A requirement for teaching fractions effectively. Fraction rules are counterintuitive without them. Among the models for fractions, circles are the best because the unit is always evident: half a pie is half a pie no matter the size of the pie. In contrast, the unit for rods, squares, or rectangles is arbitrary. For instance, for the Cuisenaire rods, if the purple or 4-rod is the unit, the red or 2-rod is 1/2, but if later the orange or 10-rod is the unit, it is 1/5.
The most distinguishing feature of the fraction circles is that they depict 12 different fractions all the way out to 16ths: 1, 1/2, 1/3, 1/4, 1/5, 1/6, 1/8, 1/9, 1/10, 1/12, 1/15, 1/16. (Sevenths, elevenths, and thirteenths were skipped because 7, 11, and 13 are prime numbers, thus severely limiting the number of problems that could be solved with them. Fourteenths were skipped because sevenths were skipped.) Having them go out that far allows students to solve lots of problems with them, and the more they solve, the more data (answers) they get from which to deduce the rules that connect the problems to the answers. Also, having 10ths, 15ths, and 16ths, in particular, make the skip counting patterns exhibited by equivalent fractions stand out. Note the equivalences of 1/2 and 2/3:
1/2 = 2/4 = 3/6 = 4/8 = 5/10 = 6/12 = 8/16
2/3 = 4/6 = 6/9 = 8/12 = 10/15
Those for 1/2 are ripe for the question "What fraction is missing in this sequence?" Ans. 7/14, because the top numbers are counting numbers, so there should be a 7 between 6 and 8, and the bottom numbers are the skip counting numbers for 2, so there should be a 14 between 12 and 16.
Think Links: Fractions • Decimals • Percent
Teaching and maintenance activities on fraction-decimal-percent equivalences in a game-like format. Presents decimals and percent as simply other ways of writing, thinking, and talking about the same thing: fractions. Answers to hundreds of equivalences in the activities themselves. Lots of pictures of fractional parts of squares that can be modeled with Ten Land blocks (for 10ths) and what are called base ten blocks (for 100ths and percent) to show the connection between fractions, decimals, and percent. Ideal for small groups and learning centers.
Focus on Pre-Algebra
Hands-on algebra activities using algebra tiles extended to 3 dimensions. Contents: positive and negative integers; adding, subtracting, multiplying, and dividing integers; algebraic expressions; adding, subtracting, multiplying, and dividing algebraic expressions; solving equations.
Math Games & Activities, Vol. 2
Activities for all major topics in number, geometry, and measurement in elementary school math. Nearly 30 games. Eighty activities, worksheets, and instructional aids. Diagnostic/prescriptive games for whole numbers, fractions, decimals, and percent. A complete program for teaching understanding of arithmetic word problems based on viewing addition, subtraction, multiplication, and division as combining and separating actions.
Answers, permission to duplicate, more than 100 pages of concise, easy-to-find instructions, and lots of examples and illustrations.
A booklet of 17 guided discovery activities for the fraction circles.