maths vocabulary homework

5 Fun activities for teaching math vocabulary

• March 8, 2024
• Rebekah Bergman
• Education Tips & Tricks

Why is teaching math vocabulary important?

Success in math isn’t only a matter of numbers; math vocabulary plays a huge role too! For students to gain true mastery of math, they need to become fluent in the language of mathematics. Becoming fluent means building a vocabulary that includes words from “addend” to the “y-axis,” understanding those words, and then being able to use them and apply them to new scenarios. Plus, a word can have one meaning inside the math classroom and an entirely different one outside of it, think of “odd” and “plane.” Math vocab also includes words and phrases that are also symbols that students need to learn how to recognize, read, and use (e.g., ℼ and √).

With many skills and standards to master, it can be tricky for math teachers to find time and opportunities to devote to vocabulary instruction . Keep reading to explore five fun ideas to teach math vocabulary.

Flocabulary for math vocabulary

At Flocabulary , vocabulary is key to our lessons and activities. Our belief in the power of vocabulary informs our approach to learning across subjects. Our hip-hop songs and engaging videos are centered around vocabulary and threaded through all the activities in each lesson. Here’s a mashup of some of the math videos Flocabulary has to offer!

Captivate students and make learning experiences memorable and interesting through Flocabulary.  Teachers can sign up below to access video lessons and activities shared in this blog post. Administrators can contact us below to learn more about the power of Flocabulary Plus.

5 Fun activities and tips for teaching math vocabulary

1. incorporate vocabulary into number talks, do nows, and your other rituals and routines..

Vocabulary instruction doesn’t have to occur in an isolated vacuum; researchers say it shouldn’t be ( File, Kieran & Adams, Rebecca, 2010 )! Exposing students to math words as they are used authentically in context is an effective strategy to build their vocabulary. It can be relatively simple to do this: you can use your existing classroom rituals and routines–like Number Talks or Do Nows–as opportunities to integrate vocabulary learning.

Exposing students to a word will not be enough to grow their vocabulary. Repetition and context are key.  As a word is used, take a moment to examine it with students. How is that vocabulary word being used in this problem or example? If the vocab word is relatively new to your students, you might provide direct instruction about its meaning and usage. If it’s a word students have seen many times already, you might pause for a quick check for understanding to reinforce the meaning and usage.

Here are some specific vocabulary activities you can implement into your classroom routines:

• Make a game of spotting the vocabulary. Ask students to keep an eye out for their math vocabulary words throughout the class. Consider creating a gesture or other signal that students can make if they see or hear one of the words used in a Number Talk or Do Now. Turn it into a friendly competition and offer prizes. Keep it easy and quick for you to implement, and this game can become its own vocabulary ritual that will foster engagement and keep the learning going and growing. 
• Use Flocabulary to spot vocabulary words in a song. Flocabulary creates standards-aligned hip-hop infused videos for K-12 subjects. Every Flocabulary lesson includes 3-10 vocabulary words. Pause the video, or have students raise their hand for you to pause the video, whenever a vocab word is used. Look at the lyrics and visuals on the screen that represent the word or phrase, and discuss the vocabulary before you continue playing the song!

2. Have students speak, write, and draw their math vocabulary words.

Math teachers know the importance of manipulatives for gaining first-hand experience with abstract mathematical concepts. Similarly, students need opportunities to practice speaking, writing and drawing new words to fully incorporate those words into their vocabulary and make them their own.

Here are a few activities that provide students with this opportunity:

• Have students apply the word to a new scenario by writing a sentence or creating their own example problem.
• Ask students to draw a visual representation of a word.
• Pair students up or put them in small groups to have conversations using their vocabulary.
• Use a Frayer model graphic organizer . This typically includes four boxes for each vocabulary word with space for students to create a definition, list examples, list non-examples, and describe features or facts.
• Assign students Flocabulary’s Vocab Cards. Inspired by the Frayer model, Vocab Cards feature a definition in student-friendly language, words, parts of speech, an image, synonyms, antonyms, and an example sentence. There is room for students to practice writing an example and drawing the word, too. Assign these Vocab Cards and have students share their work, or you can complete them front-of-class together.

3. Have students keep a journal with examples and definitions of their vocabulary words.

In a vocabulary journal, you can have students log any new words they have encountered incidentally while solving word problems, the vocabulary words you introduced, or provided direct instruction around, or a combination of both!

How much and what you have students record for each word is up to you! But again, knowing the importance of exposing students to a word in multiple contexts, you might have students create a running log with space for additional examples of the word used in context as they come across them. Having a journal is especially useful during test prep season because students can refer back to what they’ve learned.

Here’s a breakdown of how students can create a vocabulary journal:

• Adding words to the journal will help students commit the new vocabulary to memory. For each entry, students can write the word, a predicted definition from context, the real definition they find, and examples.
• Students can use the journal to self-assess. Have them set up the page with the words on one side and the definitions on the other. When they fold the page in half, they can quiz themselves!
• Use Read & Respond to record new words in their journal. After students watch a Flocabulary video, have them complete the Read & Respond accompanying activity. Instruct them to write down any additional vocabulary words from the text passages in their journal.
• Seeing this journal grow can be hugely motivational , especially for students who might struggle in other areas of mathematics. Over time, the vocabulary journal will also serve as a comprehensive and living record of their learning.

4. Gamify vocab instruction for added fun, competition, and collaboration.

Earlier, we discussed ways to create a game for math vocabulary words used throughout class time. You can also play games with students using the math terms in new contexts to test their knowledge.

