# Math Vocabulary: Coefficient

## Math vocabulary word of the day: Coefficient**!**

Coefficient. What is it? How does it work in mathematics? In this video, we’ll show you the origins of coefficient along with how works. Our definition is student-friendly too! Why is it that we oft forget the importance of math vocabulary? In reading instruction, it is always included as part of the programming but often in mathematics instruction, it is breezed over.

Neurodiverse students especially need to be taught directly the roots, prefixes, and suffixes not only in everyday reading but in math vocabulary too! This is called Morphology.

**What Is Morphology?**

Morphology, a word of Greek origin, combines “morphe,” meaning form, and “ology,” meaning the study of. Morphing creates mental pictures of children’s toys such as LEGO™ bricks that click together to create new forms beyond a rectangular prism.

Morphology works in much the same manner, with students manipulating the parts of words to create new meanings or altered, but similar, meanings.

Below in this video, we’re studying the word ‘coefficient’.

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##### Tap for Video Transcript Here

coefficient

Co Comes from

Latin origin com – which means “together, with”

efficient

comes from

Old French and Latin meaning “efficient, producing, with little waste”

What do you think coefficient means? Let’s look at other words that have co- in it

Co-work

Big projects are easier when we co-work with others.

coordinate

Planning a big party is easier if we co -ordinate with other people.

inefficient

Here’s some co-working that is inefficient

(count to 3 in your head)

Notice all the waste! This is the *opposite* of efficient.

What do you think coefficient means?

Co-efficient means to work together with little waste. Let’s see how it works in mathematics

Here we have six pencils. Without a coefficient, writing a number expression to help us talk about the quantity of pencils would be so painful and wasteful of our energy!

Let’s make this more efficient. The letter p is a variable. It’s short for pencil in this example.

hmmm….I bet we can do even better.

We can see that we have 6 pencils. Let’s put them together.

That’s better! We have six pencils and it’s written as efficiently as we can write it: 6p

In mathematics, this is what a coefficient is!

It’s the number in front of the variable.

Here I have 5 cookies plus 4 sandwiches. Let’s use our coefficient!

5c plus 4s.

I have 6 triangles plus 2 hexagons plus 3 diamonds. Let’s apply our coefficients!

6t plus 2h plus 3d

We can use this with variables too.

X plus x plus x plus y plus y

Is there a more efficient way? How can we make this have little waste? Combine our x’s and y’s!

Much better! 3x plus 2y

Coefficient – work together with little waste.