Students will develop a conceptual understanding of the equivalence of fractions as equal areas of area models and locations on number lines. They will represent equivalent fractions with given models and by generating their own models. They will extend their understanding of equivalence in whole numbers to fractional amounts. Students may struggle with representing equivalence as equal areas of the same whole.
Key Concepts:
 Equivalent fractions have the same value. They name the same amount of area of the same whole, and they are in the same position on the number line.
 Whole numbers can be named as fractions, and naming whole numbers as fractions does not change their values.
 We can name numbers in infinitely many ways.
Prior Knowledge Needed:
 Represent whole numbers in different but equivalent ways. (Grade 2, Unit 6; 2.NBT.A.2)
 Understand the meaning of the equal sign. (Grade 1, Unit 13; 1.OA.D7, 1.OA.D.8, 1.NBT.B.3)
 Understand that fractions are numbers that can be represented on the number line. (Grade 3, Unit 4; 3.NF.A.1, 3.NF.A.2a)
Units on the Horizon:
 Comparing fractions (Grade 3, Unit 11)
 Using equivalencies to compare fractions with unlike denominators (Grade 4, Unit 5)
Lessons

Lesson objective: Understand that fractions are equivalent if they represent the same amount or name the same location on a number line. Students bring prior knowledge that fractions are numbers that can be located on a number line, that the denominator...

Lesson objective: Generate equivalent fractions with area models or number lines. This lesson includes only fractions that are less than 1. This lesson helps to build procedural skill with generating equivalent fractions. An area model is used here beca...

Lesson objective: Solve problems using equivalent fractions. This lesson provides an opportunity for students to apply their knowledge and understanding of equivalent fractions to a reallife situation. Students are asked to evaluate the results from a ...

Lesson objective: Understand that equivalent fractions for whole numbers can be represented on a number line. Recognize equivalent fractions for whole numbers on a number line. Students bring prior knowledge of recognizing fractions on a number line fro...

Lesson objective: Find equivalent fractions for whole numbers. Students bring prior knowledge of equivalent fractions for one whole from 3.G.A.2. This prior knowledge is extended to generate and recognize fractions equivalent to whole numbers other than...

Lesson objective: Generate equivalent fractions for whole numbers. This lesson helps to build procedural skill with generating fractions equivalent to whole numbers. A number line is used in this lesson. Linear models are the best model for highlighting...

Lesson objective: Solve problems using equivalent fractions for whole numbers. This lesson provides an opportunity for students to apply their knowledge and understanding of generating equivalent fractions for whole numbers to a mathematical situation. ...

Lesson objective: Understand that we can name numbers, including fractions, in an infinite number of ways. Students bring prior knowledge of partitioning area models to create equivalent fractions 3.NF.A.3. This prior knowledge is extended to creating m...

Lesson objective: Generate many equivalent fractions for the same point on a number line by repeatedly partitioning the number line. This lesson helps to build procedural skill with generating equivalent fractions. A number line is used here because it ...

Lesson objective: Solve problems involving finding many equivalent fractions for the same length. This lesson provides an opportunity for students to apply their knowledge and understanding of finding many equivalent fractions for the same length to a r...