Identify Parts of an Algebraic Expression

Students identify and name the parts of an algebraic expression: terms, coefficients, constants, and factors. They describe an expression such as 2(8 + 7) as a product of 2 and (8 + 7) and explain what each part represents.

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Grade 6 · Expressions and Properties · question 1 of 3

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20 rungs. A star at the top.

In this expression in y, find the term with no variable. Ring it.

5y + 7

How it is taught

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An expression is built from terms.

A coefficient multiplies a variable; a constant stands alone.

Read it: The parts of an expression

6k + 11 has 2 terms: 6k and 11. The term with no letter is the constant, 11. The number that multiplies k is its coefficient, 6.

Split the expression at each + or −: each piece is a term.
Find the term with no letter: that is the constant.
Find the number right before a letter: that is the letter's coefficient.

6k means 6 × k, so 6 belongs to k: it is a coefficient, not a constant.

A constant never changes, whatever number k stands for.

A letter on its own has a coefficient too, even where none is written.

A constant has no letter; a coefficient multiplies one.

Circling the 6 of 6k as the constant.

6 multiplies k, so it is the coefficient of k. The constant is 11, the term with no letter.

In 15a + 18 + 14w, what is the constant? — 18. 18 is the term with no letter; 15 and 14 are coefficients.

3x + 5

An algebraic expression mixes numbers, letters, and operations. Let's pull one apart and give every piece its real name.

Here's our expression: three x plus five.

First we find the terms. Terms are the parts separated by plus or minus signs.

Three x is our first term.

And five is our second term. So this expression has two terms.

Look at the three in front of x. That's the coefficient — it tells us we have three x's.

The x is the variable. It's a letter that stands for an unknown number.

The five sits alone with no variable. That makes it a constant — its value never changes.

Because three x means three times x, the factors of that term are three and x.

Grade 6 · Terms, coefficients, variables, and constants

Two terms, one coefficient, one variable, one constant. You can name every part of an expression!

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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Standards

CCSS.6.EE.A.2

Write, read, and evaluate expressions in which letters stand for numbers

CCSS.6.EE.A.2b

Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient); view one or more parts of an expression as a single entity

Grade 6

Quoted from the Common Core State Standards.

Where this sits

Comes after

Write Algebraic Expressions from Word Phrases

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What a star here means

A star here is the top of a twenty-rung ladder, in four blocks of equal length — three of facts and one of the skill used in a real question — where a right answer climbs one rung and a wrong one drops back to the start of the block, never below it. The star is kept for good. How we grade

All of Grade 6

This is one rung of 46 in Grade 6 mathematics, in the order they build on each other.

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