The document summarizes activities from chapters 4-6 of Alice's Adventures in Wonderland involving students role-playing as characters. It includes discussion questions about deductive reasoning, ratios, symmetry, circles, and other mathematical concepts shown in the story. Character roles are provided for scenes from each chapter along with examples of how different mathematical ideas are demonstrated through the characters' dialogues and situations.

1. Alice in Wonderland Lewis Carroll (Chapters 4-6)

2. The “Play” We request everyone’s participation in this activity! Different students will be asked to play as the characters from each chapter. Don’t worry! Your dialogues will be provided. Please say them with feelings…

3. Chapter 1 Characters: Alice White Rabbit Pat Bill

4. Chapter 2 Characters: Alice The caterpillar Pigeon

5. Chapter 3 Characters: Alice The fish footman The frog footman The Duchess Cheshire Cat

6. Thank you! For performing this activity!

7. Reflexive Property of Equality -states that anything is equal to itself. “ The Duchess! The Duchess! Oh my dear paws! Oh my fur and whiskers! She’ll get me executed, as sure as ferrets are ferrets ! “ A=A; ferrets=ferrets

8. Deductive Reasoning -statement coming from a general idea which leads to a more specific conclusion “There was no label this time with the words ‘DRINK ME,’ but nevertheless she uncorked it and put it to her lips. ‘I know something interesting is sure to happen,’ she said to herself, ‘whenever I eat or drink anything; so I’ll just see what this bottle does. I do hope it’ll make me grow large again, for really I’m quite tired of being such a tiny little thing!” Here, Alice mentions that surely something interesting will happen to her whenever she drinks or eats something because of the fact that at the start of the story eating something in that world causes something weird to happen.

9. Deductive Reasoning “A likely story indeed!’ said the Pigeon in a tone of the deepest contempt. ‘I’ve seen a good many little girls in my time, but never one with such a neck as that! No, no! You’re a serpent; and there’s no use denying it. I suppose you’ll be telling me next that you never tasted an egg!” The Pigeon accuses Alice of being a serpent, and even though Alice insists she isn’t, the serpent tells her that all serpents have long necks and since Alice has a long neck, she must be a serpent.

10. Deductive Reasoning ‘To begin with,’ said the Cat, ‘a dog’s not mad. You grant that?’‘I suppose so,’ said Alice.‘Well, then,’ the Cat went on, ‘you see, a dog growls when it’s angry, and wags its tail when it’s pleased. Now I growl when I’m pleased, and wag my tail when I’m angry. Therefore I’m mad.’ Here the cat tells Alice he’s mad by telling her that dogs are not mad, and dogs wag their tails when they’re happy and growls when its mad, however it does the opposite, concluding that he must be mad. ***Deductive reasoning, from the examples is shown as relating one general fact to point out a specific one, for example we could say that all Chinese people have chinky eyes, I have chinky eyes so I must be Chinese.

11. Ratio and Proportion “Alice crouched down among the trees as well as she could, for her neck kept getting entangled among the branches, and every now and then she had to stop and untwist it. After a while she remembered that she still held the pieces of mushroom in her hands, and she set to work very carefully, nibbling first at one and then at the other, and growing sometimes taller and sometimes shorter, until she had succeeded in bringing herself down to her usual height.” After the caterpillar tells Alice of the wonder behind the mushroom, and after Alice has tested it out, she concludes that she must have a number of bites from one side of the mushroom which corresponds to another to ensure that she would somehow return to her original height. As she experiments on this, she then returns back to her original size.

12. Symmetry Property of Equality “ For the Duchess . An invitation from the Queen to play croquet.” The Frog Footman repeated, in the same solemn tone, only changing the order of the words a little, “ From the Queen . An invitation for the Duchess to play croquet.” Here, symmetry is shown by the frog’s two statements but relay the same meaning that for the duchess, there is an invitation from the queen and that from the queen, there is an invitation to the duchess, two statements: a=b and b=a

13. Circles: “Alice remained looking thoughtfully at the mushroom for a minute, trying to make out which were the two sides of it; and as it was perfectly round, she found this a very difficult question. However, at last she stretched her arms round it as far as they would go, and broke off a bit of the edge with each hand” Here, Alice shows us one of the possible properties of a circle, since a circle has no sides it shall be difficult to determine which is which. However, if we took two points in the circle, that when connected will be the diameter, we would then find that the circle would be divided in half, making one half distinct from the other, forming our sides.

14. Relative and Absolute Maximum “There ought to be a book written about me, that there ought! And when I grow up, I’ll write one—but I’m grown up now,’ she added in a sorrowful tone; ‘at least there’s no room to grow up any more here.’” Here, no room to grow up anymore here meant that in that particular place, Alice had reached its limit by growing up as big as she can and would still fit. This exemplifies relative maxima, which is the maximum in one certain part of a graph, therefore it does not necessarily mean it would be the highest point of the whole of a graph, which is called the absolute maxima.

15. Principle of Continuity “The baby grunted again, and Alice looked very anxiously into its face to see what was the matter with it. There could be no doubt that it had a very turn-up nose, much more like a snout than a real nose; also its eyes were getting extremely small for a baby: altogether Alice did not like the look of the thing at all.” The pig which Alice perceived to be a baby gradually changed into a pig. This is supported by the principle of continuity in which the idea of a figure can be shaped and contorted into something else that there would be atleast some sort of familiarity between both.

16. Quiz: The Rabbit mistakes Alice as his housemaid. What name does this housemaid go by? Bill takes up the courage to confront Alice when she was bigger than the Rabbit’s house. What kind of animal is Bill? What was the first important thing that the caterpillar wanted to tell Alice before she left? Alice accidentally insults the caterpillar by telling him that she was not happy with her height, which was the same as his. How tall was she at this time? What game will the Queen and the Duchess play? John is your good friend, both your dads are coworkers. John’s dad buys him a new DS. What best argument should you make that would assure you of a new DS? You noticed that 3 apples cost the same as 2 oranges and 2 oranges cost the same as 5 bananas. If you were to buy 18 apples, how many bananas would result from the same price? A boy wants to jog 1 mile for the day, he notices that 1 ½ rounds in the field would result to a mile. He uses a flagpole as a starting point. How does he ensure that he has completed his mile? What is the relative maxima of the given portion of a graph below? 10. X and y are two different numbers, how can you make x=y if =y