linno

Learning Target

Solve two step equations.

Example

4a + 12 = 32

1. Do the inverse of +12.

4a + 12 =32

-12

2. Then, balance it on the other side (33).

4a + 12 =32

-12        -12

            = 20

3. Bring down the a4, so that a4=21

4a + 12 = 32

-12        -12

4a         = 20

4 . Do the inverese of 4a: a4 divided by 4, and balance it.

4a =20                                                                                                                                                  

4     4 

     =5

5. Dividing 4a by 4 just leaves you with a, so a = 5. Then check it by replacing a with 5 just to make sure.

4 x 5 + 12 = 33

Remember:

The steps for solving any equation are inverse, balance, solve, check, but with two step equations, you have to do these steps twice.

When multiplying with a variable, the number always comes before the variable (4a, not a4).

The goal is to get the variable by itself.

Balance is the key to solving any problem. 

Learning Target

Graph ordered pairs of numbers on a coordinate plain.

Vocab

x-axis- a horizontal number line on a coordinate plane.  X comes first in ordered pair.

y-axis- a vertical number line on a coordinate plane.  Y comes second in ordered pair.

origin- 0,0, where the axis intersect

ordered pair- example: 5,2- used to find points on a coordinate plane

quadrant-  the 4 spaces the axis divide the coordinate plane into.

Quick Lesson

A coordinate plane is a grid split into 4 parts called quadrants.  To find a specific location, use ordered pairs.  For example (5,2) means you would go over 5 spaces and up 2.  The y and x axis have numbers on them, used to tell where to plot your dot. 

Example

The coordinates for the red dot are (2, -2)

What are the coordinates of the corners around the x on the x axis?

Bottom left: (8, 0) 

Bottom right: (9,0) 

Top left: (8,1)

Top right:  (9,1)

Check out densonr's blog for another point of view on coordinate planes.   

Have you ever looked at the sky at night and wondered what was out there, way far out there? Well, the Hubble Telescope helps us find out. But what is the Hubble Space Telescope?

Hubble Space Telescope

History

The idea for the Hubble Space Telescope originally came from Dr. Lyman Spitzer in 1946, who believed that a telescope in space would produce much clearer images than those from the ground. In the 1960s and 70s, Spitzer convinced NASA to construct a space telescope, and in 1975, NASA and the European Space Agency began developing it. In 1983 the telescope was named after astronomer Edwin Hubble, whose observations confirmed that the universe was expanding. After 8 long years the Hubble Telescope was finished.

But when the solar powered telescope was launched with and deported from the Discovery on April 24, 1990, the pictures that Hubble sent back to Earth were fuzzy and distorted. NASA discovered that one of the mirrors on the telescope was the wrong shape. Engineers designed a device to install on to the telescope to fix the mistake, bending light so that the error would not be a problem. The telescope worked perfectly after astronauts from Endeavour put the tool on the telescope in 1993.

How Does it Work?

The Hubble Space Telescope runs on solar power and can see objects in space from billions of light years away because clouds aren't in the way, unlike telescopes from Earth. The telescope is controlled by radio signals from NASA down on Earth. The telescope has a long tube, opened at one end, to take in images. Located near that end, mirrors are attached to Hubble to reflect light and focus it in one spot, bringing the light into different instruments on the telescope. Not only is the Hubble Space Telescope an extremely technical and helpful instrument, it is also a spacecraft. Along with all the various tools and instruments on the telescope, it also has the ability to orbit the earth.

Discoveries

The Hubble Telescope has had many discoveries promoting the scientific knowledge of astronomers and astrophysicists. Hubble has given NASA the first close up look at Pluto's surface, allowing them to understand what the planet will be like when we venture there. The telescope has confirmed that middleweight black holes, very large black holes, exist. The Hubble Space Telescope witnessed a super sonic shock, therefore confirming the theory that as gas rams into surrounding material, it creates a planetary nebula. It also witnessed two galaxies colliding, the result of which being the larger galaxy leaving the smaller galaxy in bad comdition

Super Sonic Shock

The Hubble Space Telescope was built to last at least 15 years. It has now operated for over 16 years and continues to send images back to Earth to enhance education about outer space.

Learning Target

Compare and order fractions

Lesson

To compare fractions:

1. Use prime factorization to find the least common multiple (LCM) of the two fractions

you are trying to compare.

2. Then create equivelent fractions using the LCM as the denominator.

    a. Find out how many times the original denominator goes into the LCM.

    b. Multiply the numerator by that number.

To order fractions:

Complete steps 1-2 with all of the fractions and put them in order.

Example

Compare:

3/6                 4/5 

 6= 3 times 2      5=5

/  \

3  2

5 times 3 times 2= LCM:30

a. 30 divided by 6=5  3/6=15/30            30 divided by 5=6   4/5=24/30           
b. 3 times 5=15                                    4 times 6=24

3/6 is less than 4/5.

To learn more, chack out this website.

Learning Target

Use stratigies to develope formulas for finding the circumferences

and diameters of circles.

Example

Multiply the diameter by π (pi) to get the circumference.

You have a can with the diameter of 14.7.

14.7 times π = 46.18  

The circumference of the can is 46.18.

Lesson

On Friday, we did an activity with the circumferences and diameters of circles.  We

took 5 circular objects, such as cans and buckets, and measured the circumferences

and diameters of them with a tape measure.  We found that the circumference divided 

by the diameter equals π.  With any circle, you can multiply the diameter by π to get the

circumference, or divide the circumference by the diameter to get π.  it is like a fact 

family.

Learn More

Visit a website to learn more about circumferences and diameters of circles.