levels of education in usa

In the USA, children start school when they are five or six years old. Depending on the state, schooling is compulsory until the age of 16 or 18. Children younger than five can go to a nursery school or preschool.
At the age of five or six, the children attend elementary school (also known as grade school or grammar school), which last six years. The fist year at elementary school is called kindergarten.

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References:

http://www.goodschoolsguide.co.uk/international/transitions/from-american-schools-to-british
http://www.mesacc.edu/international-education/future-f-1-students/us-high-school-diploma-equivalents

different types of schools in uk

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The national curriculum is a set of guidelines schools use to make sure children around the country learn the same things.
Community primary and secondary schools run by the council follow the national curriculum. Other schools, such as free schools, academies and private schools can follow a different curriculum.

References:

http://new.brighton-hove.gov.uk/children-and-learning/brighton-hove-schools/how-school-system-works
http://ukcisa.org.uk/Research–Policy/Statistics/International-student-statistics-UK-higher-education

what age is high school

In England, you can apply for a 16 to 19 Bursary Fund to help with education costs.
You must then do one of the following until you’re 18:

You can find out what year your children need to start school with our school-age calculator below.
Enrolments are now open. Contact your local public school to apply to enrol. Please return your application to your local school by Friday 24 July 2020.

This means that a child who has turned five on or by 1 January in any year must start Prep in that year, or be provided with approved home education.
Every child, from the year after they turn 5 must be enrolled at and attending school, or an approved home education program. Children can also attend Kindergarten from 4 years of age.

This information was produced by the staff of the Belin-Blank International Center for Gifted Education and Talent Development (B-BC) at the University of Iowa (belinblank.org). The resources and information listed here are for informational purposes; there is no direct or implied endorsement by the B-BC. Services provided by the B-BC include programs for academically talented K-12 and college students, professional development for teachers, the Assessment and Counseling Clinic, the Acceleration Institute (accelerationinstitute.org), and graduate programs and research in gifted education.
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References:

http://www.education.wa.edu.au/enrolling-in-school
http://www.education.tas.gov.au/parents-carers/parent-fact-sheets/age-child-startleave-school/
http://www.accelerationinstitute.org/Resources/Policy/By_State/Show_Policy.aspx?StateID=37
http://www.goodschoolsguide.co.uk/international/transitions/comparative-ages-grades-and-exams-US-vs-UK