To find how many students there will be in the upcoming school year, we need to calculate $10\%$ of the current number of seventh graders and add that to the current total.
$10\%$ of $350$ students is $0.10 \times 350 = 35$ students.
Therefore, Winchester Heights Middle School plans to have $350 + 35 = \boxed{385}$ seventh-grade students in the upcoming school year.
Currently, there are $350$ students in the seventh grade at Winchester Heights Middle School. For the upcoming school year, they are planning to increase the number of seventh graders by $10\%$ .
How many seventh-grade students does Winchester Heights Middle School plan to have in the upcoming school year?
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