Skip Counting and Number Patterns - Third Grade Mathematics

Patterns are everywhere in mathematics, forming the rhythm and music of numbers. In this chapter, you will master skip counting by 2s, 3s, 4s, 5s, 10s, and 100s, and you will learn how to uncover the hidden rules inside number sequences. Skip counting is not just fun; it is the direct bridge to mastering multiplication and division.

What Is Skip Counting?

Skip counting means counting forward or backward by a number other than 1. Instead of counting every single step, you skip a regular number of steps on each count.

Counting by 1s:  1,  2,  3,  4,  5,  6,  7,  8,  9, 10
Skip Counting by 2s: 2,  4,  6,  8, 10, 12, 14, 16, 18, 20

When you skip count by 2s on a number line, you take jumps of 2 units each:

0    1    2    3    4    5    6    7    8    9   10
+----+----+----+----+----+----+----+----+----+----+
     +-------->+-------->+-------->+-------->+---->
      Jump 2    Jump 2    Jump 2    Jump 2   Jump 2

Essential Skip Counting Patterns

Let us examine the most important skip counting patterns for third grade.

Skip Counting by 2s, 5s, and 10s

These are the most familiar patterns, and their ones digits follow special rules:
- Counting by 2s: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20... (Every number is even, ending in 2, 4, 6, 8, or 0).

- Counting by 5s: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50... (The ones digit alternates strictly between 5 and 0).

- Counting by 10s: 10, 20, 30, 40, 50, 60, 70, 80, 90, 100... (The ones digit is always 0, and the tens digit increases by 1 each time).


Skip Counting by 3s and 4s

Skip counting by 3s and 4s prepares you directly for the 3 and 4 multiplication tables:
- Counting by 3s: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36.
Notice the parity: odd, even, odd, even, odd, even...
- Counting by 4s: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48.
Notice that every single number in the 4s pattern is an even number! That is because 4 is an even number, and adding an even number always keeps the sum even.

Skip Counting by 100s

Counting by hundreds is just like counting by ones, but with two zeros attached:
- 100, 200, 300, 400, 500, 600, 700, 800, 900, 1,000.


You can also skip count by 100s starting from any number:
- Starting at 245: 245, 345, 445, 545, 645, 745.
Notice that only the hundreds digit changes; the tens and ones digits stay identical!

Discovering the Rule in a Number Sequence

When you are given an incomplete list of numbers, you can become a number detective to discover the pattern rule and fill in missing values.

The Detective Strategy

  1. Look at two consecutive numbers side by side.
  2. Determine if the numbers are increasing (getting larger) or decreasing (getting smaller).
  3. If increasing, the rule involves addition (or multiplication).
  4. If decreasing, the rule involves subtraction (or division).
  5. Find the difference between the two numbers by subtracting the smaller from the larger.
  6. Check that same difference across other pairs in the list to confirm the rule.
  7. Apply the confirmed rule to find the missing numbers.

Example 1: Finding Missing Numbers

Sequence: 14, 18, 22, ___, 30, ___

Step 1: The numbers are increasing. Step 2: Compare 18 and 14: 18 - 14 = 4. Step 3: Check next pair: 22 - 18 = 4. The rule is "Add 4". Step 4: Find first missing term: 22 + 4 = 26. Step 5: Verify next term: 26 + 4 = 30 (matches!). Step 6: Find second missing term: 30 + 4 = 34. Completed sequence: 14, 18, 22, 26, 30, 34.

Example 2: Backward Skip Counting

Sequence: 50, 45, 40, ___, 30, ___

Here the numbers are decreasing. Compare 50 and 45: 50 - 45 = 5. The rule is "Subtract 5". Missing numbers: 40 - 5 = 35, and 30 - 5 = 25. Completed sequence: 50, 45, 40, 35, 30, 25.

Chapter Practice Exercises

  1. Skip count forward and write the next three numbers: a. 6, 9, 12, 15, , , ___ b. 8, 12, 16, 20, , , ___ c. 35, 40, 45, 50, , , ___ d. 210, 310, 410, , , ___
  2. State the pattern rule and fill in the missing numbers: a. 12, 18, 24, , 36, ___ b. 80, 70, , 50, , 30 c. 105, 110, 115, , 125, ___ d. 13, 16, 19, ___, 25, ___
  3. If you start at 0 and skip count by 4s, will you ever say the number 25? Explain why or why not.
  4. A baker bakes trays of cookies. Each tray holds 6 cookies. Skip count by 6s to find how many cookies are on 1, 2, 3, 4, and 5 trays.
  5. Start at 128 and skip count forward by 10s four times. List your numbers.

Solutions and Step-by-Step Answers

  1. Next three numbers: a. 6, 9, 12, 15 -> (skip counting by 3s) -> 18, 21, 24. b. 8, 12, 16, 20 -> (skip counting by 4s) -> 24, 28, 32. c. 35, 40, 45, 50 -> (skip counting by 5s) -> 55, 60, 65. d. 210, 310, 410 -> (skip counting by 100s) -> 510, 610, 710.
  2. Rules and missing numbers: a. 18 - 12 = 6. Rule: "Add 6". Missing numbers: 30, 42. (12, 18, 24, 30, 36, 42). b. 80 - 70 = 10. Rule: "Subtract 10". Missing numbers: 60, 40. (80, 70, 60, 50, 40, 30). c. 110 - 105 = 5. Rule: "Add 5". Missing number: 120. (105, 110, 115, 120, 125, 130). d. 16 - 13 = 3. Rule: "Add 3". Missing number: 22. (13, 16, 19, 22, 25, 28).
  3. No, you will never say 25. Every multiple of 4 is an even number (0, 4, 8, 12, 16, 20, 24, 28...), but 25 is an odd number. Also, 24 + 4 = 28, so you skip right over 25.
  4. Counting by 6s:
  5. 1 tray: 6 cookies
  6. 2 trays: 12 cookies
  7. 3 trays: 18 cookies
  8. 4 trays: 24 cookies
  9. 5 trays: 30 cookies
  10. Starting at 128 and adding 10 each time: 138, 148, 158, 168.