Gameplay can be one round or many. Educational games can be especially significant when students need to reset their energy level or get up and move a bit before they’re ready to sit still or quietly focus on a different kind of task. It also creates opportunities to build classroom community through friendly competition and student collaboration. These games do not take much time away from the other math learning and practice. They also don’t require many materials or time to set up.

Here are some vocabulary games and activities students can do:

• Charades: Students can work in partners or teams to act out a vocabulary word and have their teammates guess it correctly.
• Pictionary: Students can draw a vocabulary word and have their teammates guess it correctly.
• Fil-in-the-blanks: Students can come up with a fill-in-the-blank sentence for their teammates to compete or race to identify which vocab word is being defined or described.
• Flocabulary’s Vocab Game : In this game, students complete fill-in-the-blank sentences and match definitions, images, synonyms, and antonyms with the right vocabulary word. Correct answers add new instruments to build a Flocab beat! By the end of the game, students will be able to listen to a beat they’ve created by completing the fill-in-the-blanks. Flocabulary’s Vocab Game is available in every lesson.

5. Allow room for students to get creative!

“Creating” is at the very top of Bloom’s Taxonomy and is considered to require higher-order thinking skills. While most tips on this list won’t take much time to implement, this one can take longer, but we feel the investment can be well worth the time. With that in mind, you can consider a creative vocab assignment.

You can use vocabulary activities to encourage freedom, expression, and creativity. After all, we know that students can do a lot more than write sentences and draw pictures. Often, they crave opportunities to engage more creatively with their learning.

Here are a few ways to get creative with vocab instruction with students:

• Create a picture book or other visual that could teach younger students about one or more math vocab terms while telling a story.
• Create and perform a skit that uses math vocab in a real-world context. 
• Create a poem that uses examples or definitions of math vocabulary words.
• Use Lyric Lab to have students create their own songs using their vocabulary words. Lyric Lab is a rhyme-writing tool available in every Flocabulary lesson. It includes a rhyming dictionary and beats that students can use to help them write their rap or poem. It also consists of a word bank that keeps track of which vocabulary words they’ve used. You can have students write songs in Lyric Lab and perform them to celebrate the end of a unit!

Start using these tips in your math classroom

Across all subject areas, vocabulary is essential to comprehension. It’s estimated that students need to know more than 90% of words in a text to understand it ( Schmitt et al., 2011 ). In math, this means that students need opportunities to learn the language of math to understand the problems they are solving. Fortunately, there are lots of fun and easy-to-implement ways you can build students’ math vocabulary, and Flocabulary’s videos and lesson activities can help!

Captivate students and make learning experiences memorable and interesting through Flocabulary.  Teachers can sign up below to access video lessons and activities shared in this blog post. Administrators can contact us below to learn more about the power of Flocabulary Plus.

Interested in reading more about this topic? Check out this blog post: Tips for math instruction with Flocabulary

• How to enhance your elementary STEM curriculum
• Test Prep activities and video lessons from Flocabulary

Common Math Vocabulary

Become a mathematical master by learning these common vocab terms! 

Author Chal Emery

Expert Reviewer Jill Padfield

Published: August 24, 2023

• Key takeaways
• Math has its own set of specialized “terms” – Learning them can make your child’s math experience much easier. 
• Practice, practice, practice – It’ll take time to get used to using these new terms. Practice is key to making them stick—both for you and for your child.
• Try flashcards or virtual quizzing tools – Both you and your child can benefit from frequent review using tools like vocabulary cards or quiz tools.

Table of contents

Common math vocabulary

Math can be confusing—but it doesn’t have to stay confusing! Mastering the “language of the land” can help keep your homework sessions simple, painless, and even more effective, fully immersing your student in their learning process. 

Below, we’ve rounded up the most common mathematical terms that you’ll encounter in grade levels K-8th and beyond, preparing your learner to thrive in higher-level educational settings.

Read on to learn common math words and their related definitions via our handy list: 

