Students are presented with the challenge of dividing a cake into eight separate pieces that cannot form a rectangular or square shape. Rational numbers are explored within this exercise because each section of the cake is sold for $1.59. Each part must be equal to maximize profits and to ensure that each customer is receiving the same amount of cake for the price. Encourage students to create irregular shapes for cake pieces and do their best to divide the cake up into theses unusual parts.
Students can prepare for rational number activities by using a fractional strip kit. Each kit should contain different colors of construction paper that has been cut into different sizes. White construction paper will represent the whole portion of the kit and it should be 8 1/2 by 11-inches. Other sizes should include two halves of an 8 1/2 by 11-inch sheet of orange construction paper, three 1/3 yellow sheets, four 1/4 pink sheets, six 1/6 blue sheets, eight 1/8 green sheets, sixteen 1/16 bright pink sheets, twelve 1/12 beige sheets and twenty-four 1/24 purple sheets. Have students arrange the different pieces of their kit into various fractions and whole numbers.
Rational numbers can be printed on cards and used to instruct students about their place and order. Place a number of rational and irrational numbers on cards and have students arrange themselves around the room according to their numerical values. Teachers can also pass out cards and have students divide into two groups; one group will represent rational numbers and the other group will signify irrational cards. Five students can be placed at the front of the class with rational number cards and the teacher can ask the remaining students to put their numbers in order.
Cut out circles from different colors of construction paper that includes black, yellow, brown, blue, pink, gray, white and red. Each color should be divided into various fractional sizes with the exception of one piece, which should remain whole. Students should take their circle pieces and begin to experiment with fractional parts to see if they can form rational and irrational numbers.