Guidebook - Level 9

Teacher Guide - STEM UNO Level 9 Copyright © 2026 Author: Erin Goodwin Editors: Lindsey Own and Natasha Karampela ISBN: 978-981-17737-3-0 Published by: SKOOL21 PTE. LTD. 71 Robinson Road, #14-01, 068895, Singapore First Edition published by SKOOL21 PTE LTD - Singapore, 2024 Second Edition published by SKOOL21 LLC - United States, 2026 No part of this book may be reproduced, distributed, or transmitted in any form or by any means, including photocopying, recording, or other electronic or mechanical methods, without the prior written permission of the publisher, except in the case of brief quotations embodied in critical reviews and certain other non-commercial uses permitted by copyright law.

For permissions or inquiries, please contact: Email: info@skool21.org Website: https://skool21.org Address: 600 California St, #13-021, San Francisco, CA 94108, United States

Table of Contents S. NO

CONTENT

PAGE NO.

1

PREFACE

O3

2

INTRODUCTION TO THE KIT

04

3

LESSON STRUCTURE

05

4

THE ENGINEERING DESIGN PROCESS

06

5

FOSTERING SOCIAL SKILLS

07

6

MAKERSPACE SETUP

08

7

STEM CLASSROOM MANAGEMENT

09

8

IMPLEMENTATION GUIDE

11

9

STANDARDS ALIGNMENT

15

10

CAMBRIDGE SCIENCE ALIGNMENT

16

11

NGSS ALIGNMENT

18

12

CAMBRIDGE MATHEMATICS ALIGNMENT

20

13

COMMON CORE MATHEMATICS ALIGNMENT

22

14

SCHEME OF WORK

24

15

LESSON PLANS AND ANSWER KEY

27

16

ASSESSMENT GUIDE

70

03

Preface Welcome to the Future of Teaching and Learning!

Thank you for joining us on this exciting journey! The SKOOL21 STEM Innovators series is designed not only to ignite curiosity in students but also to empower teachers to lead meaningful, hands-on STEM learning experiences. Through this series, you will guide young innovators as they explore, design, and solve real-world challenges using science, technology, engineering, and mathematics (STEM).

Building on a Strong Foundation Each level of the SKOOL21 STEM series builds upon the previous one, creating a strong continuum of learning — from simple machines to advanced 3D modeling. Students travel through key technological eras, from the Industrial Revolution to the innovations shaping our future. No matter their starting point, every learner will discover new skills and deeper understanding along the way.

Learning by Doing At SKOOL21, we believe students learn best by doing. Each book comes with a comprehensive STEM kit, enabling students to build, test, and explore concepts through hands-on challenges. As a teacher, you will facilitate engaging projects where students actively create, problem-solve, and apply critical thinking skills — all while having fun.

Making a Real-World Impact

Every project is designed to connect learning to real-world issues, inspired by the Sustainable Development Goals (SDGs). Through these challenges, students see how their ideas can contribute to solving problems like clean water access, renewable energy, and environmental conservation — empowering them to envision a better world.

Teaching Like a Pro The SKOOL21 STEM program aligns with international standards and best practices, ensuring that both teachers and students are developing the collaboration, innovation, and design thinking skills valued in today’s world. You’re not just supporting schoolwork — you’re preparing the next generation of thinkers, leaders, and changemakers.

04

Introduction to the Kit The SKOOL21 STEM UNO Learning Kit is a hands-on electronics and coding kit designed for students in Level 9. Used alongside the STEM Innovators Handbook, this kit introduces students to programming, electronics, and automation through real-world projects.

At the heart of the kit is the ATmega328P microcontroller, programmed using the C++ language through the Arduino platform. Learners explore how hardware and software work together by building projects like motor control systems, sensor-based inputs, and more.

Technical Features Microcontroller

ATmega328P

Programming Language

C++ (via Arduino IDE)

Operating Voltage

5V

Input Voltage

USB: 5V, DC: 6–12V

Digital I/O Pins

14 (6 with PWM output)

PWM Digital I/O Pins

6

Analog Input Pins

8 (A4 and A5 used for I²C communication)

DC Current per I/O Pin

20mA

Total Current Supply

USB: Max 400mA

Clock Speed

16MHz

05

DC Input: Max 1.6A

Lesson Structure Each lesson in the handbook follows a structured format to ensure clarity and effective implementation. A sample solution is also found at the end of each lesson. The structure includes:

Lesson objectives NGSS Standards Cambridge Science Standards ISTE Standards Connections Cambridge Math Standards Common Core Math Standards

Define the Problem Students are introduced to the science concept and a related real world problem they are tasked with solving.

