Repeating patterns
The next three shapes in the repeating patterns below have been drawn for you.
- Draw the next three shapes in this repeating pattern.
________ ________ ________ - The repeating pattern below has 4 shapes and 2 shades. Draw the next three shapes in this pattern.
________ ________ ________ | Y4 (10/2010) | ||
| a) | Given | |
| b) |
 |
very easy |
| c) |
 |
moderate |
Based on a representative sample of 199 Y4 students.
This resource is about continuing repeating patterns. The example given and the first pattern have only one attribute (type of shape). The second pattern has two attributes (type of shape and type of shading). Using patterns with two attributes begins at early Level 2 and by the end of Level 2 students should be able to use two attributes in a range of different scenarios (patterns, sorting attribute blocks, sorting geometric shapes, etc.). What underlies these attributes is whether students can identify a more complex "unit of repeat" of the pattern.
Most students could continue the single attribute repeating pattern. For the second pattern about 40% did not correctly incorporate the second attribute (type of shading). For both questions a small number of students restarted the shapes at the beginning to continue the pattern.
| Common response | Likely misconception | |
| b)c) |
|
Restarting the pattern at the end of the line
Student did not recognise the repeating part ("set" or "chunk") of the pattern and repeated the pattern from the beginning.
|
| c) |
 |
Working incorrectly with two attributes
Students did not take into account the shading (2nd attribute) of the pattern.
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Restarting the pattern at the end of the line
Students who completed the pattern by re-starting with the first 3 shapes and shades may either not be aware that repeating patterns can go on forwards or backwards repeating. It may also be that they can not see the repeating part (or chunk) of the pattern.
Ask the students to mark the repeating part. If they have difficulty recognising the repeating part of the pattern, circle or mark this out for students, then look at how that part is repeated and work out from that what the next shape should be. Students could explore a number of repeating patterns and just identify and describe the repeating part [ Necklace patterns or Bag of shapes]. Begin with single attribute patterns and then move on to more complex patterns.
Working incorrectly with two attributes
Ask students if the pattern they have drawn is complete or if there is something missing. If they don't identify the shading of the shapes they may need some time exploring repeating patterns using rules (both given and their own) and they may need more practice continuing and describing more simple repeating patterns [Shape patterns, Missing shapes, Bag of shapes, and working with beads, Necklace patterns] to see how repeating patterns can be built up. They could start with a single attribute (shape) and then add in another (shading). They may also need to explore different shapes using attribute blocks, or resources exploring shapes (2-dimensional shapes).
Ultimately students could explore and create simple patterns, and identify what part of the pattern is repeating. They could then move on to more complex patterns, some that may involve not showing the entire first repeating set (as with question b). Students could be asked to describe the shapes and shades in the patterns and how many of each. This may support them to recognise the relationship between the numbers of each attribute and the number of shapes in a repeating unit, e.g., for a pattern with 3 shades and 2 shapes the repeating set (chunk) will have 6 elements.
Correctly continuing the patterns
Students who can continue the patterns with two attributes could look at more complex patterns and begin to describe the pattern and work towards describing the rule for the pattern.
See the resource Continue the patterns.