# 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 ©