Rich tasks
This task requires students to continue a growing triangular pattern, identify and record the patterns. The task can be given at the start of a topic and done as the students gain enough understanding to complete it, or given as a homework task.
The phone tower
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1. The phone tower
- Encourage students to record growing patterns in systematic ways and identify a rule that will give the next term (or step) in the pattern.
- You may need to check that students are not making their towers too high (and that they are high enough). If towers are too high or not high enough the patterns are hard to find and describe.
Repeating patterns page 178
- Identify the ‘unit of repeat’ to continue a repeating pattern with two variables.
- Use repeated addition or multiplication to identify a term in a repeating pattern. For example, what will the 20th object in this pattern be?
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Teacher notes
- Before a student can continue a repeating pattern, they must identify the unit that repeats. This is sometimes referred to as the ‘core’ of the pattern.
- At this level, students are commonly encountering patterns that have two variables (or properties that change). For example, a pattern that alternates three different shapes and two different colours. When students are analysing patterns it is frequently helpful for them to focus on one variable at a time.
- Students should be encouraged to use the number of objects in the repeating element or ‘core’, and match this with an additive sequence or multiplication facts they know in order to predict which part of the pattern will occur at a particular point in the sequence rather than physically extending the pattern to this point. For example, for a pattern that repeats a triangle and circle, a student might use the 6th shape (a circle), to predict that the 12th item would also be a circle, since 6 + 6 or 2 × 6 = 12.
Number patterns page 180
- Identify a pattern or rule to continue a number pattern.
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Teacher notes
- Exposing students to a range of sequences with various starting points and gaps at different points within a pattern develops flexibility as students become aware of different types of pattern.
- Students may decide upon a rule without checking that it holds true for each step of a pattern, particularly if they struggle with counting sequences or recall of basic facts. Access to materials like number lines, hundreds boards, thousands books or calculators allow students to check their hypotheses and extend the range of patterns they are able to investigate.
Exploring patterns in systematic ways supports the development of number sense.
Growing patterns page 184
- Use a table to identify a rule and continue a growing pattern
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Teacher notes
- It is very important that students draw or build a growing pattern with materials to help them notice what changes to form each new unit and go on to construct a rule.
- A table is a useful tool for helping students track and recognise a number pattern.
Example| Number of children | 1 | 2 | 3 | 4 | 5 | |
Number of
pencils | 6 | 12 | 18 | | | |
+ 6 + 6 + 6
- By helping students recognise repeated addition or subtraction in a pattern you lay the groundwork for multiplicative thinking. For the example above, you might ask “Can you see a pattern (or relationship) between the number of children and the number of pencils? (Repeated addition of 6 pencils or x6.)
- Now students may be able to predict how many pencils 10 children would have?”
- You could ask similar questions for the relationships in the tables on the Teacher Resource sheets 40 - Koko's Codes, encouraging students to look for relationships between the top and the bottom rows.
