In order to teach fifth-graders to manipulate numbers, create a real-life scenario in which adding, subtracting, multiplying and dividing are necessary. For example, in Clara's ice cream shop, students have to order several different combinations of items, adding the cost. Take away two orders to practice subtraction, add eight orders of the same thing to practice multiplication and split the bill into pieces to practice division.
A word problem that explores numerical patterns works well for fifth-graders. Divide the class into groups and have them each work out a word problem with number patterns. For example, Bill Gates comes to the school and offers each child the chance to work for him for a month. He will either double their pay each day, starting with one cent, or he will pay a lump sum of one million dollars. Ask the kids which is better.
Have the class figure out the area of the classroom, by measuring the height, length and width. This project may involve the use of ladders to reach the ceiling, so use caution. Once the class has figured out the area of the room, compare it to other areas around the school. This project works well for a particularly rowdy or active class that needs to move around to learn.
Give the class the opportunity to devise their own number sets. They can use the heights of their classmates, the ages of all the kids in the school, or the amount of rainfall in their town over the past ten years. Whatever number set they choose, have them draw out a chart mapping the mean, median and mode of all the numbers.