Patterns and Sequences - Stage 4
This is a second collection of resources that support the teaching of Patterns and Sequences.
Here are some of the favourite activities selected by the NRICH team.
- Slick Summing Watch the video to see how Charlie works out the sum. Can you adapt his method?
- Attractive Tablecloths Charlie likes tablecloths that use as many colours as possible, but insists that his tablecloths have some symmetry. Can you work out how many colours he needs for different tablecloth designs?
- Steel Cables Some students have been working out the number of strands needed for different sizes of cable. Can you make sense of their solutions?
- Picture Story Can you see how this picture illustrates the formula for the sum of the first six cube numbers?
The activities below, taken from the STEM Learning website, complement the NRICH activities above.
Links and Resources
Number Sequences: Non-linear is an interactive program which leads students through an exploration of triangular numbers, square numbers, pentagonal patterns and matchstick problems. Students are encouraged to find the formula for each of the quadratic sequences. The data and a suggested formula for each sequence are shown on a separate worksheet.
This CIMT resource has two resources:
Sequences begins with arithmetic sequences and deals with generating a sequence from a formula and from pictures. There are further sets of questions about finding the formula for linear sequences.
Overhead Slides has pages to aid class discussion which deal with arithmetic sequences including finding the nth term.
This 'instant maths ideas' resource has a number of ideas for investigating sequences.
Points and Regions (pdf page 4) has ideas on how to generate a sequence which does not continue to follow the suggested pattern after the sixth term. More able students could then investigate a formula for the complete sequence.
This resource has some challenging and open-ended sequence questions, where students need to generate their own sequences to fit certain criteria and investigate what happens when those criteria change.