The KEY to Solving Mathematical Problems

What is the KEY?

The KEY is an instructional tool that empowers students to persevere as they engage in the process of solving complex, multi-step problems. With experience, each student will develop their own problem solving style. The value of the KEY is not for a particular type of problem nor a specific student learning style. Rather it is a generic problem solving routine that can be applied to any problem.

Videos of Introductory Lessons

Two videos demonstrate how to use the KEY as a tool in solving complex, multi-step word problems. The KEY was developed because many students do not know what an open sentence for a math problem is, nor how to write one. Also, many students have never been encouraged to investigate a problem by asking questions. These skills are critical to understanding and making sense of a problem. Specifically, what are you solving for and how do you build on the information in the problem.

Video Lesson 1 is an overview of the KEY focusing on Stop! and how to write an open sentence for a math word problem. These ideas are further developed in Chapter 8 in The Big Yellow Book. Video Lesson 2 focuses on the Think part of the KEY which is further developed in Chapter 9 in The Big Yellow Book.

Lesson 1: Stop! and Open Sentences

Lesson 2: Think

Supplemental KEY Training Worksheets

A Supplemental KEY Training Worksheet Packet is now available to those who purchased The Big Yellow Book. It contains material that was still being field tested when the book went to press in 2018.

The KEY is a powerful tool supporting perseverance in problem solving. Students need to use the KEY automatically so that it becomes routine. Learning a new routine takes time, practice, encouragement and reinforcement! The KEY Training Worksheets help develop perseverance by guiding the student through repetitive problem analysis, a new behavior for most students.

• Download the password protected file.
• The password is the last word (no period) in the last paragraph on page 71 of The Big Yellow Book.

The KEY and Common Core State Standards

Common Core State Standards for Mathematical Practices express the skills and knowledge expected of every student. The Big Yellow Book supports all eight Mathematical Practices articulated in the Common Core State Standards and is particularly effective at achieving three. The KEY supports MP1 and the Solution Strategy Worksheets support MP3 and MP6.

The KEY is a way to implement Common Core State Standards for Mathematical Practices 1:

• MP1: Make sense of problems and persevere in solving them.

MP1 states "Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary."

How the KEY Implements MP1

Teachers who use the KEY have reported dramatic improvements in perseverance in problem solving! This routine gives students permission to struggle with a problem. The Stop tells students that before they pick up their pencil they must be clear on what they are solving for. The repeated Think…Go… reminds students to keep doubling back and thinking about the problem some more as they work on it, to ensure that their work is relevant and captures all of the nuances of the problem. The dot-dot-dots in the KEY conveys to the student that they must slow down, even pause, because perseverance is a natural part of the problem solving process.