(Adds details about product pricing, release dates and software)
CHICAGO/SAN FRANCISCO, March 27 (Reuters) - Apple Inc on Tuesday rolled out a new iPad and classroom software aimed at grabbing more of the U.S. education market, but did not cut the price of the entry-level tablet despite schools flocking to laptops costing a third less.
Apple is looking to reassert its dominance in U.S. schools, where inexpensive laptops running software from Alphabet Inc's Google and Microsoft Corp now top iPad by sales, offering a cheap way to get to cloud-based productivity tools.
The new iPad has a more powerful computing chip and an extensive set of new, free software for teachers to manage students and schoolwork. But the unchanged starting price of $299 for students and $329 for the general public, without a keyboard or case, compares with less than $200 for some Windows and Google Chrome models.
Some analysts had believed Apple might cut prices, but the company stuck with its more traditional approach of packing more features into a device and maintaining its minimum price.
Despite the new software, Apple faces a tough battle in the educational market given the popularity of Google and Microsoft's productivity suites, said Carolina Milanesi of Creative Strategies. Google's G Suite fueled Chromebook sales because it was seen as easy to use to manage assignments.
"Most teachers don't look past G Suite for education," she said.
Apple, as part of its response, on Tuesday announced improvements in its iWork suite of productivity apps at an event in Chicago. School bells and announcements over a public address system directed press and more than 300 teachers into an auditorium at Lane Tech College Prep High School.
The event came during a spring buying season when many schools are making purchasing decisions for the upcoming school year.
"We've been at this for 40 years and we care deeply about education," Apple Chief Executive Tim Cook said at the event.
Apple executives said the new iPad works with its pencil accessory and features an upgraded A10 Fusion chip, the same CPU that powers the iPhone 7. It is available immediately.
The Apple Pencil remains priced at $99 for the public and $89 for schools.
Apple made up just 17 percent of the K-12 U.S. educational market in the third quarter, according to data from Futuresource Consulting. Meanwhile 60 percent of mobile computing shipments to schools ran Google's Chrome operating system, and 22 percent had Windows.
Chromebooks sold by Dell Technologies Inc cost as little as $189. Microsoft last year introduced an education-focused laptop from partner Lenovo Group Ltd running Window 10 S for a similar price.
Apple in recent years made changes to its operating system so that more than one student can log into an iPad, and to its software to let teachers better manage students.
It vastly expanded those offerings on Tuesday, updating iWork - which includes word processing, spreadsheet and presentation software - to allow students to take handwritten notes more easily, along with adding more free storage space on its iCloud service.
Apple also released a new app called Schoolwork to help teachers create assignments and track student progress.
The previously iPad-focused Classroom teacher administration app would start working on Mac computers in June, Apple said.
In the fall Apple will roll out "Everyone Can Create" lessons on video, photography, music, and drawing, joining existing "Everyone Can Code" guides for computer programming skills.
Sales of iPads made up just 8.3 percent of Apple's $229.2 billion total revenue last year, compared with the nearly 62 percent of sales generated by iPhones. (Reporting by Stephen Nellis; Editing by Meredith Mazzilli and Peter Henderson)