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 exactly one number to each object in sequence, where the last number spoken equals the total count (the cardinality of the set).

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

Read the full concept explanation →

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 tags each object with the next counting word and the final word names how many there are.

Common stuck point: The procedure for counting is the easy part; the trap is counting an object twice or skipping one. Asking "Did I touch each object exactly once and is the last number I said the total?" first is what keeps a correct-looking calculation from being attached to the wrong concept.

Sense of Study hint: Ask: Did I touch each object exactly once and is the last number I said the 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?

Answer

7

First step

Count the left side: 1, 2, 3 — there are 3 dots.

Full solution

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

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 — some letters repeat.

Example 3

easy

🍓🍓. How many strawberries?

Example 4

easy

Which numeral is this:

3

Example 5

medium

🦋. How many butterflies?

Example 6

easy

There are 9 ducks in the pond. Count them. How many ducks?

Example 7

easy

Count backward from 10 to 1. How many numbers do you say?

Example 8

medium

🍎🍎🍎🍎🍎🍎🍎🍎. How many apples?

Example 9

easy

Skip-count by 5s from 5 to 30. List the numbers.

Example 10

easy

What number comes just after 99?

Example 11

hard

Skip-count by 5s from 5 to 50. How many numbers do you say?

Example 12

easy

Skip-count by 10s from 250:

250, 260, 270, \_\_, \_\_

Example 13

easy

A jar holds 600 beads. The next jar has 100 more. How many beads are in the next jar?

Example 14

hard

Start at 480 and skip-count by 5s. What is the 4th number you say after 480?

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.

Example 3

easy

How many objects:

\bullet \bullet \bullet \bullet \bullet

Example 4

easy

Count by twos:

2, 4, 6, \_\_, \_\_

. Fill in the next two.

Example 5

easy

What number comes just before

20

Example 6

easy

Count backward from

10

6

. How many numbers do you say?

Example 7

easy

Count by tens:

10, 20, 30, \_\_

. What's next?

Example 8

easy

How many fingers on two hands?

Example 9

easy

Count by fives to

25

5, 10, 15, \_\_, \_\_

Example 10

easy

If there are

3

red balls and

4

blue balls, how many balls total?

Example 11

medium

How many whole numbers are there from

5

12

inclusive?

Example 12

medium

How many even numbers are between

1

and

20

inclusive?

Example 13

medium

A staircase has

15

steps. If you're on step

4

, how many more to reach the top?

Example 14

medium

Count by threes from

3

30

. How many numbers?

Example 15

medium

A pattern repeats every

4

beats: clap, snap, stomp, rest. On beat

10

, which action?

Example 16

medium

There are

7

houses on a street. How many gaps between adjacent houses?

Example 17

medium

Counting numbers

1

100

: how many contain the digit

7

in the ones place?

Example 18

medium

How many numbers from

1

50

are multiples of

5

Example 19

medium

A clock chimes once at 1:00, twice at 2:00, etc. How many chimes from 1:00 to 6:00?

Example 20

challenge

How many numbers from

1

100

are divisible by

2

3

Example 21

challenge

Pages numbered

1

100

. How many digits are printed in total?

Example 22

challenge

In a single-elimination tournament with

16

players, how many games are played to determine a winner?

Example 23

easy

🐝🐝🐝. How many bees?

Example 24

easy

Which numeral is this:

4

Example 25

easy

Hold up 5 fingers. Count them.

Example 26

medium

🐠🐠🐠🐠. How many fish?

Example 27

hard

🐱🐱🐱🐱🐱. How many cats?

Example 28

easy

Count to 10 out loud. What number comes after 7?

Example 29

easy

Count backward from 10:

10, 9, 8, \_\_

. What comes next?

Example 30

easy

What number comes just before 6?

Example 31

medium

Fill in the blanks:

1, 2, 3, \_\_, 5, 6, \_\_, 8, 9, 10

Example 32

medium

Count backward from 10:

10, 9, 8, 7, \_\_, 5

. What is missing?

Example 33

easy

Fill in the blanks:

47, 48, \_\_, \_\_, 51

Example 34

easy

Skip-count by 2s:

2, 4, 6, 8, \_\_, \_\_

Example 35

easy

Skip-count by 10s:

10, 20, 30, 40, \_\_

Example 36

medium

Skip-count by 2s starting at 14:

14, 16, 18, \_\_, \_\_

Example 37

medium

Sam counts his pennies by 5s:

5, 10, 15, 20, 25, 30, 35

. How many pennies in all?

Example 38

easy

Skip-count by 100s:

100, 200, 300, \_\_, \_\_

Example 39

easy

Fill in:

497, 498, 499, \_\_, 501

Example 40

easy

Skip-count by 5s starting at 425:

425, 430, 435, \_\_

Example 41

medium

Skip-count by 100s starting at 350:

350, 450, 550, \_\_, \_\_

Example 42

medium

Fill in:

789, 790, \_\_, \_\_, 793

← Back to Counting Practice Mode

Related Concepts

Addition Number Sense