Tips for Teaching Variables and Equations

Posted by David Wetzel

Math Variables and Equations

Here is one method for reinforcing middle school math terms such as variables and equations. The key is to make it visual. Start with the basics, use colors, and take it one step at a time.

Reinforcing Variables and Equations

Materials:

• unlined white paper
• black marker
• red marker

1. Begin with a simple, one-step equation. Use a black marker to write “n + 2 = 5”.

• Student must solve for “n”

Discussion:

• What is the opposite of +2?” (-2)
• What you do to one side of the equation, you must do to the other side

Show:

• n + 2 – 2 = 5 – 2 (write “- 2 “on both sides in red)
• n = 3

2. Next, practice a one-step subtraction equation

Show:

• n – 3 = 6 (using black marker)
• n – 3 + 3 = 6 + 3 (write “+3” on both sides in red)
• n = 9

3. Next, move on to two-step equations

Show:

• 5y – 10 = 5 9 (using black marker)

Discussion:

• You must get “y” by itself
• What is the opposite of - 10?  (+10)
• What you do to one side of the equation, you must do to the other side

Show:

• 5y – 10 + 10 = 5 + 10 (write “+10” to both sides in red)
• 5y = 15

Discussion:

• 5y means “5 times y”
• What is the opposite of “times”? (divide)
• To get y by itself, divide both sides by 5.

Show:

• 5y = 15 (write “/ 5” on both sides in red)
• 5y / 5 = 15 / 5
• y = 3

Additional Tips

By using colors, students can easily see and review the steps required to solve one and two-step equations.Keep practicing until the process of solving simple equations becomes automatic.

Equations quickly become more complex, requiring several steps. Be sure your middle-schooler has a concrete understanding of the basics so s/he is able to move ahead with confidence.

Resources

12 Tips for Solving Word Problems

Illuminations - An Interactive Math Website for Learning Math

General Science Misconceptions

Posted by David Wetzel

Science Misconceptions

Students are full of misconceptions about science. They learn these misconceptions from many sources, which include movies, television, siblings, parents, other family members, and school.

These misconceptions about science typically become evident when students are required to explain science in their own words and not recite memorized information. This is why it is important for students to write in science and describe their scientific observations using their own words, especially when working in groups.

Student Science Misconceptions

Here are actual answers students have given to explain scientific events and facts:

• When you breath, you inspire. When you do not breath, you expire.

• H2O is hot water, and CO2 is cold water

• When you smell an odorless gas, it is probably carbon monoxide

• Nitrogen is not found in Ireland because it is not found in a free state

• Water is composed of two gins, Oxygin and Hydrogin. Oxygin is pure gin. Hydrogin is gin and water.

• Three kinds of blood vessels are arteries, vanes and caterpillars.

• Blood flows down one leg and up the other.

• Respiration is composed of two acts, first inspiration, and then expectoration.

• The moon is a planet just like the earth, only it is even deader.

• Dew is formed on leaves when the sun shines down on them and makes them perspire.

• A super-saturated solution is one that holds more than it can hold.

• Mushrooms always grow in damp places and so they look like umbrellas.

• The body consists of three parts- the brainium, the borax and the abominable cavity. The brainium contains the brain, the borax contains the heart and lungs, and the abominable cavity contains the bowls, of which there are five - a, e, i, o, and u.

• The pistol of a flower is its only protections against insects.

• The alimentary canal is located in the northern part of Indiana.

• The skeleton is what is left after the insides have been taken out and the outsides have been taken off. The purpose of the skeleton is something to hitch meat to.

• A permanent set of teeth consists of eight canines, eight cuspids, two molars, and eight cuspidors.

• The tides are a fight between the Earth and moon. All water tends towards the moon, because there is no water in the moon, and nature abhors a vacuum. I forget where the sun joins in this fight.

• A fossil is an extinct animal. The older it is, the more extinct it is.

• Equator: A managerie lion running around the Earth through Africa.

• Germinate: To become a naturalized German.

Source

Children’s Misconceptions About Weather

The Math in Video Games

Posted by David Wetzel

Video Game Math

Video game graphics is all about geometry. Geometric shapes and interactions between geometric shapes is the basic foundation of all videos games.

Video games rely on the extensive use of circles, squares, ovals, rectangles, trapezoids, and many other geometric shapes to form shapes you see on your computer or TV screen as you play video games.

Basic Geometry

One of the basic geometric concepts you learn in school is the use is recognition of two dimensional and three dimensional objects, along with how to use them in different situations.

This is how video game programmers are able to develop a video game a sense of depth. They use a three dimensional concept called “skybox.”

This is a fixed point in which appears to be in the distance and all other graphics on in the video game are developed around this fixed point.

This point is called fixed, because it does not move, even as the figure or object you are moving appears to be in the front of the screen. This gives the video game a three dimensional look.

Video Gaming Pre-Computer Programming

When video game programmers first begin developing figures and scenes, they start with a basic geometric shape of the objects. This is the same way artists start when they begin a painting. They begin with a focal point (skybox) and draw lines that radiate from the focal point to the corners of the screen.

Next video game programmers start inserting additional lines, circles, squares, and other shapes into these original lines at places to given the video graphics depth – three dimensional look. After they draw the outline then they start inserting the colors.

This used to done by hand on pieces of paper, with each piece of paper containing the next step in the sequence.

Video Game Programming

Today this is all done on a computer working with each pixel in the screen to accomplish each the step in the process of incorporating geometric shapes into a video game.

To give you an example of how many pixels are in a TV screen, there are over 200,000 in a typical television. If you have a high definition TV for your video games, then you can have up to 18,000,000 pixels. As you can see developing video games is a complicated process.

Of course as along as you learn geometry and understand how to turn two dimensional objects into three dimensional objects then you will make a good video game programmer.

Another use of geometry used in video games is using geometric shapes which are congruent with other shapes. Also they use geometric shapes by rotating, reflecting, and the use of similarities in making the video graphics move around the screen during action sequences.

Also, video games are heavily based on patterns to present motion within the video game. These patterns are all based on the patterns within geometric shapes to give the video game action and the three dimensional look. This provides more reality to today’s video games; rather than the original video games like Pong, Space Invaders, Pacman, and other early games that came out in the 1970s.

Although these games relied heavily on geometric patterns and shapes, the games could only present a two dimensional view of the game.

Resources

Geometric Shapes are Everywhere

Illuminations - An Interactive Math  Website