Middle Years

# 2.07 Describing patterns using algebra (Investigation)

Lesson

We know that maths is a special language with numbers and symbols and knowing how to "read and write" mathematically is really important. We often use maths to describe sequences and relationships. Let's look at how we do this now.

## Describing Sequences

We could describe the pattern rule for $2,4,6,8$2,4,6,8 by saying "the number increases by $2$2 each time." We can then use this rule to find the next numbers in the sequence.

#### Activity

Create a sequence of numbers that follows that rule. Swap sequences with a friend and see if you can work out the rule and the next three numbers in the pattern.

#### Challenge

See if you work out the rule for this pattern: $1,1,2,3,5,8$1,1,2,3,5,8. What would the next three numbers in the sequence be?

## Describing Relationships

We can also describe a relationship between two things. For example, let's say I wanted to write a relationship between the number of stars and the total number of points on the stars below:

I could start by constructing a table of values:

Number of Stars ($S$S) 1 2 3
Number of Points ($P$P) 5 10 15

Now I can compare the number of stars to the number of points:

$1$1 star has $5$5 points, $2$2 stars have $10$10 points and so on.

More generally I could say,

"The number of points is $5$5 times the number of stars."

I can also write this relationship mathematically as $P=5\times N$P=5×N or more simply as $P=5N$P=5N.

We can also make our rules a bit more complex.

For example, I could say, "To find the answer ($A$A), multiply the starting number ($N$N) by $4$4. Then add $2$2." Mathematically, I can write this as $A=4\times N+2$A=4×N+2 or more simply as $A=4N+2$A=4N+2.

So here's how we would complete a table of values, with a line of working for some extra guidance (even though we don't normally show this step):

Starting Number ($N$N) $0$0 $1$1 $2$2
Working $4\times0+2$4×0+2 $4\times1+2$4×1+2 $4\times2+2$4×2+2
Answer ($A$A) $2$2 $6$6 $10$10

#### Activity

Create a rule and complete a table of values that follows that rule. Swap your table of values with a friend and see if you can work out the rule.