You cleave something when you split it along a natural grain by hitting it with a forceful blow.
The man in the picture has cleaved some wood.
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Climbing is a way of getting up something that is too high or too steep to just walk up. Things that people usually climb are cliffs, mountains or trees.
Adults usually climb cliffs, mountains or rock faces, and children usually climb trees or playground equipment. But you can climb lots of other things too.