# Multiplicative sequences

Teacher's Notes

These exercises and activities are for students to use independently of the teacher to practice number properties.

### Number Framework domain and stage:

The number work in this activity relates to applying multiplication facts. This is found in the multiplication domain at stage 7, advanced multiplicative.

### Curriculum reference:

Algebra, levels 4 and 5

### Numeracy Project book reference:

These activities do not directly follow from teaching episodes based on the Numeracy resource books.

### Prior knowledge. Students should be able to:

- Multiply by a single digit number
- Divide whole numbers and decimals by 10
- Multiply integers and decimals
- Write a rule for a sequence as a sentence, and with symbols. (See the notes with "decreasing differences" for a discussion of this).

### During these activities, students will meet:

- Sequences with multiplicative recursive formulae

### 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.