الصفوف 3–5Discrete Mathematicsمُخطَّط له

Systematic listing and counting

Finding all possibilities in an organised way (outfits, routes, arrangements, handshakes) using lists, tables and tree diagrams, and checking that nothing is missed or counted twice.

math.discrete.systematic-listing

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Whole-number arithmetic

عدد المتطلبات السابقة الإلزامية (حتى الأساس): 4

ستتعلّم

List all combinations in small problems, such as outfits from 3 shirts and 2 pairs of trousers, using a table or tree diagram.
Explain how an organised list guarantees that no possibility is missed or repeated.
Discover that 3 shirts and 2 pairs of trousers give 3 × 2 outfits, and generalise.

تعريف

A tree diagram shows each choice as a branch, so that each path from the start to an end is one possibility.

مبرهنة

If a first choice can be made in m ways and a second in n ways, there are m × n combined choices.
Three different objects can be arranged in a row in exactly 6 ways.

مفاهيم خاطئة شائعة

Counting the same possibility twice when order does not matter, as with handshakes.
Stopping when no new possibility comes to mind, instead of using a system.

يقود إلى

Counting principles

اكتشافات اختيارية

Combinatorics Systematic counting grows into permutations, combinations and the binomial theorem.