In this Grade 4 Eureka Math lesson from Chapter 22, students learn to explain fraction equivalence by using tape diagrams and number lines to visualize how fractions like one-half, two-fourths, and four-eighths represent the same value. Students connect these visual models to multiplication and division number sentences, such as multiplying or dividing both the numerator and denominator by the same number to generate equivalent fractions. The lesson builds fluency with composing and decomposing fractions across halves, fourths, eighths, fifths, and tenths.
Section 1
Representing Fractions on Tape Diagrams and Number Lines
A fraction can be represented on a tape diagram by partitioning a whole into equal parts and shading parts.
On a number line, it is the point located at the end of the -th partition when the interval from 0 to 1 is divided into equal parts.
Section 2
Finding Equivalent Fractions by Partitioning a Number Line
To decompose a non-unit fraction on a number line, divide each fractional unit into an equal number of smaller parts ().
This is equivalent to multiplying both the numerator (the number of parts considered) and the denominator (the total parts in the whole) by .
Expand to review the lesson summary and core properties.
Section 1
Representing Fractions on Tape Diagrams and Number Lines
A fraction can be represented on a tape diagram by partitioning a whole into equal parts and shading parts.
On a number line, it is the point located at the end of the -th partition when the interval from 0 to 1 is divided into equal parts.
Section 2
Finding Equivalent Fractions by Partitioning a Number Line
To decompose a non-unit fraction on a number line, divide each fractional unit into an equal number of smaller parts ().
This is equivalent to multiplying both the numerator (the number of parts considered) and the denominator (the total parts in the whole) by .