Tear the leaves of the kale away from the stems. Roll up the stacked leaves, and slice thinly crosswise. Slice Brussels sprouts crosswise thinly. Slice red cabbage in half, and then cut crosswise into thin slices to make three cups. Shred the carrot, and combine all the veggies in a large bowl.
In a cup, combine the olive oil, vinegar, maple syrup, salt and pepper. Whisk together, then pour over the veggies. Add the dried cranberries, and toss to mix.