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Number and Shape Patterns

  • Grade 4
  • Mathematics
  • 4.OA.C.5
  • Operations & Algebraic Thinking
  • Free lesson

Aligned to 4.OA.C.5 — Common Core State Standards for Mathematics.

What this lesson teaches

A pattern follows a rule that tells you how to get the next term. After you build a few terms, you can often notice extra features the rule did not mention, like 'these numbers are all even.'

Worked examples

Example 1

Rule: start at 3 and add 5 each time. Terms: 3, then 3+5=8, then 8+5=13, then 13+5=18, then 18+5=23. Pattern: 3, 8, 13, 18, 23. Extra feature not in the rule: the ones digits switch between 3 and 8.

Example 2

Rule: start at 2 and double each time. Terms: 2, 4, 8, 16, 32. Doubling grows much faster than adding does.

Example 3

Shapes make patterns too: a row of 1 square, then 2, then 3 builds a staircase, and the total squares go 1, 3, 6, 10 — each step adds one more than the last.

Practice questions

  1. Rule: start at 2 and add 4. Write the first six terms.
  2. Rule: start at 1 and multiply by 2 each time. Write the first five terms and tell one feature you notice.
  3. A shape pattern goes triangle, square, triangle, square. What is the 9th shape? Explain the rule you used.

Watch the lesson

Every lesson comes with a video taught in English and Spanish — the same video the QR code in the printed workbook opens.

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En español

Patrones de números y figuras

Un patrón sigue una regla que te dice cómo obtener el siguiente término. Después de formar unos cuantos términos, a menudo puedes notar características extra que la regla no mencionó, como 'todos estos números son pares.'

Ejemplo 1: Regla: empieza en 3 y suma 5 cada vez. Términos: 3, luego 3+5=8, luego 8+5=13, luego 13+5=18, luego 18+5=23. Patrón: 3, 8, 13, 18, 23. Característica extra que no está en la regla: la cifra de las unidades cambia entre 3 y 8.

Ejemplo 2: Regla: empieza en 2 y duplica cada vez. Términos: 2, 4, 8, 16, 32. Duplicar crece mucho más rápido que sumar.

Ejemplo 3: Las figuras también forman patrones: una fila de 1 cuadrado, luego 2, luego 3 construye una escalera, y el total de cuadrados va 1, 3, 6, 10 — cada paso agrega uno más que el anterior.

More Operations & Algebraic Thinking lessons

Multi-Digit Multiplication with Partial Products4.NBT.B.5Multi-Step Word Problems4.OA.A.3Factors, Multiples, and Patterns4.OA.B.4Times as Many: Multiplication as Comparison4.OA.A.1Word Problems with Times as Many4.OA.A.2

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