• Abacus — An abacus is a tool that usually features beads or balls on bars, which can slide across to “count” an item or value. 
• Acute Angle — These are angles that measure between 0 and 90 degrees on a protractor, often creating very “slim-looking” angles like you’d see in an acute isosceles triangle. This term covers concepts that your learners will encounter in geometry. 
• Addend — This term defines any number that’s being added with others. 
• Algebra — Algebra is a specific area of math study that swaps known values with variables, usually shown by an alphabetical letter. Your student might start math lessons around algebra topics in middle school and beyond. 
• Bar Graph — Graphs like these represent values in a data set using “bars,” making them easy to visualize. Kids often find that they are the easiest to use to reference a specific data point or set on the x-axis and y-axis of a graph. 
• BEDMAS — A handy alternative to PEMDAS, this acronym stands for Brackets, Exponents, Division, Multiplication, Addition, and Subtraction.
• Capacity — This term defines what volume of substance something can hold in itself, and is often referenced in geometry or higher-level math. 
• Centimeter — A centimeter is a metric measurement, and is about one-third of an inch in length. 
• Circumference — This term defines the total distance around a circle. 
• Common Factors — Students often encounter common factors early on, identifying factors that divide cleanly into two separate numbers. 
• Constant — Constants can be found in algebra and higher-level math, and define unchanging numbers or values. 
• Congruent — This term defines shapes that have the same shape and size. 
• Decimal — This is a mathematical mark that looks like a point (or dot), indicating a partial number or value.
• Denominator — This is the value or number that’s located at the bottom of a fraction, directly underneath the division bar. 
• Difference — This is a special term given to the final answer of a subtraction problem. 
• Digit(s) — Digits are numbers that fall on or between 0-9 in the number line. For example: The number 52 includes two digits, five (5) and two (2).  
• Divisor — This is a number that slices a number into equal parts, and is used in division functions. It sits outside of the bracket when the student is doing long division. 
• Dividend — This is the number that is being divided into equal parts during a division operation. It is located inside the division bracket. 
• End Point — An end point is the exact location where a line ends. It is indicated by a dot. 
• Equilateral — This term defines a shape in which all sides are equal in length. 
• Even Number — An even number is a number that can be divided by two. 
• Factor — A factor of a number is a number that can divide the given number evenly. For example: Factors of 4 include 2, 4, and 1. (1 x 4, 2 x 2) 
• Factoring — This is an operation that occurs when a student is breaking numbers down into their most basic components. 
• Geometry — This is an area of study in math that focuses on shapes, angles, lines, and logical application of each. 
• Greatest Common Factor — The greatest common factor is the largest number that is common to a factorial set that can divide into both cleanly. 
• Hypotenuse — The hypotenuse is the longest side on a right-angled triangle. 
• Improper Fraction — This term defines a fraction that is “top heavy” (meaning that the top number is larger than the denominator, or bottom number) or that is equal to its denominator. An example of an improper fraction in action would be 250/3. 
• Inequality — Inequalities are housed in equations that show values that are less than or greater than each other. They may also be noted as equal or unequal to each other. 
• Integers — This term defines whole numbers that are either negative or positive. It also includes the value of zero (0) in its definition. 
• Kilometer — A kilometer is equal to 1000 meters in length. For reference, one meter is about 3 feet. 
• Like Terms — Terms that are like share the same variable, as well as any associated powers or exponent notations. 
• Logic — This is a term that’s used synonymously with critical thinking or reasoning. 
• Median — This is defined as the middle number or value in a series. You can find it by putting your values in order from the least to greatest and finding the middle number. 
• Midpoint — The midpoint is the point exactly in the middle of a line segment. It can also be a point in space that is exactly in the middle of two other set points. 
• Mean — This is the average of a set of values. It can be found by adding up all numbers in a given series and dividing the sum (or the result) by the number of values present. 
• Mode — The mode of a set is the value(s) that occur the most often. 
• Multiplication — Multiplication is a math operation that repeats the addition process a certain number of times. It’s denoted by an “x” between two or more values (i.e., 4 x 4). 
• Numerator — The numerator is opposite the denominator in a fraction; sitting at the very top of the bar. 
• Odd Number — An odd number is any number that can’t be evenly divided by two. 
• Operation — This term defines any sort of processes related to division, subtraction, addition, or multiplication. 
• Order Of Operations — This term defines the set of rules that is required to fully solve a mathematical equation. It follows the BEMDAS process (as above) and is also known as PEMDAS (which is the same as BEMDAS, swapping B for brackets for P for parentheses). 
• Pentagon — This term defines a shape with five sides and five angles. 
• Percent — A percent is a “part of 100,” which is often converted to a fraction or ratio. It’s indicated using a percentage mark (%). 
• Product — This defines the final answer of a multiplication problem. 
• Proper Fraction — A proper fraction has a larger denominator (bottom number) and a smaller numerator (top number)
• Quotient — A quotient is the final answer of a division problem. 
• Ratio — A ratio is a term that defines a relationship between two separate values. It can be converted to a percentage, fraction, or decimal. 
• Repeating Decimal — This is a value that is a part of a whole, in which the digits repeat into eternity. For example: 3.555555…
• Right Angle — A right angle is an angle that measures exactly 90 degrees at its vertex. 
• Subtraction — This is a math operation in which a value is taken away from another value, resulting in the difference. For example: 4-2 = 2. 
• Symmetry — Symmetry occurs when two halves of a shape are a “perfect match” and mirror each other. 
• Unit — A unit can be used generally, defining a measurement of any type (such as centimeters or millimeters). 
• Variable — This term defines any letter or symbol that is in place of a number. For example: In x + 3 = 10, the variable is x, which stands in place of the value that would “solve” the equation (which is 7, in this case). 
• Weight — This term defines how heavy or light something is. 
• X-Axis — This axis runs horizontally (sideways or side-to-side) on a graph. 
• Y-Axis — This axis runs vertically (up and down) on a graph.
• Yard — This is a measurement unit that equates to exactly 3 feet.

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Frequently asked questions

There are many different ways that your students can learn math words for their next level of learning. Math vocabulary cards, a visual math word wall and virtual quizzing tools are popular options, for example. Your teacher can also be a helpful resource if you’re looking for tips on retention and memorization. 

This property is essential to your student’s understanding of addition. It dictates that no matter how values are grouped in an addition problem, the sum will be the same. For example: 2 + 1 + 3 = 6, just as 3 + 2 + 1 = 6. The associative property is often one of the first things your learners will be presented with as they begin to learn about addition and sums. 

Word problems are math problems that present you or your learner with a hypothetical scenario to solve using recently-learned math concepts.

An obtuse angle has an angular measurement that’s between 90-180 degrees. It can be measured using a protractor.