Getting Started Every project begins with guided first steps. This helps the student to confidently tackle the challenge with a solid foundation.

Design and Plan Students brainstorm individually, then collaborate with their team to come up with the best design plan.

Build - Test - Improve Students collaborate to build, test, and improve models. Then, they practice giving and receiving constructive feedback.

Math and Science Connection/Reflect Students connect their learning back to the academic objectives and answer guided reflection questions.

06

The Engineering Design Process The Engineering Design Process (EDP) is a systematic approach used by engineers and designers to solve problems and create innovative solutions. It provides a structured framework for developing new products, processes, or systems by following a series of well-defined steps. This process is not only applicable in engineering, but is also widely used in various STEM disciplines to tackle challenges and develop creative solutions.

For students in first grade and above, the typical Engineering Design Process follows multiple iterative steps, including identifying a problem, researching, brainstorming, designing, prototyping, testing, and refining solutions.

This structured approach encourages creativity, critical thinking, and iteration, forming a strong foundation for future STEM learning.

07

Fostering Social Skills STEM activities naturally build key social skills. Teachers can help students practice and strengthen these skills by guiding them during group work, discussions, and project challenges.

Key social skills developed include:

Collaboration

Communication

Encourage students to share ideas and assign roles during group work to build teamwork and respect for different perspectives.

Model clear communication and ask students to explain their thinking and listen carefully to teammates.

Critical Thinking

Problem-Solving

Prompt students to ask "why" and "what if" questions when solving problems or designing solutions.

Challenge students to try different strategies when they face obstacles and praise persistence.

Empathy and Respect

Time Management

Remind students to value everyone's ideas and support peers by using kind, respectful language.

Help teams set mini-deadlines and guide them to break projects into smaller, manageable tasks.

Conflict Resolution

Presentation Skills

Coach students to talk through disagreements calmly and find solutions that everyone can accept.

Give students regular chances to present their work to peers, using clear speaking and supportive feedback.

Reflection

Teamworking

Build reflection into the process by asking students what worked well, what was challenging, and what they would do differently next time.

Celebrate strong teamwork by recognizing when students share leadership, encourage each other, and solve problems together.

Teaching STEM also teaches students how to think, work, and lead. By actively supporting social skills during projects, teachers prepare students not just for academic success, but for future careers and life challenges.

08

Makerspace Setup A makerspace is a creative, hands-on area where students explore STEM concepts through building, experimenting, and solving problems together. This guide is designed for teachers who are new to STEM and looking for clear steps to set up and manage a makerspace.

Space Design: Choose a clean, well-lit space with room to move.

Arrange tables/chairs in clusters of 2–4 students.

Use low, open shelves for easy access to materials.

For 30 students, 750–900 sq ft is recommended (25–30 sq ft per student to allow movement, collaboration, and tool/machine/material use).

Materials Management: Ensure that kits are complete and accessible before each project.

Provide racks or open shelves to organize and store STEM kits for easy access.

Refer to the project instructions in the SKOOL21 book to identify if additional materials (e.g., craft items, recycled objects) are needed—plan ahead and prepare them in advance.

Shared Resources: Provide one STEM kit per small group.

Encourage teamwork by having students co-design and co-build projects.

Safety First: Set simple safety rules and review often.

Supervise all tool use closely.

Keep a first-aid kit in the space.

09

STEM Classroom Management STEM classes are hands-on, highly engaging, and often noisy—that’s a good thing! But without clear routines and structures, they can quickly become chaotic. A well-managed makerspace allows students to explore and innovate safely, responsibly, and collaboratively.

STEM Class Session Routine Set a clear and consistent structure to each session so students know what to expect and stay focused: 90-minute project (Grade 3 to Grade 12) 45-minute project ( Pre-K to Grade 2)

W

C

In t

Up

n lea s

ar

ro

m

-U

p/ 5– du c 8 3– t 5 mmins ion ins

in 5 m ins 3m 2–

Define the Problem

Reflection

5 mins 2–3 mins

5–7 mins 3–5 mins

Measure Your Success

Math & Science

5–7 mins 3–5 mins

7–10 mins 5 mins

Share & Improve

7–8 mins 3–5 mins

Getting Started

Bu

i

30 ld & – T 15– 35 m est 18 ins mi ns

ll Cha

en g

e

ins 5 m ins m 3–5

10

10 mins 5–7 mins

Space Organization: Assign specific work zones: Build Area, Supply Rack, Quiet Zone, Cleanup Station.

