Table of Contents
Simple Machines Deluxe Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
Standard Alignments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
All About Levers
What is a Lever? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
Key Words and Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
Key Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
Student Reference Sheets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
Balance
Lesson Plan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
Student Activity Sheet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
See-Saw
Lesson Plan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
Student Activity Sheet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
Catapult
Lesson Plan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
Student Activity Sheet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
Handcart
Lesson Plan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
Student Activity Sheet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
Rowboat
Lesson Plan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
Student Activity Sheet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
Scissors
Lesson Plan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
Student Activity Sheet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
Door
Lesson Plan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
Student Activity Sheet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
Wheelbarrow
Lesson Plan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
Student Activity Sheet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
Fishing Rod
Lesson Plan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
Student Activity Sheet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
Hammer
Lesson Plan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
Student Activity Sheet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
Tweezers
Lesson Plan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
Student Activity Sheet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
Lever Mobile
Lesson Plan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
Student Activity Sheet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
Rubber Band Scale . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
Part & Model List . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
Table of Contents
Simple Machines Deluxe Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
Standard Alignments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
All About Gears
What is a Gear? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
Key Words and Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
Key Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
Student Reference Sheets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
Spur Gears
Lesson Plan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
Student Activity Sheet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
Sprocket Bicycle Gear
Lesson Plan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
Student Activity Sheet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
Crown Gears
Lesson Plan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
Student Activity Sheet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
Rack and Pinion Gears
Lesson Plan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
Student Activity Sheet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
Worm and Worm Gear
Lesson Plan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
Student Activity Sheet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
Planetary Gears
Lesson Plan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
Student Activity Sheet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
Simple Transmission
Lesson Plan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
Student Activity Sheet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
Car Window
Lesson Plan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
Student Activity Sheet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
Lawnmower
Lesson Plan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
Student Activity Sheet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
Eggbeater
Lesson Plan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
Student Activity Sheet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
Food Mixer
Lesson Plan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
Student Activity Sheet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
Differential
Lesson Plan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
Student Activity Sheet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
Clock
Lesson Plan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
Student Activity Sheet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
Part & Model List . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
Table of Contents
Simple Machines Deluxe Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
Standard Alignments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
All About Inclined Planes
What is an Inclined Plane? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
What is a Screw? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
What is a Wedge? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
Key Words and Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
Key Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
Student Reference Sheets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
Roller Coaster Ramps
Lesson Plan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
Student Activity Sheet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
Moving Truck
Lesson Plan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
Student Activity Sheet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
Splitting Wedge
Lesson Plan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
Student Activity Sheet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
Chisel
Lesson Plan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
Student Activity Sheet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
Axe
Lesson Plan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
Student Activity Sheet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
Hand Drill
Lesson Plan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
Student Activity Sheet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
Archimedes Screw
Lesson Plan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
Student Activity Sheet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
Propeller
Lesson Plan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
Student Activity Sheet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
Playground Station
Lesson Plan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
Student Activity Sheet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
Part & Model List . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
Table of Contents
Simple Machines Deluxe Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
Standard Alignments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
All About Pulleys
What is a Pulley? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
Key Words and Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
Key Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
Student Reference Sheets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
Fixed Pulley
Lesson Plan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
Student Activity Sheet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
Movable Pulley
Lesson Plan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
Student Activity Sheet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
Combination Pulleys
Lesson Plan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
Student Activity Sheet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
Flagpole
Lesson Plan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
Student Activity Sheet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
Sailboat
Lesson Plan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
Student Activity Sheet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
Clothesline
Lesson Plan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
Student Activity Sheet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
Elevator
Lesson Plan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
Student Activity Sheet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
Block and Tackle
Lesson Plan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
Student Activity Sheet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
Crane
Lesson Plan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
Student Activity Sheet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
Part & Model List . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
Table of Contents
Simple Machines Deluxe Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
Standard Alignments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
All About Wheels & Axles
What is a Wheel & Axle? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
Key Words and Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
Key Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
Student Reference Sheets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
Spinning Top
Lesson Plan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
Student Activity Sheet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
Wishing Well
Lesson Plan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
Student Activity Sheet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
Wrench
Lesson Plan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
Student Activity Sheet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
Screwdriver
Lesson Plan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
Student Activity Sheet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
Ferris Wheel
Lesson Plan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
Student Activity Sheet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
Water Wheel
Lesson Plan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
Student Activity Sheet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
Paddlewheel Boat
Lesson Plan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
Student Activity Sheet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
Windmill
Lesson Plan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
Student Activity Sheet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
Measuring Wheel
Lesson Plan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
Student Activity Sheet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
Wagon
Lesson Plan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
Student Activity Sheet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
Carousel
Lesson Plan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
Student Activity Sheet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
Part & Model List . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
All About
LEVERS
What is a Lever?
