Unit 5- Exponent Rules

Summary of Knowledge:

Our goal in this investigation is make students understand everything clearly about exponents. We are going to show them four exponent rules. This is a very confusing topic, so we will put 100% effort to make it clear.

Key vocabulary:

-irrational numbers: Is an number in which the decimal porcion never ends an it doesn't repite.
-base: The basis of each place value columnin a number system.
-quotient: The answer to the division problem.
-product: The answer to the multiplication problem.
-power: The number of times a base number its multiplied by itself.

Task Analysis:
There are four rules:
-product of power property: to multiple powers having the same base, add the exponent.
-power of power property: to find the power multiply the exponents.
-qoutient of power property: To divide powers having the same base, subtratct the exponents.
-power or the product or quotient property: To find a power of a product or quotient, distribute the exponents over the factors.

Examples:
-product of power: 3^2 * 3^5= 3^(2+5)= 3^7
-power of power: (5^2) ^4= 5^(2*4) =5^8
-quotient of powers: 6^5/6^4= 6^(5-4)= 6^1= 6
-power of a product or quotient: (2/3)^2= 2^2/3^2

For more information visit:
-http://www.algebralab.org/

Exponent Rules » Quiz maker software

UNIT 6 - SURFACE AREA AND VOLUME FOR RECTANGULAR PRISMS.

Summary of Knowledge:

Do you remember the activity about the boxes that contain cans inside of them? All cans are usually packaged in a rectangular prisms where it is sombody's job to calculate the surface area and the volume of the boxes to see if all the cans will fit in it. In this investigation we will learn how to calculate the surface area and volume with the appropiate units of a rectangular prism. Also, we will know how to express the final area in the correct units, like the square units or cubic units. As well, we will learn all the steps of the surface area and volume of a rectangular prism in which we will apply the knowledge learned in real life situations.

Key Vocabulary:

1. Volume: Is the number of unit cubes that it would take to fill a box. It also is the amount of space occuppied by, or the capacity of a 3 - dimencional shape.

2. Surface Area: Is the total area of all of its faces. Also the area required to cover a 3 - dimencional shape.

3. Prism: A 3 - dimensional shape with a top and bottom that are congruent polygons and lateral faces that are parallelograms.

4. Base: The face of 3 - dimensional shape chosen to be the bottom face.

5. Rectangular Prism: A prism with a top and bottom that are congruent rectangules.

Task Analysis:

SURFACE AREA:

1. Find all the areas of the 3 distinct faces.

2. Add all the answers of the 3 - dimensional areas.

3. Multiply the answer by 2.

4. Put the corresponding units2.

5. Equation: 2 x ( L x W + W x H + H x L ) = Surface Area.

VOLUME:

1. Multiply the 3 distinct sides lengths.

2. Put the corresponding units3.

3. Equation: L x W x H = Volume.

Example:

1. Using the diagram below you will answer the following questions.

1A. Draw the prisms with the corresponding measurements.



1B. Find the volume of the rectangular prism with the correct units.

- 5 x 4 x 10 = 200 cm3

1C. Find the surface area of the rectangular prism with correct units.

- 2 x ( 5 x 4 + 4 x 10 + 10 x 5) = 2,500cm2.

surface area and volume for a rectangular prism » Quiz Maker

Unit 4 - Order of Operations

What are the goals for this investigations? What should students understand upon completion of investigation?


Order of Operations is very important because is a universal way to solve operations. It provides you an order to solve mathematical expressions involving addition, substraction, multiplication, parenthesis, division and exponents.



Key Vocabulary



- Order of Operations: Established order in which to perform mathematical operations.


1. Compute any expressions within parenthesis.


2. Compute any exponents.


3.Multiply and divide in order from left to right.


4.Add and substract in order from left to right.




How to solve a problem step by step?

(5x3) + (2x2)^2 - 6/3=30
First you solve the parenthesis " (5x3), (2x2) "
15 + 4^2 - 6/3 Then, you solve the exponents " 4^2 = 16 "
15 + 16 - 2 = 30 After that you do the division " 6/3"
And finally, you do the addition " (5x3) + (2x2)" and then the substraction "-2"

software

Order of Operations » Free online quiz softwar

Order of Operations » create assessment

http://www.mathgoodies.com/lessons/vol7/operations_exponents.html

Unit 4- Adding and Subtracting

Summary of Knowledge

Do you remember the black and red chip boards? In this investigation we used those chip boards, and numberlines to learn how to make addition and subtraction opperations with positive and negative numbers. We understood different patterns to solve there operations.Many of us noticed that if you add a positve and a positive the answer will be positive ans if you subtracta a negative and a negative the answer will be greater than the initial number. Not only this but much more.


Key Vocabulary

• Commutiative: The order of additon may change and the answer will be the same.


• Absolute value: The distance from zero on a numberline.


• Algorithim: A set of rules to preform an opperation.

• Integer: A whole number that has opposite
  Example:1/-1

• Sum: The result of an addition.
  


• Product: The result of a subtraction.

• Positive number: A number greater than zero(0).


• Negative number: A number smaller than zero(0).


• Opposites: A positive and a negative number that haved the same distance from zero(0).

Task Analysis

Positive and negative (whole) numbers

1.Write your opperation.

