a world of experience

The author received his B.Sc. from the University of California, Berkeley, in Engineering Physics. He went on to get his Ph.D. from Cornell University in Materials Science and Engineering. He has had over 30 years of experience as a practicing engineer in the fields of semiconductors, process development and materials design. He has spent a lot of time thinking about the process of learning math, physics and engineering, and is frustrated that the fields tend to be exclusive to those who already have an aptitude for them. He firmly believes that many more students would choose STEM as a career choice if the fields were presented in the right way. This book represents an approach that may appeal to anyone who likes to solve puzzles. And although the math is de-mystified, some of the problems provide a higher level of challenge to require the student to think logically. In the end, it is seeing realistic problems being solved which can give the student an entirely different view of the quantitative fields. 

1. As a Supplement to Standard Math Courses (Grades 7-12) 

• Where It Fits: Algebra I, Geometry, Algebra II, Pre-Calculus, Calculus. Flexible enough to align with the level of the class.
• How It Helps: Extensive problem sets could be used as warm-ups, homework, or extra credit to reinforce core concepts. The “what you need to know” sections tie directly to required skills (e.g., solving equations, working with functions), while the puzzle-like framing keeps students engaged. It’s a low-pressure way to practice       standards. 

                   In Short:

•       Boost student confidence in CCSS.MATH.CONTENT by  tackling bite-sized, real -world puzzles that build on classroom lessons.

2. As STEM Enrichment or Elective Classes 

• Where It Fits: Middle school STEM electives, high school engineering clubs, career-focused programs. The engineering problems at the end are designed to generate excitement about STEM careers.
• How It Helps: Gives students a hands-on taste of engineering without prerequisites. Teachers can use it as a standalone module—say, a 4-6 week unit—to let students “play engineer” and explore if it’s for them.

               In short: 

• Expose students to engineering applications early, aligning with NGSS standards like MS-ETS1-1 while building confidence through guided       problem-solving.

3. Allows Differentiated Instruction 

• Where It Fits: Mixed-ability classrooms, especially in grades 7-9 where math anxiety can start spiking.
• How It Helps: The scaffolding (rudimentary to advanced problems) and “learn by doing” approach make it perfect for students who struggle with abstract math or need a confidence boost. Teachers  could assign easier problems to students who are struggling and still challenge more advanced performers with the engineering problems.

• In Short: Meets diverse needs with tiered problems that support struggling learners and stretch high flyers - all while tying math to real-world engineering.

4. Provides a Cross-Curricular Bridge (Math + Science/Tech) 

• Where It Fits: Pair it with physics, tech ed or even computer science classes in high school.
• How It Helps: The application problems could overlap with physics (e.g., motion equations) or tech (e.g., design challenges). It’s a natural bridge between subjects, showing how math powers other fields.

• In Short: Integrate math into science and tech curricula, aligning with standards like HS-PS2 and ISTE 4a.

5. Career and Technical Education (CTE) Introduction

• Where It Fits: High school CTE programs or career exploration units in grades 9-12.
• How It Helps: The engineering focus could attract students to STEM pathways. Helps prep students for college or careers without overwhelming them.

• In Short: Gives students a low-stakes entry to engineering, supporting CTE goals and state career-readiness benchmarks.