Open Middle
Open Middle math problems, created by Robert Kaplinsky, are engaging tasks with a fixed start and single correct answer (closed beginning/end) but many paths to get there (open middle), promoting deep thinking, exploration, and rich classroom discussion.
Audience
Educators,
Students,
Caregivers
Subject
Numeracy
Grade level
Grade K - 3,
Grade 4 - 5,
Grade 6 - 8,
Grade 9 - 12,
Everyone
Approval status
Approved
Compatible devices
Chromebook,
iPad,
Mac,
Windows Desktop & Laptop
Description
Open Middle math problems, created by Robert Kaplinsky, are engaging tasks with a fixed start and single correct answer (closed beginning/end) but many paths to get there (open middle), promoting deep thinking, exploration, and rich classroom discussion by allowing diverse student strategies, unlike typical textbook problems. They involve using given digits to create a specific outcome (e.g., closest sum to 100), encouraging problem-solving and conceptual understanding across grade levels and topics.
Key Characteristics:
- Closed Beginning: All students start with the same prompt and constraints (e.g., use digits 1-9 once).
- Open Middle: Students choose their own strategies and paths to solve the problem, fostering creativity.
- Closed End: There's a single, correct, or optimal answer (e.g., the smallest possible difference, the greatest product).
How They Work (Example):
- Traditional Problem: "Solve 539 - 286".
- Open Middle Problem: "Use digits 1-9 exactly once to create two three-digit numbers with a difference as close to 329 as possible".
Benefits:
- Deeper Thinking: Moves beyond rote memorization to genuine mathematical thinking.
- Engagement: Makes math more interactive and less intimidating for many students.
- Rich Discussions: Multiple solution paths lead to valuable classroom conversations about different approaches.
- Accessibility: Adaptable for various skill levels, allowing all students to participate.
Where to Find Them:
- The main resource is the website www.openmiddle.com, which offers a large collection of problems for different topics and grades.
Cost and Access
Image
This is a free teacher resource.
It does not require a login or signup.