We continue the work done by Kalfagianni and Lee, where they gave two sided linear bounds for the crosscap number of alternating links in terms of certain coefficients of the Jones polynomial. In particular we find two-sided bounds for the crosscap number of the Conway sums of strongly alternating tangles in terms of certain coefficients of the Jones polynomial. Then we find families of links for which the crosscap number and these coefficients of the Jones polynomial grow independently. These families of links enable us to state the bounds for the crosscap number will not generalize to all links. We also study the relationship of the span of the colored Jones polynomial to the crossing number of a family of knots cablings. In particular we use the degree of the colored Jones knot polynomials to show that the crossing number of a (p,q)-cable of an adequate knotwith crossing number c is larger than q^2\ c. As an application we determine the crossing number of 2-cables of adequate knots.
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