Through work in this unit, students will come to understand that fractions referring to the samesize whole can be compared by reasoning about the size and number of pieces. They will also develop comfort with using a number of tools (such as number lines, tape diagrams, and area models) that can be utilized to reason about the size of fractions. Students will draw on their understanding of unit fractions and comparisons of whole numbers. This unit will extend those ideas to compare fractions with like numerators or like denominators.
Key Concepts:
 There are three possible relationships between two numbers a and b that are based on the same whole: a<b, a>b, a=b.
 Fractions based on the same whole with the same numerator, but different denominators have the same number of pieces, but the size of the pieces is different.
 Fractions based on the same whole with the same denominator, but different numerators, have pieces that are the same size, but the number of pieces is different.
Prior Knowledge Needed:
 Partitioning rectangles and circles into two, three, and four equal shares, describe the shares using the words halves, thirds, half of, etc. ; (Grade 2, Unit 10; 2.G.A.3)
 Understanding unit fractions; (Grade 3, Unit 4; 3.NF.A.1, 3.NF.A.2a)
 Understanding equivalent fractions (Grade 3, Unit 10; 3.NF.A.3a, 3.NF.A.3b, 3.NF.A.3c)
Units on the Horizon:
 Understand fraction equivalence and comparison (Grade 4, Unit 5)
Lessons

Lesson objective: Understand that we can compare fractions by thinking about their magnitudes. Students bring prior knowledge of understanding fractions from 3.NF.1 (Develop understanding of fractions as numbers). This prior knowledge is extended to com...

Lesson objective: Practice comparing fractions by reasoning about their size using number lines and area models. This lesson helps to build fluency with comparing fractions. Visual models are used here because it supports and develops student thinking a...

Lesson objective: Understand that when fractions have the same numerators we can compare the fractions by thinking about the size of the pieces. Students bring prior knowledge of understanding fractions from 3.NF.1 (Develop understanding of fractions as...

Lesson objective: Practice comparing fractions with like numerators using area models and number lines. This lesson helps to build fluency with comparing fractions with like numerators. A variety of word problems are used here because they support stude...

Lesson objective: Apply the strategy of common numerators to compare fractions. This lesson provides an opportunity for students to apply their knowledge and understanding of comparing fractions with like numerators in a reallife situation. Students ar...

Lesson objective: Understand that when the denominators are the same we can use the numerators to compare the number of samesize pieces. Students bring prior knowledge of understanding fractions from 3.NF.1 (Develop understanding of fractions as number...

Lesson objective: Practice comparing fractions with like denominators, including fractions greater than one. This lesson helps to build procedural skill with comparing fractions with like denominators. Visual models are used here because it supports the...

Lesson objective: Apply understanding of comparing fractions with like denominators to find fractions greater than or less than a given fraction. This lesson provides an opportunity for students to apply their knowledge and understanding of comparing fr...

Lesson objective: Practice comparing fractions using multiple strategies: reasoning about their size, common numerators, or common denominators. This lesson includes fractions greater than one. This lesson helps to build fluency with comparing fractions...