Section 1
Understanding Fractions as Division
Property
A fraction represents division. The fraction means " divided by " or "". The numerator (top number) is what we are dividing, and the denominator (bottom number) is what we are dividing by.
In this Grade 5 Illustrative Mathematics lesson from Chapter 2, students explore why a ÷ b = a/b, learning to interpret fractions as division of the numerator by the denominator. Using real-world sharing scenarios, they analyze situations where a quotient is greater than, equal to, or less than 1, and practice solving equations where the unknown may be the numerator, denominator, or quotient. This lesson directly addresses standard 5.NF.B.3 and helps students build flexible reasoning about the relationship between division and fractions.
Section 1
Understanding Fractions as Division
A fraction represents division. The fraction means " divided by " or "". The numerator (top number) is what we are dividing, and the denominator (bottom number) is what we are dividing by.
Section 2
Identifying Parts of a Fair-Share Division Problem
In a fair-share division problem, the total amount is divided into a known number of equal groups to find the size of each group.
Section 3
Distinguishing Dividend and Divisor in Word Problems
To correctly model an equal sharing situation, the division expression must be set up as:
Section 4
Creating Division Word Problems
To write a division story for an expression like , identify the total amount (the dividend, ) and what it is being divided by (the divisor, ). The story should ask a question where the answer is the quotient. The question will either be "How many groups of size are in ?" or "What is the size of each group if is shared into groups?"
Expand to review the lesson summary and core properties.
Section 1
Understanding Fractions as Division
A fraction represents division. The fraction means " divided by " or "". The numerator (top number) is what we are dividing, and the denominator (bottom number) is what we are dividing by.
Section 2
Identifying Parts of a Fair-Share Division Problem
In a fair-share division problem, the total amount is divided into a known number of equal groups to find the size of each group.
Section 3
Distinguishing Dividend and Divisor in Word Problems
To correctly model an equal sharing situation, the division expression must be set up as:
Section 4
Creating Division Word Problems
To write a division story for an expression like , identify the total amount (the dividend, ) and what it is being divided by (the divisor, ). The story should ask a question where the answer is the quotient. The question will either be "How many groups of size are in ?" or "What is the size of each group if is shared into groups?"