What are the best strategies for adding in your head?
Mental addition is fast when you stop adding the way you write. On paper you work right to left and carry. In your head it is easier to work left to right, lean on round numbers, and add one chunk at a time. The goal is recall and shortcuts, not column arithmetic.
Pick one strategy per problem rather than mixing all of them. With short daily practice the right move becomes automatic, and you stop computing and start remembering. SIXTY's adaptive difficulty pushes you toward sums you fumble and replays the ones you miss, so the gaps close fast.
How does making tens (bridging through 10 and 100) work?
Bridging means topping a number up to the next round value, then adding what is left. Crossing a 10 or a 100 cleanly removes the messy carry.
For 8 + 7, fill 8 up to 10 using 2 from the 7, which leaves 5, so 10 + 5 = 15. The same idea scales: for 76 + 47, top 76 up to 100 using 24 from the 47, leaving 23, so 100 + 23 = 123.
- Find how far the first number is from the next round number (10, 100).
- Split the second number into that gap plus the remainder.
- Add the gap to reach the round number, then add the remainder.
Why should I add left to right instead of right to left?
Working left to right gives you the biggest part of the answer first, which keeps a running total in your head and means less to hold. You add the tens, then the ones, then combine.
For 47 + 36: add the tens, 40 + 30 = 70. Add the ones, 7 + 6 = 13. Combine, 70 + 13 = 83. You never wait on a carry because you fold it in at the end.
- Add the tens (and hundreds) first to get a rough total.
- Add the ones.
- Combine the two partial sums.
What is compensation and when should I use it?
Compensation rounds an awkward number up to something friendly, adds that, then subtracts the small amount you over-added. It shines when a number ends in 7, 8, or 9.
For 68 + 27, round 68 up to 70 (that is 2 too many), add 70 + 27 = 97, then subtract the 2 you borrowed, giving 95. You can round either number, whichever is closer to a 10.
- Round the awkward number up to the nearest 10 and note how much you added.
- Add the rounded value to the other number.
- Subtract the amount you over-added.
How do I add in chunks by place value?
Break the second number into hundreds, tens, and ones, then bolt each chunk on in order. This keeps each step a single easy addition and works well for three-digit sums.
For 256 + 137: add 100 to get 356, add 30 to get 386, add 7 to get 393. Each move touches only one place, so there is nothing to carry across.
- Split the number you are adding into its place-value parts.
- Add the hundreds, then the tens, then the ones to the running total.
How do I add a long string of numbers without losing track?
Look for pairs that make a round number and group them first, then add the leftovers. Reordering is allowed because addition can be done in any order.
For 7 + 8 + 3 + 2: pair 7 + 3 = 10 and 8 + 2 = 10, so the total is 20. Spotting these tens turns a four-step chain into one quick combine.
Reading is review. Recall is what sticks.
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