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Chal Emery graduated from the University of North Carolina at Chapel Hill with a Bachelor’s in Global History and Political Science. Outside of writing, he enjoys long drives through spectacular country, and spending time getting lost in a decent film.

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Math Vocabulary for Beginners: Essential Terms and Definitions

Mathematics can be an intimidating subject for beginners, especially when it comes to understanding the vocabulary used in math problems and equations. However, having a solid grasp of math vocabulary is crucial to building a strong foundation in the subject. In this article, we’ll explore some of the key terms and definitions that beginners should know.

Number Vocabulary:

• Whole numbers: Natural numbers (1, 2, 3…) and 0.
• Integers: Whole numbers and their negative counterparts.
• Rational numbers: Numbers that can be expressed as a ratio of two integers, such as fractions.
• Irrational numbers: Numbers that cannot be expressed as a fraction or decimal, such as the square root of 2.

Algebra Terms:

• Variables: Symbols that represent unknown quantities in an equation.
• Coefficients: The numerical factor of a term in an equation, such as 3x (the coefficient is 3).
• Constants: Numbers that are fixed in value and do not change in an equation.
• Expressions: Mathematical phrases that include numbers, variables, and operators, such as 2x + 4.
• Equations: Mathematical sentences that show two expressions are equal, such as 2x + 4 = 10.

Geometry Vocabulary:

• Point: A location in space with no size or shape.
• Line: A collection of points that extends infinitely in two directions.
• Angle: The measure of the space between two intersecting lines or planes.
• Triangle: A polygon with three sides and three angles.
• Circle: A geometric shape consisting of all points equidistant from a given point, called the center.

Calculus Terms:

• Derivative: The rate of change of a function with respect to its input variable.
• Integral: The sum of an infinite number of infinitesimally small values, used to calculate area and volume.
• Limit: The value that a function approaches as its input variable approaches a certain value.
• Function: A mathematical relationship between two variables, where each input has a unique output.
• Differential Equation: An equation that relates an unknown function to its derivatives.

Probability and Statistics Terms:

• Probability: The likelihood of a certain outcome occurring, expressed as a fraction or percentage.
• Random Variable: A variable whose possible values depend on a random event or outcome.
• Mean: The average value of a set of numbers.
• Median: The middle value in a set of numbers.
• Standard Deviation: A measure of the amount of variation or dispersion of a set of numbers.

Conclusion: While this list of math vocabulary terms is by no means exhaustive, it provides a solid foundation for beginners to build upon. By understanding these key terms and definitions, beginners can begin to approach math problems with more confidence and clarity. Remember, practice makes perfect, so don’t be afraid to dive in and start using these terms in your own math work!

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Teaching Math Vocabulary that Sticks

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For math to be accessible to students, math vocabulary must be taught! Let’s talk about teaching math vocabulary in a way that sticks!

Let’s see how important math vocabulary is to understanding and solving this problem. Could you solve this problem? I covered up a vital piece of information needed to solve this problem to emulate what a student might experience without knowing the vocabulary necessary to solve.

Model Using the Math Language

If we want students to use the words we are teaching, we need to practice using it ourselves. Vocabulary requires exposure. Using the words as frequently as possible, students will hear  the words as frequently as possible, increasing their comfort with the words.

If a student uses a vocabulary word incorrectly, then make sure to correct it. “Bottom number” is a “denominator.”

As teachers, we can jump ahead to the solving of a problem, but using the STAAR test question above, we should start by asking students – “What does surface area mean?”

Annotating word problems or questions is also a way to practice math vocabulary. Anytime we read the word “percent,” we wrote “/100” to remember that percent meant “out of 100.”Let’s look at another math vocabulary rich problem: 

Here are some questions you can ask to practice that math vocabulary. 

• What makes a number an integer?
• Is -53 an integer?
• What does absolute value mean?

Get Ahead By Previewing Vocabulary

If you are a Texas teacher, you can use this excellent document that will show you which vocabulary words are new to the grade level as well as words from previous grade levels. This is a great place to start for a word wall. 

• 6th grade 

Previewing the vocabulary for an upcoming unit is a great place to start when teaching math vocabulary. In my experience, students copying definitions killed the energy in class, but offering students a “kid-friendly” definition that you referenced daily and had them practice (using some of the ideas in this post) was much more successful. 

Display a Word Wall

Update 7/28/2023: maneuvering the middle now has a middle school math + algebra 1 word wall..

As you can see in the video below, our Word Wall includes 190 essential math terms, their clear-cut definitions, and their visual representations.

We’ve included Spanish translations for all terms and definitions, ensuring a supportive and accessible learning experience for English Language Learners.

They were designed to be minimal prep and flexible to customize the formatting to suit your students’ unique needs.

Word walls are a vital part of any math classroom. You can learn more about word walls in this post .  If students are taking a brain break and staring off into space, they are likely staring at some math content. To have the most useful word wall, make sure words include a short definition, picture, and can be visible from the furthest spot in the classroom.

My word wall was constantly building. The wall started with 3 words in unit 1 and eventually built to just under 100 by the end of the school year. I purchased my sixth grade TEKS word wall here . 

Pointing out the addition of new words to the word wall and where students can access help if needed lets students know that the word wall is for their use! It is meant to be used!

Provide Opportunities to Use the Words in Context

When asking students questions, prompt the response to include vocabulary in their answer. This is the lowest lift, but it is so effective! Use a turn and talk and a cold call to get every student responding.