Provide racks or open shelves to store kits neatly and accessibly.

Keep a project material checklist to make sure kits are complete before starting.

Tool and Materials Rules: Use tools with care – no playing or misusing materials.

Return everything to its labeled place.

Ask before taking extra supplies.

Hands to yourself—respect others’ creations and space.

Only one group member (Material Manager) may collect materials at a time.

Group Management with Team Roles Group work can be messy without structure. SKOOL21 encourages student collaboration, so rotating roles helps balance responsibility and ensure active participation: Leader

Keeps team on task, tracks time, encourages collaboration.

Material Manager

Collects kits/materials from the teacher, ensures supplies are returned post-build.

Reporter

Shares outcomes, challenges, and solutions with the class.

Testing Supervisor

Evaluates the model, gives feedback, suggests changes.

11

Implementation Guide The SKOOL21 STEM Innovators Handbook offers project-based STEM lessons for Pre-K through Grade 12. Teachers can use three main models to implement these projects:

Integrated Approach Embed STEM projects into existing science and math lessons. For example, a science unit on plants might include a hands-on engineering challenge from the handbook. This aligns STEM activities directly with curriculum standards and learning objectives. Research shows that teaching STEM subjects together (as with integrated lessons) deepens understanding and retention and makes learning more relevant and connected to the real world.

Advantages: Reinforces required science/math standards with hands-on application.

Builds problem-solving and critical-thinking skills through project-based learning.

Helps students see connections across subjects (an “interconnected viewpoint”). viewpoint”)​ Uses existing class time (no extra periods needed), so STEM isn’t an add-on but part of the curriculum.

Practical Tips: Align projects to lessons: Choose SKOOL21 projects that match your unit goals (e.g. use a simple machine project during a forces & motion unit).

Start small: Begin with a short STEM activity (one 45-minute session) in a science or math lesson, then build up to longer projects.

Co-teach if possible: Collaborate with a science or math colleague to share planning and bring in different expertise.

Use grade-appropriate pacing: For Pre-K–Grade 2, integrate a 45-min STEM mini-project each week; for Grade 3+, you might split a 90-min science period into lecture + project time.

Emphasize standards: SKOOL21 projects are designed to align with NGSS, Common Core standards, Cambridge math and science. Highlight these connections in your lesson plan to meet academic goals.

12

Stand-Alone Class Approach Schedule a dedicated STEM class or makerspace session (e.g. a weekly 90minute lab period or rotating STEM special). In this model, students work in a makerspace or lab with tools and machines (like robotics kits, 3D printers, craft materials, etc.). A makerspace is “a collaborative workspace inside a school for making, learning, and exploring” exploring”​. Students in teams tackle SKOOL21 projects from start to finish, using hands-on materials rather than just textbooks.

Advantages: Focused hands-on learning: Students can take abstract concepts and make them concrete (for example, learning circuitry by actually building a paper circuit).

Resilience and creativity: The trial-and-error nature of making teaches perseverance; students learn to iterate on designs when things don’t work and thus develop grit​ grit.

Equity and access: A well-stocked STEM lab gives all students (including girls and under-represented groups) equal access to tech and engineering tools. tools​ Practical Tips: Schedule regularly: Block out a consistent STEM lab period (45–90 minutes) each week or rotate classes in/out of the lab.

Prepare materials in advance: Keep common kits (e.g. robotics, simple circuits, design sets) ready so each session isn’t delayed by setup and leave time for cleanup during class Train teachers: Provide basic training or guides on the SKOOL21 projects so teachers feel confident using the equipment and managing hands-on activities.

Group students thoughtfully: Mix skill levels in teams; older students can mentor younger ones in a makerspace project.

Blend with curriculum: Even in a stand-alone class, tie projects to standards (e.g. a coding project that teaches math logic or a design challenge that reinforces physical science concepts).

13

Extra-Curricular Approach Run STEM projects as after-school clubs, lunch-time activities, or summer camps. These are optional programs (STEM clubs, robotics teams, coding camps, etc.) where interested students can explore SKOOL21 challenges more freely. After-school STEM “engages students in hands-on, real-world projects,” making STEM feel exciting and relevant.

