Reviewing And Explaining Solutions

When you finish a problem, you are not quite done yet. You still need to look back at your work, check that it makes sense, and explain your thinking in words that other people can follow. This lesson builds on skills from Reflecting On Learning Communication Strategy and helps you turn a quiet thought into a clear explanation.

Reviewing means looking back at something you already did. When you review a solution, you read each step again and ask, "Does this make sense?" You check for small mistakes, like a number you copied wrong or a step you forgot.

Imagine you solved \(3 \times 4 = 12\). To review it, you could count by fours three times: 4, 8, 12. If your counting matches your answer, you know your solution is correct. If it does not match, you found a mistake to fix.

A good explanation tells why an answer is true, not only what the answer is. Instead of saying "The answer is 12," you can say, "The answer is 12 because 3 groups of 4 make 12, and \(3 \times 4 = 12\)."

Words like because, so, and first help you connect your steps to your answer. These small words show your reasoning and help someone else follow along, even if they were not there when you solved the problem. This kind of thinking also appears in Explaining Math Thinking Clearly, where you practice putting your math steps into full sentences.

Revising means fixing your explanation so it is clearer. After you write or say your first explanation, ask yourself: "Would a classmate understand this?" If some steps are missing, add them. If a sentence is confusing, say it a simpler way.

Notice how the revised explanation on the right includes both the answer and the reason. This small change makes a big difference for anyone reading or listening to your work.

You can use a short checklist every time you finish a problem or an answer. Ask yourself these three questions.

• Did I check each step for mistakes?
• Did I explain why my answer is correct, using words like because?
• Would someone else understand my explanation without asking me questions?

If you can answer yes to all three, your solution is ready to share. If not, go back and revise the part that is unclear.

Review: Looking back at your finished work to check it for mistakes.

Solution: The answer to a problem, along with the steps used to get there.

Justify: Giving a good reason to show why your answer is correct.

Explain: Using words to describe your steps and thinking so others can follow.

Revise: Changing your work to make it clearer or more correct.

Reasoning: The thinking and steps that lead you to an answer.

Try solving a simple problem, such as \(15 - 6 = 9\). Write one sentence with just the answer. Then write a second sentence that explains why the answer is correct. Compare the two sentences and notice how the second one gives more information.

You can also read a partner's explanation and ask them one question about a step that is unclear. Answering that question is a form of revising, because it helps make the explanation clearer for the next reader.

Related lessons

• Reflecting On Learning Communication Strategy