Guess my number!

A great game to play is to guess my number with students. They solve equations without even realizing it.

Example

I think of a number, I multiply it by 7, and then I take away 4. My answer is 17. What number did I think of?

For students to answer this, there are several methods. We could use trial and improvement.

Number

Answer

Too big or small

5

5 x 7 – 4 = 31

Too big (must be smaller!)

2

2 x 7 – 4 = 10

Too small (must be bigger!)

3

3 x 7 – 4 = 17

Correct, so the answer must be 3!

This method is excellent for primary students – the brightest students will notice the quickest way to do this is to work it backward! Embrace this, and it is the key to solving equations!

Using Function machines

Function machines will have probably been seen before and can be adapted to solve simple linear equations.

For example, to solve the equation 5x + 6 = 16

Imagine you are the x; what has happened to you to get the answer 16.

Think about working backward using the reverse operations to find out what the input is. The opposite of add 6 would subtract 6, and the opposite of multiply by 5 is to divide by 5.

So (16 - 6) / 5 = 2 so x must be 2!

Balancing method – this is the best method for developing onto more challenging equations at a later date.

An equation consists of an unknown quantity, often defined with a letter, and to solve it; you need to find the value of the unknown.

Example: 3x+4 = 19

This equation can look daunting, so let us simplify it. Imagine a set of balancing scales – an equation must always balance. On one plate of our system, you would have 3 x's and 4 boxes. On the other side, you will have 19 boxes. The scales must always remain balanced, so you must do precisely the same to the other side if you remove or add something from one side.

Looking at the picture, you have 4 weights on each side that we have absolutely the same on both plates, so we remove it from each side without losing the balance.

This operation is leaving you with 3x=15. Let's get rid of the 3, so we have pure x on the left side of our equation; I mean scales. So, 3x divided by 3 gets us just clean x, but without reducing the value of the right side, which is 15 by 3, our right plate will take a nosedive, right? And everything here is about balance. So 15 divided by 3 equals 5. So our answer looks like X=5

Mathematically we set it up as follows

3x + 4 = 19

3x = 15

X = 5