Question 1

Can you think of other examples where mathematics helps us in our everyday lives?

Accepted Answer

Mathematics is everywhere and plays a crucial role in our everyday lives. Here are some examples:Budgeting and shopping: We use maths to manage our money. Math is useful for calculating discounts, comparing prices, or tracking expenses.Cooking and baking: Recipes often require measurements, proportions, and timing.Time management: We use math to plan our schedules, calculate travel time, estimate how long tasks will take, etc.Understanding patterns: Recognising patterns in weather, traffic, or daily routines involves mathematical thinking.

Question 2

How has mathematics helped propel humanity forward? (You might think of examples involving: carrying out scientific experiments; running our economy and democracy; building bridges, houses, or other complex structures; making TVs, mobile phones, computers, bicycles, trains, cars, planes, calendars, clocks, etc.)

Accepted Answer

Mathematics is everywhere. Mathematics has propelled humanity by economic development eradication of diseases and increase in living standards.1.2 Patterns in Numbers Figure it Out (Page No. 3)

Question 3

Can you recognize the pattern in each of the sequences in Table 1?

Accepted Answer

Yes,PatternsRecognization of patterns1, 1, 1, 1, 1, 1, 1,… (All l’s)Sequence of all 1 ’s1, 2, 3, 4, 5, 6, 7, … (Counting numbers)A sequence of consecutive counting numbers starting from 11, 3, 5, 7, 9, 11, 13, … (Odd numbers)A sequence of consecutive odd numbers starting from 12, 4, 6, 8, 10, 12, 14, … (Even numbers)A sequence of consecutive even numbers starting from 21, 3, 6, 10, 15, 21, 28, … (Triangular numbers)In the sequence, each term is the sum of first n consecutive counting numbers1,4, 9, 16, 25,36, 49, … (Squares)In the sequence, each term is the product of counting number by itself starting from 11, 8, 27, 64, 125, 216, … (Cubes)In the sequence, each term is the product of counting number by itself thrice starting from 11, 2, 3, 5, 8, 13, 21, … (Virahanka numbers)In the sequence, each term (starting from third term) is the sum of previous two terms

Question 4

Rewrite each sequence of Table 1 in your notebook, along with the next three numbers in each sequence! After each sequence, write in your own words what is the rule for forming the numbers in the sequence.

Accepted Answer

All l’s 1, 1, 1, 1,… (The next three numbers are 1, 1, 1. The rule is that every number is 1.)Counting numbers 1, 2, 3, 4, 5, 6, 7,… (The next three numbers are 8, 9,10. The rule is to add 1 to the previous number.)Odd numbers 1, 3, 5, 7, 9, 1,… (The next three numbers are 15, 17, 19. The rs to add 2 to the previous number.)n numbers 2, 4, 6, 8, 10, 12, 14,… (The next three is to add 2 to the previous number.)Triangular numbers 1, 3, 6,10,15, 21, 28,…(The next three numbers are 36,45, 55. The rule is to add the next natural number is sequence.)Squares 1, 4, 9, 16, 25, 36, 49,… (The next three numbers are 64, 81, 100. The rule is to square the next natural number.)Cubes 1, 8, 27, 64, 125, 216,… (The next three numbers are 343, 512, 729. The rule is to cube the next natural number.)Virahanka numbers 1, 2, 3, 5, 8, 13, 21,… (The next three numbers are 34, 55, 89. The rule is to add the last two numbers.)Powers of 2 1, 2, 4, 8, 16, 32, 64,… (The next three numbers are 128, 256, 512. The rule is to multiply the last number by 2.)Powers of 3 1, 3, 9, 27, 81, 243, 729,… (The next three numbers are 2187, 6561, 19683. The rule is to multiply the last number by 3.)1.3 Visualising Number Sequences Figure it Out (Page No. 5-6)

Question 5

(a) Why are 1, 3, 6, 10, 15,…… called triangular numbers?
(b) Why are 1, 4, 9, 16, 25,…….. called square numbers or squares?
(c) Why are 1, 8, 27, 64, 125,…….. called cubes?

