Good question, and one I'm passionate about!
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Yes, you do need a reading program, but I'm not sure what you're doing with BJU Reading exactly. BJU generally uses anthologies alongside worksheets, which didn't fit with the CM philosophy we've come to love that uses whole living books. But that would be a personal choice up to you as you consider your reading goals.
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There is so much more to reading than just reading well! There is an entire body of reading instruction to be taught, and it is pretty important. I just googled "reading state standards", and these are the ones that came up first, so here's a copy of the state standards for fourth grade reading in these states:
Here is AZ's:
http://www.ade.state.az.us/standards/la ... RdgGr4.pdf
Here is CA's:
http://www.sdcoe.k12.ca.us/score/stand/std.html#4WA
Here is WI's:
http://dpi.wi.gov/standards/elaa4.html
There's a lot there, isn't there?!?
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The good news is HOD considers state standards when they write, so through "Drawn into the Heart of Reading", R & S English, writing instruction, and CM-style LA instruction, you should be fine, though it is up to each of us to be sure we are meeting standards. However, when considering state standards it is good to keep in mind that the very most important goal of teaching children to read is to help them to read with moral discernment, and blessedly DITHOR meets that higher standard beautifully, even though it is not a
state standard.
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HTH as you consider reading for your fourth grader!
In Christ,
Julie