PERTS Elevate Resource Library

Open-Ended Math Tasks

Select math problems that offer students multiple pathways to explore a concept, solve a problem, or justify their reasoning.

Grades 6-8, 9-12 Math Video · 1:34

Overview

Open-Ended Tasks in mathematics offer students multiple pathways to explore a concept, solve a problem, or justify their reasoning. These tasks are intentionally designed with more than one correct answer or more than one valid method of solving, encouraging creativity, critical thinking, and authentic engagement with mathematics.

Through this practice you will be able to:

  • Foster an engaging and inviting learning environment where students are encouraged to take ownership of their learning.
  • Gather evidence of student thinking to better support independent and self-regulated learning.
  • Integrate real-world context to increase student motivation and relevance.
  • Support a student-centered classroom that empowers learners to guide their own learning pathways.

Materials

A well-crafted open-ended task aligned to your current unit. See the Task Identification Checklist Here are some examples:

  • Design a garden using any shape(s) with a fixed perimeter; compare different designs for area and explain your reasoning. [CCSS.MATH.CONTENT.7.G.B.4 Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle.]
  • Create a data display (graph, chart, or visual model) to represent a real-world situation of your choice; justify your choices and interpretations. [CCSS.Math.Content.6.SP.B.4 Display numerical data in plots on a number line, including dot plots, histograms, and box plots.]
  • Develop a budget for a class event with a set amount of money; decide how to allocate funds and justify trade-offs and priorities. [CCSS.MATH.CONTENT.7.EE.B.3 Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers... and assess the reasonableness of answers using mental computation and estimation strategies.]

Chart paper, whiteboards, or notebooks for brainstorming and recording

(Optional) Graphing tools: calculators, graph paper, or software

Sticky notes or reflection prompts

Self-Evaluation Form for students to self-evaluate their process and reasoning

Day Before Prep (~40 min)

  1. Select rich, open-ended tasks with your students that allow for multiple solutions, strategies, and/or representations. The Task Identification Checklist provides guidance for selecting a task. Explore the task(s) yourself to ensure that you are familiar with multiple methods for solving the problem. As you work through it, ask yourself:

    • What strategies might students use?
    • What ideas or mistakes might come up while students work on this?
    • How can I help students think for themselves without giving away the answer?

  2. Prepare materials that students might use for planning and design. These could be included as problem handouts, tools for visual or algebraic work, and reflection prompts. Also prepare a Self-Evaluation Form for students to self-evaluate their process and reasoning.

  3. Create a few sample student responses or exemplars to anticipate different approaches.

  4. Plan how students will share their work (e.g., gallery walk, small groups, whole-class discussion/presentation).

  5. Consider grouping structures (pairs, triads, or open choice) based on your goals for collaboration.

Conducting the Practice (35-50 min)

  1. Introduce the Task (5-10 minutes): Present the open-ended task (or choice of tasks) clearly. Emphasize that there is no single right answer or method and that students will choose how to approach the problem. Here is sample language:

    "This task is designed so you can explore and make your own choices about how to solve it. There isn't just one right answer or way to do it. You will get to decide the path that makes the most sense to you. This gives you a chance to take charge of your problem solving and try out different ideas, which helps you become a stronger and more independent thinker."

  2. Work Time (15-20 minutes): Students can work independently or in groups. Provide access to various tools and resources for problem-solving. Circulate to ask probing questions and support student thinking.

  3. Share Strategies (5-10 minutes): Have students present their solutions and explain their reasoning. This could be done through posters, whiteboards, gallery walks, or peer discussions/presentations.

  4. Reflection (5 minutes): Ask students to reflect in writing or discussion: What strategy did they choose and why? What did they learn from their own approach and from seeing others' approaches?

  5. Wrap-Up (5 minutes): Summarize key mathematical ideas and celebrate the variety of thinking in the room.

Pitfalls to Avoid

  • Over-scaffolding the task: Avoid giving too much direction, which can limit autonomy. Let students interpret and make decisions.
  • Tasks that are too vague or unaligned: Ensure the task is rigorous, relevant, and connected to content goals.
  • Uneven participation in groups: Set norms and expectations to promote shared responsibility in collaborative work.
  • Skipping reflection time: Processing how and why students approached the task is essential for building understanding.
  • Assessing only the end product: Use rubrics or checklists that value process, reasoning, and communication—not just the answer.

What to Look For

  • Students making intentional choices about how to approach the task
  • Use of varied representations (tables, graphs, equations, visuals) and solution methods
  • Peer discussions that involve comparing strategies
  • Student work that shows depth of reasoning, not just final answers
  • Increased student confidence and willingness to share ideas
  • Creativity in problem-solving and solutions

Additional Inspiration

This practice was developed in collaboration with WestEd.