Description
Sometimes the quickest way to count something is not to count it directly.
In Lesson 6 of Counting & Combinatorics, learners bring together the ideas from the course and explore a collection of powerful counting strategies.
They investigate counting the opposite, splitting a problem into cases, using symmetry, counting the same thing in two ways and replacing a complicated object with a simpler one.
This lesson includes
- complementary counting — counting what is easier instead;
- splitting problems into separate cases;
- using symmetry to avoid repeated work;
- double counting and counting the same set in two ways;
- matching complicated objects with simpler objects;
- problems involving coin tosses, codes, handshakes, diagonals and subsets;
- a rectangle-counting challenge;
- answers and discussion;
- supplementary exercises for extra practice and revision.
Suitable for learners aged 10 and over. This lesson draws on ideas developed throughout Lessons 1–5.
☕ Free to download
This resource is completely free. If you find it useful and would like to
support the creation of more free mathematics resources, you can
support Sumthing Else on Ko-fi
.
This is Lesson 6 of the 6-part Beyond Curriculum: Counting & Combinatorics course.
