# Creating Rich Tasks at Mathspace: A Guide for Teachers

How does the Mathspace team create rich tasks and what lessons are there for teachers who want to do the same?

At Mathspace, we prioritize creating rich tasks that align with educational standards and foster deep conceptual understanding. Our rich tasks are designed to engage students in exploratory and hands-on learning, providing teachers with valuable classroom resources. For teachers interested in developing their own rich tasks and those who just want a peek behind the curtain, here are some insights into how we select topics and structure our rich tasks, along with guidance for effective implementation.

#### Selecting Topics and Standards

We begin our process by thoroughly examining the new Virginia Standards of Learning (SOLs), identifying those that would benefit from a more conceptual or exploratory approach. We focus on standards that use terms like “represent,” "describe," "explain," and "derive," (among others) as these indicate opportunities for deeper understanding.

For the rich task we'll walk through today, we focus on the 8th grade standards relating to square roots, specifically non-perfect squares: 8.NS.1a and 8.NS.1b. Associated content for these same standards can be found in the Mathspace textbook here: VA Grade 8: 1.02 Estimate square roots.

Rich tasks can be demanding to implement at the best of times, and without a well-defined structure, it can be even more challenging. A well-structured rich task is essential for effective teaching and learning.

Our goal with these rich tasks is that teachers can read through the task guide shortly before class and feel confident that they can successfully implement it with their students. It shouldn't feel overwhelming or overly complex.

Here's how we structure our tasks:

1. Task Name and Blurb: The first page includes the task name and critical concept.
1. Standards and Objectives: Standards are clearly stated and the task is briefly described so that teachers understand the purpose and goals.
2. Vocabulary: Relevant vocabulary is listed, focusing on terms necessary for understanding the task rather than the target concepts. For example, in our square roots task, our vocabulary terms don't include "perfect square" but instead focus on more basic prior knowledge required to access the task (Area of a square and side length of a square).
3. Materials and Preparation: A comprehensive list of materials is provided, including optional items and a preparation checklist, to ensure that teachers are well-prepared to deliver the task.
3. Task Instructions: A student-friendly presentation of the task gives clear, step-by-step instructions. For example, students might work with sets of numbers to create and compare squares, using graph paper and scissors to explore the concept of square roots.
4. Sample Student Responses: Examples of possible student responses guide teachers in anticipating and addressing student misconceptions. These aren't meant to provide the only correct answer, but they allow teachers to anticipate what students might say.
5. Discussion and Reflection:
1. Discussion Guide: A discussion guide suggests questions to facilitate student engagement and critical thinking during and after the task. This guide includes strategies to help students who may struggle and to challenge those who progress quickly.
2. Post-Task Questions: Post-task questions help teachers tie the activity back to broader mathematical concepts and vocabulary.
6. Additional Resources: Printable handouts and editable slides support various teaching preferences. While some teachers may prefer guiding the class collectively using slides, others might opt for group-based activities with handouts. We want to be flexible enough to accommodate multiple types of classrooms.

Check out the Guide for the Square Roots Task here.

#### Implementing Rich Tasks in the Classroom

1. Preparation:
1. Quick Read-Through: Teachers with limited time can quickly read through the task overview and gather necessary materials using the preparation checklist.
2. Task Familiarization: Ideally, teachers should familiarize themselves with the task beforehand to better facilitate student learning.
2. Classroom Delivery:
1. Flexible Approaches: Teachers can use slides for whole-class instruction or distribute handouts for group work depending on their teaching style.
2. Guided Exploration: Encourage students to explore and experiment with the task, offering support and prompting critical thinking without providing direct answers.
3. Facilitating Discussion:
1. Encouraging Exploration: Use the discussion guide to prompt students to share their findings and reasoning, fostering a collaborative learning environment.
2. Connecting Concepts: Help students draw connections between the task and broader mathematical concepts, preparing them for more formal instruction.

By carefully selecting standards, structuring tasks thoughtfully, and providing comprehensive implementation support, Mathspace aims to empower teachers and enhance student learning through rich, engaging mathematical experiences.