Fourth graders should know that numbers can be expressed in many different ways. Fractions are an important concept of mathematical expression at this level. Students should know that the number 2 can be expressed as 46/23 and vice versa. Play a fraction game to review this form of mathematical expression. Have the students rewrite fractions as whole numbers or other fractions or simplify fractions by writing them as whole numbers. Design 3-by-3 tic-tac-toe boards with fractions written on them. Pair up students and have them play tic-tac-toe by placing crosses and circles over the fractions that they are able to correctly rewrite.
Children at this level are learning to express mathematical relationships in the form of equations. Story games are useful catalysts for practicing this form of expression. You can perform story games as a class, presenting problems in common language and having students write the problem as an equation. Tell the class that you will have a barbecue this weekend and 24 people are coming. You need to buy 24 hamburger patties and 24 buns. Hamburger patties cost 50 cents each, while buns cost 10 cents each. Elicit from the students the correct equation to compute how much the barbecue will cost (y=.5x24+.1x24).
Basic logic is a part of the mathematics used at the fourth-grade level (such as geometry and algebra). Introduce basic logic through puzzles and games. Demonstrate through quiz games how logical thinking can be related to the real world. An example of a question that may be asked in a logic game is a "True or False" question, such as "All frogs are green. George is a frog. George is green. True or false?" coupled with "All frogs are green. George is green. George is a frog. True or false?"
Students at the fourth-grade level are becoming much more familiar with how the real world works. Use games that mimic reality to help children internalize the mathematical concepts taught in class. In this game, students must use mathematical expressions to make decisions regarding money. Place students into groups and have them make decisions given a certain set of choices with a fixed amount of money. Tell students that they have $10 and need to buy enough food for the group. Give each group a list of items with different prices and tell the groups that they need to present their decisions as to what to buy along with their equations that show how much money they spent and how much is left over.