These exercises and activities are for students to use independently of the teacher to practice number properties.
- Continue multiplicative sequences.
Proportions and Ratios, AP (Stage 8)
- Practice exercises with answers (PDF or Word)
Prior knowledge.
- Multiply by a single digit number
- Divide whole numbers and decimals by 10
- Write a rule for a sequence as a sentence, and with symbols. (See the notes with "decreasing differences" for a discussion of this).
Background
Students meeting non-linear sequences for the first time often want to continue looking for additive patterns, which can be easy to continue. However, these additive patterns do not generalise or provide an explanation of how to go from one term to the next in a sequence. Talking of "finding a pattern" when a student looking at 1, 2, 4, 8, explains that the pattern is +1, +2, +4, and that this is not as helpful as "finding a rule" (which will always tell us how to get to the next number) is a useful approach.
Some of the problems in exercise 2 involve multiplying by a decimal. This is found at stage 8 of the multiplication domain, so is likely to be tricky for some students.
Comments on the Exercises
Exercise 1
Asks students to find the rule that links the terms then use it to work out the next two terms in the sequence.
Exercise 2
Asks students to fill in the missing number in the sequence.