D.C. Public Schools is introducing a slew of new classroom lessons designed to give students more in-depth and engaging learning opportunities across the school system starting next year.

The activities, called “cornerstones,” could include a Socratic seminar, a hands-on science task, a short piece of writing or a weeks-long research project. They are designed to be memorable or inspiring learning experiences that help students make connections to the real world or encourage breakthroughs in their thinking.

Such activities are already happening in a lot of classrooms, but school officials said they want to make them a standard part of every child’s education.

At a training for principals on Thursday, D.C. Schools Chancellor Kaya Henderson said the school system has made strides in increasing the rigor of curriculum, which is aligned to new Common Core academic standards, but lessons aren’t equally challenging across the District.

“If I go to one side of town, I might see the same lesson being taught very differently than on another side of town,” she said.

Citing an example of a lesson that was memorable to her, Henderson sang a jazzy song that she wrote in the eighth grade about the water cycle for a science project.

“Clearly powerful, if, at 44, I still remember it,” she said. She said she hated her science classes until they got to that creative lesson about the water cycle.

Some of the most popular charter schools in the District emphasize project-based learning that helps students apply what they learn and make connections across different subjects. The new academic standards being used in the District and many states emphasize depth of knowledge, and many schools are looking for ways to encourage higher-order thinking skills.

The District is hiring teachers to develop and contribute projects that can be shared. The school system has amassed more than 200 lesson plans on a Web site that can be used by teachers in more than 60 courses.

For example, in a high school algebra class, students could be assigned to create scatter plots and find regression equations using data related to space shuttle flight. In a fourth- grade science class, they might learn about machines and design windmills and sailboats powered by wind. In a sixth-grade health class, they could study the impact of violence in their communities and come up with plans for addressing violence and bullying at school that they can propose to the principal.

Many teachers will be expected to teach four of the lessons a year. Some activities could take a day, others much longer.

Teachers will receive training before they introduce the lessons and then meet afterward to share work samples and reflect on how the activities went.

In some cases, students might also be able to share their work by, for example, reading essays aloud on a stage.

Heidi Haggerty, principal at J.O. Wilson Elementary School in Capitol Hill, said she likes the idea of the new lessons and the opportunity to share work with teachers from across the city.

“This gives us a chance to show what our kids can do,” she said.

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