Justifying mathematical reasoning
Construct and follow multi-step mathematical arguments; identify errors in reasoning and explain why a method works or does not work
What a learner can do afterwards
- Explain step by step why a columnar addition method gives the correct answer
- Find and explain an error in a worked example (e.g. incorrect regrouping)
- Construct a simple argument for why a general statement is true (e.g. 'adding two even numbers always gives an even number')
The lesson
When someone shows you how they solved a maths problem, you can check if their thinking makes sense. Look at each step, not just the final answer. If every step follows the rules, the whole answer is right too.
Look at 27 + 15 added in columns. First add the ones: 7 + 5 = 12. Since 12 is more than 9, write the 2 and carry a ten to the tens column. Then add the tens: 1 carried, plus 2, plus 1, makes 4. The answer is 42. Each step follows from the one before, so the method works.
Now look at 46 + 38 done wrong. The ones were added as 6 + 8 = 14, but 14 was written straight into the ones column with no carry. Then the tens were added as 4 + 3 = 7, giving 714. The mistake is the step where the ten hiding inside 14 never moved to the tens column. Fixing that one step gives 84.
When you check someone's maths, follow the reasoning one step at a time. The exact step that breaks the rule is where the mistake is, even if the rest of the working looks neat.
Check every step, not just the final answer, and you can find exactly where reasoning breaks down.
Watch it
Where it sits
Where this leads
Jobs that lean on this skill. Follow one to see everything it is built on.
8 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.