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# Pattern Makers

Purpose:

In this unit, students are introduced to the notion of a repeating pattern. This is done by a number of means including the use of everyday objects. They are encouraged to create, describe and continue patterns.

Achievement Objectives:

Achievement Objective: NA1-6: Create and continue sequential patterns.
AO elaboration and other teaching resources

Specific Learning Outcomes:
• describe patterns
• continue a pattern
• create patterns
Description of mathematics:

In this unit, students are introduced to the concept of a pattern - a fundamental notion in mathematics. This notion is especially prevalent in research mathematics. Research mathematicians are trying to find things that occur regularly in some way. The results that they produce as theorems tell us about the patterns that will always occur under given circumstances.

For instance, Pythagoras’ Theorem tells us that in a right-angled triangle the square of the hypotenuse is equal to the sum of the squares on the other two sides. So in the diagram below 52 = 32 + 42. But Pythagoras saw a general pattern. For any right-angled triangle (not just the one below or a couple of others), there is the same link between the length of the hypotenuse and the lengths of the other two sides.

But here we’re not worried about anything so complicated. Here we are concerned with introducing the basic ideas of a pattern. These are that patterns involve something that repeats, like ‘clap, shout, clap, shout, clap, …’ or ‘red, blue, yellow, yellow, red, blue, yellow, yellow, red, …’ or ‘5, 8, 11, 14, 17, …’ Now because patterns repeat there must be a rule that describes the repetition. For instance, after you’ve shouted, you clap and after you’ve clapped, you shout, or add 3 to get the next number.

As the students progress through their school career, they will meet many number patterns like 5, 8, 11, 14, 17, … and will be able to predict the next term by knowing the relationship between consecutive terms or by using a formula for finding the next term. This will eventually require algebra as algebra gives a succinct way of expressing such relations.

Required Resource Materials:
paper
glue
pasta shapes
cubes
toothpicks
nursery sticks
found equipment (Lego blocks, bottle tops, leaves, etc.)
paint
digital (or other) camera
chart paper and pens
Key Vocabulary:

pattern, next, create, copy, repeating,

Activity:

#### Session 1

This lesson is to be used to lay the foundation for the concept of pattern.

1. Share a picture book with illustrations that show patterns.
What is a pattern? Can you see any patterns in our class.
2. Go for a pattern walk. If available take a digital (or other) camera so patterns can be recorded, for example, path tiles laid in a repeating pattern, a repeating koru pattern on a traditional design.
3. Return to class and construct an experience chart of the patterns observed.

#### Session 2

Students are introduced to the idea of repeating patterns.

1. Read the chart made yesterday. Make comparisons between geometric patterns and patterns that repeat. Be sure to explore repeating elements in cultural patterns such as tukutuku, kowhaiwhai or tapa cloth (siapo, ngatu, hiapo) patterns.
2. Spend time as a class creating and talking about repeating patterns. Some ideas are:
• clapping patterns;
• body patterns (arms out, arms up, arms out, arms up);
• building colour patterns use counters, cubes;
• follow-the-leader patterns (hop, hop, jump, hop, hop, jump; stamp, stamp, clap, stamp, stamp, clap; etc.,);
• joining dots to create patterns.
3. Remember to encourage verbalization of the pattern. Encourage students to predict what will come next.

#### Session 3

Students will freely create and explore repeating patterns.

1. Begin this session with some of the pattern activities used in the previous session.
2. Pattern making materials are spread around the room. Students are free to move to any centre and create repeating patterns. Go from student to student and ask:
What will come next?
How do you know?

3. Watch for students who are unable to create repeating patterns. These students will need to spend some time copying and chanting patterns.
4. Let the students share their patterns with the class. Encourage other class members to continue some of these patterns and describe the pattern.

#### Sessions 4 & 5

Students are given tasks to complete that require them to construct repeating patterns.

1. Review repeating patterns. Read some patterns from the previous session.
2. Give the students a choice of pattern tasks to do. Challenge the students to create patterns with more than two elements.