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Here are lots of good ideas from all over the place for introducing the letter H. Most of these activities use the across-the-curriculum approach. These ideas are not just for preschoolers, but can be used remedially for any level, and for teaching students whose first language is not English.
Lesson Ideas & Activities:
Play Hide the H. Cut a large, capital or lower case letter H out of poster board or construction paper. Hide the letter somewhere, either in the open and slightly camouflaged or near an object that would begin with the letter H. Let the child(ren) look for the letter. You can say getting warm as they get closer to finding the letter or you can clap faster or slower depending on how close they are to the letter.
Think of all the names that start with the letter H: Henry, Harriet, Hercules, Howard, Heidi, Harrison, Harry, Hank, Henrietta, etc.
Pretend you are on a treasure hunt. Find things around the house that start with the letter H that could be the treasure.
Create your own book. You could make a picture book by letting them cut pictures of things that start with H out of magazines or they could draw their own pictures.
Go on a make believe trip to cities, countries or continents that begin with the letter H. Some examples could be Hawaii, Honolulu, Honduras, etc. You could find these on a globe or map, pretend to take an airplane trip there and then sample foods from that area or learn something new about that geographic area. This would be a great way to introduce geography and map skills. You could also watch a video or tv broadcast about that area. Check your local library for what’s available.