Accepted Answer

(a) Triangular numbers are called so because these numbers of dots can be arranged to make a triangle.1, 3, 6, 10,…….. are triangular numbers.1, 3, 6, 10,……… dots can be arranged to make a triangle. (see figure below)(b) Square numbers are called so because these numbers of dots can be arranged to make a square.1, 4, 9, 16,………. are square numbers.1, 4, 9, 16,……… dots can be arranged to make a square (see fig. below)(c) Cubes are called so because these many unit cubes can be arranged to make a cube.1, 8, 27, 64,…… are cube numbers.1, 8, 27, 64,……. unit cubes can be arranged to make cubes. (see figure below)

Question 6

You will have noticed that 36 is both a triangular number and a square number! That is, 36 dots can be arranged perfectly both in a triangle and a square. Make pictures in your notebook illustrating this!
This shows that the same number can be represented differently and play different roles, depending on the context. Try representing some other numbers pictorially in different ways!

Accepted Answer

It’s fascinating that 36 can be both a triangular number and a square number! Let’s explore this by visualizing how 36 dots can be arranged in both shapes and then represent other numbers in different ways:Other numbers that can be represented pictorially in different ways are: 99 as both a square and a cross:

Question 7

Can you think of pictorial ways to visualise the sequence of Powers of 2? Powers of 3?
Here is one possible way of thinking about Powers of 2:

Accepted Answer

Intext Questions

Source: This question is from Patterns in Mathematics, Mathematics &mdash; Class 6, CBSE Board.
Key Concepts CoveredThis question tests your understanding of the following concepts from the chapter Patterns in Mathematics: Think, Pictorial, Ways, Visualise, Sequence, Powers. These are fundamental topics in Mathematics that students are expected to master as part of the CBSE Class 6 curriculum.A thorough understanding of these concepts will help you answer similar questions confidently in your CBSE examinations. These topics are frequently tested in both objective and subjective sections of Mathematics papers. We recommend revising the relevant section of your textbook alongside practising these solved examples to build a strong foundation.
How to Approach This QuestionRead the question carefully and identify what is being asked. Break down complex questions into smaller parts. Use the terminology and concepts discussed in this chapter. Structure your answer logically — begin with a definition or key statement, then provide supporting details. Review your answer to ensure it addresses all parts of the question completely.
Key Points to RememberAlways show your working steps clearly.
Verify your answer by substituting values back into the equation.
Practice similar problems from the textbook exercises.
Memorise important formulae and their conditions of applicability.
Related Questions from Patterns in MathematicsQ1: Can you think of other examples where mathematics helps us in our everyday lives?
Q11: Now by imagining a similar picture, or by drawing it partially, as needed, can you say what is the...
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Question 8

(Page 7)
By drawing a similar picture, can you say what is the sum of the first 10 odd numbers?

Accepted Answer

1 + 3+ 5+ 7 + 9 + 11 + 13 + 15 + 17 + 19 = 100

Source: This question is from Patterns in Mathematics, Mathematics &mdash; Class 6, CBSE Board.
Key Concepts CoveredThis question tests your understanding of the following concepts from the chapter Patterns in Mathematics: Page, Drawing, Similar, Picture, Say, Sum. These are fundamental topics in Mathematics that students are expected to master as part of the CBSE Class 6 curriculum.A thorough understanding of these concepts will help you answer similar questions confidently in your CBSE examinations. These topics are frequently tested in both objective and subjective sections of Mathematics papers. We recommend revising the relevant section of your textbook alongside practising these solved examples to build a strong foundation.
How to Approach This QuestionRead the question carefully and identify what is being asked. Break down complex questions into smaller parts. Use the terminology and concepts discussed in this chapter. Structure your answer logically — begin with a definition or key statement, then provide supporting details. Review your answer to ensure it addresses all parts of the question completely.
Key Points to RememberAlways show your working steps clearly.
Verify your answer by substituting values back into the equation.
Practice similar problems from the textbook exercises.
Memorise important formulae and their conditions of applicability.
Related Questions from Patterns in MathematicsQ1: Can you think of other examples where mathematics helps us in our everyday lives?
Q11: Now by imagining a similar picture, or by drawing it partially, as needed, can you say what is the...
Q12: Can you find a similar pictorial explanation for why adding counting numbers up and down, i.e., 1,...
Q13: By imagining a large version of your picture or drawing it partially, as needed, can you see what...
Q14: Which sequence do you get when you start to add the All 1’s sequence up? What sequence do you get...
Practice more questions from Patterns in Mathematics &mdash; Mathematics, Class 6 CBSE

Question 9

Now by imagining a similar picture, or by drawing it partially, as needed, can you say what is the sum of the first 100 odd numbers?