• Instead of: how do we divide fractions?
• Try: Using the word reciprocal, explain how we divide fractions.
• Instead of: What sides of the triangle are congruent?
• Try: Using the word congruent, describe what you notice about the sides of this triangle.

I read that you need to use a new word about 10 times before you remember it!  Teaching math vocabulary is something that you build into your instruction.

Fun Practice for Spiraling Definitions

To keep vocabulary and definitions fresh, use any of these activities in the last few minutes of class:

• Flyswatter Games – If you want students to get familiar with your word wall, use the Flyswatter Game.  This is a very engaging review game. If you are like me and don’t bother to cover up anything in your room before a test, this will help remind students where to look when they are stuck.  Two students face off with fly swatters in hand.  You give them a prompt such as “2, 4, 6, 8” are examples of ______” And the first student to swat the word ‘multiples’ earns their team a point.
• Flashlight Game -This game is great for those last few minutes of class as a sponge activity.  Turn off the lights and use a flashlight to point to a word on the wall.  Students can then shout out an example, the definition, or even a counter-example. 
• Guess the Word – I played this in a PD, and immediately implemented it in my classroom. One student stands with the white board behind them facing the rest of the classroom. You write (or have a slide deck prepared) a vocabulary word behind the student. Students in the classroom take turns giving the students hints to what vocabulary word is written behind them. You see how many words the student can guess in a given amount of time. 
• Quizziz or Kahoot – Both have a vast library of vocabulary rich games.

How do you teach math vocabulary to your students?

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The BIG List of Math Terms and Definitions

This list will be updated by Jesse as new math terms make their way into Matter of Math’s lessons.

A – B – C – D – E – F G – H – I – J – K – L M – N – O – P – Q – R S – T – U – V – W – X Y – Z

A branch of math that uses letters to show numbers that may change, depending on the situation.

A straight line that is approached by a curve, but never actually reached.

For \(y=\large\frac{1}{x}\) there are asymptotes at \(x=0\), as \(y\) approaches ∞, and at \(y=0\), as \(x\) approaches ∞.

To divide a shape, line, or angle into two exactly equal parts.

Brackets (Parentheses)

There are 3 types of brackets that are used in math.

• () – Parentheses or “round brackets”
• [] – Brackets, “box brackets” or “square brackets”
• {} – Braces or “curly brackets”

Coordinates

A set of one, two, or three values that show you the exact position of an object.

Cube (Shape)

A 3-dimensional shape, with 6 square sides.

Cube (Number)

The result of multiplying a number by itself 3 times. The first 10 cube numbers are

Cube (Root)

A number that would be multiplied by itself 3 times (cubed) to make the number in question.

Decimal Expansion

The decimal expansion of a number shows it in base 10. This often involves numbers after the decimal point, separating whole numbers (units, tens, hundreds, thousands, etc.) on the left from decimals (tenths, hundredths, thousandths, etc.) on the right.

Displacement ( Vector )

Both the magnitude and direction of an object’s change in position.

Distance ( Scalar )

The measurement of an object’s movement, without direction.

Divisibility test

Simple mental math tricks that tell you if a number is divisible by another. Print the divisibility rules from 1 to 15 here .

The number that divides another exactly – without leaving a remainder. 2 divides 10 exactly, so 2 is a factor of 10.

Factor Pair

Two factors that multiply together to give the target number, shown in brackets separated by a comma. 10 and 11 multiply to make 110, so (10, 11) is one of 110’s factor pairs.

Fractional exponent

A power, or index, that is a fraction with a numerator on the top (multiplier) and a denominator on the bottom (divisor).

A mathematical relationship between one or more variables , where each value in the input set relates to exactly one value in the output set. Functions can be one-to-one or many-to-one .

The longest side of a right-angle triangle. The side that is always opposite the right-angle.

The function inside the integral.

Integration by Substitution

Integration by Parts

Integration by parts uses an easy-to-integrate function (\(g’\)) to break down a more complex function into smaller parts that can be integrated bit by bit, like this:

For a more detailed explanation, see Integration by Parts .

Inverse Function

A function \(f{-1}\) that reverses or the action of another function \(f\).

If \(f=x\)  then the inverse is  \(f^{-1}=\large\frac{1}{x}\normalsize, x\neq0\).

If \(f=x^3\)  then the inverse is  \(f^{-1}=x^{\large\frac{1}{3}}\).

If \(f=e^x\)   then the inverse is  \(f^{-1}=\ln x\).

A process that is repeated on the value last found by itself. Numerical analysis often uses many iterations to build a close approximation.

Another term for size.

Negative number

A number that is less than zero .

Numerical Method

A math tool that calculates an approximation of a problem.

One-to-One (Function)

A function is one-to-one if every input value gives one and only one output value. If it is one-to-one, then it has an inverse function .

Ordinary Differential Equation (ODE)

A differential equation with only one independent variable.

Oscillation

A regular, rhythmic movement back and forth around a central point (the rest, or equilibrium).

A parabola is a symmetrical curve made by slicing down the side of a cone. The orange curves show the parabolas made by the plane \(x=-1.3\) intersects the double cone \(z^2=x^2+y^2\).

Parentheses

See Brackets .

Prime factorization/decomposition

The unique combination of prime numbers that multiply together to make a number. Every number has its own prime factorization.

A unit for measuring angles, similar to degrees. 1 radian ≈ 57.3°.

What makes radians special is this: An arc with an angle of 1 radian will have a radius (side length) that is the same as the arc length. A full circle has 2π radians, so 2π=360°.

