Unit 1.1

Mathematics as a study of

creating, discerning and

generalizing Patterns

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Understanding what is mathematics

• Mathematics as a study of patterns:

Example 1:

Stacey's example of working on numbers like 87:

• 87; 8+7=15; 87-15=72

• 86; 8+6=14; 86-14=72

• 79; 7+9=16; 79-16=63

• 78; 7+8=15; 78-15=63

• 65; 6+5=11; 65-11=54

• 69; 6+9=15; 69-15=54

• 23; 2+3=5; 23-5=18

• 28; 2+8=10; 28-10=18

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• Would this work for all two digit numbers?

• Would this work for all three digit numbers?

• How do you show that?

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Mathematics Pattern

• Mathematics is the study of patterns.

• Studying pattern is an opportunity to:

observe

hypothesise

experiment

discover

and create generalizations

• Study of patterns alternatively termed as a study of generalizations

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What are Patterns in Mathematics?

• In Mathematics, patterns are related to the type of any event or objects.

• If we take a set of elements or numbers in which all these elements or numbers are related to each other in a specific rule, then this rule or manner is called the pattern.

• Sometimes patterns are called as sequence.

• Patterns are finite or infinite in numbers.

• For example, in the sequence 2,4,6,8, ? ,

• each number is increasing by sequence 2. Here the pattern rule is start at 2. Add 2 to each time. So, last number will be 8+2 =10.

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Pattern Rule

• Pattern rule tells how to build a pattern. We

may be able to state a pattern rule in more

than one way.

• 1,3,5,7,9,11…

• Here one pattern rule is start at 1 & add 2

each ti e .

• Another pattern rule is The odd numbers

starting at 1

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Core of a pattern

• The core of a pattern is the smallest string of elements that repeats.

In this pattern the shape and colour changes

• The core of this pattern is

• The pattern rule is black triangle & white circle.

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Numerical patterns (Number Patterns)

• A sequence of numbers which follows a certain

pattern is called number patter.

• Like , , , , , ……… is a u ber patter whose first term is 1 and add 4 every time to get

the other terms.

Examples:

• Fibonacci Number Pattern

• Growing number pattern

• Repeating number pattern

• Geometric number pattern etc.

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Geometric pattern (Patterns of shapes)

• A geometric pattern is a kind of pattern

formed of geometric shapes and typically

repeating like a wallpaper.

• The geometric pattern is used in a variety of

ways in our daily life.

• For example, a dress pattern is a template,

and a wall paper pattern may be an infinitely

repeating design.

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Abstract Patterns

• Any of the five senses may directly observe

patterns.

• Conversely, abstract patterns in science,

mathematics, or language may be observable

only by analysis.

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Types of Patterns

• Repeating

• Growing

• Shrinking

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1. Examples • 1, 1, 2, 2, 1, 1,…….

• It is of the form AA, BB, AA,….

• The core is 1,1, 2,2,

Repeating Patterns

• A repeating pattern is a cyclical repetition of

an identifiable core.

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2. Examples

• 120, 121, 123, 126, 130, 135, 141,…………..

• The pattern rule is start at 120 and Add 1. The amount you add increases by 1 each ti e .

• 870, 880, 889, 897, 904, 910,………

• 2, 3, 5, 8, 12, 17,……….

Growing Patterns:

• Growing pattern is a pattern in which the numbers increase, and the amount added changes each time in a predictable way.

• A growing pattern happens when something is added each time. It can be shapes, picture, objects, numbers, etc.

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3. Examples • , , , , , …………

• The pattern rule is start at 81. Subtract 9. The amount you subtract decrease by 1 each ti e .

• , , , , , ,……. Shrinking Patterns

• A shrinking pattern is a pattern in which the numbers decrease, and the amount subtracted changes each time in a particular way.

• A shrinking pattern happens when something is taken away each time.

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Patterns of Reflection

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Patterns of Translation, Rotation and Reflection

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Patterns in Daily Life

• What patterns are present?

• Are they from the natural or manmade world?

• What are the elements of pattern?

• What shapes do we see?

• How are colours used?

• Do the patterns have meaning or purpose?

• How many varieties are there?

• How do they differ?

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