• A lever is a stiff bar often made of metal,
plastic or wood.
• The lever pivots on one point, the fulcrum–up,
down or side to side –to produce the motion
that helps do work.
• To use a lever, you provide effort and the lever
helps you work against the resistance.
• Levers can change the amount of force needed to do work,
the direction of the applied forces and the work that is produced.
Key Words and Definitions
Effort - the force that is applied to do work; the push, pull, squeeze or lift provided
to use a lever on an object
Effort Arm (EA)- distance on the lever from the fulcrum to the point where
the effort is applied
Resistance - the force provided by the object on which one is trying to do work;
the object works against (pushes back) the effort
Resistance Arm (RA) - distance on the lever from the fulcrum to the point
where the resistance is applied
Fulcrum - the spot along the lever that sits still as the rest of the bar rotates or
pivots around it
Mechanical Advantage (MA) - a mathematical calculation that reveals how
many times easier a job is to do when a lever is used; EA ÷ RA = MA
Work - the job being done while using the lever
Load - the object (weight) lifted or moved; provides resistance to the lever
Force - any kind of push or pull applied to an object
Double lever- two levers attached to each other at the fulcrum; might be a pair
of 1st, 2nd or 3rd-class levers; work together to do one job
8
Graphics courtesy of ClickArt® 65,000 Incredible Image PakTM; ©1996-97,T/Maker Co.
knexeducation.com
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Balance L
Objectives
Lesson Length: 30-45 minutes
• Identify the fulcrum, resistance and effort on a balance
• Determine the lever class of a balance
• Demonstrate how the Balance functions as a 1st-class lever
• Measure forces applied to the Balance using weights
• Manipulate the Balance to determine the effects on required force
• Graph results of experiments
• Infer how the Balance does work based on measurements
• Experiment with the Balance to distinguish between classes of levers
• Manipulate the Balance to compare and contrast lever classes
Materials
-3 blank dot stickers or pieces
of masking tape
-marker
-small object, such as a pencil,
chalk or eraser
-5 -10 pennies, green Rods or
other small unit weights
-2 paper clips
-K’NEX Rubber Band Scale
• Measure forces with a Rubber Band Scale
Every lever has a job to do
Balances, similar to the K’NEX Balance, are very helpful in situations where you need to compare the
weights of different objects.The balance is a pair of scales. Comparable loads will put the balance in
equilibrium and the arm will be perfectly horizontal.This type of machine is often found in a science lab
or grocery store.
What class of lever is it?
The Balance can be used as a 1st, 2nd or 3rd-class
lever, depending on the placement of the Balance
arm and the weights. As built according to the
instructions, it is a 1st-class lever. Direct students
to the “Student Reference Sheets”.
R
F
E
16
Graphics courtesy of ClickArt® 65,000 Incredible Image PakTM; ©1996-97,T/Maker Co.
ents
nce measurem
ta
is
d
d
n
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rc
o
✓ F
ment results
re
su
a
e
m
f
o
h
✓ Grap
e nt
on of experim
ti
ta
re
rp
te
In
✓
results
graph for how
ra
a
p
y
r
to
a
n
la
✓ Exp
d to serve as
re
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lt
a
s
a
w
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n
Bala
f levers
other classes o
ck
Journal Che
knexeducation.com
11
22
QUESTIONS
Weigh a small object, such as a pencil, by
placing it on one of the Balance trays (gray
Hub). Use pennies or K’NEX pieces as
weights on the other tray. Make sure each
tray is set at the same distance from the
middle of the Balance arm.Weigh and
compare other objects. Design a graph to
record and compare your results.
a. Measure the distance from the center of
the Balance to the end of the arm where the
object is weighed. Record this length.This is
the resistance arm because the object being
weighed resists or works against the lever.
11
22
b. Then, measure from the center to the end
of the other arm, where the weights are.This
is the effort arm because the weights supply
the effort or work to make both sides equal
and balanced. Record this length.Are the two
distances the same? What does this show?
33
When built according to the instructions,
what class lever is your Balance? Alter your
Balance so it functions as each of the other
class levers. Explain.
1-888-ABC-KNEX
To place objects and weights on the Balance,
students might use the hanging gray Hubs as
trays, connect weights to the upright Rod or
hang weights below.A larger object might be
suspended below the Hub by hooking the
object on a paper clip that hangs from the
gray Connector.
The graph should compare the variables, how
many of the small weights it takes to balance
the weight of the object.
a. Review the terms resistance arm and
effort arm to help students differentiate
between the two sides of the lever.
b. Help students see that the arms will
balance when both sides are equal, in weight
and in distance from the center. If the
distance on one side changes, its weight must
also change to keep in balance. Have students
experiment with placing small objects on
both sides of the Balance and shifting the
trays to different positions.
c. Shorten the effort arm by sliding the tray
with the weights closer to the middle.