Advantages: Extra time to explore: Students get more hours to question, tinker, and learn beyond the limited school day. For example, a weekly robotics club might meet for an hour after school.

Builds interest and identity: Fun club activities spark motivation and a positive attitude toward STEM, helping students develop a STEM identity​ identity.

Flexible and student-driven: Students self-select; they work at their own pace on creative projects (e.g. coding a game, building a model bridge).

Reaches diverse learners: Clubs can target different age groups and skill levels – from basic science for younger kids to advanced robotics for teens.

This helps bridge enrichment gaps (making STEM opportunities available to all students)​ students).

Practical Tips: Keep it low-stakes: Emphasize fun and curiosity over grades. Short, handson projects (like mini-challenges) keep students engaged.

Advertise widely: Invite all students, not just high-achievers. Use school announcements, flyers, and parent newsletters to raise awareness.

Tie to competitions or showcases: Use events (science fairs, robotics tournaments) to motivate the extra effort.

Leverage summer or camp time: If resources allow, run a week-long STEM summer camp using several SKOOL21 projects for deeper immersion.

Collaborate with community: Invite guest speakers (engineers, makers) or partner with local libraries/museums for materials and inspiration.

14

Hybrid Approach (Blending All Models) In practice, many schools use a mix of models. A hybrid approach might integrate simple STEM tasks into regular lessons and also offer a dedicated STEM lab plus an after-school club. This way, every student gets some STEM exposure and those who love it can dive deeper.

When to integrate: Use curriculum-linked projects during core classes. For example, in a Grade 4 math class you might use a SKOOL21 project on gears to teach ratios, or in science class students might build a model ecosystem. Smaller or single-session activities fit well here.

When to do stand-alone: Reserve longer, open-ended projects for STEM class or the makerspace. Complex engineering challenges (robot design, 3D modeling, advanced coding) need longer blocks, so these suit a 90-min STEM period or series of lab sessions.

When to use clubs: Offer students a space for exploration that doesn’t fit the curriculum or timeline. These projects can be driven by student interest and can span several weeks without pressure to “cover the curriculum.”

Using a hybrid plan ensures flexibility. Teachers can adapt: if a semester is heavy with testing, lean on after-school clubs for enrichment; when covering standards, weave STEM into lessons. Always check that even free-form projects still touch academic goals.

(Note: SKOOL21 projects are already aligned to NGSS and Common Core standards, Cambridge Mathematics and Cambridge Science, so whether standards​ integrated or stand-alone, they support learning objectives.)

15

16

Moments

Partcle Model

Reflection

Magnetometer

Wind Turbines

Weather Seesaw

Asteroids

Global Science Impact

9

10

11

12

13

14

15

Endothermic or Exothermic

6

8

Chromatography

5

Solubility Predictor

60 - 90 min

Gold Foil Experiment

4

7

60 - 90 min

Ecosystems

3

60 - 90 min

60 - 90 min

60 - 90 min

60 - 90 min

60 - 90 min

60 - 90 min

60 - 90 min

60 - 90 min

60 - 90 min

60 - 90 min

60 - 90 min

60 - 90 min

Weight Machine

2

60 - 90 min

Duration

Joints

Topic

1

Lesson #

SDG 16

SDG 13

SDG 13

SDG 7

SDG 8

SDG 9

SDG 12

SDG 12

SDG 11

SDG 7

SDG 8

SDG 8

SDG 15

SDG 3

SDG 3

SDG

HS-PS4-5

HS-ESS1-4

HS-ESS2-4

HS-PS3-3

HS-PS2-5

HS-PS4-5

HS-PS3-2

HS-PS2-1

HS-PS1-6

HS-PS1-5

HS-PS4-1

HS-PS1-8

HS-LS2-4

HS-PS3-3

HS-LS1-2

NGSS

9SIC.05

9ESs.01, 9ESs.02

8ESc.01

8ESp.02

8Pe.01

8Ps.01

9Cc.04

9TWSa.04

9Cc.04

5.1.4

12.3.1

2.2.1

19.2

11.1.5

1.7.2

Cambridge Science

1.3.d.

1.7.c.

1.3.d.

1.3.d.

1.6.c.

1.4.a., 1.4.c.,

1.3.d., 1.7.c.

1.4.a., 1.4.c.

