Grade 5 has some exciting updates with the addition of Module 5 Topic C: Area of Rectangular Figures with Fractional Side Lengths!

In this new lesson, Grade 5 students put their understanding of adding and multiplying fractions to work as they calculate the areas of rectangular figures and apply this to real-world scenarios.

Students begin this new topic by reviewing how to find the area of basic rectangles. They find that, even if one or both of the side lengths are written as unit fractions, the process of finding the area as a product of the side lengths remains the same. Then, they encounter an important symbol for area, A, that they use throughout the remainder of the tasks. 

When new fractions come into play–a side length written as a mixed number–students also add a new step: rewriting the mixed number as an improper fraction before multiplying to find the area. Once the product is found, the students rewrite the improper fraction as a mixed number again. And, don’t forget the units! Students always ensure that the area is labeled in sq units.

But, students quickly learn that there is a second approach for finding the area when the side length(s) of a rectangle is a mixed number. First, they break the larger rectangle into smaller rectangles, simplifying their factors into whole-number or unit-fraction side lengths. Next, they find the area of each smaller rectangle, then add the products to find the total area. After completing this task, they have established an important principle: we can find the area of a rectangle by summing the areas of its parts.

By comparing the results from one task to another, students learn that despite using different methods to find the area of a figure, the results remain the same.

In the next task, students decompose rectangles where the side lengths are both mixed numbers. First, they break the rectangles down into even more pieces by dragging tiles of various sizes to fill the original shape. Then, they break down mixed numbers into parts with whole-number or unit-fraction side lengths, practicing the steps necessary before actually solving. Soon, they’re completing the entire process–solving for the area of each part and then adding them to solve for the total area.

The final tasks in the module have students demonstrate their understanding as they solve word problems. Students use both methods for finding area as they encounter scenarios where they must find the area of a garden bed and a piece of fabric.

In the final task, there is an additional challenge: the shape they’re finding the area of is not a perfect rectangle. Students use their critical thinking skills to apply their understanding of area to scenarios like painting a wall with a window or the floor of a room with a balcony. In both cases, students must use an additional operation–addition or subtraction–to find the total area of the composite shape.

For Students: This new module encourages students to combine several previously taught skills: finding the area of rectangles, using the distributive property of multiplication, and converting and multiplying fractions. As they complete word problems with area, they are also seeing the practical applications of the math they are learning, translated into real-world scenarios.

For Teachers: Through this module, teachers can identify any persistent gaps in their students’ understanding of fraction operations. Students must not only demonstrate these skills in isolation, but also apply them to real-world scenarios, where any breakdowns become evident. If gaps exist, teachers can quickly address them in small groups using our Assignments feature. 

If you have any questions about these new updates, please don’t hesitate to reach out to us at support@happynumbers.com. We’re here to help you and your students make as much progress in math as possible! 

Explore the updates in Grade 5 Module 5 Topic C today to help your students become area experts!