Mat 5:27-28 See Mat 5:20: what is the second example that Jesus gives in which our righteousness must surpass that of the scribes and Pharisees if we are to enter the kingdom of heaven? See Mat 5:17; with what fullness did Jesus fill the seventh commandment of Moses? How does this and the fullness with which Jesus filled the sixth commandment in the previous verses demonstrate the superiority of Christ’s law written on people’s hearts to the law of Moses written on tablets of stone? Cf. 1Sa 16:7. 
Borrowing terms from mathematics, in what sense might the law of Moses be described as “discrete”, but the higher law of Christ “continuous”, and how does that help us understand the superiority of Christ’s law? See Phil 3:6-9, 1Ti 1:15-16 and observe how a few discrete points on a graph representing our obedience to a law written in stone still allows for an infinite amount of deviation from the straight path of obedience to God’s will. Instead of marking discrete points that men must obey as does the law of Moses, what simple “formula” does the continuous law of Christ give? See Rom 13:8-10. Notice that on the continuum of Christ’s royal law of love, there are no longer any discrete points to mark our righteousness—what matters is being in Christ (on the line) where one point flows continuously to the next. This is the righteousness which comes from God on the basis of faith—that faith by which one abides in Christ.
Mat 5:29-30 What is the great danger of an adulterous heart? See 1Co 6:9-10, Heb 13:4, Rev 21:8. In light of this great danger, what does Jesus teach in these verses about the importance of avoiding temptations to such? Are His words here meant to be taken literally, or as hyperbole to emphasize the seriousness of an adulterous heart? What things in our world today cause men to stumble, especially in regard to lust, and what serious actions ought we take to “cut them off”? What do these verses teach us about the unthinkable awfulness of the judgment of hell (Gehenna)? Of what great value to a person are his eyes or hands? What would physical life be like without them? Consider the manifold afflictions of the wicked in this life, especially as the result of sexual sins; if one’s whole being when cast into Gehenna is simply consumed and the person annihilated, why would it be better for a sinner to add to his afflictions in this life by losing his eyes or hands than to simply seek release from all afflictions through annihilation? Is this not the very thinking of the wicked that deceives them to commit suicide?
Mat 5:31-32 What is the clear connection between these verses and the preceding? What is the great danger to one’s soul of entering into an adulterous marriage by marrying one who has been divorced? See again 1Co 6:9-10, Heb 13:4, Rev 21:8. For what one exception does Matthew record that Jesus said a divorce did not constitute adultery? What is meant by unchastity? Note: the Greek word used means fornication, as it is always translated by the KJV; in every other instance it is translated as immorality or fornication by the NASB. Is it significant that this exception clause is found only in Matthew’s gospel to the Jews, and not in any of the other gospels that were written to Gentiles, or in Paul’s writings to Gentiles? See Mat 19:8-9, Mar 10:11-12, Luk 16:18, Rom 7:3, 1Co 7:10-11. What was different about Jewish marriage from Gentile marriage that would warrant an exception clause for fornication, considering that once a marriage has been consummated such immorality is more properly called adultery? See Mat 1:18-19, 24-25. Would Joseph, a righteous man, have been sinning against God in desiring to “put away” (same word as used here in Mat 5:32 for divorce) Mary because he thought she had committed fornication during the time of their betrothal when they were technically considered to be married though the marriage had not been consummated? What does literal adultery in a marriage covenant teach us about spiritual adultery in our covenant relationship with God? See Jer 3:1-10, 5:7, 23:10-11,14, Eze 16:30-32, 23:43-45, Hos 3:1, etc…, Rev 17:1,5, 18:1-4, etc…. Are the dangers of spiritual adultery less, or even more serious than the dangers of physical adultery? See Jam 4:4. Whereas people may seek to justify their literal adultery against an unloving or unfaithful spouse, can they ever justify their spiritual adultery in the same way?