1.6.c. , 1.4.a.,

1.4.a., 1.4.c.

1.3.d., 1.7.c.

1.6.c., 1.7.c.

1.6.C 1.7.C

1.7.c.

1.3.d.

ISTE

Standards Alignment

HSS.CP.A.5

HSS-ID.B.5

HSF.IF.C.9

HSG.CO.A.2

HSG-GMD.B.4

HSG-SRT.C.8

HSG-SRT.C.8

HSG.GMD.A.3

HSS.ID.C.7

HSS.ID.B.6.c

HSA.CED.A.2

HSN.RN.A.2

HSF.BF.B3

HSF.LE.B.5

HSG.MG.A.1

CCSS- Math

9Ss.05

9Ss.03

9As.04

9Gp.06

9Gp.03

9Gp.02

9Gg.10

9Gg.04

9As.06

9Ss.05

E2.5

E2.2

E7.1

E5.1

C2.6

Cambridge Math

Lesson Plans and Answer key

28

Project 1: Joints Lesson Plan Duration: 60 - 90 minutes

Learning Content

Students will explore the functionality of hinge and ball-and-socket joints through coding and building models. They will use servo motors and physical materials to simulate joint movements and connect their learning to real-world applications in biomechanics and engineering.

Learning Content By the end of the lesson, students will: 1. Identify and differentiate between hinge and ball-and-socket joints in the human body and mechanical systems.

2. Program a servo motor to mimic joint movements.

3. Build functional joint models to demonstrate movement.

4. Reflect on the real-world applications of joint models in physical therapy and robotics.

Vocabulary Meaning

Word Joint Hinge Joint

The point where two bones connect, allowing movement.

A joint allowing movement along one axis, like a door or elbow.

Ball-and-Socket Joint A joint allowing multi-directional movement, like a shoulder or hip.

Materials

Computer

Arduino IDE Software

Level 9 Kit

STEM Book

Learning Activities (Session 1) Introduction 1. Ask students to observe how their arm and leg joints move. Discuss which joints allow circular motion (ball-and-socket) and which allow linear motion (hinge).

2. Show examples of how these biological joints inspire engineering designs, like car steering mechanisms (ball-and-socket) and door hinges (hinge).

Problem Khali, a physical therapist, needs models to teach her patients about joint movements.

Students will help by designing and programming models of hinge and ball-and-socket joints using servo motors and building materials.

29

Wire 1. Distribute KidsUno microcontrollers and servo motors.

2. Guide students to connect the KidsUno to their computers using a USB cable.

3. Assist students in plugging the servo motor into port 13 on the KidsUno: Brown wire GND Red wire V Orange wire D13

→

→ →

Code 1. Open the Arduino IDE and demonstrate: Selecting "Arduino Uno" as the board and ensuring the correct USB port is selected.

Opening the “Servo Sweep” example.

2. Walk students through modifying the code to use port 13 and upload it to the KidsUno. Build

1. Guide students in creating a hinge joint model: Use building blocks and a servo motor to replicate the movement of a hinge joint.

Ensure the servo motor is securely attached and functional.

2. Ask them to integrate the servo motor into the model so it moves when powered by the code.

Discover 1. Ask students to test their hinge joint models.

2. Discuss how changing the code or structure affects the movement.

3. Prompt questions like: “How does reducing the delay affect the joint’s speed?”

Challenge 1. Guide Students to Build a Ball-and-Socket Joint.

2. Move around the classroom to observe students as they cut, assemble, and attach their components.

3. Provide individualized support for students who are struggling with specific steps, such as cutting or stabilizing the structure.

Share and Improve (10 minutes) 1. Have students present their joint models to the class, explaining the design process and functionality.

2. Use a feedback table to highlight design strengths and suggest improvements.

3. Allow students time to refine their models based on peer and teacher feedback.

30

Answer Key MATH AND SCIENCE CONNECTION ANSWER 1 The formula for the circumference of a circle is: C = 2πr Substitute r = 1 and π = 3.14 C = 2 × 3.14 × 1= 6.28 units A 3/4 circle is 75% of the full circle's circumference: 3 × 6.28 = 4.71 units 4 The formula to convert degrees to radians is: π Radians = Degrees × 180 3.14 180 Radians = 270 × 0.01744 = 4.71 radians Radians = 270 ×

Answer: The value of 270 degrees is 4.71 radians.

