In this unit, students will extend their understanding of equivalent fractions and addition and subtraction of fractions with like denominators (including mixed numbers) to create expressions that are equivalent using fractions with unlike denominators. They will then combine their existing number sense of benchmark fractions on the number line with whole number composition concepts to estimate where a sum or difference may fall on the number line. Finally, students will apply these equivalency and operations concepts to model and solve addition and subtraction of fractions and mixed numbers with different denominators.
Key Concepts:
 If \(\frac ab=\frac{an}{bn}\)and \(\frac cd =\frac{cm}{dm}\), then \(\frac ab + \frac cd = \frac{an}{bn}+\frac{cm}{dm}\). This is why rewriting fractions as equivalent fractions produces the same sum. (Lesson 1)
 We can use the magnitude of fractions to be added or subtracted to estimate the sum or difference as less than or greater than some whole number, or to tell what two whole numbers the result should fall between. (Lesson 3)
 Naming the sum or difference of two fractions as one number requires rewriting the fractions with same size pieces. (Lesson 4)
Prior Knowledge Needed:
 Understanding equivalent fractions (Grade 3, Unit 10; 3.NF.A.3)
 Comparing fractions (Grade 3, Unit 11; 3.NF.A.3)
 Decomposing and composing fractions for addition and subtraction (Grade 4, Unit 3; 4.NF.B.3)
 Understanding fraction equivalence and comparison (Grade 4, Unit 5; 4.NF.A.1)
 Comparing fractions to benchmarks of zero, half, and one (Grade 4, Unit 5; 4.NF.A.2)
 Solving addition and subtraction word problems involving fractions and mixed numbers (Grade 4, Unit 9; 4.NF.B.3)
Units on the Horizon:
 Solving problems with fractional quantities (Grade 5, Unit 12)
 Addition and subtraction of decimals (Grade 6, Unit 3)
 Addition and subtraction of rational numbers (Grade 7, Unit 4, Unit 5)
Lessons in this unit have been temporarily archived as they undergo maintenance work.
Lessons

Objective: Subtract fractions with unlike denominators using equivalent representations that use equalsized pieces. This optional activity can be used after Unit 3 Lesson 6. Math concept addressed: In this Guided Collaborative Task, students will use t...

Objective: Find sums and differences of mixed numbers with unlike denominators by combining equalsized pieces that can be easily subtracted or added. This optional activity can be used before or after Unit 3 lesson 8. Math concept addressed: In this Gu...