Balance the arms again. Do you have to add
or remove weights? What does this tell you?
Choose the right word in this sentence to
explain your findings:
When the effort arm is shorter than the
resistance arm, (more/less) effort is needed
to do the work.
ANSWERS
33.
c. Students should complete the sentence:
When the effort arm is shorter than the
resistance arm, more effort is needed to
do the work. If you decrease the length of the
effort arm, you have to increase the effort.
As built according to the instructions, it is a
1st-class lever. Students’ answers will vary but
should include an explanation of the
resistance being in the center for a 2nd-class
lever and the effort being in the center for a
3rd class lever.
17
s
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Balance E
to differentiate class and function
• Identify fulcrum, effort and load (resistance)
in different Balance configurations
• Identify, reinforce and solidify understanding of effort
and resistance arms
L2= Left 2 yellow Connector
L1= Left 1
C= Center yellow Connector
R1= Right 1
R2= Right 2
R1
• Compare and contrast performance and results for
each lever class of the Balance
• Measure force and distance for each lever class of the
Balance
R2 E
• Calculate Mechanical Advantage and work efficiency
for the lever classes
C
L1
L2
Objectives • Conduct experiments with the Balance
F
R
Additional Activities using the K’NEX Balance
There are two different ways to change the lever class of the Balance:
(1) slide the load on the gray Rods to change their position from the
fulcrum; (2) disconnect the whole arm from the base of the Balance
and snap it into one of the other sets of yellow Connectors on the top
bar.This allows you to change the placement of the fulcrum.
1st-Class
L2
L1
F
C
R1
Feeling the Force: 1st, 2nd & 3rd-Class Balances
11.
R2
R
E
2nd-Class
L2
a. Set the fulcrum on the Balance in Position L2. Label the
fulcrum and the resistance.
b. Remove the entire hanging arm and Tire load on the left side
of the Balance, up to the orange Connector.Add the large Hub
and Tire and four small Hubs and Tires as extra weights on the
right hanging arm. Snap the right hanging arm onto the yellow
Rods of the under arm of the Balance. (see 2nd-class photo)
c. Lift the load by applying effort to the opposite end of the arm.
In what direction do you apply the effort? Record and explain
your observations.Which class of lever is the Balance now? Why?
L1
C
R1
F
d. Lift the load by applying the effort at the end of the long arm.
In what direction was the effort applied? Record and explain
your observations. Compare these results to the previous test
and explain what you find.
e. Which class of lever is the Balance now? Why?
R2
f. For both tests, in which direction does the resistance move?
g. Use the K’NEX Rubber Band Scale to measure the forces and
verify your results. Explain your findings.
E
3rd- Class
18
R
[Push down on the opposite end of the arm and the resistance goes up.
The Balance is a 1st-class lever which changes the direction of the force.
The Balance becomes a 2nd-class lever when applying the effort by pulling
or pushing up the end of the long arm.The resistance also goes up.This
takes less force because the effort arm is longer than the resistance arm.]
Graphics courtesy of ClickArt® 65,000 Incredible Image PakTM; ©1996-97,T/Maker Co.
knexeducation.com
Materials
-K’NEX Balance
-weights (small & large
Hubs and Tires)
-K’NEX Rubber Band Scale
-two metric rulers
-calculator (optional)
-masking tape
-markers
22.
alance
r class of the B
ve
le
h
ac
e
r
fo
bels
nd and
✓ F, E and R la
ments for 1st, 2
re
su
ea
m
ce
n
ing
ta
✓ Chart of dis
and correspond
ce
an
st
si
re
d
an
3rd-class effort
sistance rises
re
e
for
distances th
of test results
s
n
io
at
n
la
p
x
e
ns and
vers
✓ Observatio
ree classes of le
th
l
al
g
in
ar
p
e
m
co
ance as all thre
al
B
e
th
r
fo
ts
remen
✓ Force measu
rk
classes of levers
vantage and wo
d
A
al
ic
an
ch
e
s for M
of EA
✓ Calculation
ses and lengths
as
cl
t
n
re
e
iff
d
efficiency for
and RA
ck
Journal Che
a. Set the fulcrum on the Balance in Position L1. Label
the fulcrum and resistance.
c. Calculate the Mechanical Advantage for the Balance
in this position. (Use the “What’s the Mechanical
Advantage” Reference Card for help.)
b. Repeat step 1b. Let the weights hang from the end
of the right arm. (see 3rd-class photo)
c. Lift the load by using the Balance as a 1st-class lever.
Where and in what direction do you apply the effort?
