Unit 6 - Making Nets

Summary of Knowledge
The goals of the investigation are:

• To learn and comprehend about making nets and boxes.



• Learn new vocabulary and understand them.



• Drawing 3D shapes.

They should understand that this unit of investigation even though it is just shapes they may help you in your life.

Key Vocabulary

Base: Is the bottom face of a 3 dimensional figure.

Rectangular Prism : Is a 3 dimensional shape with 6 faces.

Cube: is a three dimensional figure with six identical square faces.

Surface Area: is the total area of all its faces.

Net: is a two dimensional pattern that can be folded to form a three dimensional figure.

TASK ANALYSIS

Find surface area of net.

1. Find dimensions of net.



2. Multiply L* W of each face.



3. Add them all up.

How to draw a net.

1. If it is a typed question just multiply L* W * W * H and L * H.
   



2. Add them all up and multiply it by 2.

HELPFUL WEBSITES

http://www.ixl.com/
This is a website to study for tests or quizzes.

http://gwydir.demon.co.uk/jo/solid/cube.htm
This other website helps you practice nets by playing a game.



QUIZ

Unit 6 - Making Nets » online quizzes

Unit 4 - Multiplying and Dividing

Summary of Knowledge:

In unit 4, Accentuate the Negative we learned how to work with positive and negative numbers. Although negative numbers are not very common in daily life experiences, they are very important information. As well, we learned how to work with exponents when adding, subtracting, multiplying, and dividing. We noticed certain rules to solve the problems in this unit.

Key Vocabulary

Commutative Property: The order of the addition or multiplication of two numbers that does not change the results or its product.

Examples:

2 + 3 = 5 / 3 + 2 = 5 / 4 x 2 = 8 / 2 x 4 = 8

Absolute Value: The absolute value of a number is its distance from zero on a number line.

Examples:

/-3/ 3

Task Analisis: for multiplying and dividing negative numbers.

1. 
   
   
   
   
   
   First multiply/divide the numbers like if there were not negative or positive signs(do a normal division/multiplication).






2. 
   
   
   
   
   
   
   If there is an even number of negative signs, then the product will be positive, but if there is an odd number of negative signs, then the product will be negative.

Examples:


Multiplication : -2 x 6 = -12 , -12 x -3 = 36

Division: -144 /12 = -12 , -56 / -8 = 7

Here are some fact families

12 x 3 = -36 2/100 /

3 x -12 = -36

-36 / -12 = 3

-36 / 3 = -12

Next you will show your abilities and skills in this quiz that we have prepared for you...

GOOD LUCK ! ! !

Multiplying and Dividing Negative Numbers. » test maker

Unit 5 - Scientific Notation

Summary of knowledge:

The goals for this investigation are to remember all what we learned in this unit and help our classmates and us to study for the final exam. Students should understand the difference between scientific notation and standard notation and how to work them.



Key Vocabulary:
Exponent: A number, letter, or any quantity written on the right hand of and and above another quantity and the denoting how many times the latter is repeated as a factor to produce the power indicated.

Scientific Notation: A short way to write very large or very small numbers. A number written in scientific notation is expressed in this form: A number greater than or equal to one but less than 10x10 raised to an exponent.

Standard Notation: The most common form of written numbers. For example 254 is the standard notation for 2 hundreds, 5 tens, and 4 ones.



Task Analysis:

Scientific notation to standard notation:

1.- Rewrite the number that is multiplied by ten.
2.- If the exponent next to the ten is positive, move that number of times from the decimal to the right, and if it is negative from from decimal to the left.

Examples:


10^8=100,000,000

3.6 x 10^11 = 360,000,000,000

7 x 10^3 = 7,000

7.56 x 10^-7 = .000000756

4.5 x 10^-2 = .045

6 x 10^-5 = .00006

Standard notation to scientific notation:
1.- Put a decimal point after the first number of the number sentence.
2.- From there count now how many spaces there are till the end of the number.
3.- The you eliminate the zeros at the end and you write the number times ten and then you put the number of spaces counted as the exponent.

Examples:

10,000,000= 1 x 10^7

7,534,000= 7.534 x 10^6

8,007,000= 8.007 x 10^6

.0005768= 5.768 x 10^-4

.057 = 5.7 x 10^-2

.0008 = 8 x 10^-4

Example problem and solution:

Scientific Notation » create exams

This video shows what is scientific notation, and how to manage small and big numbers.
It will explain to you why this works, and show you a task analysis.
It includes examples and clear explanations.


