Practice and Review — Chapter 1 - Patterns in Mathematics

Use these questions to practise and revise "Chapter 1 - Patterns in Mathematics". Write your answers in your notebook. Your teacher has the answers.

AI-generated practice questions

1. According to the text, what is the key characteristic that makes an arrangement a pattern rather than a random jumble?
   • a) It must involve numbers only
   • b) It must repeat exactly the same way forever
   • c) It follows a rule so that what comes next is predictable
   • d) It must be created by humans
2. Which of the following is described in the text as a 'repeating pattern'?
   • a) 2, 4, 6, 8, 10
   • b) 100, 90, 80, 70
   • c) red-blue-red-blue-red-blue
   • d) 1, 3, 6, 10, 15
3. In a 10×10 number grid, why do multiples of 3 form diagonal stripes?
   • a) Because 10 is a multiple of 3
   • b) Because 10 is not a multiple of 3
   • c) Because 3 is a multiple of 10
   • d) Because the grid has 10 rows
4. What is the rule for generating triangular numbers?
   • a) Multiply the term number by itself
   • b) Add the next counting number to the previous total
   • c) Add the two previous terms together
   • d) Double the previous term
5. Which sequence represents the doubling pattern (powers of two)?
   • a) 1, 3, 6, 10, 15
   • b) 1, 2, 4, 8, 16, 32
   • c) 1, 1, 2, 3, 5, 8
   • d) 1, 4, 9, 16, 25
6. The Virahanka numbers (Fibonacci sequence) are formed by adding the two terms immediately before it to get the next term. (True / False)
7. Square numbers can be built by adding consecutive odd numbers starting from 1 (1, 3, 5, 7...). (True / False)
8. The sum of any two consecutive triangular numbers is always a square number. (True / False)
9. What number comes next in the sequence 3, 6, 9, 12? What rule did you use? Extra Practice
10. If you shade multiples of 4 on a 10×10 grid, will the shaded squares form diagonal stripes? Explain why or why not. Extra Practice
11. Why does the doubling pattern (1, 2, 4, 8, 16...) grow much faster than a skip-counting pattern like 2, 4, 6, 8...? Extra Practice

Multiple-choice questions

12. Which of the following best describes pattern?
    • a) An arrangement of numbers, shapes, colours, or events that follows a rule, so that once you know the…
    • b) Multiply the previous term by 2
    • c) A term-to-term rule, which explains how to get from one term to the very next one
    • d) Today, this sequence is often called the Fibonacci sequence, but in recognition of its Indian origin, it
13. Which term matches this description: "The earliest kind of pattern most of us ever learn, often before we can even read, and they…"?
    • a) Doubling Pattern
    • b) First way
    • c) Virahanka numbers
    • d) Skip-counting patterns
14. Which of the following best describes virahanka numbers?
    • a) The earliest kind of pattern most of us ever learn, often before we can even read, and they…
    • b) Multiply the previous term by 2
    • c) A term-to-term rule, which explains how to get from one term to the very next one
    • d) Today, this sequence is often called the Fibonacci sequence, but in recognition of its Indian origin, it
15. Which term matches this description: "A term-to-term rule, which explains how to get from one term to the very next one"?
    • a) Doubling Pattern
    • b) Skip-counting patterns
    • c) Pattern
    • d) First way
16. Which of the following best describes Doubling Pattern?
    • a) Multiply the previous term by 2
    • b) Today, this sequence is often called the Fibonacci sequence, but in recognition of its Indian origin, it
    • c) The earliest kind of pattern most of us ever learn, often before we can even read, and they…
    • d) An arrangement of numbers, shapes, colours, or events that follows a rule, so that once you know the…

Fill in the blanks

17. A ________ is an arrangement of numbers, shapes, colours, or events that follows a rule, so that once you know the rule, you can say with confidence what comes next.
18. Today, this sequence is often called the Fibonacci sequence, but in recognition of its Indian origin, it is also known as the ________.
19. The ________ is a term-to-term rule, which explains how to get from one term to the very next one.
20. ________: Multiply the previous term by 2
21. Chances are you will find a rangoli — a design made of coloured powder or flower petals, built from dots and lines arranged in a repeating, symmetric ________.
22. A rangoli, a timetable, and a traffic signal look nothing alike, yet all three are built on the same idea: something arranged so that it repeats, grows, or changes according to a ________.
23. Recognising a ________ lets us do something powerful: predict what comes next without having to see it for ourselves.
24. Consider the sequence of ________ 5, 10, 15, 20.

