List<TheBaseClass> items = new List<TheBaseClass>()

public class ProcessingStep1()
{
    Dictionary<Type, CalculateDelegate> lookupTable = new Dictionary<Type, CalculateDelegate>();

    public ProcessingStep1()
    {
        lookupTable.Add(typeof(ItemA), ProcessItemA);
        lookupTable.Add(typeof(ItemB), ProcessItemB);
        // ...
    }

    public method CalculateAThing(IEnumerable<TheBaseClass> items)
    {
        foreach (TheBaseClass item in items)
        {
            // desired to throw an exception if the key is not found
            CalculateDelegate calculate = lookupTable[item.GetType()];
        }
    }

    public ProcessItemA(TheBaseClass item)
    {
        // need to cast to access a property from the derived type
        var something = (item as ItemA).PropertyOnItemA;
        item.BaseClassProperty = doMath(something);
    }

    public ProcessItemB(TheBaseClass item)
    {
        // no need to cast, but the behavior is different for ItemB than others
        item.BaseClassProperty = somethingSpecific;

    }

    // ...
}

public abstract class TheBaseClass
{
    public abstract void CalculateAThing();
}