Learn on PengienVision, Mathematics, Grade 4Chapter 14: Algebra: Generate and Analyze Patterns

Lesson 3: Patterns: Repeating Shapes

In Grade 4 math (enVision Mathematics, Chapter 14), students learn how to identify and extend repeating patterns made up of shapes or numbers, then use division to predict any specific term in the pattern, such as the 49th or 100th item. The lesson covers recognizing that positions of each shape correspond to multiples or near-multiples of the pattern's cycle length, and applying that relationship to solve problems efficiently. Students also practice constructing math arguments to justify their predictions.

Section 1

Finding an Element in a Repeating Pattern

Property

To find the element at position NN in a pattern with a repeating unit of length LL:

  1. Divide the position number by the length of the repeating unit: N÷LN \div L.
  2. If the remainder is RR and R>0R > 0, the element is the RR-th element in the repeating unit.
  3. If the remainder is 00, the element is the LL-th (last) element in the repeating unit.

Examples

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Chapter 14: Algebra: Generate and Analyze Patterns

  1. Lesson 1

    Lesson 1: Number Sequences

  2. Lesson 2

    Lesson 2: Patterns: Number Rules

  3. Lesson 3Current

    Lesson 3: Patterns: Repeating Shapes

Lesson overview

Expand to review the lesson summary and core properties.

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Section 1

Finding an Element in a Repeating Pattern

Property

To find the element at position NN in a pattern with a repeating unit of length LL:

  1. Divide the position number by the length of the repeating unit: N÷LN \div L.
  2. If the remainder is RR and R>0R > 0, the element is the RR-th element in the repeating unit.
  3. If the remainder is 00, the element is the LL-th (last) element in the repeating unit.

Examples

Book overview

Jump across lessons in the current chapter without opening the full course modal.

Continue this chapter

Chapter 14: Algebra: Generate and Analyze Patterns

  1. Lesson 1

    Lesson 1: Number Sequences

  2. Lesson 2

    Lesson 2: Patterns: Number Rules

  3. Lesson 3Current

    Lesson 3: Patterns: Repeating Shapes