Mathematical terms and their representations with Cuisenaire Rods

Mathematical term Represented with Cuisenaire Rods as -
Patterns Arrangement of rods in an arithmetic progresion, geometric progression, repetative colorization, ...
Even numbers Any train represented by a train of red rods
Odd numbers Any number which can not be made by a train of red rods
Sequence Stair cases
Inequalities Collections, trains, Venn diagrams, sets, groups
Equalities Collections, trains, Venn diagrams, sets, groups
Addition Trains, regrouping with mats
Subtraction What's missing?, take away, regrouping with mats
Associative property  
Commutative property  
Multiplication Repeated addition, squares and rectangles, towers, place mat
Distributive property  
Division Repeated subtraction (How many can be taken away?) How many groups? How big of groups? Tear down a tower. Place mat division.
Place value Grouping game, trading game, place mats with rods, squares and cubes, towers *see exponents to do decimal numbers with towers.
Fractions If then equations, puzzles, guess my mind (if red is 2/3 what is one?)
Addition of fractions Create fractions with identical rods a denomenator or value of one, then join the rods representing the numerator.
Subtraction of fractions Create fractions with identical rods a denomenator or value of one, then separate the rods representing the numerator.
Multiplication of fractions Repeated addition, of, four ways,
Division of fractions How many in? How many groups can be taken away? (repeated subtraction) How big of groups? 1/3 divided into three equal groups is 1/9? 4 divided into equal groups of 2/3 = 6 (make train of four light green rods and put red rods(2/3) under to match (6). 7/8 divided by 3/4 use eighths, 7/8 and 6/8, how many 6/8 in 7/8? one and one part of the 6 = 1 1/6.
Decimals If then equations, puzzles
Fractional equalities Rectangles
Primes A number that can not be formed by a train of any one color except white
Composite Any number that can be formed by a tower of factors
Greatest common factor Candy sacks - If all the rods that represent the factor for eeach number were put into a separate sack and each represents a candy, then what would be the largetest candy that is in all the sacks? Can be done with primes as well as all common factors.
Least common multiple Candy sacks - If the primes of multiples are put into sacks, which sacks would have the least number of rods and would exactly match? Multipes of 3 are (g * w) (g * r) (g * g) (g * p) (g * y) Multiples of 5 are (y * w) (y * r) (y * g).
Exponents Towers of rods, for positive use white base and for negative put white on top of tower to show negative (3 - 1=1/3, 3 - 2=1/9)
Mean, median, mode Line up rods to represent data, locate, count, move to balance.

Dr. Robert Sweetland's Notes ©