“How do you know?”: getting kids to explain their math thinking

Why explaining matters

The Common Core’s practice standards describe what good math thinking looks like at every grade. The third one is about arguments: students justify their conclusions, communicate them to others, and respond to the arguments of others ^[1]. The first one adds a habit worth copying at home: proficient students keep asking themselves, “Does this make sense?” ^[1].

Explaining also shows you where the thinking went wrong. A wrong answer with a reason is far easier to fix than a wrong answer alone.

Questions to ask, in order

1. “How did you get that?” Ask it after right answers too, or your child will learn the question means “wrong.”
2. “Can you show me?” Fingers, blocks, a drawing. For young children this counts as an explanation ^[1].
3. “What did you do first?” Breaks “I just know” into steps.
4. “Does that make sense?” Ask them to check the answer against the story: can Mia have more shells than both girls together?
5. “Is there another way?” A second method is the best check there is.

What to listen for

• A reason, not a feeling. “Because 8 and 2 make 10” is a reason. “It felt right” is a start: ask what they did.
• The right words, gently. If your child says “the take-away,” you can echo back “the difference.” The practice guide recommends teaching clear, precise math words and helping children use them when they explain ^[2].
• A guess, said honestly. “I guessed” is useful to hear. Thank them, then ask what they could check.

How Kizupi does it

After a first wrong answer, Kizupi asks the child how they got it, because children often fix a mistake themselves while explaining. It asks after right answers too: always the first time a child gets a new skill right, and now and then after that. A child who says they guessed is thanked for being honest (“A guess is a fine place to start. Let’s figure it out together.”), never told off.

If a child is stuck, help comes one rung at a time on a fixed seven-step ladder: wait, read it again, a focus question, a picture, a partial step, a similar problem worked through, and only then a full walkthrough.

Questions parents ask

My child gets the right answer but can’t explain it. Is that a problem?

Not at first. Many children can do more than they can say. Ask them to show it with objects or a drawing, which counts as an explanation for young children ^[1].

At what age can kids explain their math?

From the start of school. The practice standards apply from kindergarten, and elementary students can make arguments using objects, drawings, diagrams and actions ^[1].

What if my child says “I just know”?

Ask “What did you do first?” or “Can you show me?” Smaller questions are easier to answer than “explain.”

Should I ask “how do you know?” when the answer is right?

Yes. If you ask only after mistakes, your child will hear the question as “you’re wrong.”

Keep going

• Free printable math word problem worksheets, Grades 1–6, with an answer key checked by Kizupi’s math engine.
• How to help your child with math word problems
• What the equal sign really means: early algebra in first grade
• Kizupi, the math tutor app for kids that asks why, and how Kizupi is different from drill apps and AI homework helpers.

Sources

1. Common Core State Standards Initiative, Standards for Mathematical Practice. Read October 26, 2026.
2. What Works Clearinghouse, Institute of Education Sciences, U.S. Department of Education, Assisting Students Struggling with Mathematics: Intervention in the Elementary Grades (WWC 2021006), practice guide summary. Read October 26, 2026.

Cite this page: The Kizupi team, ““How do you know?”: getting kids to explain their math thinking,” Kizupi, updated October 26, 2026, https://kizupi.com/guides/how-do-you-know-explain-math-thinking.