Accepted Answer

Do it yourself by referring the above image.We know that adding up consecutive odd numbers gives square numbers.So, while adding up 100 odd number, we get a number which is square of 100.1 + 3 + 5 + 7 + 9+ 11 + … + 197 + 199 = 100001.4 Relations Among Number Sequences Figure it Out (Page No. 8-9)

Question 10

Can you find a similar pictorial explanation for why adding counting numbers up and down, i.e., 1, 1 + 2 + 1, 1 + 2 + 3 + 2 + 1,……., gives square numbers?

Accepted Answer

1 = 1 = (1)21 + 2 + 1 = 4 = (2)21 + 2 + 3 + 2 + 1 = 9 = (3)21 + 2 + 3 + 4 + 3 + 2 + 1 = 16 = (4)21 + 2 + 3 + 4 + 5 + 4 + 3 + 2 + 1 = 25 = (5)21 + 2 + 3 + 4 + 5 + 6 + 5 + 4 + 3 + 2 + 1 = 36 = (6)2and so on.

Question 11

By imagining a large version of your picture or drawing it partially, as needed, can you see what will be the value of 1 + 2 + 3 + … + 99 + 100 + 99 + …. + 3 + 2 + 1?

Accepted Answer

We know that by adding the counting numbers up and down, we get perfect squares as these sequences are to be thought of as forming a symmetric pattern around a central line. So, by adding counting numbers up and down to 100, we will get our central line with 100 dots and the rest above and below that line.So 1 + 2 + 3 + ….. + 99 + 100 + 99 + …… + 3 + 2 + 1 = 1002= 10,000

Question 12

Which sequence do you get when you start to add the All 1’s sequence up? What sequence do you get when you add the All 1’s sequence up and down?

Accepted Answer

Adding up: 1 + 1 + 1 + 1 = 4Adding down: 1 + 1 + 1 + 1 = 4The sum is the same in both ways.

Source: This question is from Patterns in Mathematics, Mathematics &mdash; Class 6, CBSE Board.
Key Concepts CoveredThis question tests your understanding of the following concepts from the chapter Patterns in Mathematics: Sequence, Get, Start, Add, Down, Patterns in Mathematics. These are fundamental topics in Mathematics that students are expected to master as part of the CBSE Class 6 curriculum.A thorough understanding of these concepts will help you answer similar questions confidently in your CBSE examinations. These topics are frequently tested in both objective and subjective sections of Mathematics papers. We recommend revising the relevant section of your textbook alongside practising these solved examples to build a strong foundation.
How to Approach This QuestionRead the question carefully and identify what is being asked. Break down complex questions into smaller parts. Use the terminology and concepts discussed in this chapter. Structure your answer logically — begin with a definition or key statement, then provide supporting details. Review your answer to ensure it addresses all parts of the question completely.
Key Points to RememberAlways show your working steps clearly.
Verify your answer by substituting values back into the equation.
Practice similar problems from the textbook exercises.
Memorise important formulae and their conditions of applicability.
Related Questions from Patterns in MathematicsQ1: Can you think of other examples where mathematics helps us in our everyday lives?
Q11: Now by imagining a similar picture, or by drawing it partially, as needed, can you say what is the...
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Q13: By imagining a large version of your picture or drawing it partially, as needed, can you see what...
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Question 13

Which sequence do you get when you start to add the counting numbers up? Can you give a smaller pictorial explanation?

Accepted Answer

When we start adding the counting numbers cumulatively, we get the sequence of triangular numbers.1: 11 + 2: 31 + 2 + 3: 61 + 2 + 3 + 4: 101 + 2 + 3 + 4 + 5: 15This sequence is known as the triangular numbers.

Question 14

What happens when you add up pairs of consecutive triangular numbers? That is, take 1 + 3, 3 + 6, 6 + 10, 10 + 15,… ? Which sequence do you get? Why? Can you explain it with a picture?

