--- title: "Explaining Mathematical Reasoning" description: "With teacher prompting, explain and justify mathematical reasoning using drawings, number sentences, or words" canonical: https://lightmysky.com/learn/mathematics/explaining-mathematical-reasoning-mt_kJ5wYzO8qC source: https://lightmysky.com/learn/mathematics/explaining-mathematical-reasoning-mt_kJ5wYzO8qC.md retrieved: 2026-11-12 --- > **Agent view.** This is the Markdown twin of the page, for tools and assistants. > When to use this site, and the call that answers each job: https://lightmysky.com/agent-instructions.md > API description (OpenAPI 3.1): https://lightmysky.com/openapi.json · Authentication: https://lightmysky.com/auth.md > Pricing: https://lightmysky.com/pricing.md · Catalog: https://lightmysky.com/llms.txt · Full catalog: https://lightmysky.com/llms-full.txt > Every machine-readable file on this domain: https://lightmysky.com/.well-known/ai-catalog.json > Ask for Markdown with `Accept: text/markdown`, a `.md` address, or `?mode=agent`. # Explaining Mathematical Reasoning With teacher prompting, explain and justify mathematical reasoning using drawings, number sentences, or words Subject: Mathematics · Area: Mathematical Thinking · Ages 6 to 7 Page: https://lightmysky.com/learn/mathematics/explaining-mathematical-reasoning-mt_kJ5wYzO8qC ## Ready when they can - Explain a solution strategy using a drawing or number sentence (e.g. 'I made ten first, then added the rest') - Justify why an answer is correct by showing an alternative method that gives the same result - Identify and explain an error in a worked example or a peer's solution ## Lesson: Telling how you got your answer You have shown your working with objects and drawings. A number sentence uses numbers and signs: + means add, - means take away, and = means 'is the same as'. Explain each step. Check by solving the same problem another way. Compare the answers and the steps. Matching answers help, but both methods can have a slip. **Example.** Mia has 8 stickers and gets 5 more. Split 5 into 2 and 3. Add 2 to 8 to make 10. Add the 3 left to get 13. Her number sentences are 8 + 2 = 10 and 10 + 3 = 13. *(drawing: Count on 5 from 8: 9, 10, 11, 12, 13. Start at 8, then make 5 hops. This check also gives 13.)* **Example.** Check the work against the problem. Do the drawn groups match its numbers? For taking away, count only objects without crosses. When counting on, count new hops, not the start. Ben adds 3 to 6 but counts '6, 7, 8'. He counted the start. He needs three new counts: 7, 8, 9. A double adds a number to itself. 5 + 5 = 10. For 5 + 6, one group has one more, so add 1 to the double: 10 + 1 = 11. For 5 + 4, one group has one fewer, so take 1 from the double: 10 - 1 = 9. You can add the same two groups in either order. 2 + 6 and 6 + 2 both make 8. To check using the other order, work it out again. Copying the first answer beside the reversed numbers is not another calculation. Addition and taking away can check each other. If 10 - 3 = 7, adding back the 3 should give 10: 7 + 3 = 10. To check an addition, take one added group away from the total. The other group should remain. Count the objects to check each step. To add 9, you can add 10 and then take away 1. Adding 10 puts in one more than you need. For 3 + 9, first find 3 + 10 = 13. Then take away the extra 1: 13 - 1 = 12. **Recap.** You can show your math thinking with a drawing, a number sentence, or words, and use it to check answers and find mistakes. *Original lesson, questions and flashcards written for this learning dataset.* ## Practice 18 questions on this page, each with its working shown. ## Needs first - [Showing Your Working](https://lightmysky.com/learn/mathematics/showing-your-working-mt_nyK25mNOeR) ## Optional connections - [What the equals sign means](https://lightmysky.com/learn/mathematics/what-the-equals-sign-means-mt_oIzycTBeE4) - [Addition in any order](https://lightmysky.com/learn/mathematics/addition-in-any-order-mt_QCgbiVrwnp) ## Opens up - [Teaching It Back](https://lightmysky.com/learn/learning-to-learn/teaching-it-back-mt_6eTZUwKQZr) - [Justifying mathematical reasoning](https://lightmysky.com/learn/mathematics/justifying-mathematical-reasoning-mt_pyMD_SIiYO)