Grade 6 (age 11-12)

grade 6 Variables and Expressions

Writing a number that is unknown or that can change as a letter such as x or y, instead of □, lets one expression cover many cases. x + 3 is the number you get by adding 3 to x, and when a number multiplies a letter the × is left out, so 2 × x is written 2x. If each bag holds 6 candies, x bags hold 6 × x = 6x candies: when x is 4 there are 24, and when x is 10 there are 60. In the picture, change the value of x and watch how the values of x + 3 and 2 × x change with it.

Expressions with letters

📦 Letters for unknown numbers

①A number we do not know yet is written with a letter such as x or y instead of □

②x + 3 means "3 added to x", and 2 × x means "2 times x"

③With the starting value in the picture, x = 5, we get x + 3 = 8 and 2 × x = 10

④Each time x goes up by 1, x + 3 goes up by 1 and 2 × x goes up by 2

Value of x5

From sentences to expressions

✏️ From sentences to expressions

①"5 more than a number" is x + 5

②"3 times a number" is 3 × x, or 3x without the ×

③"2 less than a number" is x - 2

④"The number of candies in x bags of 6" is 6x

⑤In a product of a number and a letter, the number goes first: write 3x, not x × 3

Summary

Expressions with letters

x + 3, 2x, x - 5

Expressions that use letters for unknown or changing numbers

Value of an expression

When x = 4, 2x + 1 = 9

Put a number in place of the letter and calculate to get the value

🎯 Key points

①Unknown or changing numbers are written with letters such as x and y

②In a product of a number and a letter, leave out ×: 3 × x is written 3x

③Putting a number in place of a letter and calculating is called substitution, and the result is the value of the expression

④When turning a sentence into an expression, first find which operation words like "more than", "times" and "less than" stand for

⑤Expressions with letters are the starting point for the equations learned in middle school

Examples & Unit Review

Example 1

Each bag holds 6 candies and there are x bags. Write an expression for the total number of candies.

The number of candies is the number in one bag × the number of bags, so it is 6 × x.

Leave out × and put the number first: 6x candies.

▸ 6x candies

Put a number in for x to get the actual count: with 4 bags, 6 × 4 = 24 candies.

Example 2

When x = 4, what is the value of 2x + 1?

Put 4 in place of x: 2x + 1 = 2 × 4 + 1.

2 × 4 = 8, and 8 + 1 = 9.

▸ 9

Set x to 4 in the picture and 2 × x = 8 appears; adding 1 gives 9, the value of 2x + 1.

Unit Review

When x = 3, what is the value of 5x - 2?

①13

②15

③10

④6

▸ ① 13

Put 3 in place of x: 5x - 2 = 5 × 3 - 2.

5 × 3 = 15, and 15 - 2 = 13.

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Ratio & Rate

Last updated 2026-10-17