What happens? Record and explain your observations.
Length of EA ______ cm
Length of RA ______ cm
d. Repeat step 2c for a 3rd-class lever.
e. For both tests, in which direction does the resistance
move?
[Push down on the short end of the arm and the load goes up
so the Balance is a 1st-class lever.
Exploring Distance for Each Lever Class
11.
a. Stand a ruler behind the resistance (load) and have
a partner stand a second ruler behind the place
where the effort is applied.Apply the effort and
measure how the load and effort move. Compare the
results.What do they show?
b. Describe, measure and record the length of the
effort arm and resistance arm.
1-888-ABC-KNEX
The Load
Rises:
____ cm
____ cm
____ cm
d. Which is greater, the distance the effort arm moved
or the distance the load rises? Verify your results by
testing at least three other points along the effort arm
of your lever. Record these results and add them to
the chart.
f. Repeat step 1g. Compare these results to the
previous test and the tests in Activity 1. Draw a
conclusion about levers based on these comparisons.
The Balance is a 3rd-class lever when pushing or pulling up on
the arm between the fulcrum and the resistance.The resistance
goes up also. Rubber Band Scale measurements will verify that
the 3rd-class lever requires more force to lift the load than the
1st-class lever.]
Pull the
EA Up:
15cm
10cm
5cm
Etc.
23.
e. Alter the Balance to function as a 2nd and 3rd-class
lever. Repeat the test for each of these lever classes.
Record and compare your results.What conclusions
can you draw from these experiments? Describe how
the EA moves for each class of lever.
There is a direct relationship between work and
distance.The formula for this relationship is very easy
to use for levers. Use these formulas to calculate the
efficiency of the Balance as each class of lever.
Work output = Force (weight of load) x Distance (distance
load rises)
Work input = Force (measurement) x Distance (EA
moves)
Efficiency = Work output x 100
Work input
19
STUDENT ACTIVITY SHEET
e
c
n
a
l
a
B
e
Th
Every lever has a job to do
A balance helps you weigh things like letters or apples. It also
helps you compare the weights of two different objects.To make
a balance work, you put the object you want to weigh on one
side of the balance.Then, on the other side of the balance, you
place something else – usually gram weights.When the objects
on each side weigh the same amount – the long arm of the
balance is perfectly horizontal.
Label your lever
Use stickers or tape to label
the parts of the balance:
F
Fulcrum
R Resistance
E
Effort
* See Building Instructions for help
11
22
What class of lever is it?
Is your balance a 1st, 2nd, or 3rd class lever? Use these clues:
R
R
E
F
E
Graphics courtesy of ClickArt® 65,000 Incredible Image PakTM; ©1996-97,T/Maker Co.
R
3rd class
weights supply the effort or work to make
both sides equal and balanced. Record this
length.Are the two distances the same?
What does this show?
Weigh a small object, such as a pencil, by
placing it on one of the Balance trays (gray
Hub). Use pennies or K’NEX pieces as
weights on the other tray. Make sure each
tray is set at the same distance from the
middle of the Balance arm.Weigh and
compare other objects. Design a graph to
record and compare your results.
a. Measure the distance from the center of
the Balance to the end of the arm where
the object is weighed. Record this length.
This is the resistance arm because the
object being weighed resists or works
against the lever.
F
2nd class
1st class
b. Then, measure from the center to the
end of the other arm, where the weights
are.This is the effort arm because the
20
F
E
c. Shorten the effort arm by sliding the
tray with the weights closer to the middle.
Balance the arms again. Do you have to
add or remove weights? What does this
tell you? Choose the right word in this
sentence to explain your findings:
33
When the effort arm is shorter than the
resistance arm, (more/less) effort is
needed to do the work.
When built according to the instructions,
what class lever is your Balance? Alter
your Balance so it functions as each of the
other class levers. Explain.
knexeducation.com
National Science Education Standards (Grades K - 4)
Students will develop an understanding of:
Unifying Concepts and Processes
• Systems, order, and organization
• Evidence, models, and explanation
• Change and measurement
• Form and function
PHYSICAL SCIENCE
• Properties of objects and materials
• Position and motion of objects
SCIENCE AND TECHNOLOGY
SIMPLE machines DELUXE 79520
NSES Content Standards Alignments
• Abilities of technological design
• Understanding about science and technology
National Science Education Standards (Grades 5 - 8)
Students will develop an understanding of:
Unifying Concepts and Processes
• Systems, order and organization
• Evidence, models and explanation
• Change and measurement
• Form and function
SCIENCE AS INQUIRY
• Abilities necessary to do scientific inquiry
• Understanding about scientific inquiry
PHYSICAL SCIENCE
• Motions and Forces
• Transfer of Energy
SCIENCE AND TECHNOLOGY
• Abilities of technological design
• Understanding about science and technology
Reprinted with permission from 1996 National Science Education Standards by the National Academy of Sciences,
Courtesy of the National Academies Press, Washington, D.C.
