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## What are we targeting?

Through a series of lessons using different contexts, manipulatives, and models, students will learn to add and subtract fractions with unlike denominators. Adding and subtracting fractions with unlike denominators is a key concept for students to understand, yet students typically only learn a procedure to do so. They lack the conceptual understanding of why finding the common whole (or common denominator) is essential.

The two main models that help represent adding and subtracting fractions are the bar model and the number line model. In the early phases of learning this concept, the contexts of time and money are a great universal context that help students engage in what the denominator represents, while the importance of the numbers that are chosen is critical towards a student's ability to grasp this concept.

Adding time:

The learning progression of these lessons begins by representing expressions with money and time as contexts on rods models so that students develop a deep understanding of a common whole and common denominators for unlike fractions.

The objective of these lessons is for students to think about fractions in relationship to time or money initially. We accomplish this by being very intentional with the denominators chosen for each problem. First, it is the relationship of the denominators to the context. When we present coins, the denominator will be 100 to represent the whole. By doing so, we will have 1/20 = nickel, 1/10 = dime, 1/4 = quarter, 1/2 = 50 cent piece and 1/100 = penny.

Adding money:

Subtracting money:

When students think about fractions as money in relationship to the denominator, adding 1/4 + 1/10 becomes a mental calculation of 25 + 10.

Students then use this understanding of a common whole with the bar model and transition into using a double open number line to add and subtract unlike fractions.

Finally, they will be able to create equivalent expressions without the use of manipulatives and models to solve for adding and subtracting unlike fractions.

The intended learning outcome of these lessons is that students become flexible in how they solve these problems. By working with various bar models, a number line, and then the equation only, students form a deeper sense of numeracy about what a fraction represents, equivalent fractions, and common wholes.

## How will students see these lessons?

This content has been added to 5th-grade lessons, and these lessons have been carefully integrated into the full suite of DreamBox lessons. Students who are working in lessons beyond these will not need to complete these lessons. If a student is currently working on content at this grade level, then they will see these lessons on their lesson chooser at the appropriate time.