This is a level 2 algebra strand activity from the Figure It Out series.
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continue a spatial pattern
continue a sequential pattern
Activities One and Two
Using a table to organise the attributes of members in a sequential pattern is an important strategy in solving problems of the type found in these activities. This is particularly true where several attributes are involved in a single pattern. Another useful strategy is to identify the repeating element in the pattern.
For example, pattern a has an element of , which means that multiples can be used to predict the tenth and twentieth object. Since occurs at every multiple of two, both the tenth and twentieth objects must be purple circles. Similarly, the repeating element in pattern b is , so the multiples of three can be applied. The ninth member of the pattern is , so the tenth member must be . The eighteenth member of the pattern is , so the twentieth member must be .
In pattern c, two attributes are involved, so it is useful to make a table.
Once students can see a pattern of colour and position in the table, they can use the multiples. The colour pattern repeats in an element of three, the position repeats in an element of two. Therefore, the tenth member will be on its side and purple, and the twentieth member will be upright and orange.
The tenth and twentieth objects in the other patterns can be established by similar means.
Answers to Activity
1. a. purple circle
b. red trapezium
2. a. purple circle
b. orange hexagon
c. orange sideways
3. Answers will vary.
1. Answers will vary.
2. Answers will vary.