888-ABC-KNEX
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1
Standards for Technological Literacy: Content for the Study of Technology (Grades 3-5)
Students will develop an understanding of:
the nature of technology
Core Concepts of Technology
• Systems
• Processes
• Requirements
Relationships Among Technologies
• Technologies integrated
design
The Attributes of design
simple machines deluxe 79520
Standards for Technological Literacy:
Content for the Study of Technology
• Requirements of design
Engineering Design
• Engineering design process
• Creativity and considering all ideas
• Models
The Role of Troubleshooting, Research and Development, Invention and Innovation,and
Experimentation in Problem Solving
• Troubleshooting
• Invention and innovation
• Experimentation
Abilities for a Technological World
Apply Design Process
• Collecting information
• Visualize a solution
• Test and evaluate solutions
• Improve a design
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1
Students will develop an understanding of:
the nature of technology
Core Concepts of Technology
• Systems
• Processes
• Requirements
Relationships Among Technologies
• Interaction of systems
• Knowledge from other fields of study and technology
Design
The Attributes of design
• Design leads to useful products and systems
• There is no perfect design
simple machines deluxe 79520
Standards for Technological Literacy: Content for the Study of Technology (Grades 6-8)
Engineering Design
• Brainstorming
• Modeling, testing, evaluating, and modifying
The Role of Troubleshooting, Research and Development, Invention and Innovation, and
Experimentation in Problem Solving.
• Troubleshooting
• Invention and innovation
• Experimentation
Abilities of a Technological World
Apply Design Process
• Identify criteria and constraints
• Test and evaluate
• Make a product or system
Used with permission of the ITEEA (www.iteea.org)
888-ABC-KNEX
2
National Council of Teachers of Mathematics Education
Standards and Expectations for Grades 3 - 9
NUMBER AND OPERATIONS
Instructional programs from pre-kindergarten through grade 12 should enable all students to:
• U
nderstand numbers, ways of representing numbers, relationships among numbers, and
number systems.
• Understand meanings of operations and how they relate to one another.
• Compute fluently and make reasonable estimates.
Grades 3 - 5 Expectations: In grades 3 - 5 all students should:
Understand numbers, ways of representing numbers, relationships among numbers, and
number systems.
•Understand the place-value structure of the base-ten number system and be able to represent
and compare whole numbers and decimals.
•Develop understanding of fractions as parts of unit wholes, as parts of a collection, as locations
on number lines, and as divisions of whole numbers.
• Use models, benchmarks, and equivalent forms to judge the size of fractions.
• Recognize and generate equivalent forms of commonly used fractions, decimals, and percents.
Grades 3 - 5 Expectations: In grades 3 - 5 all students should:
Understand meanings of operations and how they relate to one another.
• Understand various meanings of multiplication and division.
• Understand the effects of multiplying and dividing whole numbers.
•Identify and use relationships between operations, such as division as the inverse of
multiplication, to solve problems.
Grades 3 - 5 Expectations: In grades 3 - 5 all students should:
Compute fluently and make reasonable estimates.
•Develop fluency with basic number combinations for multiplication and division and use these
combinations to mentally compute related problems, such as 30 × 50.
•Develop fluency in adding, subtracting, multiplying, and dividing whole numbers.
•Develop and use strategies to estimate computations involving fractions and decimals in
situations relevant to students’ experience.
•Select appropriate methods and tools for computing with whole numbers from among mental
computation, estimation, calculators, and paper and pencil according to the context and nature
of the computation and use the selected method or tools.
ALGEBRA
Instructional programs from pre-kindergarten through grade 12 should enable all students to:
• Understand patterns, relations, and functions.
• Represent and analyze mathematical situations and structures using algebraic symbols.
• Use mathematical models to represent and understand quantitative relationships.
• Analyze change in various contexts.
Grades 3 - 5 Expectations: In grades 3 - 5 all students should:
Understand patterns, relations, and functions.
• Represent and analyze patterns and functions, using words, tables, and graphs.
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SIMPLE MACHINES DELUXE 79520
NCTM Standards Alignments
Represent and analyze mathematical situations and structures using algebraic symbols.
• Represent the idea of a variable as an unknown quantity using a letter or a symbol.
• Express mathematical relationships using equations.
Grades 3 - 5 Expectations: In grades 3 - 5 all students should:
Use mathematical models to represent and understand quantitative relationships.
•Model problem situations with objects and use representations such as graphs, tables, and
equations to draw conclusions.
Grades 3 - 5 Expectations: In grades 3 - 5 all students should:
Analyze change in various contexts.
