--- title: "Counting & Cardinality" description: "14 topics in Mathematics, in the order they build on each other." canonical: https://lightmysky.com/learn/mathematics/areas/counting-and-cardinality source: https://lightmysky.com/learn/mathematics/areas/counting-and-cardinality.md retrieved: 2026-10-19 --- > **Agent view.** This is the Markdown twin of the page, for tools and assistants. > When to use this site, and the call that answers each job: https://lightmysky.com/agent-instructions.md > API description (OpenAPI 3.1): https://lightmysky.com/openapi.json · Authentication: https://lightmysky.com/auth.md > Pricing: https://lightmysky.com/pricing.md · Catalog: https://lightmysky.com/llms.txt · Full catalog: https://lightmysky.com/llms-full.txt > Every machine-readable file on this domain: https://lightmysky.com/.well-known/ai-catalog.json > Ask for Markdown with `Accept: text/markdown`, a `.md` address, or `?mode=agent`. # Counting & Cardinality 14 topics in Mathematics, in the order they build on each other. Page: https://lightmysky.com/learn/mathematics/areas/counting-and-cardinality - [One-to-one counting](https://lightmysky.com/learn/mathematics/one-to-one-counting-mt_WcfaSfVT33): One-to-one correspondence when counting objects: each object is paired with exactly one number name - [How Many in Total?](https://lightmysky.com/learn/mathematics/how-many-in-total-mt_dmNvjroCPT): Cardinality principle: the last number said when counting a set tells how many objects are in the set, regardless of arrangement or order counted - [One More Each Time](https://lightmysky.com/learn/mathematics/one-more-each-time-mt_sYpKWbq5ra): Each successive counting number represents a quantity that is one larger than the previous number - [Showing numbers many ways](https://lightmysky.com/learn/mathematics/showing-numbers-many-ways-mt_pAcaehday5): Represent numbers using objects, pictorial representations, and the number line - [Counting objects to 20](https://lightmysky.com/learn/mathematics/counting-objects-to-20-mt_yqAL6O5i_v): Count up to 20 objects in structured arrangements, count up to 10 scattered objects, and count out a requested amount from 1 to 20. - [Comparing groups: more or fewer](https://lightmysky.com/learn/mathematics/comparing-groups-more-or-fewer-mt__h7hvT4tEb): Compare two groups of objects to determine which has more, fewer, or whether they are equal, using matching and counting strategies - [Rote counting to 100](https://lightmysky.com/learn/mathematics/rote-counting-to-100-mt_M5PPDJStGm): Rote count forwards and backwards from 0 to 100, beginning from 0, 1, or any given number, by ones - [Counting in 2s, 5s and 10s](https://lightmysky.com/learn/mathematics/counting-in-2s-5s-and-10s-mt_nvdpxAJTBG): Count in multiples of 2, 5, and 10 (skip counting) - [Two written numerals between 1 and 10](https://lightmysky.com/learn/mathematics/two-written-numerals-between-1-and-10-mt__YRJ23GuIK): Compare two written numerals between 1 and 10 to determine which is greater or less - [Counting forwards and backwards](https://lightmysky.com/learn/mathematics/counting-forwards-and-backwards-mt_aHAM29nidj): Count forwards and backwards in steps of 3 from 0 - [Skip Counting (4s, 8s, 50s, 100s)](https://lightmysky.com/learn/mathematics/skip-counting-4s-8s-50s-100s-mt_IzQvs7k_sE): Count from 0 in multiples of 4, 8, 50, and 100 - [Counting in 6s](https://lightmysky.com/learn/mathematics/counting-in-6s-mt_7rJM8eWUfw): Count in multiples of 6, 7, 9, 25, and 1000 - [Counting forwards and backwards (age 6+)](https://lightmysky.com/learn/mathematics/counting-forwards-and-backwards-age-6-mt_OkSJfrmFb_): Count forwards and backwards in tens from any number (not just multiples of 10) - [Counting Within 1,000](https://lightmysky.com/learn/mathematics/counting-within-1-000-mt_M2v1A9OEuM): Count within 1000, including skip-counting by 5s, 10s, and 100s