When using π, the term radians isn’t needed.

Refers to a number that uses the radical symbol, √ , to show a fractional exponent or root.

The number or function inside the radical symbol, √ .

The result of dividing 1 by the number or function . The reciprocal of 5 is 1 / 5 , and the reciprocal of 1 / 5 is 5.

Any left-over after dividing one whole number by another. This is given as a whole number and not a decimal or fraction. So, for 14÷4 , the answer would be 2 remainder 2, because 4 goes into 12 three times and there is 2 left-over.

A measurement that only includes magnitude (size).

See Vector .

A list or arrangement of numbers in a special order. The order must be able to be written as an equation. For example

For each term, replace the k in the square brackets with k=0, k=1, k=2, etc, up to k=6 for the first set and keep going infinitely for the second.

Square Root

The number that, when multiplied by itself, gives the number in question. For example, 5 is the square root of 25 because 5 × 5 = 25 .

This would most often be written using a radical , like this:

A number that is not rational, and a radical ( √ ) is needed to express it.

\(\sqrt2\) uses a radical and cannot be simplified, so it is a surd .

\(\sqrt4\) represents the rational number 2 so, even though it uses a radical , it is not a surd .

Translation

A sliding movement of an object or shape with no stretching, squashing, rotation, or flipping.

A measurement that had both size and direction.

See Scalar .

4 thoughts on “The BIG List of Math Terms and Definitions”

Missing the term INTERGRAL and INTEGER. Both important mathematical terms. Integration by Parts is not in your listing so why instruct readers to go to it?

Thank you for your feedback.

I assume you came from our Integration by Parts lesson – the links to this page help explain “integration by substitution” and the “integrand.”

This page is also a work in progress, there are many very important terms that haven’t been clarified yet, amongst them “integral” and “integer.” Watch this space! Jesse

what is a cerd(serd) in matematical terms?

Hi Leon, I have added a definition of Surd to the list – I hope it helps! Jesse

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Teaching with Jillian Starr

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FREE Number Talks

First grade teachers, access 20 FREE Number Talk Prompts to enhance your place value unit and get your students engaged in conversation.

6 Ways to Build Math Vocabulary in the Classroom

Math vocabulary is often an overlooked, but integral part of developing strong mathematicians. Let’s just take a look at this real interaction with a student toward the end of our lesson on parallel lines:

“Which two lines in this diagram are parallel?” *Head scratch* “What does parallel mean??”

The student couldn’t answer the question because they didn’t know what the word parallel meant even though they knew the concept of parallel. It got me thinking about the importance of building math vocabulary in the classroom. 

Supporting students in building math vocabulary through explicit vocabulary instruction is an important part of growing their math learning. It provides them with a common language to communicate about their mathematical thinking (and we know how important math discourse is!).

Without this shared language, students have difficulty communicating and comprehending what is being asked of them.

You’re probably familiar with previewing vocabulary so you might be wondering if students need to know the math vocabulary before learning the related content. Well, yes and no. While previewing vocabulary is important, we don’t need students to master all the words before discussing math concepts.

Instead, as we are working through math content, I introduce the related vocabulary word and then encourage students to use the word. When students are learning these new words, they are practicing using them in context rather than in isolation and are more likely to learn them.

While vocabulary is clearly important, I’ll share one very important caveat: don’t teach keywords as a strategy for solving word problems. As I shared in a previous post, I used to teach keywords until I learned that they aren’t actually very helpful. *cringe* Lesson learned!

The activities and teacher moves I share below will support all students, but are also incredibly important for multilingual learners. Even multilingual learners who appear fluent in English need continued instruction in academic language. For example, a student may know the word “right” to mean correct or the direction opposite of left, but in math, the word “right” as it relates to angles has a very different meaning! Explicitly teaching vocabulary will greatly support your multilingual learners. Ok, let’s dig in!

Modeling Math Vocabulary

Teaching math vocabulary starts with us, the teachers. It’s important for us to model using the vocabulary words we want kids to be using. It gives students the opportunity to hear the word in context and reinforces the expectation of using math academic vocabulary. 

In addition to just using the words we want students to learn, it’s also important to reinforce words that students are referring to. For example, if a student says “I counted the biggest coin first and then the smallest coin and got 35,” we can rephrase what they said but replace the vague language with the math vocabulary word we want them to use: “So are you saying that you first counted the quarter and then the dime to get 35 cents?” If you use this rephrasing move, you’ll also want to do some prompting to ensure students are also getting the opportunity to use the words themselves. 

Prompting for Math Vocabulary

When students are responding to questions or having partner or small group discussions, they’ll often have to refer to math concepts but they may not always be able to recall the precise words they need to communicate effectively. Whether you do this proactively or reactively, prompting can be an effective strategy.

To be proactive, prompt students to use specific words during partner or group discussions. Say, “In a moment you’ll talk to your partner/group about (topic). When you are discussing, be sure to use the word (vocabulary word) in your explanation.” Prompting students in this way will help keep the vocabulary word at the forefront of their minds as they begin talking.

*Bonus points if you display the word you want them to use just in case they forget!

Sometimes even with the best proactive teaching strategies, students will still not use precise vocabulary. In this case, you can prompt students to rephrase their thought while using the vocabulary word. Let’s go back to my earlier example.

If a student says “I counted the biggest coin and then the smallest coin and got 35,” you might respond by saying, “Can you say that again but use the names of the coins you are talking about so we can really follow your thinking?” Students can then use any reference they have available to them to rephrase using that academic vocabulary. Speaking of references… 

Math Vocabulary Notes

Now, when I say notes, I’m not talking about the kind of notes you took in high school. I just mean all the different ways you can have kids record the vocabulary words they have learned.

For writing, my students keep personal dictionaries. These dictionaries are nothing fancy and are actually just small spiral-bound pages that I assemble myself. In them, students write the words they are learning to spell so that they can reference them as they are writing. Of course, these don’t need to be their own notebooks, but can be index cards on rings, the back of their regular notebooks, or even stapled pages.

Math personal dictionaries are a little different than the ones we use in writing though because we aren’t super concerned with spelling, but with the connection of the word with the meaning. So instead of just writing words, I’ll have kids include a definition in their own words, a picture, an example, or some combination of those. Putting vocabulary into their own words helps students to internalize math vocabulary because in order to use their own words, they have to have a deeper understanding of them.

Math Vocabulary Word Walls

Similar to vocabulary notes, a word wall contains the words we want students to learn. Unlike word walls we might use for reading or writing, we want to make sure our math word walls also have a student-friendly definition and if appropriate, a picture. That way students do not have to try to recall the meaning of the word when they are trying to use precise language.

Having words up on the wall isn’t enough though! Many students won’t naturally use the word wall so they need to be taught how to use it as a reference. As the teacher, you should refer to it often, prompt students to refer to it when appropriate, and provide positive feedback when students use it, especially independently. When deciding what words to include on your word wall, consider the words required by your state standards as well as any additional words your math program includes.

Don’t worry, I’ve got your back on this one. If you’d like to start math word wall in your classroom, I have them available at each grade level K-6, and a bundle if you teach multiple grades. With visual representations and student-friendly definitions, the cards help students remember key vocabulary. 

Internalize Math Vocabulary with Gestures

Multi-sensory instruction is really impactful! Adding gestures to the mix when teaching math vocabulary can help students to internalize the meaning of the words. In fact, years ago our art teacher had kids put their arms out like an airplane anytime he or someone else said the word “horizontal” and straight up and down when someone said “vertical.” He really needed kids to learn these words because of how often they came up in art class.

Every single year when we got to our geometry unit, the kids already knew what those two words meant and as soon as I began introducing horizontal and vertical lines, their arms started flying. I was so amazed at how well they knew the words and how engaged they were.

So, consider what other gestures you can use when introducing vocabulary words. There are so many ways we can incorporate gestures to help students learn important vocabulary words!

Math Vocabulary Games

Who doesn’t love games? Using games when teaching vocabulary can help to engage students while learning. Some of my favorites are memory, crossword puzzles, and charades. For memory, have kids match up a math vocabulary word and a definition. I’ve even had kids use the index cards they created for their words as cards. They can play independently or with others – it’s fun either way!

Crossword puzzles are easier to create than you might think. There are so many free crossword puzzle creators out there and all you have to do is type in the word and the clue and they create the puzzle for you. Easy!

Finally, remember the gestures we just talked about? Make them into a game of charades! This can be fun in small groups or as a whole class activity.

Do you have other favorite ways of building math vocabulary in the classroom? I’d love to hear them in the comments!

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I enjoyed your article because I regularly utilized at least 4 of your strategies without giving it reasonable thought. Reading your explanations made me feel justified in my choices and gave me more insight on increasing the ways to implement these. I am a secondary mathematics teacher.

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hello I'm Jillian

I’m so happy you’re here. I want every child to feel confident in their math abilities, and that happens when every teacher feels confident in their ability to teach math.

In my fifteen years of teaching, I sought every opportunity to learn more about teaching math. I wanted to know HOW students develop math concepts, just like I had been taught how students learn to read. I want every teacher to experience the same math transformation I did, and have the confidence to teach any student that steps foot in their classroom. I’m excited to be alongside you in your math journey!

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Teaching Precise Math Vocabulary

By Mary Montero

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A few years ago, I was heavily pregnant, and my students were scheduled to go on a field trip three hours away from the school.  Since I was so close to my due date (and we all know how school buses are…), we decided it would be best if the interventionist and I swapped duties for the day. As she was going through her schedule with me, she made a quick aside.

“Make sure they say 5 plus 5 EQUALS 10, and not 5 plus 5  is  ten,” she reminded me before quickly apologizing with an abrupt, “I know you know that. Sorry.” It gave me pause because, while I did, in fact, know that many educators believe this to be best practice, it occurred to me that I rarely put this into action in my own classroom. It was just the reminder I needed about the importance of math vocabulary and just how critical it is to use formal math vocabulary as much as possible during everyday conversation with my students…and encourage them to do the same.

I know I’ve seen it said that using math vocabulary isn’t crucial to student success- some opponents even argue that it is confusing for kids and adds an extra degree of difficulty to math tasks. However, I truly believe that encouraging students to use correct, precise math vocabulary increases their comprehension and ability to tackle math word problems, improves performance on standardized tests (which almost always  use proper, precise math vocabulary), and gives every child a little boost as they progress through the grade levels.

Teaching Precise Math Vocabulary The Upper Elementary Classroom

While it takes a bit of extra time to incorporate this vocabulary as you are teaching concepts, my students love  it when they sound like official mathematicians! I do a lot of pre-teaching to explain that while some of the more informal terms aren’t always inaccurate and certainly not wrong , it’s so much more impressive to use formal math terms. Also explain to them that it will help them in the long run and helps them better understand math concepts. I make a big deal out of it (you don’t usually learn this until 6th grade, but we’re tackling it today, because I know  you can handle it). They eat it up!