• Investigate how a change in one variable relates to a change in a second variable.
• Identify and describe situations with constant or varying rates of change and compare them.
MEASUREMENT STANDARD
Instructional programs from pre-kindergarten through grade 12 should enable all students to:
•Understand measurable attributes of objects and the units, systems, and processes of
measurement.
• Apply appropriate techniques , tools, and formulas to determine measurements.
Grades 3 - 5 Expectations: In grades 3 - 5 all students should:
Understand measurable attributes of objects and the units, systems, and processes of measurement.
•Understand such attributes as length, and select the appropriate type of unit for measuring
each attribute.
•Understand the need for measuring with standard units and become familiar with standard
units in the customary and metric systems.
•Carry out simple unit conversions, such as from centimeters to meters, within a system of
measurement.
•Understand that measurements are approximations and how differences in units affect
precision.
DATA ANALYSIS AND PROBABILITY
Instructional programs from pre-kindergarten through grade 12 should enable all students to:
•Formulate questions that can be addressed with data and collect, organize, and display
relevant data to answer them.
• Select and use appropriate statistical methods to analyze data.
• Develop and evaluate inferences and predictions that are based on data.
• Understand and apply basic concepts of probability.
Grades 3 - 5 Expectations: In grades 3 - 5 all students should:
Formulate questions that can be addressed with data and collect, organize, and display relevant
data to answer them.
• Collect data using observations, surveys, and experiments.
• Represent data using tables and graphs such as line plots, bar graphs, and line graphs.
Grades 3 - 5 Expectations: In grades 3 - 5 all students should:
Select and use appropriate statistical methods to analyze data.
•Describe the shape and important features of a set of data and compare related data sets,
with an emphasis on how the data are distributed.
888-ABC-KNEX
SIMPLE MACHINES DELUXE 79520
Grades 3 - 5 Expectations: In grades 3 - 5 all students should:
Develop and evaluate inferences and predictions that are based on data.
•Propose and justify conclusions and predictions that are based on data and design studies to
further investigate the conclusions or predictions.
GRADES 6 - 8
NUMBERS AND OPERATIONS
Instructional programs from pre-kindergarten through grade 12 should enable all students to:
•Understand numbers, ways of representing numbers, relationships among numbers, and
number systems
• Understand meanings of operations and how they relate to one another.
• Compute fluently and make reasonable estimates.
Grades 6 - 8 Expectations: In grades 6 - 8 all students should:
Understand numbers, ways of representing numbers, relationships among numbers, and
number systems
• Work flexibly with fractions, decimals, and percents to solve problems.
• Understand and use ratios and proportions to represent quantitative relationships.
• Develop meaning for integers and represent and compare quantities with them.
Grades 6 - 8 Expectations: In grades 6 - 8 all students should:
Understand meanings of operations and how they relate to one another.
•Understand the meaning and effects of arithmetic operations with fractions, decimals,
and integers.
Grades 6 - 8 Expectations: In grades 6 - 8 all students should:
Compute fluently and make reasonable estimates.
•Select appropriate methods and tools for computing with fractions and decimals from among
mental computation, estimation, calculators or computers, and paper and pencil, depending on
the situation, and apply the selected methods.
ALGEBRA
Instructional programs from pre-kindergarten through grade 12 should enable all students to:
• Understand patterns, relations, and functions.
• Represent and analyze mathematical situations and structures using algebraic symbols.
• Use mathematical models to represent and understand quantitative relationships.
• Analyze change in various contexts.
Grades 6 - 8 Expectations: In grades 6 - 8 all students should:
Understand patterns, relations, and functions.
•Represent, analyze, and generalize a variety of patterns with tables, graphs, words, and, when
possible, symbolic rules.
• Relate and compare different forms of representation for a relationship.
Grades 6 - 8 Expectations: In grades 6 - 8 all students should:
Represent and analyze mathematical situations and structures using algebraic symbols.
• Develop an initial conceptual understanding of different uses of variables.
•Use symbolic algebra to represent situations and to solve problems, especially those that
involve linear relationships.
•Recognise and generate equivalent forms for simple algebraic expressions and solve linear
equations.
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Grades 3 - 5 Expectations: In grades 3 - 5 all students should:
Use mathematical models to represent and understand quantitative relationships.
•Model and solve contextualized problems using various representations, such as graphs,
tables, and equations.
Grades 6 - 8 Expectations: In grades 6 - 8 all students should:
Analyze change in various contexts
• Use graphs to analyze the nature of changes in quantities in linear relationships.
MEASUREMENT STANDARD
Instructional programs from pre-kindergarten through grade 12 should enable all students to:
•Understand measurable attributes of objects and the units, systems, and processes of
measurement.
