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How Delta is expected to change given a $1 move in the underlying is called Gamma. An investor can see how the Delta will affect an option's price given a $1 move in the underlying, but to see how the Delta on that option might change given the $1.00 move, we refer to Gamma. Gamma will be a number anywhere from 0 to 1.00. Since Delta cannot be over 1.00, Gamma cannot be greater than 1.00 either as Gamma represents the anticipated change in Delta.
Looking at the hypothetical example, XYZ is trading at $50. The XYZ Jan 50 call is trading for $2, has a Delta of .50 and a Gamma of .06. Should XYZ go up to $51, an investor can estimate that the 50 strike call will now be worth around $2.50. The new Delta of this 50 strike call at an XYZ price of $51 should be around 0.56 (simply adding the Gamma of .06 to the old Delta of .50).
