Exam 2..

Our second exam is on this coming Monday. In class yesterday some of the students brainstormed ideas of what they thought was going to be on the exam. Here is a list of the ideas that they came up with....

• Divisibility Rules
• Divisibility Properties
• Prime & Composite Numbers
• Sieve of Eratosthenes
• Number systems
o Egyptian
o Babylonian
o Roman
o Mayan
• Calculations in Base 12
• Calculations in Base 5
• Addition, Subtraction, and Multiplication using number lines
• Addition, subtraction, multiplication and division using manipulatives
(exchanges, regrouping, using rectangles, etc.)
• Partial Sums
• Partial Products
• Partial Quotients
• Factor trees
• Using number rods
• GCF and LCM
• Properties of Addition
• Properties of Multiplication
• Number Sets

Prime Numbers and Factorization

A prime number is a natural number that possesses exactly 2 different factors. These factors include 1 and itself. This rule makes the smallest prime number 2.

Prime Factorization: writing a number as its unique product of prime factors. Click here to see an example of how this is done using a factor tree.

PRIME FACTORIZATION TREE:

Divisibility

Divisibility: if a and b are whole numbers with a not = to 0, then a is a factor of b if and only if there is a whole number c such that a * c = b, we can say "a divides b" or "b is a multiply of a".

To find out if a large number is divisible by 2 without using a calculator, you can add up the sum of all of the digits, and if that number is divisible by 2, then the number as a whole is divisible by 2.

Example: 24,593
2+4+5+9+3 = 23
23 is not evenly divisible by 2...
therefore, 24,593 can not be evenly divided by 2.

multiplication, multiply, times, product, double, triple....

There are many different ways that you can multiply numbers. A method that we were just taught in class is known as the lattice method for multiplication. The Lattice Method can be time consuming, but yet very efficient. Click here to see a visual of how the Lattice Method works!

Back to the basics..

Today in class we had a student presenter who helped us to learn how to divide with the grouping method. We had candy corn, and divided them into even groups. For example, for the problem 24/2, we started by making 2 groups. From there, we evenly disperse the remaining candy corn into the two groups. So when all of your candy corn is gone, you should have 2 groups with 12 candy corn in each.

Addition

There are numbers EVERYWHERE! We are constantly doing math, even when we don't realize it. Yesterday we learned about the different properties of addition and multiplication.

Properties of Addition

1. closure: any number in the set added with a different number in the set, remains a number located in the set
2. identity
3. commutative: order of the numbers does not matter
ex. 3+4+5 or 5+3+4
4. associative: regrouping numbers
ex. (2+3x)+5x or 2+(3x+5x)

Click Here to see the associative and commutative properties demonstrated in the classroom.

Yesterday in class we learned how to add and subtract in both base 5 and base 12. In our base 10 system, we have 10 digits including: 0,1,2,3,4,5,6,7,8, and 9. In the base 5 system there are 5 digits: 0,1,2,3, and 4.