Fundamental Concepts and Initial Applications

 Theory: Arithmetic expressions combine numbers using addition, subtraction, multiplication, or division to describe calculations clearly.
Example:
Question: Express Mallika’s weekly lunch expenses if she spends ₹25 daily from Monday to Friday.
Solution: Total expense = ₹25 × 5 = ₹125

Subtopic Name: Evaluating Simple Arithmetic Expressions
Theory: Arithmetic expressions have specific values obtained by performing the indicated operations.
Example:
Question: Evaluate the expression 13 + 2.
Solution: 13 + 2 = 15

Subtopic Name: Equality Sign Usage in Expressions
Theory: The equality sign denotes that two expressions have identical values.
Example:
Question: Confirm the equality: 24 ÷ 2 and 6 × 2.
Solution: 24 ÷ 2 = 12, 6 × 2 = 12, thus 24 ÷ 2 = 6 × 2

Subtopic Name: Expressing Numbers in Multiple Ways
Theory: A number can be represented by different arithmetic expressions using basic operations.
Example:
Question: Write three different expressions that equal 20.
Solution: 15 + 5, 40 ÷ 2, 4 × 5

Subtopic Name: Comparing Arithmetic Expressions
Theory: Expressions can be compared based on their evaluated values using greater than, less than, or equal signs.
Example:
Question: Which is greater: 10 + 2 or 7 + 1?
Solution: 10 + 2 = 12, 7 + 1 = 8, thus 10 + 2 > 7 + 1

Subtopic Name: Contextual Understanding of Arithmetic Expressions
Theory: Real-life situations provide context to arithmetic expressions, helping us interpret their meanings.
Example:
Question: Raja has 1023 marbles, gains 125 more. Joy has 1022 marbles, gains 128 more. Who has more?
Solution: Raja: 1023 + 125 = 1148, Joy: 1022 + 128 = 1150, thus Joy has more.

Subtopic Name: Visual Representation of Arithmetic Comparisons
Theory: Visual aids help clarify arithmetic comparisons by representing quantities physically or graphically.
Example:
Question: Represent visually: 113 – 25 compared with 112 – 24.
Solution: Both equal 88, visually indicating equal marbles remaining.

Subtopic Name: Expressing Daily Life Situations Mathematically
Theory: Arithmetic expressions can model daily life scenarios to solve practical problems.
Example:
Question: Write an expression for the amount spent by Ruby if she buys four dosas each costing ₹23 and tips ₹5.
Solution: Total amount = 4 × 23 + 5 = ₹97

Subtopic Name: Arranging Expressions in Ascending Order
Theory: Expressions can be ordered based on their evaluated numerical values.
Example:
Question: Arrange in ascending order: 67 – 19, 67 – 20, 35 + 25, 5 × 11, 120 ÷ 3.
Solution: Evaluations: 67 – 20 = 47, 67 – 19 = 48, 5 × 11 = 55, 120 ÷ 3 = 40, 35 + 25 = 60. Ascending: 120 ÷ 3, 67 – 20, 67 – 19, 5 × 11, 35 + 25

 Theory: Logical reasoning allows comparison of expressions without full calculation, saving time and effort.
Example:
Question: Without calculation, which is greater: 245 + 289 or 246 + 285?
Solution: Initially, 246 > 245, but 289 > 285 by a greater margin, thus 245 + 289 is greater.