Learn on PengiPengi Math (Grade 4)Chapter 5: Factors, Multiples, and Patterns

Lesson 4: Patterns in Motion

In this Grade 4 Pengi Math lesson from Chapter 5, students learn to generate number patterns by applying rules such as "Add 3" and use input-output tables to identify function rules. They explore arithmetic sequences by defining a start term and common difference, then practice recognizing implicit features of patterns, like alternating odd and even numbers, that go beyond the stated rule.

Section 1

Using Input-Output Tables

Property

An input-output table organizes pairs of numbers that are related by a rule. The 'input' is the number you start with, and the 'output' is the result after applying the rule. We often use variables like xx for the input and yy for the output.

Input (x)Output (y)value 1value 1value 2value 2\begin{array}{|c|c|} \hline \textbf{Input (x)} & \textbf{Output (y)} \\ \hline \text{value 1} & \text{value 1} \\ \hline \text{value 2} & \text{value 2} \\ \hline \end{array}

Section 2

Finding the Rule of an Arithmetic Sequence

Property

To find the rule for a simple number sequence, calculate the difference between any two consecutive terms. If the sequence is a1,a2,a3,…a_1, a_2, a_3, \dots, the rule is to add the common difference, d=a2−a1d = a_2 - a_1, to each term to find the next one.

Examples

Section 3

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 5: Factors, Multiples, and Patterns

  1. Lesson 1

    Lesson 1: Understanding Factors and Factor Pairs

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  2. Lesson 2

    Lesson 2: Understanding Multiples

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  3. Lesson 3

    Lesson 3: Prime and Composite Numbers

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  4. Lesson 4Current

    Lesson 4: Patterns in Motion

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Section 1

Using Input-Output Tables

Property

An input-output table organizes pairs of numbers that are related by a rule. The 'input' is the number you start with, and the 'output' is the result after applying the rule. We often use variables like xx for the input and yy for the output.

Input (x)Output (y)value 1value 1value 2value 2\begin{array}{|c|c|} \hline \textbf{Input (x)} & \textbf{Output (y)} \\ \hline \text{value 1} & \text{value 1} \\ \hline \text{value 2} & \text{value 2} \\ \hline \end{array}

Section 2

Finding the Rule of an Arithmetic Sequence

Property

To find the rule for a simple number sequence, calculate the difference between any two consecutive terms. If the sequence is a1,a2,a3,…a_1, a_2, a_3, \dots, the rule is to add the common difference, d=a2−a1d = a_2 - a_1, to each term to find the next one.

Examples

Section 3

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 5: Factors, Multiples, and Patterns

  1. Lesson 1

    Lesson 1: Understanding Factors and Factor Pairs

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  2. Lesson 2

    Lesson 2: Understanding Multiples

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  3. Lesson 3

    Lesson 3: Prime and Composite Numbers

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  4. Lesson 4Current

    Lesson 4: Patterns in Motion

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