M3U3D1 Warmup: List as many mathematical symbols as you can. These can be algebraic or geometric. Be prepared to share and defend your choices. Answers will vary. List answers on the side board.

M3U3D1 Logical Steps OBJECTIVE: To prove algebraic statements using logical steps.

Getting Blood From a Stone The rules of writing a mathematical proof are very similar to the rules of "getting blood from a stone". The old saying "You can't get blood from a stone” means that nobody can give you anything that they, themselves, do not have.

The "rules of the game", and how these rules relate to mathematical proof: 1)You must start with the word STONE and end up with the word BLOOD by a series of logical steps (much like the steps in a mathematical proof). 2)You must change one letter in each step. Each step must follow directly from the previous step. (In a proof, you must address one concept at a time. Each step in a proof must follow directly from the step before it - including from the 'Given', and lead to the next.) CONT…

3)The word in each step must be a real word, and in the dictionary. (In a proof, each step must be true: a definition, postulate, or theorem). If you use an unusual word, you must write the definition. 4)In this game, some people can do this in 10 steps; others may take 15, and both can be correct. There is more than one route, and no one way is necessarily better than another. One may be longer, but the best one is the one that the student "sees" when trying to do the problem! (This is very true of proof; there are dozens of proofs of the Pythagorean Theorem, for example, and even in classroom assignments there is often more than one method.)

5)In this game, some people like to work backwards, or even from both ends toward the middle. (This works very well with proofs, too!) Example: Can you get a DOG from a CAT? (Can you go from the word CAT to the word DOG?)

Here are some possible solutions to this problem: Solution 1: CAT - BAT - BAG - BOG – DOG Solution 2: CAT - COT - DOT – DOG BLOOD STONE Now that you know what to do, see if you can get BLOOD from a STONE

Solution 1: STONE BLOOD STONE-STORE-SNORE-SNORT-SNOOT-SNOOP- SLOOP-BLOOP-BLOOD Solution 2: STONE BLOOD STONE-SHONE-SHINE-THINE-TRINE-BRINE- BRANE-BRAND-BLAND-BLOND-BLOOD There are many more solutions. These are the ones I came up with!!!

STUDENT SOLUTIONS!!! Solution 3: STONE BLOOD STONE-STORE-STORK-STARK-STANK-STINK- SLINK-BLINK-BLIND-BLOND-BLOOD Solution 4: STONE BLOOD STONE-SHONE-SHINE-CHINE-CHINK-CLINK- BLINK-BLIND-BLOND-BLOOD

Now let’s check your geometry knowledge. On the worksheet I just gave you, complete the Matching Definitions on page 3. You will have a few minutes. Then we will discuss this!

F J N H K L O B M D E C G A

Take a minute and read through page 4. We will discuss this in a minute.

Now look at page 5. Let’s try these together! 1. Symmetric 2. Subtraction Prop. Of = 3. Reflexive 4. Division Prop. Of = 5. Addition Prop. Of =6. Distributive 7. Substitution 8. Transitive

You try page 5 #9. Given Distributive Addition Prop. Of = Division Prop. Of =

Now look at page 5 #10. You try then we will check it together! Given Multiplication Prop. Of = Distributive Subtraction POE Addition Prop. Of = Division Prop. Of =

Classwork: M3U3D1 page 5

Homework: M3U3D1 page 6