Lesson 6 — Activity 2:

Using Simple Formulas to Make Patterns



Getting Ready


Besides using pictures and numbers in a sequence to find patterns, we can also find patterns in simple formulas.


Try This:

Look at the formula below. Can you solve for the variable a?

a + 2 = 4


If you said a = 2, you would be correct, because 2 + 2 = 4!

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. You will learn more about variables in the upcoming lessons, however for this lesson, you will work with variables using simple formulas.

Courtesy of ADLC

Let's look at an example to find patterns using a formula. Remember, any letter or symbol can be used as the variable in an equation. In the examples below, you will look at using different letters as your variables.

If the formula is: c + 8 = d

If c is 3, what is d?
  • 3 + 8 = 11
If c is 4, what is d?
  • 4 + 8 = 12
If c is 5, what is d?
  • 5 + 8 = 13


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


Let's try another one!


If the formula is: x – 3 = y

If x is 8, what is y?
  • 8 – 3 = 5
If x is 9, what is y?
  • 9 – 3 = 6
If x is 10, what is y?
  • 10 – 3 = 7


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

So, if we followed this logic, if the variable (x) 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 – 3 = 10

Is 10 three more than 7? 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.

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

For example, if the formula is:

a = 3b (which means 3 x b)

We would answer this formula as follows:

If a = 2, then b = 6 (3 x 2 = 6)

If a = 3, then b = 9 ( 3 x 3 = 9)

We can do the same for division equations!

For example, if the formula is:

c ÷ d = e

We would answer this formula as follows:

If b = 6 and c = 2, then e = 3 (6 ÷ 2 = 3)

If b = 18 and c = 3, then d = 6 (18 ÷ 3 = 6)



  Self-check!

Try this!

Complete the following equations using the formulas below.

j + 8 = k
If j is 4, what is k?
If j is 10, what is k?


m – 2 = n
If m is 4, what is n?
If m is 18, what is n?


a = 5r

If r is 3, what is a?

If r is 5, what is a?


k = 12
k = 18

  n= 2
  n= 16

  a = 15

a = 25