# Patterns and Sequences - Stage 3

This collection of resources supports the teaching of Patterns and Sequences.

Here are some of the favourite activities selected by the NRICH team.

- Odds, Evens and More Evens Alison, Bernard and Charlie have been exploring sequences of odd and even numbers, which raise some intriguing questions...
- Seven Squares Watch these videos to see how Phoebe, Alice and Luke chose to draw 7 squares. How would they draw 100?
- Shifting Times Tables Can you find a way to identify times tables after they have been shifted up?
- Charlie’s Delightful Machine Here is a machine with four coloured lights. Can you develop a strategy to work out the rules controlling each light?

These are just a few of the activities on Patterns and Sequences that you can find on the NRICH curriculum pages.

The activities below, taken from the STEM Learning website, complement the NRICH activities above.

### Year Nine Booster Kit

**Year Nine Booster Kit** has teachers notes and resources for a lesson on linear sequences. (Pdf pages 27-29). Students use a pattern shown on a handout to investigate how the pattern develops.

### Number Patterns and Sequences

**Number Patterns and Sequences** contains explanations, examples and exercises where students find missing numbers in sequences and use function machines to generate sequences. Students also find the nth term of an arithmetic sequence and attempt to explain how the nth term is found and used.

**Overhead Slides** has two pages about linear sequences which are suitable to aid whole class discussion.

### Sequences

**Sequences pack one** (pdf page 7) is Smile card 1312 which shows sets of patterns which develop as arithmetic sequences. Students are expected to state each term to term rule but this could be extended to finding the nth term.

### Number and Algebra 2

**Number and Algebra 2** (pdf page 118) gives an example of a strategy for solving a problem involving a sequence. This is followed by a series of related problems where students are encouraged to find the nth term of each sequence. Other questions involve using first and second differences to continue given non-linear sequences.

The **Resource and Assessment Pack** has a revision sheet of similar questions (pdf page 21) and two extension questions (pdf page 33), one of which relates to triangular numbers.