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

Lesson objective: Extend understanding of equivalent fractions to see that writing equivalent fractions is useful for comparing sums of two fractions. Students bring prior knowledge of decomposition of fractions to find sums and differences of fractions...

Lesson objective: Identify and create equivalent sums and differences using fractions with unlike units. This lesson helps to build fluency with computation of equivalent fractional values and deepen conceptual understanding that expressions composed of...

Lesson objective: Understand that we can use the magnitude of fractions to be added or subtracted to estimate between which two whole numbers the result will fall. Students bring prior knowledge of estimation with benchmarks of 0, \(\frac12\), and 1 fro...

Lesson objective: Estimate the sum of fractional values as greater or less than a given whole number. This lesson provides an opportunity for students to apply their knowledge and understanding of estimation of fractional sums to a reallife situation. ...

Lesson objective: Use fraction equivalence strategies to find the best expressions for adding fractions with different sized pieces. Students bring prior knowledge of equivalent fractions from 3.NF.A.3a/bc. This prior knowledge is extended to to include...

Lesson objective: Compute sums and differences of fractions with different sized pieces whose values are between one and two. This lesson helps to build fluency with adding and subtracting fractions with different sized pieces (unlike denominators). Fra...

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...

Lesson objective: Use benchmark values of 0, half, and 1 to estimate sums of fractional values, and check estimates with exact calculations. This lesson provides an opportunity for students to apply their knowledge and understanding of estimation and ad...

Lesson objective: Compute sums and differences of fractions with different sized pieces (unlike units) whose values are between one and ten. This lesson helps to build fluency with fractional addition and subtraction. Multiplication strategies for equiv...

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...

Lesson objective: Calculate sums and differences of fractions in multistep expressions. This lesson helps to build towards fluency with addition and subtraction of fractions and mixed numbers whose pieces are different sizes (with unlike units). Multip...

Lesson objective: Solve multistep problems involving sums and differences of fractions with different sized pieces. This lesson provides an opportunity for students to apply their knowledge and understanding of addition and subtraction of fractions wit...