Addition and subtraction strategies (age 7+)
Explain why addition and subtraction strategies work, using place value and the properties of operations
What a learner can do afterwards
- Explain why adding tens and ones separately gives the correct total
- Describe why a compensation strategy works (e.g. 'I added 1 too many, so I subtract 1')
- Use place-value language to justify a written method step by step
The lesson
When you add two numbers like 67 and 24, you can split each one into tens and ones, add the tens together, add the ones together, then join the two answers. This works because of place value: the tens digit always means 'how many tens' and the ones digit always means 'how many ones,' so tens only ever combine with tens, and ones only ever combine with ones.
Look at 67 + 24. Split it into 60 + 20 and 7 + 4. 60 + 20 = 80. 7 + 4 = 11. Now join them: 80 + 11 = 91. Splitting works because 60 and 20 are both tens, and 7 and 4 are both ones, so nothing gets mixed up.
Compensation is another good strategy. For 29 + 15, you might add 1 to 29 to make 30, because 30 is easier to work with. But adding that 1 changes the total, so you must take it back off at the end: 30 + 15 = 45, then 45 minus 1 = 44. Whatever extra you add, you must remove later.
Splitting and compensation both work because they keep track of place value, so the total stays exactly right.
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.