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Children also develop spacial awareness, the ability to see how things might fit together. Will this piece fit into that spot? (Will all of this 'stuff' fit in the trunk of the car?) Spacial awareness comes in later when children are learning about geometry and area.
Process of elimination is also learned. For example if this piece goes here, then this piece must go there. I have one piece left and one spot left, that must be where the piece goes.
Children also learn patience. Some children get frustrated when working with puzzles. You can model for them how to turn the piece to make it fit. Patience is a skill they will use forever!
If you haven't bought a puzzle go buy one. Start out with the chunky pieces and maybe only 3-5 pieces. If your child is a little older, teach them how to find all the corner and straight edge pieces first.
Every home should have puzzles. Puzzles are some of the best learning tools around!
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