Number Play Class 7 Notes

Number Play Class 7 Notes

Number Play Class 7 Notes

Stick Figure Cutouts

Assign numbers to some given stick figures Cutouts, arranged in some order, as per their heights Paste stick figure cutouts according to a given number arrangement

Parity of Numbers

Even : Writing expression for even numbers 2n

Odd: Writing expression for odd numbers (2n -1)

Parity of sum of some given odd and even numbers Parity of product of some given odd and even number

Magic Square

Magic sum

Constructing 3 × 3 magic squares for 9 given consecutive numbers

Constructing 3 × 3 magic squares with a given magic sum

With 9 consecutive numbers With any 9 numbers

Filling grids

Filling 3 × 3 grids with numbers with the given sum of each column and each row.

Cryptarithm (Digits in disquise)

Finding the values of some digits in problems involving sum and product of two or three numbers

Virahanka Sequence 1, 2, 3, 5,...

Rhythm as a sequence of beats representing a sum of short syllable (1 beat) and of long syllable (2 beats) in magic.

Numbers of this sequence appears in nature, art, music, etc.

Finding a given term the Virahanka sequence.

CHAPTER AT A GLANCE

Important Terms and Their Meanings

1. Rhythm : A rhythm is a sequence of beats that can be represented as a sum of short syllables (1 beat) and long syllables (2 beats).

2. Virahanka-Fibonacci Numbers

1. The sequence 1, 2, 3, 5, 8, 13, 21, 34, ... is known as the Virahanka-Fibonacci sequence.
2. These numbers appear in nature, art, and mathematics.
3. Real-world example : The number of petals on a flower often follows this sequence.

Applications of Fibonacci Numbers

1. Fibonacci numbers are used in computer algorithms, especially in sorting and searching.
2. They appear in biological settings, such as the arrangement of leaves on a stem.

3. Magic Squares and Their Properties

1. A magic square is a grid where the sums of numbers in each row, column, and diagonal are equal.
2. In a 3 × 3 magic square using numbers 1-9, the magic sum is 15.

4. Magic Sum : The magic sum is the constant sum that is obtained when adding the numbers in any row, column or diagonal of a magic square.

5. Consecutive Numbers : These are numbers that follow one another in order without any gaps (e.g., 1, 2, 3, 4).

6. Cryptarithm : A type of mathematical puzzle where the digits in a numerical equation are replaced by letters. Each letter represents a unique digit.

7. Alphametic : A specific type of cryptarithm where the letters represent digits in an arithmetic equation. For example, in the equation (T + T + T = UT), the letters T and U must be replaced by digits to make the equation true.

8. Syllable : A unit of language that typically consists of a vowel sound, with or without surrounding consonants.

Picking Parity

1. Parity:

Even Numbers: Numbers that can be divided by 2 without a remainder (e.g., 0, 2, 4, 6,...).

Odd Numbers : Numbers that cannot be divided by 2 evenly (e.g., 1, 3, 5,7,...).

The sum of even numbers is always even, and the sum of odd numbers may be even or odd.

2. Sum of Numbers :

The sum of an odd number of odd numbers is odd.

The sum of an even number of odd numbers is even.

The sum of an even number of even numbers is even.