1 Up ahead, the road divided into three and, as if in reply to Milo’s question, an enormous road sign, pointing in all three directions, stated clearly:
2 Digitopolis
5 Miles
1,600 Rods
8,800 Yards
26,400 Feet
316,800 Inches
633,600 Half Inches
AND THEN SOME
3 “Let’s travel by miles,” advised the Humbug, “it’s shorter.”
4 “Let’s travel by half inches,” suggested Milo, “it’s quicker.”
5 “But which road should we take?” asked Tock. “It must make a difference.”
6 As they argued, a most peculiar little figure stepped nimbly from behind the sign and approached them, talking all the while. “Yes, indeed: indeed it does; certainly; my; yes; it does make a difference, undoubtedly.”
7 He was constructed (for that’s really the only way to describe him) of a large assortment of lines and angles connected together into one solid many sided shape -somewhat like a cube that’s had all of its corners cut off and then had all its corners cut off again. Each of the edges was neatly labelled with a small letter, and each of the angles with a large one. He wore a handsome beret on top, and peering intently from one of his several surfaces was a very serious face. Perhaps if you look at the picture you’ll know what I mean.
8 When he reached the car the figure doffed his cap and recited in a loud clear voice:
9 “My angles are many,
10 My sides are not few,
11 I’m the Dodecahedron.
12 Who are you?”
13 What’s a Dodecahedron?” asked Milo, who was barely able to pronounce the strange word.
14 “See for yourself,” he said, turning around slowly. “A Dodecahedron is a mathematical shape with twelve faces.”
15 Just as he said it, eleven other faces appeared, one on each surface, and each one wore a different expression.
16 “I usually use one at a time,” he confided, as all but the smiling one disappeared again. “It saves wear and tear. What are you called?”
17 “Milo,” said Milo.
19 “That is an odd name,” he said, changing his smiling face for a frowning one. “And you only have one face.”
19 “Is that bad?” asked Milo, making sure it was still there.
20 “You’ll soon wear it out using it for everything,” replied the Dodecahedron. “Now, I have one for smiling, one for laughing, one for crying, one for frowning, one for thinking, one for pouting, and six more besides. Is everyone with one face called a Milo?”
21 “Oh no,” Milo replied; “some are called Henry or George or Robert or John or lots of other things.”
22 “How terribly confusing. he cried. “Everything here is called exactly what it is. The triangles are called triangles, the circles are called circles, and even the same numbers have the same name. Why, can you imagine what would happen if we named all the twos Henry or George or Robert or John or lots of other things?” You’d have to say Robert plus John equals four, and if the four’s name were Albert, things would be hopeless.”
23 “I never thought of it that way,” Milo admitted.
24 “Then I suggest you begin at once,” admonished the Dodecahedron from his admonishing face, “for here in the Digitopolis everything is quite precis.”
25 “Then perhaps you can help us decide which road to take,” said Milo.
26 “By all means,” he replied happily. “There’s nothing to it. If a small car carrying three people at thirty miles an hour for ten minutes along a road five miles long at 11.35 in the morning starts at the same time as three people who have been traveling in a little automobile at twenty miles an hour for fifteen minutes on another road and exactly twice as long as one half the distance of the other, while a dog, a bug, and a boy travel an equal distance in the same time or the same distance in an equal time along a third rald in mid-October, then which one arrives first and which is the best way to go?”
27 “Seventeen!” shouted the Humbug scribbling furiously on a piece of paper.
28 “Well, I’m not sure, but--” Milo stammered after several minutes of frantic calculating.
29 “You’ll have to do better than that,” scolded the Dodecahedron, “or you’ll never know how far you’ve gone or whether or not you’ve ever got there.”
30 “I’m not very good at problems,” admitted Milo.
31 “What a shame,” sighed the Dodecahedron. “They’re so very useful. Why, did you know that if a beaver two feet long with a tail a foot and a half long can build a dam twelve feet high and six feet wide in two days, all you would need to build the Kariba Dam is a beaver sixty-eight feet long with a fifty one foot tail?”
32 “Where would you find a beaver as big as that?” grumbled the Humbug as his pencil point snapped.
33 “I’m sure I don’t know,” he replied, “but if you did, you’d certainly know what to do with him.”
34 “That’s absurd,” objected Milo, whose head was spinning from all the numbers and questions.
35 “That may be true,” he said, “but it’s completely accurate, and as long as the answer is right, who cares if the question is wrong? If you want sense, you’ll have to make it yourself.”
36 “All three roads arrive at the same place at the same time, " interrupted Tock, who had patiently been doing the first problem.
37 “Correct!” shouted the Dodecahedron. “And I’ll take you there myself. Now you can see how important problems are. If you hadn’t done this one properly, you might have gone the wrong way.”
38 “I can see where I made my mistake,” said the Humbug, frantically rechecking his figures.
