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n

Variables in Context
Letters That Stand for Numbers

Learn how a letter like \( n \) can stand for a number we do not know yet, and how to turn a real story into a math sentence.

ISEE Lower Level: Quantitative Reasoning

What Is a Variable?

A variable is a letter that stands for a number. We use it when we do not know the number yet, or when the number can change.

n a letter stands for ? a number

Why Do We Use Letters?

Stories often have a number we do not know yet. Instead of leaving a blank, we use a letter to hold its place. Then we can write a clear math sentence about the story.

Unknown amount
"Maya has some marbles." We do not know how many, so we write \( m \).
Changing amount
"The number of students" can change each day, so we call it \( s \).

From a Story to a Letter

"Sam has some stickers." Let \( s \) = number of stickers

The Big Idea

"3 more than a number \( n \)" \( n + 3 \)

Words That Mean Operations

Word in the StoryOperationWith \( n \)
more than, sum, totaladd\( n + 5 \)
less than, fewer, take awaysubtract\( n - 5 \)
times, groups of, doublemultiply\( 2 \times n \)
shared equally, split intodivide\( n \div 4 \)

Expression vs. Equation

Expression
A math phrase with no equals sign. It just describes an amount. Example: \( n + 4 \).
Equation
A math sentence with an equals sign. It says two amounts are the same. Example: \( n + 4 = 10 \).

How to Build a Math Sentence

1
Find the unknown. What amount do we not know? Give it a letter.
2
Write what the letter means. Such as "Let \( c \) = number of cookies."
3
Spot the action words. "more," "fewer," "times," "shared" tell you the operation.
4
Write the expression or equation using the letter and the operation.

Example 1: Marbles

Story: Ben has some marbles. His friend gives him 6 more. Write an expression for how many marbles Ben has now.

m marbles + 6 more \( = m + 6 \)

Example 2: Equal Groups

Story: There are some bags. Each bag holds 4 apples. Write an expression for the total number of apples.

b bags × 4 each \( = 4b \)

Example 3: An Equation

Story: Lily has a number of stamps. After she buys 5 more, she has 12 stamps. Write an equation.

\( s + 5 \) = \( 12 \)

Common Mistakes

✕ Mixing up the order
"5 less than \( n \)" is \( n - 5 \), not \( 5 - n \). Read carefully!
✕ Forgetting the meaning
Always write what your letter stands for, like "Let \( c \) = cookies."
✕ Wrong operation
"Groups of" means multiply, not add. Watch the action words.

Quick Summary

Story PhraseMath
A number \( n \) plus 7\( n + 7 \)
4 fewer than \( n \)\( n - 4 \)
Triple a number \( n \)\( 3n \)
\( n \) shared by 2 people\( n \div 2 \)
\( n \) and 3 equals 10\( n + 3 = 10 \)

Question 1 of 5

Tom has some toy cars. He buys 8 more. If \( t \) is the number he started with, which expression shows how many he has now?

Question 2 of 5

Which expression means "5 less than a number \( n \)"?

Question 3 of 5

There are \( p \) plates. Each plate holds 3 cookies. Which expression shows the total number of cookies?

Question 4 of 5

Anna has some shells. After she finds 4 more, she has 15 shells. If \( h \) is her starting number, which equation fits?

Question 5 of 5

A pizza is cut so that \( z \) people share it equally. Which expression shows each person's share if there are 8 slices?

You've Got It!

1
A variable is a letter that stands for an unknown or changing number.
2
Action words tell you whether to add, subtract, multiply, or divide.
3
An equation uses an equals sign to say two amounts are the same.
4
Always write down what your letter means before you solve.

Great Work, Mathematician!