True or false

25. A pattern is an arrangement of numbers, shapes, colours, or events that follows a rule, so that once you know the rule, you can say with confidence what comes next. (True / False)
26. The first way is not a term-to-term rule, which explains how to get from one term to the very next one. (True / False)
27. Doubling Pattern: Multiply the previous term by 2 (True / False)
28. Chances are not you will find a rangoli — a design made of coloured powder or flower petals, built from dots and lines arranged in a repeating, symmetric pattern. (True / False)
29. Recognising a pattern lets us do something powerful: predict what comes next without having to see it for ourselves. (True / False)
30. Growing patterns, where each term is not larger than the one before, following a fixed rule, such as 2, 4, 6, 8. (True / False)
31. Shrinking patterns, where each term becomes smaller according to a rule, such as 100, 90, 80, 70. (True / False)
32. In the second term, there are not two hexagons above three diamonds. (True / False)

Short-answer questions

33. What is meant by "pattern"?
34. What is meant by "skip-counting patterns"?
35. What is meant by "virahanka numbers"?
36. What is meant by "first way"?
37. What is meant by "Doubling Pattern"?

Think and explain

38. Explain why: In this chapter, we begin with numbers, grids, and shapes.
39. Explain why: Even without being told, most of us can sense that the next number should be 25.
40. Explain why: Patterns generally fall into a few broad families, and it helps to know their names.
41. Explain why: Mathematicians spend a great deal of time trying to uncover the rule behind a set of terms.
42. What is the difference between pattern and Doubling Pattern?

Problem solving

43. Calculate: 1 × 1
44. Calculate: 50 × 50
45. Calculate: 30 + 12
46. Calculate: 1 × 2

Application questions

47. Give one example of how rule is used in everyday life.
48. Give one example of how pattern is used in everyday life.
49. Give one example from everyday life of the ideas in this chapter.

Questions from the textbook

50. What is the next term in the sequence 1, 3, 6, 10, ___? Options: 12 (b) 14 (c) 15 (d) 16
51. Which of these is a square number? Options: 15 (b) 21 (c) 36 (d) 40
52. In the doubling pattern 1, 2, 4, 8, 16, what is the 7th term? Options: 32 (b) 64 (c) 128 (d) 96
53. In the Virahanka numbers 1, 1, 2, 3, 5, 8, 13, which rule connects one term to the next? Options: Multiply the term by 2 (b) Add the two previous terms (c) Add 3 each time Subtract 1 each time A position-to-term rule is more useful than a term-to-term rule mainly because it: Uses smaller numbers (b) Lets us find any term directly, without finding every earlier term (c) Only works for shapes (d) Cannot be used for square numbers
54. What is the 4th cube number? Options: 16 (b) 24 (c) 64 (d) 81
55. Along which diagonal of Pascal's Triangle do the triangular numbers appear? Options: The outer edge of 1s (b) The second diagonal (counting numbers) (c) The third diagonal (d) They do not appear in Pascal's Triangle A pattern is an arrangement that follows a fixed _____________. The sequence 1, 4, 9, 16 is known as the _____________ numbers. Triangular numbers are formed by adding one _____________ than the previous time. The Virahanka numbers are also widely known, outside India, as the _____________ sequence. The four steps of the pattern-thinking process are Observe, Identify, Predict, and _____________. A square number can be rebuilt as the sum of consecutive _____________ numbers, called gnomons.
56. Define a pattern in your own words and give one example from daily life that is not mentioned in this chapter.
57. What is the difference between a term-to-term rule and a position-to-term rule? Give one example of each.
58. Write the first five terms of the square numbers and explain how each term is formed.
59. Explain, using the chessboard story, why the doubling pattern can be misleading if we judge it only by its first few terms.
60. List, in order, the four steps of the pattern-thinking process described in this chapter.
61. What is a gnomon, and how does it help explain why square numbers grow the way they do?
62. Name two places, other than a mathematics textbook, where the Virahanka numbers or the golden ratio have been observed.
63. Explain, with a labelled diagram or dot arrangement of your own, why adding two consecutive triangular numbers always produces a square number.
64. is only useful in mathematics class. Do you agree or disagree? Support your answer with one example from outside mathematics.

Revision exercises

65. Write three important points about "Introduction: The World Runs on Patterns".
66. Write three important points about "1.1 What Is a Pattern?".
67. Write three important points about "1.2 Patterns in Numbers".
68. Write three important points about "1.3 Patterns in Shapes".
69. Write three important points about "1.4 From Patterns to Rules".
70. Write three important points about "1.5 The Pattern-Thinking Process".
71. Write three important points about "1.6 Patterns in Nature and Everyday Technology".
72. Write three important points about "1.7 Patterns and Computational Thinking".
73. Write three important points about "Discussion Questions".
74. Write three important points about "Practical Activity: The Matchstick Tower".
75. Write three important points about "Extension Activity: The Golden Ratio Hunt".

These questions are based on the lesson content. “Extra Practice” questions have been newly created by the course generator to give students more opportunities to apply what they have learned.