Purplemath: Quadratic Formula

During my study in secondary school, I find it is easy to solve quadratic equations. Maybe it is because of the quadratic formula I memorized. But some other students find it difficult to solve quadratic equations even though they knew the formula. So, it not enough by just memorized the formula. We also need to know how to use it.

I think Purplemath is one of the good sites that provide an explanation about quadratic formula.

Pyramid Puzzles

In order to solve that puzzle, please follow the instruction: Insert a number 1-9 in each vacant square so that the number in each square is the sum or difference of the numbers in the two squares immediately below it. Digits in similarly colored squares will be the same.

I am quite confuse at first. But now I able to solve the puzzle. Maybe you should try too. Thanks to Erich Friedman.

Source: Click here.

MATHEMATICA & Integration

I always like MATHEMATICA. For me MATHEMATICA is a great calculator. It can solve so many problems. But of course you have to know the MATHEMATICA language. The language is quite simple actually. I think the school students also able to learn MATHEMATICA quickly.

The picture above shown one of MATHEMATICA ability, that is to solve integration's problem. You can try it here.

The Zen of the Labyrinth by Dave Phillips

The maze above was taken from this book The Zen of the Labyrinth by Dave Phillips.

To solve this maze you must follow this rules:

Enter by the bottom red path and end on the center gray square. You may retrace your path but may not make a U-turn on a pathway. You must follow the paths in the order red, blue, yellow and then red, blue, yellow again, as needed, changing color on the white squares.

Continued Fraction again

Continued fraction was my final project in university. It is really interesting topic to learn. However, many peoples seem abandoned this area. Believe me, even though the research was implemented by me in university, several parts in continued fraction I think suitable for school students. It is worth to try.

Tower of Hanoi

I still remember during my study in university, one of my lecturer use this game Tower of Hanoi as an introduction to teach algebra. I don't like algebra, so it is quite difficult for me to relate the game with algebra.

I think this is a good game. It will be good, if you can expose this game to your students.

Source: Cut the Knot.

Optical Illusion again

Please focus on the picture. Do you think the page is moving?

I really like this web page MURDEROUS MATH.

Mathematics Song

I am not sure whether this video will help students to understand arithmetic better. But I am sure the song is quite funny.

Binary Clock

The picture above depicts a clock. A binary clock actually. The time was 1.15am. How to read the clock?

1. 1st line (top line) > each circle represent 6 hours

2. 2nd line > each circle represent 2 hours

3. 3rd line > each circle represent 30 minutes

4. 4th line > each circle represent 6 minutes

5. 5th line > each circle represent 1 minute

6. Green = AM, Red = PM

Can you try to read the binary clock below,


Why we can display clock by using this method? If you are interested click here.

Cast Vortex

The image above depicts a metal puzzle. I am not sure how to solve it. But the idea is "The three pieces each have a spiral (vortex) body and two protrusions. When assembled together, each piece is unified into a flat object. In order to undo this complex entanglement it will be necessary to unbind them three dimensionally".

I got this from online puzzle shop.

Maze

In order to solve that maze, you must follow this sequence:

If you want to start from the top and exist at the bottom
1. Cross the blue bars.
2. Cross the green bars.
3. Cross the red bars.

Or, if you want to start from the bottom and exist at the top
1. Cross the red bars.
2. Cross the green bars.
3. Cross the blue bars.

Idea simplified from MathPuzzle.com.

Golden Number

That symbol is what we called it 'phi' which is a symbol for 'golden number'. Some peoples might call it 'golden ratio' and some other peoples might call it 'golden mean' and some other peoples might call it 'golden section'. No matter how many different names we call for 'phi', it is only represent one number. I knew about 'phi' when I did a project about continued fraction. 'Phi' has a close relationship with continued fraction but I am not going to talk about it here.

Here, I am just interested with 'phi' and how it affect our daily life. 'Phi' even affect the arrangement of our nose, ears, eyes, etc. Do you believe me? I am also hard to believe and still curious about it. If you are eager to know, visit Golden Number.

Calculator Chaos

The problem above is at level 1. For me it is quite easy to generate all the numbers except number 50 (need little time to think). I think this kind of game is really interesting to attract school students (primary or secondary) to practice their arithmetic skill.

If you are interested, visit Math Playground.

Your eyes got problem?

Look carefully at the lines that connect all the dots. Are the line straight? Look again. Are you sure?

Actually this kind of trick was used by me as an introduction to teach parallel lines. It works for me, maybe it works for you.

I got this from Cut the Knot.

Clinometer's problem

1. In order to construct a clinometer, you will need things like clear plastic ruler, clear plastic protractor, string, adhesive tape, small weight and tape measure. Then try to construct a clinometer shown below.
2. When you already have a clinometer, you can find a height of something by using that clinometer. If you are in school, I think you can measure the height of flag pole, tree, building, etc. The picture below depicts on how to use clinometer, it is clear enough I guess. In order to calculate the height of something, you must know the distance between you and that thing, also the angle measured by the clinometer. After that you will know the height by using the formula of tangent.3. Try to solve the problem like below.
4. The problem above is quite a simple problem. If you want a difficult one, try to find a height of something without knowing the distance between you and that thing. It is involving algebra in order to solve that problem.