Neft Teacher · Notes Packet
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Unit 10 · Standard MPP.4

Math is Ingenuity

Lesson 10-4

My Notes Level 1 Support Level 2 Standard Level 3 Enrichment

Today's objectives

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 ___.'

📖 See Learn It for the explanation and worked examples, and the Vocab tab for the words. These are your notes to fill in and keep.

✏️ Fill in each blank as we go. Use the Word Bank to help you.

📚 Word Bank — fill each blank with the best word

👆 Tap any word to see its meaning and a picture.

Level 3: try the blanks from memory first, then check the bank.

  1. 1Coming up with a different, sometimes unique solution is .
  2. 2One full turn of a wheel, gear, or pedal is a .
  3. 3A toothed wheel that passes motion through a chain is a .
  4. 4A comparison of two quantities, like pedal turns to wheel turns, is a .
  5. 5Ratios that make the same comparison with different numbers are .

Write About the Math

How will your future vehicle be powered, and what math will be used in its design or use?¿Con qué funcionará tu vehículo del futuro, y qué matemáticas se usarán en su diseño o su uso?

Say your answer to a partner first. Then write it, using at least two of these words:

Model: One pedal rotation makes one wheel rotation, so a bigger wheel's longer perimeter carries the bicycle farther with each pedal push. — A strong answer connects the 1-to-1 ratio to the wheel's perimeter, explaining a bigger wheel travels farther per pedal push. A weak answer just says 'bigger is faster' without naming the ratio or perimeter.

Start

Complete the frames. Use the word bank.Completa las oraciones. Usa el banco de palabras.

  • Describe a future mode of individual transportation. A complete answer says how it is ___, names a ___ (or rate) that shapes it, and explains where that math appears in the vehicle's ___.
  • My answer is ___ because ___.Mi respuesta es ___ porque ___.

Build

Write two connected sentences. Use because, so, or but.Escribe dos oraciones conectadas. Usa porque, entonces o pero.

  • My claim is ___.Mi afirmación es ___.
  • My evidence is ___, so ___.Mi evidencia es ___, entonces ___.

Explain

Write a claim, give math evidence, and explain your reasoning.Escribe una afirmación, da evidencia matemática y explica tu razonamiento.