ANSWER 2 2. Help students to label the value on the number line. π 3. Radians = Degrees × 180 3.14 Radians = −270 × 180 Radians= −270 × 0.01744 Radians = −4.71 radians Answer: −270-270−270 degrees is equivalent to -4.71 radians.

Reflect Question # 1

2

Answer key For Physical Therapists: Joint models help patients understand their injuries and recovery, improving rehabilitation outcomes.

For Biomedical Engineers: They aid in designing prosthetics and joint replacements that enhance mobility and quality of life.

Physical Therapists: Use joint models to teach proper movement and prevent future injuries.

Biomedical Engineers: Create cost-effective prosthetics and devices that improve access to healthcare solutions.

31

Project 2: Weight machine Lesson Plan Duration: 60 - 90 minutes

Learning Content

Students will explore the mechanics of pulleys and weight-lifting machines. They will design and build a weight-lifting mechanism using a servo motor and evaluate how pulleys reduce the effort required to lift a load. Students will connect their learning to the importance of weight machines in promoting health and strength, especially for the young and elderly.

Learning Content By the end of the lesson, students will: 1. Understand the function of pulleys and how they reduce effort.

2. Program a servo motor to simulate weight-lifting motions.

3. Build a weight-lifting machine using the KidsUno microcontroller and evaluate its performance.

4. Relate weight machines to health benefits and the importance of exercise.

Vocabulary Meaning

Word Congenital

A condition or trait present from birth.

Diet

The food and drink regularly consumed.

Muscle Weight machine

Body tissues that contract and relax to enable movement.

Equipment used to build strength by lifting or pushing weights.

Materials

Computer

Arduino IDE Software

Level 9 Kit

STEM Book

Learning Activities (Session 1) Introduction 1. Begin by discussing how lifestyle choices influence health, highlighting the importance of exercise for muscle and bone strength.

2. Explain that weight machines are crucial for improving strength, mobility, and injury prevention, particularly for elderly individuals.

Problem Ham, a fitness trainer, wants to design a weight-lifting machine to help his clients build muscle and strengthen their bones. Students are tasked with creating a mechanical weightlifting machine to simulate this function.

32

Predict 1. Show the images of the fixed pulley and the system of two pulleys.

2. Ask students: Which pulley system do you think reduces the effort required to lift the load?

Why? 3. Encourage students to reason how the arrangement of pulleys affects the force needed to lift a weight.

Challenge 1. Guide students to inspect the large crane design and identify the pulley section.

2. Ask them to modify the crane into a mechanical weight-lifting machine: The design should lift the suspended weight when pulling down on one side.

Focus only on the mechanical design, excluding sensors or bricks for now.

Design and Plan 1. Provide students with a space to draw and describe their plan.

2. Encourage collaboration: Ensure every team member contributes ideas to the final plan.

Discuss how they will implement pulleys and servo motors to lift weights efficiently.

Build and Code 1. Help students to wrap the wire around the 270° servo motor to create the weight-lifting mechanism and assemble the pulley system using building blocks.

2. Help students to modify the code to program the servo motor for up-and-down motions.

3. Help them to install the OLED display libraries and program the screen to show “Weight Machine.”

Test and Evaluate 1. Does the pulley system reduce the effort required to lift the weight?

2. How does the design mimic real-life weight machines?

Share and Improve 1. Guide presentations by ensuring all students share their designs and peers provide constructive feedback.

2. Monitor engagement during feedback, encouraging actionable and respectful suggestions.

3. Support refinement by helping students implement key feedback and improve their designs.

33

Answer Key MATH AND SCIENCE CONNECTION ANSWER 1 a. The “2” likely represents the base weight of the handle. b. s2 represents the contribution of the cube's side length to the weight. c. s2 + 2 = 29 s2 = 29 – 2 = 27 s = 27 ​≈ 5.2 d. Side length is irrational value.

⇒

⇒

ANSWER 2 a. 4πr2 = 1

1 ⇒ r = 4π1 = 12.56 ≈ 0.0796 ⇒ r = 0.0796 ≈ 0.28 2

b. Radius r is an irrational value.

Reflect Question #

Answer key

1

It helps the elderly improve bone strength, preventing injury.It promotes physical fitness among younger individuals, reducing the risk of lifestylerelated diseases.

2

Fitness Trainers use weight machines to design personalized strength-building programs. Biomedical Engineers create innovative weight machines tailored for rehabilitation and elderly care.

34