Mathematics

Grade Levels: 6th Grade, 7th Grade, 8th Grade, 9th Grade, 10th Grade, 11th Grade, 12th Grade,

Topics: AlgebraExpressions and Equations

Common Core State Standard: A-CED.2, A-CED.4,

Knowledge and Skills:

· Can evaluate expressions by substituting values for variables

· Can simplify expressions using correct order of operations

· Can do basic operations on both sides of an equation in such a way as to preserve the equality

Lesson:

**Objects and Images**

The focal length of a lens (f) is related to the distance from the lens to the object (D_{o}) and the distance from the lens to the image that is created (D_{i}) by this equation:

1. Determine the focal length of each lens:

lens |
D_{o} (inches) |
D_{i} (inches) |
f |

#1 | 25 | 3 | |

#2 | 30 | 3.5 | |

#3 | 100 | 2.75 | |

#4 | 50 | 3.25 |

2. Find the missing value in each case:

lens |
D_{o} (inches) |
D_{i} (inches) |
f |

#5 | ? | 2.25 | 2.09 |

#6 | 40 | ? | 2.57 |

#7 | 10 | ? | 2.45 |

#8 | ? | 2 | 1.94 |

#9 | ? | 2 | 1.96 |

#10 | 10 | ? | 3.00 |

#10 | 25 | ? | 3.00 |

#10 | 50 | ? | 3.00 |

#10 | 100 | ? | 3.00 |

#10 | 200 | ? | 3.00 |

#10 | 500 | ? | 3.00 |

#10 | 1000 | ? | 3.00 |

#10 | 2000 | ? | 3.00 |

For lens #10, what happens to the value of D_{i} as D_{o} gets very large? (Compare D_{i} to the value of f.)