# An In-Depth Look: Plato Courseware and Standards-Based Mathematical Practice

## An In-Depth Look: Plato Courseware and Standards-Based Mathematical Practice

Plato Courseware for mathematics is designed to meet rigorous content standards and also provide ample opportunity for students to practice, apply, and stretch their understanding. Content standards define what students should learn, but state and Common Core standards also provide clear direction on *how* students can best build knowledge. At all grade levels, students simultaneously build their mathematical knowledge and hone their mathematical skills by repeatedly applying eight critical mathematical practices.

Our new Math 8 course exemplifies Edmentum’s approach to online mathematics content by requiring students to apply multiple mathematical practices in every single lesson. Each lesson includes activities that encourage students to learn how to approach the topic at hand but that also guide students toward thinking deeply, enabling them to build abstract understanding from concrete problems and experiences. One example of this can be seen in our first lesson on reflections. In the lesson activity, we present students with the following diagram:

The goal of the content standard is for students to know how to reflect points and shapes across a line. We could teach them a simple formula for this practice, but turning it into a rote process doesn’t develop deep mathematical understanding. Instead, we encourage students to make sense of reflecting a triangle by thinking about the reflection process abstractly and figure out *why* a given triangle could or could not be the reflection of this triangle. So how do we encourage students to think about what is going on when the triangle ABC is reflected across the line MN? We ask them questions such as…

- What shape will the reflected figure be?
- After reflecting the triangle ABC across the line MN, which point will be the rightmost point?
- Which point will be the topmost point?
- Which point will be the leftmost point?

Questions like these lay a foundation for the student. Now, students know that when they reflect the triangle, the result will be a triangle of similar shape. They will also know that the point B′ will be the *rightmost* point, rather than the leftmost point and that the point A′ will be the topmost point. We then ask students about the following three triangles and ask them to explain their reasoning for why each of the triangles either could or could not be a copy of the reflected triangle.

- Image 1 could not be the reflected triangle. While it’s similar in shape, B′ isn’t on the rightmost side of the triangle.
- Image 2 could be a reflection. It’s both the correct shape and size, and the points are situated correctly.
- Image 3 could not be a reflection. While the order of the points are reversed, the triangle itself is not the same shape as the original triangle.

Throughout Math 8, we use lesson activities and unit activities as opportunities to allow students to think through problems in a scaffolded way. By asking students smaller questions about the nature of the problem at hand, we prepare them to take the logical leaps required to solve problems using these practices. As students progress through the course, it’s our hope that this inquisitive approach to mathematics becomes second nature, helping to fuel their desire to learn and practice mathematics.

Interested in learning more about Edmentum’s updated mathematics content from Plato Courseware? Check out this video for a sneak peek! Or, take a look at this brochure to learn about Plato Courseware’s engaging online courses, which are proven to achieve real results!