No, you don’t have to take pre-algebra prior to taking algebra.
I was looking through the table of contents for the Teaching Book series, and this is what I found:
Pre-Algebra
Chapters 1-6 seem to be a recap of grades 6 and 7
Chapters 7-17 are virtually the same as Algebra 1
Algebra 1
Seems to cover everything in chapters 7-17 of Pre-Algebra, and probably a little more (presumably in greater detail)
Here is the link to the Pre-Algebra table of contents: http://184.168.83.81/Assets/PreAlgebraTOC.pdf
Here is the link to the Algebra 1 table of contents: http://184.168.83.81/Assets/Algebra1TOC.pdf
I personally have never used the Teaching Book series; however, from personal experience with other pre-algebra curricula and textbooks, I recommend you go straight to algebra 1. If your child needs to review any previous subjects, you could probably just review the previous lessons.
Hope this helps and God bless!
Pre algebra or algebra?
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You Don’t Need Pre-Algebra to take Algebra
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