• Apply appropriate techniques, tools, and formulas to determine measurements.
Grades 6 - 8 Expectations: In grades 6 - 8 all students should:
Understand measurable attributes of objects and the units, systems, and processes of
measurement.
• Understand both metric and customary systems of measurement
•Understand relationships among units and convert from one unit to another within the
same system.
Grades 6 - 8 Expectations: In grades 6 - 8 all students should:
Apply appropriate techniques, tools, and formulas to determine measurements.
•Select and apply techniques and tools to accurately find length, area, volume, and angle
measures to appropriate levels of precision.
DATA ANALYSIS AND PROBABILITY
Grades 6 - 8 Expectations: In grades 6 - 8 all students should:
Instructional programs from pre-kindergarten through grade 12 should enable all students to:
•Formulate questions that can be addressed with data and collect, organize, and display
relevant data to answer them.
• Select and use appropriate statistical methods to analyze data.
Grades 6 - 8 Expectations: In grades 6 - 8 all students should:
Formulate questions that can be addressed with data and collect, organize, and display relevant
data to answer them.
•Formulate questions, design studies, and collect data about a characteristic shared by two
populations or different characteristics within one population.
NUMBERS AND OPERATIONS
High School Expectations: In high school all students should:
•Understand numbers, ways of representing numbers, relationships among numbers and
number systems.
• Compute fluently and make reasonable estimates.
ALGEBRA
High School Expectations: In high school all students should:
• Understand patterns, relations, and functions.
• Use mathematical models to represent and understand quantitative relationships.
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Grades 6 - 8 Expectations: In grades 6 - 8 all students should:
High School Expectations: In high school all students should:
•Understand measurable attributes of objects and the units, systems, and processes of
measurement.
• Apply appropriate techniques, tools, and formulas to determine measurements.
DATA ANALYSIS AND PROBABILITY
High School Expectations: In high school all students should:
•Formulate questions that can be addressed with data and collect, organize and display data to
answer them.
• Develop and evaluate inferences and predictions that are based on data.
PROCESS STANDARDS
Problem Solving
Instructional programs from pre-kindergarten through grade 12 should enable all students to:
• Build new mathematical knowledge through problem solving.
• Solve problems that arise in mathematics and in other contexts.
• Apply and adapt a variety of appropriate strategies to solve problems.
• Monitor and reflect on the process of mathematical problem solving.
Reasoning and Proof
Instructional programs from pre-kindergarten through grade 12 should enable all students to:
• Recognize reasoning and proof as fundamental aspects of mathematics.
• Select and use various types of reasoning and methods of proof.
Communication
Instructional programs from pre-kindergarten through grade 12 should enable all students to:
• Organize and consolidate their mathematical thinking through communication.
• Communicate their mathematical thinking coherently and clearly to peers, teachers, and others.
• Analyze and evaluate the mathematical thinking and strategies of others.
• Use the language of mathematics to express mathematical ideas precisely.
Connections
Instructional programs from pre-kindergarten through grade 12 should enable all students to:
• Recognize and use connections among mathematical ideas.
• Recognize and apply mathematics in contexts outside of mathematics.
Representation
Instructional programs from pre-kindergarten through grade 12 should enable all students to:
• Create and use representations to organize, record, and communicate mathematical ideas.
• Select, apply, and translate among mathematical representations to solve problems.
• Use representations to model and interpret physical, social, and mathematical phenomena.
Standards are reprinted with permission from Principles and Standards for School Mathematics, copyright 2000 by the
National Council of Teachers of Mathematics (NCTM). All rights reserved. NCTM does not endorse the content or validity of
these alignments.
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MEASUREMENT
Common Core State Standards for Mathematics in Grades 3 - 9
GRADE 3
Operations and Algebraic Thinking
• Represent and solve problems involving multiplication and division.
• Understand properties of multiplication and the relationship between multiplication and division.
• Multiply and divide within 100.
• Solve problems involving the four operations, and identify and explain patterns in arithmetic.
Number and Operations in Base Ten
• Use place value understanding and properties of operations to perform multi-digit arithmetic.
Number and Operations—Fractions
• Develop understanding of fractions as numbers.
Measurement and Data
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Common Core Standards Alignments
• Solve problems involving measurement
• Represent and interpret data.
MATHEMATICAL PRACTICES - ASSOCIATED WITH MATHEMATICS AT ALL GRADE LEVELS
1. Make sense of problems and persevere in solving them
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the reasoning of others.
4. Model with mathematics.
5. Use appropriate tools strategically.
6. Attend to precision.
7. Look for and make use of structure.
8. Look for and express regularity in repeated reasoning.
GRADE 4
Operations and Algebraic Thinking
• Use the four operations with whole numbers to solve problems.
