Math is Ingenuity

MPP.4 · Unit 10 · Lesson 4

Name   Period

Objectives / Objetivos

Content Objective: I can use ratios and models to explain how the Penny Farthing and gear-driven bicycles were ingenious solutions to a real problem.

Language Objective: I can explain a gear ratio using the words rotation, teeth, and 'for each ___, the wheel turns ___.'

Key Idea / Idea clave

Gear Ratios, Circumference & Mechanical Advantage. Formula: Distance = Rotations × Circumference | Gear Ratio = Teeth_Driver / Teeth_Driven. 1. Circumference is the distance traveled in one full wheel rotation. 2. Gear ratios determine speed and rotational force (torque). 3. Apply proportional reasoning to calculate travel distance and mechanical advantage

Vocabulary / Vocabulario

Term / TérminoDefinition / Definición
ingenuity
ingenio		Coming up with different, and sometimes unique, solutions to problems.
Idear soluciones diferentes, y a veces únicas, a los problemas.
rotation
rotación		One full turn of a wheel, gear, or pedal all the way around.
Una vuelta completa de una rueda, un engranaje o un pedal.
gear
engranaje		A toothed wheel that passes motion to another toothed wheel through a chain.
Una rueda con dientes que transmite el movimiento a otra rueda con dientes por medio de una cadena.
ratio
razón		A comparison of two quantities, like pedal rotations to wheel rotations.
Una comparación de dos cantidades, como rotaciones del pedal y rotaciones de la rueda.
equivalent ratios
razones equivalentes		Ratios that make the same comparison using different numbers.
Razones que hacen la misma comparación con números diferentes.

Practice Preview / Vista previa de práctica

  1. On the Penny Farthing, what is the ratio of pedal rotations to front-wheel rotations?
    1. 1 to 1
    2. 1 to 2
    3. 2 to 1
    4. 1 to 4
  2. The pedal gear turns 48 teeth per rotation. The largest rear gear needs 32 teeth for one full rotation. How many rotations does the rear wheel make for each pedal rotation?
    1. 1.5 rotations
    2. 16 rotations
    3. 0.5 rotations
    4. 2 rotations
  3. The smallest rear gear has 12 teeth. How many rotations will the rear wheel make for each rotation of the 48-tooth pedal gear?
    1. 4 rotations
    2. 36 rotations
    3. 3 rotations
    4. 0.25 rotations
  4. The rider makes 3 full pedal rotations with the chain on the 32-tooth gear. How many rotations does the rear wheel make?
    1. 4.5 rotations
    2. 3 rotations
    3. 96 rotations
    4. 6 rotations

Reflection / Reflexión

One thing I learned today / Una cosa que aprendí hoy: