Explaining Mathematical Reasoning
With teacher prompting, explain and justify mathematical reasoning using drawings, number sentences, or words
What a learner can do afterwards
- 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
1 · Read
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.
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.
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.
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.
Readings and practice questions written for this learning dataset.
More to read
Explain where each part went
To add 6 and 5, split the 5 into 4 and 1. Add 4 to the 6 to reach 10. Then add the remaining 1 to reach 11. Explain why you split the number and where each part went. Someone can check that you used all 5.
Do the check
Try another calculation to check your answer. You could count objects first, then count on from the starting number. Check that both methods use the numbers in the problem. Compare their steps and results. Copying your first answer does not give you a second calculation.
Look at the work
An answer alone may not tell you how someone got it. Look at their drawing or listen to their counts. Check each part against the problem. A group might need another object. A count might need another hop. Explain which part needs changing and why.
Change a double
If you know 3 + 3 = 6, you can use it to explain 3 + 4. The second group has one more, so the total has one more: 7. If that group has one fewer instead, take one from the double's total. Say which group changed.
2 · Watch
En anglaisTake it off screen
Where it sits
Learn first
Optional connections
This opens up
Where this leads
Jobs that lean on this skill. Follow one to see everything it is built on.
18 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.