'For all have sinned, and come short of the glory of God; Being justified freely by his grace through the redemption that is in Christ Jesus: Whom God hath set forth to be a propitiation through faith in his blood, to declare his righteousness for the remission of sins that are past, through the forbearance of God; To declare, I say, at this time his righteousness: that he might be just, and the justifier of him which believeth in Jesus.'
To make sure we understand, Paul uses two words to show that justification is a gift. The word freely and the word grace. The word freely is not to be substituted with the word 'only' because 'freely' is used to describe redemption in Christ as a gift of grace.
In Sunday School we listened to an explanation that justification is like a 3-legged stool or mathematical equation: Works + Faith + Grace = Justification. To those who have not read Romans it makes sense that works must be thrown in the mix, that our deeds have a part in our justification, that we must add works into the equation. But this is not biblical. Isaiah prompts us: 'But all our righteousnesses are as filthy rags; and we all do fade as a leaf; and our iniquities, like the wind, have taken us away.' Isaiah 64:6
Therefore works is not the component that yields justification. Paul taught that faith in the blood of Jesus = Justification.
The explanation can be better represented by a chemical equation. It would look like this: Add two components: the component Faith to the component Grace which yields a reaction. That reaction is works. The symbol for yield is an arrow with a delta symbol over it. Faith + Grace ^ Justification.
Those who believe that redemption is gifted upon faith in the blood of Jesus Christ are made righteous by His righteousness, and will do good works linked to justification. The point is good works do not make us justified before God.
Many people practice the old covenant formula while living in the times of the new covenant. Not understanding the new covenant, we rehearse the old over and over again.