The Meadows School was Summerlin's first constructed facility of any kind, opening in 1988 on 40 acres donated by the Howard Hughes Corporation, several years before the community's first residents moved in. Summerlin's first public school, William R. Lummis Elementary, followed in 1993 and was named for Howard Hughes' cousin and the executor of his estate. The Howard Hughes Corporation donated $250,000 to Clark County School District at the time to help fund a new school building prototype that CCSD went on to use across the district.
According to Danielle Bisterfeldt, Senior Vice President of Marketing and Consumer Experience for Summerlin, in the developer's own published statement, planning for both public and private schools was part of the master plan from its earliest stages, with land specifically set aside for both. Summerlin's developer has published a total figure of 26 schools operating within the community; its own current schools directory names 14 schools operated by CCSD, 2 public charter schools, and 9 private schools, which totals 25, one fewer than the published figure of 26.
Those three categories work differently for a buyer or renter to understand. CCSD's public elementary, middle, and high schools are assigned by a home's exact address under the district's zoning system. Nevada's public charter schools are open to any eligible student through a lottery, regardless of address. Private schools set their own independent admissions and tuition, separate from both CCSD zoning and the charter lottery.
For a broader look at Summerlin's neighborhoods, amenities, and real estate market beyond schools specifically, my Living in Summerlin Las Vegas: Community Overview covers the community as a whole. That guide is a useful starting point before narrowing in on a specific neighborhood based on school proximity.