Perfect Patterns

Activities One, Two, and Three

The aim of these activities is for students to focus on the relationships between numbers in different positions within a family of equations. Most students are likely to see relationships down the equations rather than within the equations themselves. For example, consider the set:
1 = 3 – 2
2 = 4 – 2
3 = 5 – 2
4 = 6 – 2
Students will see that the left-hand numbers are “increasing by one” as are those immediately to the right of the equals sign. The “subtract two” part of each equation remains constant. This makes writing the next equation a patterning exercise.
The problem of writing an equation much further down encourages students to look for relationships within the equations and is much more difficult. Many students will wish to keep writing equations down in the pattern; encourage them to think around this. For example, with the pattern above, they might note that the number immediately to the right of the equals sign is always two greater than the left-hand number. This enables any number of equations in this pattern to be written:

Answers to Activities

Activity One
a. Yes.
b. The pattern is + 1.
Activity Two
a. 5 + 0 = 5
b. 5 – 0 = 5
c. 5 x 1 = 5
d. 5 + 5 = 10
e. 5 + 6 = 11
f. 5 = 7 – 2
g. 5 ÷ 5 = 1
Answers will vary for the equations further down for each pattern.
Activity Three
Answers will vary.