Deepening Our Understanding of Mathematical Properties and Relationships

In our final weeks of school, our focus has turned back to nurturing and developing essential understandings in mathematics. Our students should be very confident with the following categories of numbers:

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 (odd x even = even, even x odd = even, and even x even = even)

Prime Numbers:
* only have 2 factors (one and itself), 2 is the only even prime number

Composite Numbers:
* have more than two factors, can be even or odd

Square Numbers:
* make a square array and have an odd number of factors (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)

Our current Scott Foresman Investigation in Math (Number Puzzles and Factoring) challenges students to identify numbers that contain one or more of the above-listed categories.These have been presented to the students as "puzzles"...
For example, Think of a number that is even and square.......4 works (produces a 2x2 array, 4 is even).....16 also works (produces a 4x4 array, 16 is even).

In working through number puzzles, students must also distinguish between factors and multiples. 
Factors of 8 are 1, 2, 4, and 8
Multiples of 8 are 8, 16, 24, 32.....(and so on)


Our puzzles have extended to considering FOUR CLUES at a time! We love BRAIN GYM. :-)
*Example: Think of a number that is even, a multiple of 3, less than 100, and a square number (the number 36 would work in this puzzle).


As these ideas have been reviewed and developed, we have used them to build our understanding of prime factorization. The kids REALLY are enjoying this! What an engaging and powerful way to integrate our understanding of factors, prime and composite numbers.

Our 5th grade teachers are SO excited that these "rising 5th graders" will be coming to them with a solid foundation build upon understanding of fundamental properties and relationships of numbers.

Our students are so excited and empowered too- they are even using their understanding of number to find all of the factors for large numbers such as 180 (which has EIGHTEEN factors, by the way)!!

Math Rocks!