Grade 6 (age 11-12)

grade 6 Variables and Expressions

Variables and Expressions

Letters like x and y stand for unknown numbers. In x + 3 you add 3 to a number, and the times sign is dropped, so 3 times x becomes 3x. Just as x candies at 500 won each cost 500x won, one line holds an unset quantity. Move the slider to change x and the results of x + 3 and 2 times x shift.

Expressions with Letters

📦 Unknown Numbers as Letters!

①Use letters x, y instead of □ for unknown numbers

②x + 3 means "add 3 to some number"

③Substitute a value to compute the result

Value of x5

Building Expressions

✏️ Sentences to Expressions

①"5 more than a number" → x + 5

②"3 times a number" → 3 × x = 3x

③"a number minus 2" → x - 2

④Omit ×: 3 × x = 3x

⑤x candies at 500 won each → 500x

Summary

Variables & Expressions

x + 3, 2x, x - 5

Expressions with unknown numbers as letters

Value of Expression

When x = 4, 2x + 1 = 9

Substitute a number into a letter to evaluate

🎯 Key Points

①Express unknowns with letters like x, y

②Omit ×: 3 × x → 3x

③Substitute to evaluate

④Practice translating sentences to expressions

⑤Foundation for middle-school equations

Examples & Unit Review

Example 1

Write an expression for the price of x candies that cost 500 won each.

Multiply the price of one by the number, so write 500 × x.

The multiplication sign × can be omitted, so write 500x won.

▸ 500x won

A letter like x stands for a changing number, and the multiplication sign is omitted.

Example 2

Find the value of 2x + 1 when x = 4.

Substitute 4 for x: 2 × 4 + 1.

8 + 1 = 9.

▸ 9

Replacing a letter with a number to find the value is called substitution.

Unit Review

What is the value of 5x - 2 when x = 3?

①13

②15

③10

④6

▸ ① 13

Substitute 3 for x: 5 × 3 - 2.

15 - 2 = 13.

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Decimal Division

Ratio & Rate