TOEIC - Level 2
Tags: toeic
The passage says that many problems in life, like learning difficulties or relationship troubles, do not have a single clear answer, and people often disagree about how to solve them. In contrast, mathematics always has a definite answer that does not change, such as 5 + 7 = 12. Even when there are different ways to solve a math problem—like choosing different sides as the base and height of a triangle—the result is still the same. Math also helps us organize messy information, turning random numbers into patterns, averages, and graphs. Because of this reliability and order, the author believes math is a useful tool that can improve our lives.
- answer
- Definition: the single correct result that mathematics provides for a question or calculation, contrasted with unclear solutions in life
- Example: The answer to “What is five plus seven?” is twelve.
- problem
- Definition: a situation or difficulty that lacks an obvious solution, especially in personal or life contexts
- Example: A child who has trouble learning is described as a problem.
- math
- Definition: the discipline that uses numbers, formulas, and logical steps to produce exact results and organize data
- Example: In math there is a single answer that is right.
- triangle
- Definition: a three‑sided geometric figure used in the passage to illustrate different ways of calculating area
- Example: The triangle has a right angle with sides measuring 20 mm and 30 mm.
- pattern
- Definition: an organized arrangement or regularity that emerges when numbers or measurements are sorted by mathematics
- Example: Mathematics turns a chaotic set of numbers into a pattern.
- Which of the following is cited in the passage as an example of a problem that may lack a single answer?
- Calculating the area of a triangle
- A child having trouble learning
- Determining the sum of five and seven
- Measuring the height of a triangle
- What answer does the author give for “What is five plus seven?”
- Ten
- Eleven
- Twelve
- Thirteen
- In the triangle example, what are the lengths of the two sides that form the right angle?
- 15 mm and 25 mm
- 20 mm and 30 mm
- 30 mm and 40 mm
- 20 mm and 40 mm
- How does the author compare the act of applying mathematics to a household chore?
- Cooking a meal
- Painting a room
- Washing and sorting dishes
- Building a house
- Which statement about mathematics is supported by the passage?
- It can have multiple correct answers that differ in value.
- It organizes numbers into patterns and can calculate averages.
- It is described as a source of conflict.
- It never uses formulas.
- Do you agree that math always has a single correct answer? Why or why not?
- Have you ever faced a problem in life that seemed to have no clear answer? Share your experience.
- Why do you think the author compares solving math problems to washing and sorting dishes?
- In the triangle example, how does changing the base and height still give the same area? Explain.
- The author says math should be our friend. Do you think everyone should rely on math for life decisions? Why or why not?
- Is it better to have many opinions on a personal problem, or to look for a single clear solution? Discuss.
- If you could add a new subject to school that combines math and emotions, what would it be called and what would you teach?
- Rewrite the ending of the paragraph about math bringing order, using a different metaphor than dishes.
- Imagine a world where math gave different answers every time you calculated. How would daily life be different?
- After reading the text, how has your view of math’s role in solving real‑world problems changed?
Why Do I Like Mathematics?
Sometimes there is a problem in life that has no answer. Perhaps a child has trouble learning. Perhaps someone becomes ill. Perhaps there was love, but now there is conflict. These problems are hard to solve. There is no single answer. Many people have opinions on what is the best answer.
But in mathematics there is an answer: a single answer that is right. There is no doubt; there is no argument; this answer is right. If we ask, “What is five plus seven?” The answer is twelve. If we ask,
“How do you raise a child?” The answer would depend on the child and the parents.
Sometimes there is more than one way to reach an answer. Imagine we want to find the area of a triangle. The triangle has a right angle; the two sides surrounding the right angle are 20mm and 30mm. The formula for the area of a triangle is one half of (base)(height). We could consider the 20mm side as the base and 30 mm as the height.
We could consider the 30mm side as the base and the 20mm side as the height. Both ways would produce the same answer. The area is 300 square mm. Alternatively, we could consider the base as the third side of the triangle and then we would have to draw a height and measure it. The height would be neither 20 nor 30. But still we would end with the same answer. In math, the answer does not change.
Another reason I like math is the way it brings order. There can be a whole set of numbers or a whole set of measurements that mean nothing until mathematics organizes them into a pattern. An average number can be found; graphs can be drawn; the spread of the numbers and probabilities of a certain number happening can be calculated. This is like having a whole lot of dirty dishes after supper.
Applying math is like washing and sorting the dishes and putting them back into the cupboard. Math is a powerful tool. Math should be our friend, and we will find more ways to use it to better our lives.
