- It helps teachers see your thinking and identify any mistakes in your approach
- It builds stronger mathematical reasoning skills for harder problems later
- It's a valuable life skill for explaining your thinking in many situations
Plus, explaining helps you catch errors and strengthens your memory of the process!
Question: How do I know if my explanation is detailed enough?
Answer: A good explanation should answer these key questions:
- What is the problem asking?
- What strategy did you choose and why?
- What steps did you take to solve it?
- How do you know your answer is correct?
If someone who didn't solve the problem could understand your explanation and follow your thinking, then it's detailed enough!
Question: What if I don't know how to explain something I just figured out in my head?
Answer: That's completely normal! When you figure something out in your head, try these steps:
- Slow down and think about what your brain did
- Try solving the same type of problem with smaller numbers to see the steps
- Draw a picture or use objects to represent your thinking
- Practice explaining your mental process out loud first
Remember, explaining your thinking is a skill that improves with practice!