Accepted Answer

Adding up pairs of consecutive triangular numbers.1 + 3 = 43 + 6 = 96 + 10 = 1610 + 15 = 25…………………………………………and so on.Here, we get a sequence of squares.

Source: This question is from Patterns in Mathematics, Mathematics &mdash; Class 6, CBSE Board.
Key Concepts CoveredThis question tests your understanding of the following concepts from the chapter Patterns in Mathematics: Happens, Add, Pairs, Consecutive, Triangular, Numbers. These are fundamental topics in Mathematics that students are expected to master as part of the CBSE Class 6 curriculum.A thorough understanding of these concepts will help you answer similar questions confidently in your CBSE examinations. These topics are frequently tested in both objective and subjective sections of Mathematics papers. We recommend revising the relevant section of your textbook alongside practising these solved examples to build a strong foundation.
How to Approach This QuestionRead the question carefully and identify what is being asked. Break down complex questions into smaller parts. Use the terminology and concepts discussed in this chapter. Structure your answer logically — begin with a definition or key statement, then provide supporting details. Review your answer to ensure it addresses all parts of the question completely.
Key Points to RememberAlways show your working steps clearly.
Verify your answer by substituting values back into the equation.
Practice similar problems from the textbook exercises.
Memorise important formulae and their conditions of applicability.
Related Questions from Patterns in MathematicsQ1: Can you think of other examples where mathematics helps us in our everyday lives?
Q11: Now by imagining a similar picture, or by drawing it partially, as needed, can you say what is the...
Q12: Can you find a similar pictorial explanation for why adding counting numbers up and down, i.e., 1,...
Q13: By imagining a large version of your picture or drawing it partially, as needed, can you see what...
Q14: Which sequence do you get when you start to add the All 1’s sequence up? What sequence do you get...
Practice more questions from Patterns in Mathematics &mdash; Mathematics, Class 6 CBSE

Question 15

What happens when you start to add up powers of 2 starting with 1, i.e., take 1, 1 + 2, 1 + 2 + 4, 1 + 2 + 4 + 8,…..? Now add 1 to each of these numbers — what numbers do you get? Why does this happen?

Accepted Answer

Let us add powers of 2 starting with 1Here 1 = 11 + 2 = 31 + 2 + 4 = 71 + 2 + 4 + 8 = 151 + 2 + 4 + 8 + 16 = 31Hence series 1, 3, 7, 15, 31,….. is formed.Now let us add 1 to each of the above numbers1 + 1 = 2 = 211 + 2 + 1 = 4 = 2 × 2 = 221 + 2 + 4 + 1 = 8 = 2 × 2 × 2 = 231 + 2 + 4 + 8 + 1 = 16 = 2 × 2 × 2 × 2 = 24This happens because we are adding (1 + 1 = 2), hence the power of 2 increases.

Question 16

What happens when you multiply the triangular numbers by 6 and add 1? Which sequence do you get? Can you explain it with a picture?

Accepted Answer

Triangular numbers are 1, 3, 6, 10, 15, 21,…….1 × 6 + 1 = 73 × 6 + 1 = 19 (increase of 12 i.e. 6 × 2)6 × 6 + 1 = 37 (increase of 18 i.e. 6 × 3)10 × 6 + 1 = 61 (increase of 24 i.e. 6 × 4)15 × 6 + 1 = 91 (increase of 30 i.e. 6 × 5)We get the sequence: 7, 19, 37, 61, 91,………..

Question 17

What happens when you start to add up hexagonal numbers, i.e., take 1, 1 + 7, 1 + 7 + 19, 1 + 7 + 19 + 37,….? Which sequence do you get? Can you explain it using a picture of a cube?

Accepted Answer

When you start to add up hexagonal numbers, you obtain a sequence of cubic numbers.Let’s add them up cumulatively:1. Sum of first hexagonal number: 12. Sum of first two hexagonal numbers: 1 + 7 = 83. Sum of first three hexagonal numbers: 1 + 7 + 19 = 274. Sum of first four hexagonal numbers: 1 + 7 + 19 + 37 = 64This sequence is 1, 8, 27, 64,…..The sequence 1, 8, 27, 64,…. is the sequence of cubic numbers: 13, 23, 33, 43, 53,…..The cube number: Cn= n3

Question 18

Find your patterns or relationships in and among the sequences in Table 1. Can you explain why they happen with a picture or otherwise?

