Tuesday, June 7, 2011
Monday, May 23, 2011
Unit 5- Scientific Notation
The purpose of scientific natation is make numbers easier to work with.
with scientific notation we can represent and display really large and small numbers easier
KEY VOCABULARY
Scientific Notation= a short way to write very large or very small numbers.
Standard Notation= the most common way of writing numbers.
EX. 254= 2 hundreds 5 tens 4 ones
TASK ANALYSIS
Standard-Scientific
make the number smaller than 10 but bigger than 1 and put the number of zeros on the exponent and *10 before the exponent
EXAMPLES
1. Standard-Scientific
2.5*10^-5= 0+0+0+0+2.5= .000025
Useful Links
http://www.math.toronto.edu/mathnet/plain/questionCorner/scinot.html
http://www.mathace.net/misc/scientific-notation
http://science.widener.edu/svb/tutorial/scinot.html
Unit 6 - Making Nets
The goal for this project is to make a blog explaining people how to de nets wich is our theme, students should understand the concept of a net and how to do it for rectangular prisms.
Unit 4 - Extending the Number Line
Summary of Knowledge:
Students should identify negative and positive numbers.
Students should identify the value of positive, negative, and rational numbers in order to place them on a number line.
Students should be able to know the relationship between positive or negative numbers and their opposites.
Key Vocabulary:
Negative Numbers: A number less than 0. On a number line, negative numbers are located to the left of 0. On a vertical number line, negative numbers are located below 0.
Positive Numbers: A number greater than 0. 0 is neither positive nor negative. On a number line, positive numbers are located to the right of 0. On a vertical number line, positive numbers are located above 0.
Opposites: Two numbers whose sum is 0. For example: -3 and 3 are opposites. On a number line, opposites are the same distance from 0, but in different directions from 0. The number 0 is its own opposite.
Integers: The whole numbers and their opposites. 0 is an integer, but is neither positive nor negative.
Rational Numbers: numbers that can be expressed as a quotient of 2 integers where a divisor is not 0.
Task Analysis of how to Place Numbers on the Number Line:
Examples :
Kate and brad have a project of measuring the temperature in the Sahara desert on their new film. They recorded these temperatures : 40 , 20 , 0 , -20 , -40. Do a number line and plot the temperatures in it.
Juanes is doing a number line and which he has to record the numbers : -2,0,2,4,-4. Do a number line , and plot the numbers.
Web References :
Web References :
http://www.helpingwithmath.com/resources/oth_number_lines.htm
www.funbrain.com/linejump/index.html
www.mathsisfun.com/number-line.html
By Juan Andres Zepeda and Nicolas Chavez
Unit 5 - Exponent Rules
The goal for this investigation was to understand exponents and learn how to use them. By completing this unit students shoul understand why and how the exponents work and the task analysis or algorithms to solve a problem.
Key Vocabulary:
Base - The face of a 3-Dimensional shape, chosen to be the bottom base.
Exponent - A symbol or number placed above and after another symbol or number to denote the power in which later is to be raised.
Task Analysis:
Multiplication Properties of Exponents:
1) Product of Powers property
To multiply powers having the same base, add the exponent.
In General: a^m*a^n=a^m+^n
2. 3*3^5=3^1+^5=3^6
3. (-2)^2+(-2)^4=(-2)^6
4. x^2*x^3*x^4=x^9
2) Power of a Power Property
To find a power of a power,multiply the exponent.
In General: (a^m)^n=a^m*^n
Examples:
1. (5^2)^4=5^2*4=3^8
2. (y^3)^4=y^12
3. [(y^3)^3]^2=-3^6
1) Quotient of Powers Property
To divide powers having the same base, subtract exponents.
In General: a^m/a^n=a^m-n
Ex:
1. 6^5/6^4=6^1=6
2. 9^4*9^2/9^7=9^6/9^7=9^-1
3. (-5^2)/(-5^2)=(-5^0)=1
4. y^3/y^5=y^-2
2) Power of a Product or Quotient Property:
To find a power of a product or quotient, distribute the exponent over the factors.
