In this unit, students begin to integrate their understanding of fractions with their understanding of comparing numbers. They use and build on their knowledge of fractions to discover different strategies for comparing and building equivalent fractions. By partitioning proportionally and exploring the idea of transitivity, students deepen their understanding of equivalence and comparison.
Key Concepts:
 There are three possible relationships between two given numbers with the same unit of reference, a and b: \(a<b\), \(a>b\), \(a=b\)
 We can compare two numbers indirectly by comparing them both to a common benchmark.
 a/b = (nxa)/(nxb) because we have n times as many pieces in the whole. Each piece is n times smaller, so we need n times as many of them to cover the same distance or the same area.
 Finding common denominators is helpful in comparing fractions because it enables us to compare samesized pieces.
Prior Knowledge Needed:
 Compare two twodigit numbers; (Grade 1, Unit 13; 1.NBT.B.3)
 Understand fractions as numbers; (Grade 3, Unit 4, 3.NF.A.1)
 Recognize and generate equivalent fractions; (Grade 3, Unit 10; 3.NF.A.2)
 Understand whole numbers as fraction; (Grade 3, Unit 10; 3.NF.A.2)
 Compare 2 fractions by reasoning about their size; (Grade 3, Unit 11; 3.NF.A.3)
Units on the Horizon:
 Using equivalency to add and subtract fractions with unlike denominators (Grade 5, Unit 3)
 Understanding the concept of multiplying fractions by fractions (Grade 5, Unit 5)
 Developing the concept of dividing unit fractions (Grade 5, Unit 8)
Lessons

Lesson objective: Extend understanding that fractions can be compared as less than, equal to, or greater than another fraction that has unlike numerators and denominators. Students bring prior knowledge of comparing fractions from 3.NF.A.3.ad. This pri...

Lesson objective: Compare and order fractions with unlike numerators and denominators. This lesson helps to build procedural skill comparing fractions with unlike numerators and denominators. Area models and number lines are used here because it support...

Lesson objective: Apply comparing and ordering fractions in a realworld problem context. This lesson provides an opportunity for students to apply their knowledge and understanding of comparing and ordering fractions to a reallife situation. Students ...

Lesson objective: Extend understanding that fractions can be compared using its comparison to a benchmark fraction. Students bring prior knowledge of comparing fractions from 3.NF.A.3.ad. This prior knowledge is extended to using a benchmark as student...

Lesson objective: Compare fractions to common benchmarks of 0, half, or 1. This lesson helps to build procedural skill with comparing fractions to a benchmark fraction. A number line is used here because it highlights a fraction's distance from the benc...

Lesson objective: Apply choosing a reasonable benchmark that may not be half or 1 to make fraction comparisons. This lesson provides an opportunity for students to apply their knowledge and understanding of comparing fractions with using a benchmark to ...

Lesson objective: Extend fraction understanding by recognizing that equivalent fractions can be generated by partitioning or combining each equal share of a fraction. Students will understand that when naming equivalent fractions the denominator changes...

Lesson objective: Combine or partition each equal piece of a whole to generate equivalent fractions. This lesson helps to build procedural skill with generating equivalent fractions. Area models and number lines are used here because it hightlights how ...

Lesson objective: Apply multiplication and division to generating equivalent fractions. This lesson provides an opportunity for students to apply their knowledge and understanding of generating equivalent fractions to a mathematical situation. Students ...

Lesson objective: Multiply or divide the numerator and denominator by the same number to generate equivalent fractions. This lesson helps to build procedural skill with generating equivalent fractions. The area model is used here because it visually sup...

Lesson objective: Compare fractions with unlike denominators by finding common denominators. Students bring prior knowledge of comparing two fractions with like denominators by reasoning about their size from (Grade 3, Unit 11; 3.NF.A.3). This prior kno...

Lesson objective: Compare fractions with unlike denominators in problems where the denominators are compatible, meaning one of the numbers is a multiple of the other. This lesson helps to build procedural skill with comparing fractions with unlike denom...

Lesson objective: Compare fractions with unlike denominators in problems where the denominators are not compatible, meaning one of the numbers is not a multiple of the other number. This lesson helps to build procedural skill with comparing fractions wi...

Lesson objective: Compare fractions with unlike denominators using the most appropriate strategy based on the fractions being compared. This lesson helps to build fluency with comparing fractions with unlike denominators. Comparing indirectly to a bench...

Lesson objective: Apply the skill of comparing fractions with unlike denominators using the most appropriate strategy based on the fractions being compared. This lesson provides an opportunity for students to apply their knowledge and understanding of c...