Counting Examples in Math

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Counting.

This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Math.

Concept Recap

Determining the total number of objects in a set by assigning one number to each object.

Like pointing to each toy and saying '1, 2, 3...' to know how many toys you have.

Read the full concept explanation โ†’

How to Use These Examples

  • Read the first worked example with the solution open so the structure is clear.
  • Try the practice problems before revealing each solution.
  • Use the related concepts and background knowledge badges if you feel stuck.

What to Focus On

Core idea: Counting establishes a one-to-one correspondence between objects and numbers.

Common stuck point: Confusing 'how many' with 'which number' (cardinal vs ordinal).

Sense of Study hint: Try touching or moving each object as you count it, then say the last number out loud โ€” that's your total.

Worked Examples

Example 1

easy
A student counts the dots on a domino. The left side has 3 dots and the right side has 4 dots. How many dots are there in total?

Solution

  1. 1
    Count the left side: 1, 2, 3 โ€” there are 3 dots.
  2. 2
    Count the right side: 1, 2, 3, 4 โ€” there are 4 dots.
  3. 3
    Count all dots together starting from 1: 1, 2, 3, 4, 5, 6, 7 โ€” the total is 7 dots.

Answer

7
Counting assigns one number to each object in sequence. The last number spoken is the total (cardinality). Counting on from the first group (starting at 3 and continuing 4, 5, 6, 7) is a key efficiency strategy.

Example 2

medium
How many letters are in the word MATHEMATICS? Count carefully โ€” some letters repeat.

Practice Problems

Try these problems on your own first, then open the solution to compare your method.

Example 1

easy
Skip-count by 5s starting at 5 and list the first six multiples.

Example 2

medium
A bag contains red, blue, and green marbles. There are 4 red, 3 blue, and 5 green marbles. Without counting the whole bag at once, use grouping to find the total.