In General: (a*b)^m=a^m*b^m
(a/b)^m=a^m/b^m
Ex:
1. (6*5)^2=6^2*5^2
2. (4yz)^3=4^3*y^3*z^3
3. (2/3)^2=2^2/3^2
4. (7/4)^-3=7^-3/4^-3=4^3/7^3
http://www.algebralab.org/lessons/lesson.aspx?file=Algebra_ExponentsRules.xml
Unit 6 - Surface Area and Volume for Rectangular Prisms
The goal of this investigation is to be able to create a net, be able to create a box, and create net with given bow or create a box with a given net.This is very important because it may help us in the future specially if we decide to become architects. The main key terms that appear in this section are Surface Area and The Volume of a rectangular prism.
Key V0cabulary:
cube: A three-dimensional shape with six identical square faces
8 vertice
- 12 edges
net: A net is a two-dimensional shape pattern that can be folded to form a three-dimensional shape.
rectangular prism: A prism with a top and a bottom that are congruent rectangles.
base: The face of the three-dimensional shape chosen to be the bottom face
Task Analysis:
Suface Area: first you must find the are of each face of the rectangular prism. Then you add them up and you have the surface area. You could also find the surface area by getting the area of the three distinct faces and then multiply them by two.
Volume:to find the volume of a rectangular prism yopu must multiply the dimensions.
The equation for finding the volume of a rectangular prism is (lxwxh)
Examples:
The volume of this box is 8 sinse the dimensions are 2x2x2 (lxwxh)
The surface are of this cube 12 since the dimension of an face is 2x2=4 sinse its a cube you multiply times 6 that equals 12.
Unit 5 - Square and Cube Roots
Summary of Knowledge:
The goal for this investigation is to use square roots to find the side lengths of a square using the given area. You know that a square has two same sides and multiply both to give you thre area (x^2 ) (x*x)
Cube roots are important to find the side lengths of a cube by a given area.
Ex: volume : 27
side length: 3
( 3*3*3 = 27)
Key Vocabulary:
Irrational Number: A number in the decimal portion that never ends and does not repeat.
Cube roots: A number that must be multiplied by itself three times to equal a given number.
Ex: 27 the cube roots of 27 is 3 (3*3*3)
Square Roots: A nonnegative numner that must be multiplied by itself to equal a given number.
Ex: 4 the square root of 4 is 2 (2*2)
Task Analysis Square Roots:
1 Numbers should be perfect squares. This means that the product of a number multiplied by itself ( use nultiplication tables to help you know which numbers are square roots.)
2 If a number is not a square number write the two square roots in between.
Ex:
√20 Irrational in between 4 and 5
4*4 =16 5*5=25
20 is in between 16 and 25
Task Analysis of Cube Roots
1: Think of 2 factors that make the number that you are finding the cube roots.
Ex:
∛8
Factors: 2 AND 4
2: Then see if the small number can be used to divide the big number( the answer has to be the same as the small number). Also you can think if the big number is a square number. And of the square root is the small number.
Ex:
∛8 Factors: 2 AND 4
Factors of 4 : 2, 2 (2x2= 4)
3:Then multiply the 3 small numbers and the number should be the cubed number in the beggining.
Ex: 2x2x2 = 8 ( the cubed root of 8= 2)
4:If the number its irrational think of two numbers that are in between the cubed number.
Ex:
∛16
The 2 cube numbers are: 8 and 27
The cube root f 8: 2 (2x2x2) The cube roots of 27 : 3 (3x3x3)
The answer is : irrational in between 2 and 3
Examples of Square and Cube roots
∛27:= 3 this means that 3x3x3=27
√30 = irrational in between 5 and 6
Take this quiz to test your knowledge : if you need more help go to this useful links below.
style="FONT-SIZE: 10px; COLOR: #000; FONT-FAMILY: Arial, Helvetica, sans-serif">Square and Cube Roots » Make A Quiz
Very Useful Links!!!!
Square roots: http://www.ixl.com/1f?gclid=CK7-xbXcsakCFced7QodjWUoKQ
Cube Roots: http://www.onlinemathlearning.com/cube-roots.html