Accepted Answer

Squares are generated by adding consecutive odd numbers.For example:12= 122= 1 + 3 = 432= 1 + 3 + 5 = 942= 1 + 3 + 5 + 7 = 161 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 = 1001.5 Patterns in Shapes Figure it Out (Page No. 11)

Question 19

Can you recognise the pattern in each of the sequences in Table 3?

Accepted Answer

Yes, we can recognise the pattern in each of the sequence in Table 3.

Source: This question is from Patterns in Mathematics, Mathematics &mdash; Class 6, CBSE Board.
Key Concepts CoveredThis question tests your understanding of the following concepts from the chapter Patterns in Mathematics: Recognise, Pattern, Sequences, Table, Patterns in Mathematics, Mathematics. These are fundamental topics in Mathematics that students are expected to master as part of the CBSE Class 6 curriculum.A thorough understanding of these concepts will help you answer similar questions confidently in your CBSE examinations. These topics are frequently tested in both objective and subjective sections of Mathematics papers. We recommend revising the relevant section of your textbook alongside practising these solved examples to build a strong foundation.
How to Approach This QuestionRead the question carefully and identify what is being asked. Break down complex questions into smaller parts. Use the terminology and concepts discussed in this chapter. Structure your answer logically — begin with a definition or key statement, then provide supporting details. Review your answer to ensure it addresses all parts of the question completely.
Key Points to RememberAlways show your working steps clearly.
Verify your answer by substituting values back into the equation.
Practice similar problems from the textbook exercises.
Memorise important formulae and their conditions of applicability.
Related Questions from Patterns in MathematicsQ1: Can you think of other examples where mathematics helps us in our everyday lives?
Q11: Now by imagining a similar picture, or by drawing it partially, as needed, can you say what is the...
Q12: Can you find a similar pictorial explanation for why adding counting numbers up and down, i.e., 1,...
Q13: By imagining a large version of your picture or drawing it partially, as needed, can you see what...
Q14: Which sequence do you get when you start to add the All 1’s sequence up? What sequence do you get...
Practice more questions from Patterns in Mathematics &mdash; Mathematics, Class 6 CBSE

Question 20

Try and redraw each sequence in Table 3 in your notebook. Can you draw the next shape in each sequence? Why or why not? After each sequence, describe in your own words what is the rule or pattern for forming the shapes in the sequence.

Accepted Answer

Answer:Regular Polygons:1.6 Relation to Number Sequences Figure it Out (Page No. 11-12)

Source: This question is from Patterns in Mathematics, Mathematics &mdash; Class 6, CBSE Board.
Key Concepts CoveredThis question tests your understanding of the following concepts from the chapter Patterns in Mathematics: Try, Redraw, Sequence, Table, Notebook, Next. These are fundamental topics in Mathematics that students are expected to master as part of the CBSE Class 6 curriculum.A thorough understanding of these concepts will help you answer similar questions confidently in your CBSE examinations. These topics are frequently tested in both objective and subjective sections of Mathematics papers. We recommend revising the relevant section of your textbook alongside practising these solved examples to build a strong foundation.
How to Approach This QuestionRead the question carefully and identify what is being asked. Break down complex questions into smaller parts. Use the terminology and concepts discussed in this chapter. Structure your answer logically — begin with a definition or key statement, then provide supporting details. Review your answer to ensure it addresses all parts of the question completely.
Key Points to RememberAlways show your working steps clearly.
Verify your answer by substituting values back into the equation.
Practice similar problems from the textbook exercises.
Memorise important formulae and their conditions of applicability.
Related Questions from Patterns in MathematicsQ1: Can you think of other examples where mathematics helps us in our everyday lives?
Q11: Now by imagining a similar picture, or by drawing it partially, as needed, can you say what is the...
Q12: Can you find a similar pictorial explanation for why adding counting numbers up and down, i.e., 1,...
Q13: By imagining a large version of your picture or drawing it partially, as needed, can you see what...
Q14: Which sequence do you get when you start to add the All 1’s sequence up? What sequence do you get...
Practice more questions from Patterns in Mathematics &mdash; Mathematics, Class 6 CBSE