Patterns

Haese MYP 2 Mathematics - Chapter 8I, page 171

Patterns Beyond School:

You will use these skills in research and scientific reports, meterology, biology, computer science, aeronautics, physics

Success Criteria:

You will be able to:

Identify a pattern
create a rule from a pattern and vice versa
Use and read input/output tables

Prior Knowledge/Warm Up Activity:

Key Vocabulary:

Input, output, rule, formula

Answer:

Read the problem first...

Find all of the important information: ladders, same length, increasing pattern

Find the instruction: How many pieces needed

i) 4 rung: find the pattern (increasing by 3) from 11 pieces

1 2 3 4

5, 8, 11, 14

ii) 5 rung: +3 17 pieces

iii) 12 rungs: counting from n=1 to 12 = 38 pieces

same as Un = Un-1 + 3

next ans previous ans

slow way, can do this quicker

12 rungs = Un = U0 + 3 x 11

U12 = 5 + 33 = 38 pieces of metal

b) let m represent # metal pieces and r represent # rungs

5 + 3 x r(n-1) = m

New Knowledge:

Mathematical patterns can be found in almost every part of everyday life.

A pattern is a repeated arrangement of numbers, colours, shapes etc.

If the set of numbers are related to each other in a specific rule, then the rule or manner is called a pattern. Sometimes, patterns are also known as a sequence. Patterns are finite or infinite in numbers.

Rules for Patterns in Maths

To construct a pattern, we have to know about some rules. To know about the rule for any pattern, we have to understand the nature of the sequence and the difference between the two successive terms.

Types of Patterns

In Discrete Mathematics, we have three types of patterns as follows:

Repeating – A type of pattern, in which the rule keeps repeating over and over is called a repeating pattern.
Growing – If the numbers are present in the increasing form, then the pattern is known as a growing pattern. Example 34, 40, 46, 52, …..
Shrinking – In the shrinking pattern, the numbers are in decreasing form. Example: 42, 40, 38, 36 …..

Worked Examples:

Rules from patterns.pdf

Input output tables

1st rule - expression is 2 x input, difference is +2

2nd rule - 3 x exp. + 1, difference is +3

Let's go through some more.....

Notes:

Find the pattern from the input (initial number) by using standard operations to calculate the output
Find the difference in each output number and search for the common multiple or divisor
Always check your rule
2 things to remember; need a starting number or value and an operating value

Application Tasks:

Textbook Questions: Chapter 8I questions (all)
Patterns worksheet above

A number is multiplied by 2 then subtracted from 3. Write this rule in mathematical notation

Write a short paper analysis justifying the reason why we should learn the skill of creating general rules from patterns and where would we see them in everyday life (250 words approximately)

Additional Resources

Google Sites

Report abuse