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 (Do) and the distance from the lens to the image that is created (Di) by this equation:
1. Determine the focal length of each lens:
| lens | Do (inches) | Di (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 | Do (inches) | Di (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 Di as Do gets very large? (Compare Di to the value of f.)