Use Variables to Represent Unknown Quantities

Students write and interpret equations in which a variable represents an unknown quantity. They translate a real-world situation into an equation using a variable, choosing an appropriate letter and explaining what the variable represents.

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Grade 6 · Equations and Inequalities · question 1 of 3

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20 rungs. A star at the top.

n − 2 = 14, n =

How it is taught

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A variable is a letter that stands for an unknown number.

The letter is defined before it is used.

An expression uses that letter to show a calculation.

Read it: A letter for the number you do not know

"4 less than a number x" starts with x and takes 4 away. On a tape, 4 comes off the end of the x bar, and the part that is left is x − 4.

Give the unknown number a letter and a bar of its own.
Ask what happens to it: add, take away, multiply or divide.
Write it in that order: x − 4 is x with 4 taken away.

A letter stands for a number we do not know yet, so the expression works for any value of it.

Adding and multiplying can go either way around: x + 4 and 4 + x are the same.

Taking away and dividing cannot: x − 4 and 4 − x are different numbers.

Start with what you have, then do what the words say to it.

Writing 4 − x for "4 less than a number x".

Less than takes 4 away from x, so x comes first: x − 4.

Write "a number y divided by 6" as an expression. — y ÷ 6. y ÷ 6, not 6 ÷ y: y is the bar that is cut.

a + 8 = 20

Lena has some apples in her basket. She buys eight more. Now she has twenty apples.

We don't know how many apples Lena started with — that's the unknown number.

When a number is unknown, we can use a letter to stand for it. Let's pick the letter a.

We say: let a equal the number of apples Lena started with.

We start the equation with a — the apples she had at the beginning.

Then she bought eight more, so we add eight.

All of that equals twenty, the apples she has now.

Our equation reads: a plus eight equals twenty.

The variable a represents the unknown — the apples Lena started with.

Grade 6 · Naming an unknown with a letter

Variables let us write equations even when a number is unknown. Nice work!

What you see

While they climb, your page writes one true line to ask about tonight, and a short note each Sunday.

MayaGrade 3 · Mathematics

Did you know?

A chessboard has 64 squares — share them out between the 8 rows and each row holds exactly 8.

Today’s goal: 1 star — one skill mastered, every rung of its ladder climbed
Climbing now: Divide within 100

An example student.

MayaGrade 3 · Mathematics

Maya earned 2 stars this week — Interpret multiplication as equal groups, which took 6 answers over 3 days before its star landed 3 days ago and Multiply by 6, 7, 8 and 9. Next up: Divide within 100.

An example week.

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