The National Building museum I think is much more suitable for that age. They have hands-on rooms with soft building blocks and right now they have a fun house exhibit with a huge ball pit and things to climb on!
Yeas is eez
Possibly. When I visited about a month ago, they were doing a lot of construction - part of it did look like a children's area, but it might be suited for kids a few years older. Most of the other exhibits would likely not be interesting for kids.
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