Pattern makers
This unit introduces students to the notion of a repeating pattern. They are encouraged to create, describe, and continue patterns.
About this resource
Specific learning outcomes:
- Describe patterns.
- Continue patterns.
- Create patterns.
Pattern makers
Achievement objectives
NA1-6: Create and continue sequential patterns.
Description of mathematics
In this unit, students are introduced to the concept of a pattern. This is a fundamental notion in mathematics and is especially prevalent in research mathematics. Research mathematicians try 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.
Here we are concerned with introducing the basic ideas of a pattern. These are patterns that 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,...' Since 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 you add 3 to get the next number.
As the students progress through mathematics, they will meet more complex 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 an understanding of algebra, as algebra gives a succinct way of expressing such relations.
Opportunities for adaptation and differentiation
The learning opportunities in this unit can be differentiated by providing or removing support for students and by varying the task requirements. Ways to extend students include:
- encouraging students to use more items in their pattern; for example, use four different colours of Lego instead of just two.
- challenging students to copy and continue patterns made by other students
- providing opportunities for students to work in pairs and small groups in order to encourage peer learning, scaffolding, extension, and the modelling and sharing of patterns
- working alongside individual students (or groups of students) who require further support with specific areas of knowledge or activities.
The context for this unit can be adapted to suit the interests and experiences of your students. For example, you might collect objects from the school playground or local area for making patterns or encourage students to bring examples of patterns that they find at home (photos may be easier than actual objects in some cases).
Te reo Māori kupu, such as tauira (pattern) and tatau (count), could be introduced in this unit and used throughout other mathematical learning. You could also encourage students who speak a language other than English at home to share the words related to patterns that they use at home. They might be able to describe the shapes used in a pattern in their home language, or they might be able to share an example of a pattern that is relevant to their culture.
Required materials
- a picture book with illustrations of patterns (for example, Pitter Pattern by Joyce Hesselberth, I Went Walking by Sue Williams).
- paper
- glue
- pasta shapes
- cubes
- toothpicks
- nursery sticks
- equipment to be used in creating patterns (for example, Lego blocks, bottle tops, leaves, etc.)
- paint
- camera
- chart paper and pens
Activity
This lesson lays the foundation for the concept of pattern.
1.
Share a picture book with illustrations that show patterns.
- What is a pattern?
- What patterns can we see in this book?
- Can you see any patterns in our class?
2.
Go for a pattern walk. If available, take a camera so patterns can be recorded, for example, path tiles laid in a repeating pattern or a repeating koru pattern on a traditional design.
3.
Return to the class and construct a chart of the patterns observed. You might use a writing lesson to construct statements describing the patterns students can see.
This session introduces students 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, and 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 using counters and cubes
- follow-the-leader patterns (hop, hop, jump, hop, hop, jump; stamp, stamp, clap, stamp, stamp, clap, etc.)
- joining dots to create patterns.
3.
Encourage verbalisation of each pattern and encourage students to predict what will come next.
This session provides time for students to freely create and explore repeating patterns.
1.
Begin this session with some of the pattern activities used in the previous session.
2.
Spread pattern-making materials around the room. Allow students to move to any centre and create repeating patterns. Alternatively, you could structure this more (for example, by organising students into groups and having them rotate around centres) in reflection of the needs of your class. Encourage students to start with a simple two-object unit of repeat, but extend this for students who are ready for extension.
3.
Go from student to student and ask:
- Can you read your pattern to me?
- What will come next?
- How do you know?
4.
Watch for students who need support to create repeating patterns. These students will need to spend some time copying and chanting patterns.
5.
Let the students share their patterns with the class. Encourage other class members to continue some of these patterns and describe them. Reflect on the understandings demonstrated. Use any misconceptions as the basis for subsequent teaching.
This session requires students to construct repeating patterns.
1.
Review repeating patterns. Read some patterns from the previous session. Address any misconceptions that were evidenced in the previous session.
2.
Give the students a choice of pattern tasks to do. Model the completion of the tasks as necessary. Challenge the students to create patterns with more than two elements.
The tasks might include:
- creating a tī rakau repeating patten
- creating wallpaper for the dolls’ house
- making a patterned headband using a cultural design
- designing a pattern for a dinner plate
- creating a frieze for the classroom
- creating your own tie with a repeating pattern
- creating a belt with a repeating pattern
- a pattern for the edge of a small tapa cloth.
3.
These tasks may be completed over several days. Follow each session with class sharing and discussion time, focusing on the repeating patterns.
Home link
Dear parents and whānau,
This week in math, we have been making up patterns. Your child will be able to tell you what a pattern is.
You and your child might like to explore your home and see how many repeating patterns you can find on clothing, furnishings, wall hangings, art work, (etc.) You may have special family patterns that you'd like to explore. Take time to talk about the elements that are repeated in the patterns that you find.
You might like to work with your child to draw, cut out, create a pattern of your own, or copy a favourite pattern.
Enjoy finding, making, and talking about patterns with your child.
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