Number and Shape Patterns

4th Grade MathFactors and Multiples4 pages

About this worksheet

Pattern work for 4th grade on Common Core 4.OA.5, where the point is the feature the rule never stated. Students extend add-3, multiply-by-2 and add-10 sequences from printed starts, then answer a detective question about each: a checkbox list for the odd-even alternation, an observation about the doubling sequence, and a description of what the ones and tens digits do under add 10. A repeating star-square-triangle-circle strip asks for the 12th and 17th shapes without drawing them all. The reasoning section has Leo proving even-plus-4-stays-even with help from a printed clue box, and Maya predicting whether her 20th term is odd or even. Answers included.

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$Number and Shape Patterns: Factors and Multiples - page 1$

$Number and Shape Patterns: Factors and Multiples - page 2$

$Number and Shape Patterns: Factors and Multiples - page 3$

$Number and Shape Patterns: Factors and Multiples - page 4$

Curriculum objectives covered

4.OA.5

“Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. For example, given the rule "Add 3" and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way.”

All seven questions generate from a stated rule and then name an unstated feature; question 1 is the standard's own add-3-from-1 alternation example, checkboxes included.

What's inside this worksheet

Part 1: Generate Number Patterns

Start at 1 and add 3, start at 4 and multiply by 2, start at 5 and add 10, each extended in printed grids. Every sequence carries its own hidden-feature question, and the first offers four checkbox options.

Part 2: Shape Patterns

Eight shapes are printed and numbered: star, square, triangle, circle, repeating. Question 4 wants the 12th shape and question 5 the 17th, with an explanation that avoids drawing all seventeen.

Part 3: Pattern Reasoning Challenge

Leo's add-4-from-2 sequence stays even, and students explain why with a clue box supplying Even + Even = Even and Odd + Odd = Even. Maya starts at 3 and adds 5; students write her first five numbers and predict the parity of the 20th.

How teachers use it

The why matters

Accept an extension only with its feature question answered. Writing 16, 32, 64, 128 is the easy half; noticing every term stays even is the standard.

Remainder preview

The 17th-shape question is secretly division with remainder: 17 ÷ 4 leaves 1, so it matches position 1, the star. Let students discover that shortcut rather than presenting it.

Parity vocabulary

Post Even + Even = Even from the clue box on the wall during this unit. Maya's 20th-term prediction is answerable from parity alone, no listing required.

More 4th Grade Math worksheets

Multi-Digit Operations Fractions and Decimals Measurement and Data Geometry

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