River is a multi-part sign. First, make the sign for water with your dominant hand (by tapping the ASL letter W against your chin), then hold your hand open and flat, palms either facing down or facing each other in front of you, running parallel to each other as they shimmy in a synchronized curved manner, somewhat similar to how you sign hall or street, but in a sinuous way instead.
Teach your child the sign for river when you are actually out for a stroll in the woods or at a park that's lucky enough to have a river or stream running through it.
We use the sign for river when we have one in close proximity to home, or the first time we go on vacation with our little ones.
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