• Gain familiarity with factors and multiples.
• Generate and analyze patterns.
Number and Operations in Base Ten
• Use place value understanding and properties of operations to perform multi-digit arithmetic.
Number and Operations—Fractions
• Understand decimal notation for fractions, and compare decimal fractions.
Measurement and Data
• Solve problems involving measurement and conversion of measurements from a larger unit to a
smaller unit.
• Represent and interpret data.
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Operations and Algebraic Thinking
• Write and interpret numerical expressions.
• Analyze patterns and relationships.
Number and Operations in Base Ten
• Perform operations with multi-digit whole numbers and with decimals to hundredths.
Measurement and Data
• Convert like measurement units within a given measurement system.
• Represent and interpret data.
Geometry
• Graph points on the coordinate plane to solve real-world and mathematical problems.
Mathematics Grade 6
In Grade 6, instructional time should focus on four critical areas:
• C
onnecting ratio and rate to whole number multiplication and division and using concepts of
ratio and rate to solve problems.
• Writing, interpreting, and using expressions and equations.
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grade 5
• Developing understanding of statistical thinking.
grade 6
Ratios and Proportional Relationships
• Understand ratio concepts and use ratio reasoning to solve problems.
The Number System
• Compute fluently with multi-digit numbers and find common factors and multiples.
Expressions and Equations
• Apply and extend previous understandings of arithmetic to algebraic expressions.
• Reason about and solve one-variable equations
• Represent and analyze quantitative relationships between dependent and independent variables.
Statistics and Probability
• Develop understanding of statistical variability.
Mathematics Grade 7
In Grade 7, instructional time should focus on four critical areas:
• Developing understanding of and applying proportional relationships
• Developing understanding of operations with rational numbers
• Drawing inferences about populations based on samples.
GRADE 7
Ratios and Proportional Relationships
• Analyze proportional relationships and use them to solve real-world and mathematical problems.
The Number System
• Apply and extend previous understandings of operations with fractions to add, subtract, multiply,
and divide rational numbers.
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• Use properties of operations to generate equivalent expressions.
• Solve real-life and mathematical problems using numerical and algebraic expressions and equations.
MATHEMATICS GRADE 8
In Grade 8, instructional time should focus on three critical areas:
• Grasping the concept of a function and using functions to describe quantitative relationships.
GRADE 8
Expressions and Equations
• Analyze and solve linear equations.
Functions
• Define, evaluate, and compare functions.
• Use functions to model relationships between quantities.
Statistics and Probability
• Investigate patterns of association in bivariate data.
Common Core State Standards for Mathematics in High School
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Expressions and Equations
NUMBER AND QUANTITY
The Real Number System
• Use properties of rational and irrational numbers.
Quantities
• Reason quantitatively and use units solve problems.
ALGEBRA
Seeing Structure in Expressions
• Write expressions in equivalent forms to solve problems.
Creating Equations
• Create equations that describe numbers or relationships.
Reasoning with Equations and Inequalities
• Understand solving equations as a process of reasoning and explain the reasoning.
• Solve equations and inequalities in one variable.
• Solve systems of equations.
• Represent and solve equations graphically.
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• M
odeling links classroom mathematics and statistics to everyday life, work, and decision-making.
Modeling is the process of choosing and using appropriate mathematics and statistics to analyze
empirical situations, to understand the better, and to improve decisions. Quantities and their
relationships in physical, economic, public policy, social, and everyday situations can be modeled
using mathematical and statistical methods. When making mathematical models, technology is
valuable for varying assumptions, exploring consequences, and comparing predictions with data.
• A
model can be very simple, such as writing total cost as a product unit price and number bought,
or using a geometric shape to describe a physical object like a coin. Even such simple models
involve making choices. It is up to us whether to model a coin as a three-dimensional cylinder, or
whether a two-dimensional disk works well enough for our purposes. Other situations- modeling
a delivery route, a production schedule, or a comparison of loan amortizations- need more
elaborate models that use other tools from the mathematical sciences. Real-world situations are
not organized and labeled for analysis; formulating tractable models, representing such models,
and analyzing them is appropriately a creative process.
STATISTICS AND PROBABILITY
Interpreting Categorical and Quantitative Data
• Summarize, represent, and interpret data on a single count or measurement variable.
• Interpret linear models.
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MODELING
Making Inferences and Justifying Conclusions
• M
ake inferences and justify conclusions from sample surveys, experiments and observational
studies.
Authors: National Governors Association Center for Best Practices, Council of Chief State School Officers; Title: Common Core
State Standards (insert specific content area if you are using only one); Publisher: National Governors Association Center for
Best Practices, Council of Chief State School Officers, Washington D.C.; Copyright Date: 2010
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