Lesson 8 — Activity 3:

Using Formulas to Make Patterns

and Draw Conclusions


In this activity, you will use various formulas to develop patterns and draw conclusions. Formulas are handy ways of telling people what to expect. They ensure that everyone uses the set of numbers in the same way.


When writing formulas, we use variables. A variable is a letter or symbol that is used to represent an unknown quantity.

In the example on the right, the variable in each of the questions is the letter "x." We use the letter "x" in this example as our variable to represent the number in the formula that we do not yet know. Any letter or symbol can be used to represent the variable.

We can then use these formulas to find patterns. For example, this formula gives us a pattern shown in the following table (using "m" and "n" as our variables):

m + 2 = n


This table can also be made by using numbers only.



Let's try some more examples to find patterns using formulas.


If the formula is: A + 8 = B

If A is 4, what is B? 4 + 8 = 12

If A is 5, what is B? 5 + 8 = 13


Can you see the pattern in the formula? Each time the variable "A" goes up by one number in the formula, the answer ("B") also goes up by one number. 

Let's try another one!


If the formula is: L - 2 = M

If L is 8, what is M? 8 – 2 = 6

If L is 9, what is M? 9 – 2 = 7

If L is 10, what is M? 10 – 2 = 8


Can you see the pattern in the formula? Each time the variable "L" goes up by one number in the formula, the answer ("M") also goes up by one number.


So, if we followed this logic, if the variable "L" went up by three numbers (to 13), how much do you think the answer would go up by? According, to the pattern, the answer would also go up by three. Let's check to see if we are correct.

13 – 2 = 11

Is 11 three more than 8? Yes it is! We are correct!




This is called drawing a conclusion. A conclusion is a statement arrived at by applying a set of logical rules.



In the example above, L – 2 = M, our conclusion would be:

If L is 13, then M is 11 (13 – 2 = 11).


We can use our conclusion to answer any question.

For example:

If L is 15, then M is 13 (15 – 2 = 13).


You can use formulas like the above to answer multiplication and division equations as well.

For example, if the formula is:

T = 3R (which means 3 x R)

We would answer this formula as follows:

If R = 2, then T = 6 (3 x 2 = 6)

If R = 3, then T = 9 ( 3 x 3 = 9)

We can do the same for division equations!

For example, if the formula is:

B ÷ C = D

We would answer this formula as follows:

If B = 8 and C = 2, then D = 4 (8 ÷ 2 = 4)

If B = 15 and C = 3, then D = 5 (15 ÷ 3 = 5)



  Self-check!

Try this!

Answer these questions on your own first.

When you are finished, click on the tabs below to check your answers!


J + 10 = K
If J is 4, what is K?
If J is 10, what is K?

If J is 4, what is K? 14
If J is 10, what is K? 20


M – 5 = N
If M is 5, what is N?
If M is 21, what is N?

If M is 5, what is N? 0
If M is 21, what is N? 16


The perimeter of a square (the distance around the outside edge) is given by the equation P = 4S. What is the perimeter for the following length of sides:

S = 2, then P = ?
S = 8, then P = ?

S = 2, then P = 8 (P = 4 x 2)
S = 8, then P = 32 (P = 4 x 8)


If you know the area (A) and the width of a rectangle, then you can find the length of a side.
A ÷ W = L
If A = 12 and W = 2, then L = ?

If A = 12 and W = 2, then L = 6

12 ÷ 2 = 6