For I delivered to you [b]as of first importance what I also received, that Christ died for our sins according to the Scriptures,
Makes sense to me.
When Paul refers to 'according to the scriptures', it is generally accepted that he is referring to what we call the 'Old Testament' encoded instructions of Messiah coming to bring the Gospel of The Grace of God in The Christ. Jesus, during the period following His resurrection, before His Ascension, 'opened the scriptures' to show how The Gospel of Grace is foretold and how He fulfilled it.
http://garyhabermas.com/video/habermas_unc_04-11-07_pt1.wmv
http://garyhabermas.com/video/video.htm
There is a glorious wealth of spiritually instructive and uplifting material at Dr. Habermas's website.