Numbers & the Number System • Topic 1 of 9

Counting

Counting looks trivial to an adult, but it rests on a handful of principles that CTET tests directly. To count a set of objects a child must recite number names in a fixed order (the stable-order principle), tag each object once and only once (one-to-one correspondence), and understand that the last number said is the total (cardinality) - and that the total does not change if you start from a different object (order irrelevance). Three kinds of counting matter for the exam. Forward counting recites numbers in increasing order from any starting point (start at 5, go three steps: 5, 6, 7, 8) and builds the idea of 'one more', the seed of addition. Backward counting goes the other way (12, 11, 10, 9) and underpins subtraction and 'one less'; children often stall crossing a decade, getting stuck going 21, 20, then hesitating. Skip counting jumps by a fixed amount - 2, 4, 6, 8 or 5, 10, 15, 20 or 10, 20, 30 - and is the bridge to multiplication tables and equal grouping. The teaching order runs concrete to abstract: real counters and number-line hops first, charts and mental counting later.

✅ Solved examples

1. A child counting a row of seven beads points to two beads while saying 'four'. Which counting principle has she broken?
One-to-one correspondence - each object must be tagged with exactly one number word. Pointing to two beads on a single count violates it, so the total will be wrong.
2. Complete the skip-counting series: 5, 10, 15, 20, __ . What is the rule and the next term?
The rule is add 5 each time (skip counting by 5s). The next term is 20 + 5 = 25.
3. Counting backward from 22: 22, 21, 20, __ . A child says '10'. What likely went wrong, and what is correct?
The child confused the decade boundary. The correct term is 19 - after 20 comes 19, not a jump to 10. Crossing decades backward is a known sticking point.
4. Why is skip counting by 2s considered a foundation for multiplication?
Each jump represents one equal group of 2, so 2, 4, 6, 8 is really 1, 2, 3, 4 groups of two. That equal-grouping idea is exactly what multiplication formalises.

✏️ Practice — try these, take hints as needed

1. Forward counting from 8 by single steps gives 8, 9, __, 11. Fill the blank.
Add one each step.
It sits between 9 and 11.
10
2. Skip counting by 10s starting at 10: 10, 20, 30, __ . Next term?
Add ten each time.
Two tens after 20.
40
3. The principle that the last number you say while counting is the total number of objects is called:
Not order, not correspondence.
It answers "how many".
Cardinality
4. Counting backward from 15 by ones: 15, 14, 13, __ . Fill the blank.
Subtract one.
One less than 13.
12

📝 Topic test — 8 questions

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