Learn on PengiPengi Math (Grade 4)Chapter 3: Understanding Multiplication and Division

Lesson 1: Understanding Multiplication and Division as Equal Groups

In this Grade 4 lesson from Pengi Math Chapter 3, students explore division as equal groups by learning two types of division: partitive (sharing) and quotative (measurement). Students represent division problems using drawings, tables, and equations, then connect division to multiplication as its inverse operation.

Section 1

Relating Factors to Equal Groups

Property

In a multiplication equation, the numbers being multiplied are called factors.
One factor represents the number of equal groups, and the other factor represents the size of each group.

(number of groups)×(size of each group)=total(\text{number of groups}) \times (\text{size of each group}) = \text{total}

Examples

Section 2

Two Meanings of Division: Quotative and Partitive

Property

Division word problems can be categorized into two types based on the unknown information:

  1. Group Size Unknown (Partitive Division): The total is divided into a known number of groups. The goal is to find the size of each group.
Total÷Number of Groups=? (Group Size)Total \div Number\ of\ Groups = ?\ (Group\ Size)
  1. Number of Groups Unknown (Quotative Division): The total is divided by a known group size. The goal is to find the number of groups.
Total÷Group Size=? (Number of Groups)Total \div Group\ Size = ?\ (Number\ of\ Groups)

Section 3

Relating Division to Finding a Missing Factor

Property

Solving a division problem, such as A÷B=?A \div B = ?, is the same as finding the unknown factor in the related multiplication equation, B×?=AB \times ? = A.
The quotient of the division is the unknown factor.

Examples

Lesson overview

Expand to review the lesson summary and core properties.

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Section 1

Relating Factors to Equal Groups

Property

In a multiplication equation, the numbers being multiplied are called factors.
One factor represents the number of equal groups, and the other factor represents the size of each group.

(number of groups)×(size of each group)=total(\text{number of groups}) \times (\text{size of each group}) = \text{total}

Examples

Section 2

Two Meanings of Division: Quotative and Partitive

Property

Division word problems can be categorized into two types based on the unknown information:

  1. Group Size Unknown (Partitive Division): The total is divided into a known number of groups. The goal is to find the size of each group.
Total÷Number of Groups=? (Group Size)Total \div Number\ of\ Groups = ?\ (Group\ Size)
  1. Number of Groups Unknown (Quotative Division): The total is divided by a known group size. The goal is to find the number of groups.
Total÷Group Size=? (Number of Groups)Total \div Group\ Size = ?\ (Number\ of\ Groups)

Section 3

Relating Division to Finding a Missing Factor

Property

Solving a division problem, such as A÷B=?A \div B = ?, is the same as finding the unknown factor in the related multiplication equation, B×?=AB \times ? = A.
The quotient of the division is the unknown factor.

Examples