Useful links:
This is a website that explains what is scientific notation.
This is a scientific notation problem generator. Create your own problems and solve them!
This website gives your exercises and explanations

Unit 5- Exponent Rules

SUMMARY OF KNOWLEDGE
One of the main and primary goals for this investigation was to learn the order of operations. This included exponents. Exponents need a complex process in order to work out. Students should understand multiplication to work with exponents. Another goal was to use exponents to shorten equations for easier solving.
KEY VOCABULARY:

Exponents: Small number (in size) located on the top right part of another number, to represent the power to which the second is to be raised up.
Ex: 6^4= 6×6×6×6= 1296
Base: The bigger number below the exponent, called factor too, that is multiplied by itself.
Ex: 6^4= 6 is the base of this example

TASK ANALYSIS:

When we want to solve a number called Base (B) "Powered" to Exponent (E). (y=B^e)
First we must see the value of "E". If it is zero, then any base "powered" to zero is (1). (y=B^0=1)
If "e" is greater than zero, then B^e=B*B*B...*B. The result is the multiplication of B*B as many times as the value of "e" indicates.
If "e" is less than zero, (negative number) then B^-e
1/(B^e)
EXAMPLES:
1._ 6^0 = 1
2._ 6^4 = 6x6x6x6
3._ 6^-2 = -2/6^-2 = 6x6

1._ 6^0 = 1
2._ 6^4= 6x6x6x6x
1._ 3^2x3^7=3^9
2._ [(5^2)^3] ^2=5^3×2=5^6
3._ y^3/y^5=y^-2
4._ (6×5)^3=6^3×5^3

Here are some useful links that will help you with exponents for the final exam:
http://www.algebralab.org/lessons/lesson.aspx?file=Algebra_ExponentsRules.xml
http://www.purplemath.com/modules/exponent.htm

Exponent Rules » Online test maker

Unit 6- Order of Operations

SUMMARY OF KNOWLEDGE:


The goal of this investiagation is to get to know how to multiply , divide , add , and substract negative and positive numbers together.
By this we learn how to solve MATHEMATICAL EXPRESSIONS!

KEY VOCABULARY:
ORDER OF OPERTATIONS:
Established order in which to perform mathematical OPERATIONS!

TASK ANALYSIS:

1. First do parenthesis.
2. Then do exponents.
3. Then you do multiplications or division!
4. Then additions or susbtractions left to right!
5. When you are done with all these steps and their answers you add the ones that were in parenthesis with exponents with multiplication or division and or addition and substraction.

EXAMPLES:








[72*(36/ 40)]+10=11








7*7=49








36/40=0.9








49*9=44.1+10=11








([(44*4)+3]+-15) /140








((4*4*4*4*4)+3]+-15) /140








([256*4]+3)+-15) /140








([1,024]+3)+-15)/140








(1,027)+-15)/140








(1,012)/140=7.22

Unit 6-Order of Operations Quiz! » funny quizzes

Unit 6-Order of Operations Quiz! » fun quizzes

Unit 5 - Square and Cube Roots.

Summary of Knowledge.

When finished the unit you should know that to find the square root of a number, you want to find some number that when multiplied by itself, gives you the original number, the cube root of a number is some number that when multiplied by itself 3 times, gives you the original number.

Key Vocabulary.

Square Root: A divisor of a quantity that when squared gives the quantity. For example, the square roots of 25 are 5 and −5 because 5 × 5 = 25 and (−5) × (−5) = 25.

Cube Root:the number or quantity whose cube is a given number or quantity: 2 is the cube root of 8 (usually written 3square root 8 or 81/3).

Irrational Number: A number that cannot be expressed as a ratio between two integers and is not an imaginary number. If written in decimal notation, an irrational number would have an infinite number of digits to the right of the decimal point, without repetition.

Task Analysis.

Square Root

1. Have number of which you want to find square root.
2. Find the numbers square, a number that when multiplied by itself gives the initial number.
3. Plot number on problem.

Cubic Root

1. Have number of which you want to find cube root.
2. Find the numbers cube, a number that when multiplied by itself three times gives the initial number.
3. Plot number on problem.

Examples.
Square Root of 9 = 3, because 3 x 3 = 9.
Cube Root of 27 = 3, because 3 x 3 = 9 x 3 = 27, that equals 3 x 3 x 3.

Practice Quiz.

Square and cube roots » quiz builder

This Video Is So You Get It.

This video is just for fun so you hear good music untill you finish the exam.

This is for cube roots and how to get them.

Unit 6- Surface Area and Volume for Cylinders

Summary of Knowledge:
The goal of our investigation is to understand how to get the surface areaand the volume of figures. We made a project with 14 cans and 1 big piece of cardboard. We donated the box to the poor people of Ecuador.

All students should complete all of the investigation because after, you will need to review your notes to study.

Vocabulary:
surfae area:is the total area of all of its faces.
cylinder:is a three dimentional shape with a top and a base that are congruent circles.

Task Analysis:
Volume of a Cylinder

• Measure the diameter of the cylinder

• Divide the measurement by 2 (radius)

• Measure the height

• Multiply radius *radius*3.14*height.

Task Analysis:
Surface Area of a Cylinder:

• Measure the diameter of the cylinder.

• Divide the measurement by 2(radius)

• Measure the height.

• Multiply by 2* (radius*radius*3.14)+height*2*3.14*radius



Examples:

1.






R: 5 H:11

SA:2*(5*5*3.14)+11*2*3.14*5=502.65cm3
V: 5*5*3.14*11=863.94cm2

2.

R:15 H: 20

SA: 2*(15*15*3.14)+20*2*3.14*15=3298.67cm3

V: 15*15*3.14*20=14137.17cm2

Area and volume for Cylinders » fun quizzes

Unit 6 / Area and Volume of Rectangular Prisms