During our first investigation in our unit Factors, Multiples, and Arrays, our classes created posters of the arrays for various numbers. Using these posters, students put numbers into different categories based on the kind and number of arrays they could make. Students identified numbers that made "only one array", numbers that made "square arrays", and numbers that made "many different arrays". These initial ideas then developed into classifying numbers in five ways: odd, even, prime, composite, and square. Numbers may fall into as many as three different categories. Here is a list of the mathematical ideas that are being developed during Math Workshop as a result of these student-made posters:
Odd Numbers: * have a 1, 3, 5, 7, or 9 in the ones place * have only odd factors * odd x odd = odd
Even Numbers: * have a 2, 4, 6, 8, or 0 in the ones place * always have a factor of 2 * each factor pair must have at least one even factor * odd x even = even, even x odd = even, and even x even = even
Prime Numbers: * only have 2 factors (one and itself) * only produce one array * 2 is the only even prime number
Composite Numbers: * have more than two factors * make at least 2 different arrays * can be even or odd
Square Numbers: * make a square array * have an odd number of factors * follow a pattern of odd, even, odd, even, ... * can be made by multiplying a number by itself (ex: 1 x 1 = 1, 2 x 2 =4, 3 x 3 = 9, therefore, 1, 4, and 9 are square numbers)
Students, can you identify a number between 100-200 that is composite and square? Leave a comment and share your answer (and your reasoning)!!