- Expand this lesson into a writing assignment by having students write their observations and conclusions about
the theorems in narrative form. - If time allows, have students share their conclusions with the whole class or in small groups.
Indirect Proofs
I.SectionObjectives
- Reason indirectly to develop proofs of statement.
II.MultipleIntelligences
- This is a short lesson but scaffold it into three sections. This will work for both multiple intelligences and for
special needs students. - Begin by defining an indirect proof.
- Define conjecture and what is meant by a conjecture.
- Begin by writing if- then statements using real life examples.
- For example- “If Mary plays soccer then she is an athlete.”
- Request that the students write three if- then statements in their notebooks.
- Allow time for the students to share their work.
- Algebraic Examples- use the one in the text to begin with.
- Then have students write three more algebraic examples.
- Exchange papers with a partner.
- Each partner must prove the if- then statement as true or false.
- Allow time for students to share their work.
- This helps students to make the connection between if- then statements and whether the statement is true or
false.
- Geometric Examples- use the example in the text.
- Then divide students into small groups.
- Request that they prove the following using the same diagram from the text.
-^62 =^63 - After students are finished writing the proof, allow time for sharing.
- Take the best parts of each written proof to compose a proof on the board.
- Intelligences- linguistic, logical- mathematical, visual- spatial, interpersonal, intrapersonal.
III.SpecialNeeds/Modifications
- Write all theorems on the board.
- Use the above activity to scaffold this lesson for the students.
IV.AlternativeAssessment
- Prior to teaching the lesson, compose a list of essential elements for the proof that the students are going to
write. - When composing the group proof on the board, be sure that the final example has each of these elements in it.
- Request that students copy this proof into their notebooks.
Chapter 4. Geometry TE - Differentiated Instruction