39 “But if all roads arrive at the same place at the same time, then aren’t they all the right way?” asked Milo.
40 “Certainly not!” he shouted, glaring from his most upset face. “They are all the wrong way. Just because you have a choice, it doesn’t mean that any of them has to be right.”
1. Read this sentence from the passage.
34 “That’s absurd,” objected Milo, whose head was spinning from all the numbers and questions.
How does the phrase “head was spinning” contribute to the meaning of the passage?
A It reveals that Milo thinks the Dodecahedron is funny.
B It expresses that Milo is confused by the math problems.
C It highlights that Milo is interested in discovering the truth.
D It implies that Milo thinks the Humbug needs help with math.
2. What are two ways that the imagery in paragraph 7 contributes to the meaning of the passage?
A It reveals how unusual the Dodecahedron looks.
B It implies that Milo helped build the Dodecahedron.
C It describes how the Dodecahedron teaches numbers.
D It suggests that Milo and the Dodecahedron are similar.
E It introduces how the Dodecahedron expresses himself.
3. Read this sentence from the passage.
“‘That may be true,’ he acknowledged, ‘but it’s completely accurate, and as long as the answer is right, who cares if the question is wrong?’” (paragraph 35)
The word “accurate” comes from the Latin root accuratus, meaning “done with care.” Based on the root, what is the definition of the word accurate?
A balanced
B correct
C finished
D interesting
4. Which detail from the passage supports the theme that a person can learn to view the world differently through math?
A “As they argued, a most peculiar little figure stepped nimbly from behind the sign and approached them, talking all the while.” (paragraph 6)
B “‘Is that bad?’ asked Milo, making sure it was still there.” (paragraph 19)
C “‘I never thought of it that way,’ Milo admitted.” (paragraph 23)
D “‘I’m sure I don’t know,’ he replied, ‘but if you did, you’d certainly know what to do with him.’” (paragraph 33)
5. In paragraph 22, how does the Dodecahedron use a logical appeal?
A by describing why some shape names lead to frustration
B by suggesting how people ought to create their own names
C by suggesting why people should be named for their features
D by describing how authorities determine the names of objects
6. Read this sentence from the passage.
“Perhaps if you look at the picture you’ll know what I mean.” (paragraph 7)
How does the switch to addressing the reader affect the passage?
A It hints at the Dodecahedron’s opinions of other characters.
B It demonstrates the narrator’s feelings toward the Dodecahedron.
C It highlights the narrator’s limit of words to describe the Dodecahedron.
D It suggests that the other characters struggle to understand the Dodecahedron.
7. This question has two parts. First, answer Part A. Then, answer Part B.
Part A: What is revealed by the conversation between Milo, the Humbug, and Tock about the three different roads?
A The characters are tired from their long journey.
B The characters disagree about the right way to go.
C The characters are eager to meet new people in the city.
D The characters distrust the information presented on the sign.
Part B: How does the conversation in Part A affect the plot?
A It causes them to take a break.
B It causes them to take the shortest trip.
C It causes the Dodecahedron to talk to them.
D It causes the Dodecahedron to read the sign.
8. Which statement expresses a theme that is found in paragraphs 34–35 and 39–40?
A Difficult questions can lead to confusion.
B New people can make traveling impossible.
C Education is an easy way to make new friends.
D Choosing a path can be done without much thought.
1 answer
Here are the answers to the questions based on the excerpt from The Phantom Tollbooth:
B It expresses that Milo is confused by the math problems.
The phrase "head was spinning" suggests Milo's confusion as he struggles to understand the complex mathematical concepts being discussed.
A It reveals how unusual the Dodecahedron looks. E It introduces how the Dodecahedron expresses himself.
The imagery in paragraph 7 describes the Dodecahedron's unique physical appearance and how he communicates, emphasizing his unusual nature.
B correct
The root “accuratus” means “done with care,” which aligns closely with the definition of “accurate” as being correct.
C “‘I never thought of it that way,’ Milo admitted.” (paragraph 23)
This detail shows Milo's realization, suggesting that through the interaction with the Dodecahedron, he begins to see the world—and mathematics—in a new light.
A by describing why some shape names lead to frustration
The Dodecahedron explains the confusion that arises from arbitrary naming, highlighting the logical reasoning behind consistent naming conventions.
C It highlights the narrator’s limit of words to describe the Dodecahedron.
The switch to addressing the reader acknowledges that the narrator may struggle to adequately convey the Dodecahedron's complexity.
Part A: B The characters disagree about the right way to go. Part B: C It causes the Dodecahedron to talk to them.
The disagreement about which road to take prompts the Dodecahedron to approach them and offer assistance.
A Difficult questions can lead to confusion.
The discussions about the complexities of math and the confusion they generate capture the theme of how challenging questions can make things unclear.
