Creating patterns from a single shape
The purpose of this activity is to support students in establishing structure within one shape. That shape then becomes the foundation for creating a growth pattern.
About this resource
These activities are intended for students who use a small range of strategies for the addition, subtraction, and multiplication of whole numbers. They should know most of their basic facts for addition, subtraction, and multiplication.
Creating patterns from a single shape
Achievement objectives
NA3-8: Connect members of sequential patterns with their ordinal position and use tables, graphs, and diagrams to find relationships between successive elements of number and spatial patterns.
Required materials
- square tiles or squared paper
See Materials that come with this resource to download:
- Creating patterns from a single shape (.pptx) in paper form or displayed on a shared screen
1.
Show the students slide 1 of Creating patterns from a single shape.
- Here is shape 3 in a growing pattern.
- Describe how the shape is made up.
- Draw what shape 4 might look like.
2.
Let students use squared paper to create shape 4.
There are many possible designs, including (see slides 2 and 3):
- Adding one square to each of the four arms.
- Adding one square to each of the horizontal arms.
- Adding one square to each of the vertical arms.
Students may come up with other creative variations, such as taking some squares away.
In each case, discuss these key questions:
- What stays the same as the pattern grows?
- What changes as the pattern grows?
3.
Let students choose a shape and extend the pattern in both directions to show shapes 1, 2, 3, 4, 5, and 6. Other students can check the patterns for consistency.
- Are the constant (same) features kept?
- Are the changes (differences) made in a consistent way?
4.
Use the shape 3 designs on slides 4 to 6 as the start of a similar process. For each shape, discuss the features of the shape.
Ask students to draw shapes 2 and 4, then check that the changes are consistent.
1.
Provide students with examples and non-examples of growth patterns. Non-examples are sequences where the changes are not applied consistently, or some constant features are lost as the pattern grows. Here is a non-example of a growth pattern (slide 7).
- What is wrong with this pattern?
- Can you fix it?
Look for students to recognise that each side of the right-angled triangle increases by one square in each step. That change is not consistently applied in the step from shape 3 to shape 4. The pattern should look like this (slide 8):
2.
Explore more complex growth patterns in which changes to colours or orientations of squares occur. For example:
- What will shape 5 look like?
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