Virginia SOL Math / Grade 4 / Patterns, Functions & Algebra

4.PFA.1

Patterns

What you'll learn

  • Identify, describe, extend, and create addition and subtraction patterns
  • Identify, describe, extend, and create multiplication patterns
  • Find the rule for a number pattern and use it

Words to know

Pattern —
an ordered set that follows a rule
Rule —
what to do to get the next term
Term —
one number or item in a pattern
Increasing —
the terms grow larger
Decreasing —
the terms get smaller

Why it matters Finding a pattern's rule lets us predict what comes next, in numbers, savings, or a growing design.

Worked examples

Model ItI do

Find the rule and the next term: 3, 6, 12, 24, ...

Each term is doubled: 3 x 2 = 6, 6 x 2 = 12, 12 x 2 = 24. The rule is multiply by 2, so the next term is 24 x 2 = 48.

Try It TogetherWe do

Describe the rule and extend: 100, 90, 80, ___, ___.

Each term is 10 less than the one before, so the rule is subtract 10. The next terms are 70 and 60.

Now YouYou do

Find the rule and the next term: 5, 10, 20, 40, ...

Compare each term to the one before it to find what you multiply by. Check your answer in the back.

Practice

Mastered 0 of 11

Warm-up

Ease in with the basics.

  1. 1.Extend the pattern: 5, 10, 15, 20, ___.

  2. 2.What is the rule for 20, 18, 16, 14?

  3. 3.Extend the pattern: 1, 2, 4, 8, ___.

On Level

The core Quick Check from the book.

  1. 1.Extend the pattern: 2, 4, 8, 16, ___.

  2. 2.What is the rule for 81, 72, 63, 54?

  3. 3.Fill the blank: 4, 12, ___, 108. (rule: multiply by 3)

  4. 4.Is 5, 15, 45, 135 increasing or decreasing?

  5. 5.Create a pattern that starts at 3 and multiplies by 2. Write the first four terms.

Challenge

Stretch your thinking.

  1. 1.Find the rule and the next term: 4, 12, 36, 108, ___.

  2. 2.Fill the blank: 2, 6, ___, 54, 162. (rule: multiply by 3)

  3. 3.A pattern starts at 3 and follows the rule 'multiply by 2, then subtract 1.' Write the first four terms.