2. Locate the first number on a numberline( on a paper or your head).

3. Change the opperation to a single sign( task analisys #2).

4.Answer.

5. Check by repeating process.

How to Change the Sign
1. When you have:
(+n)+(-n) =(+n)-(+n)

• (+n)-(-n)= (+n)+(+n)
• (+n)+(+n)= (+n)+(+n)
• (+n)-(+n)= (+n)-(+n)
• Addition is commutative so if negative sign is first you can put it second then change the sign.

2. Opposites

*(-s)+(+s)=0

* When both numbers,(not the sign) are the same digit, the answer will always be zero.

Example:(-4)+(+4)=0

Fractions adding and subtracting

1. Write down the problem.

2. Convert mixed number into improper fractions.

3. Find the common denominator.

4. Solve the numerators(with main sign)(not the denominators).

5. Put the answer over the denominator.

6. Check.

Examples

1.(-100)-(+3)=(-103)

2.(-10,043.5)+(-75)=(-10,118.5)

3.(-50)+(12)=(-48)

Links that can Help

http://s4zygxf.edu.glogster.com/adding-and-subtracting-integers/

http://www.mathsisfun.com/positive-negative-integers.html

http://www.phschool.com/atschool/cmp2/active_math/site/Grade7/Chip/index.html

Adding and Subtracting » online exam

Unit 5- Scientific Notation

Michelle Ramirez

Daniel Peña

Summary of Knowledge:

Scientific notation is a goood way to abrbiate long numbers and shrt numbers. Scientific notation is imporatnt because mathematicians need a better way to simplify numbers without taking the value. For mathematicians is better to simplify than count the zeros.


Key Vocabulary:

Scientific Notation: is a short way to wrte the very large or very small numbers.

Standard Notation: the most common form of written numbers. ex: 254= 2 hundreds, 5 tens, and 4 ones.


Task Analysis:

Scientific- Standard

1.You see the number
2.Then you see the exponent that are the number os place value the decimal moves.
3.If you move to the ricght is positive and if you move to the left is negative.

Standard- Scientific

1. You need to move the decimal place so the decimal is in between the place value of one and ten.
2. And to know the exponents you count the number of place values you moved.
3. end should end like this: c*〖10〗^n , where c should from one to ten, and n is the exponent.

Examples:

hange from standard to scietnific:

1,000,000,000,000 = 1*10^ 12

Change to standard:

7 *10^ 8 = 700,000,000

Scientific Notation » Free online quiz software

Unit 4 - Multiplying and Dividing

Summary of Knowladge

In this investigation we will unmask the mystery behind negative numbers and we will learn to multiply and divide them. We will do it by applying real life examples in questions and problems to solve.

Vocabulary

Negative number: A number less than 0 and on a number line its located to the left of 0.


Absolute value: The absolute value of a number is the distance from 0 in a number line.


Positive number: A number greater than 0 and on a number line it is located on the right of 0.

Comutative property: Order of addition or multiplication that does not change the result.



Task Analysis

Multiplying a negative with a positive number


1. Take out the negative sign of the negative number.

2. Multiply the two factors

3.Put the negative sign to the final result

Multiplying negative numbers

1. Multiply the number as if it woulde be positive

2. If the amount of negative numbers is even the answer will be positive and if the number os negative numbers is odd the answer will be nagative.

Dividing negative numbers

1. Divide the number as if it was positive

2. If the amount of negative numbers is even the answer will be positive and if the number of negative numbers is odd the answer will be negative.

Example

-4*-2*-6*-8*-10= take out all the negative and fing the result signs so.....



4*2*6*8*10= 3840 because there are a odd amount of negative number the answer is negative



-4*-2*-6*-8*-10= -3840




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-8/-7/-1= croos out the negative sign. 8/7/1= 1.14 add negative sign to result because the amount of negative numbers are odd -1.14

OTHER HELPFUL SITES

Multiplying and Dividing » make test

Unit 5 - Square and Cube Roots

Summary of knowledge:
The goal was to be able to understand the concept of square and cubic roots, and be able to find the root of any given number. You should know that any number has a square and cubic root, even if the square root is irrational. When it's not perfect it's an irrational number between two numbers.

Key Vocabulary:
Irrational Number: Number in which decimal portion never ends and doesn't repeat.

Task Analysis:
1. Memorize the square roots from 1-12 and the cubic roots from 1-5.
2. Check if it would be a perfect or irrational number.
3. See in between which two numbers or what number your square/cubic roots is.
4. If perfect put the number. If irrational put between what numbers and write "irrational."

Examples:
1). √25 = 5 (5*5 = 25)
2). ∛27 = 3 (3*3*3 = 27)
3). √10 = between 3 and 4 (3*3 = 9 / 4*4 = 16) IRRATIONAL
4). ∛15 = between 2 and 3 (2*2*2 = 8 / 3*3*3 = 27) IRRATIONAL



USEFUL LINKS:

http://www.math-videos-online.com/algebra-square-roots.html

http://www.mathvids.com/lesson/mathhelp/664-square-roots

http://www.ixl.com/math/grade-7/square-roots-of-perfect-squares

http://www.ixl.com/math/grade-7/estimate-square-roots


Practice Quiz:

Square and Cube Roots » ProProfs Quizzes