Start with the larger number
For 5 + 3, start at 5 and count on three: 6, 7, 8. Counting on means you do not need to begin again at 1.
Make ten when a sum crosses ten
For 8 + 5, split 5 into 2 and 3. First use 8 + 2 to make 10, then add the remaining 3 to reach 13. Making ten can turn a less familiar sum into two easier steps.
The ten-question round moves from sums within 10 to non-crossing sums within 20, then mixes in crossing-ten facts. If an answer is not right yet, keep it in view, adjust it, and try again.