Here are a few ways that I encourage my students to routinely infuse formal math vocabulary in the classroom, and a few terms that I’m a particular stickler about with my students. You can also download this free guide with more tips and practice activities!

Expression, Equation, Number Sentence

I’ll admit that I previously used these terms interchangeably, just hoping my students would recognize them when it came time for testing season. I know there are still anchor charts on my blog that use the terms incorrectly, and I cringe every time I see one (note to self: fix that!). Eventually, though, I decided I needed to explicitly teach these terms to my 4th and 5th graders, and they did an amazing job! Here’s a sample anchor chart to teach students the difference between an expression and an equation.

You’ll notice that “Express” is underlined under Expression and “Equa” is underlined under Equation. Expressions are short, hence the “express” and “equa” is similar to equal. This helps my students remember the difference.

Decimal Points

If you were to ask my former students what I’m MOST picky about when it comes to math talk, this would probably be it.

1.24 is not one point two four or one point twenty-four.

Well, technically, it is, but my students know they need “permission to use point,” which is granted only in specific (and usually hurried) situations.

1.24 is one and twenty-four hundredths.

Reading Whole Numbers

Along the same lines as the decimals points, I am hyper picky about students not adding “and” when they are reading whole numbers.  105 is not one hundred and five, just one hundred five.  “And” is reserved only for decimals, even with my young students who don’t know how to read decimals yet.

Reading Fractions

If I student reads 1/4 as one over four, I usually ask them to rephrase it to either one fourth or a quarter.

If a student tells me the “top number” of a fraction is one, I ask them to rephrase it to, “the numerator” is one.  Same goes if they tell me the “bottom number” of a fraction is four.  They rephrase it to “the denominator” is four.

Greater Than > and Less Than <

So often I hear kids say, “The arrow is pointing at the smaller number!” or “The alligator is eating the smaller number.”  I know these are all techniques we use to teach young students how to use the symbols, but as they get older, it’s so important that they can read an expression like 456 > 87 as “456 is greater than 87.”

Regroup and Decompose

I know this one is controversial, but they aren’t borrowing any numbers, they are regrouping the numbers. This definitely causes a bit of a generational divide, as I grew up with the term borrowing and carrying, as did most of our students’ parents. However, if we are really focusing on using math vocabulary to help our students understand the math concepts, they will learn to understand what “regrouping” and “decomposing” mean just as we understood the function of “borrow” and “carry.” The only difference is that as they get older, they will understand that these terms are literal (and they are great for mini lessons on prefixes, too!)

Improper Fraction and Fraction Greater than One

I’m going to admit that I’m still not completely fluent with this change, but did you know that the more up-to-date and accurate term for an improper fraction is a “fraction greater than one?”  It’s literal, and it’s a great teaching moment.  Since “improper fraction” is still used regularly in textbooks and other resources, I teach both terms and use them interchangeably.

Reduced and Simplified Fractions

This one is very similar to the one above. I still use both terms interchangeably and make sure that my students understand that we really aren’t reducing  the fraction or making it smaller, but putting it into its simplest form.

Geometry Terms

Those aren’t corners. Those are vertices. 🙂

Dimensions (Area & Perimeter)

I can’t tell you how many times I’ve had students get to me in 4th grade and have a good grasp on perimeter and area concepts but have no  idea what a dimension is or how to read dimensions (ie. 4 x 3 is four by three or length times width). This is an easy, easy fix, and there’s something that kids love about the word dimension.

Along the same lines, I tend to always refer to the “outside” of a shape as the perimeter of it and the inside of it as the area.

I constantly ask my students, “What operation did you use to solve this problem?”

I have also stopped saying, “What’s the answer?” whenever possible and replaced that with, “What’s the sum/difference/product/quotient?” anywhere that I can.

This is another important one. There are three DIGITS in the number 453. It’s so important that students understand the difference between the digits and the number, just like they understand that letters are different than words.

Attending to Precision with Informal vs. Formal Math Talk

I want to emphasize that I don’t call my students out as wrong or tell them that the more informal terms are inaccurate (unless they are). To me, having my students practice their math vocabulary during conversations and math discussions is just like having them practice their reading fluency, and it becomes just that– fluent.

Do you teach the Standards of Mathematical Practice in your classroom? If so, you’ll recognize that this all really comes down to the Mathematical Practice of attending to precision. When students say, “To solve this problem, I did take away,” I think it’s completely reasonable to ask them to be more precise with their language and say, “To solve this problem, I subtracted…”

What are you a stickler for when it comes to math vocabulary?

A special note: Please note that I have used these strategies and expectations with all students, but students needing extra support or English Language Learners may need additional scaffolds, support, and accommodations.

Formal vs. Informal Math Talk Anchor Chart Inspiration:

Building a  Bridge to Academic Math Vocabulary

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Mary Montero

I’m so glad you are here. I’m a current gifted and talented teacher in a small town in Colorado, and I’ve been in education since 2009. My passion (other than my family and cookies) is for making teachers’ lives easier and classrooms more engaging.

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7th Grade Math Vocabulary: A Guide for Students and Parents

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In 7th grade, students further their understanding of proportional relationships, equations and 2-D and 3-D figures. Along with new material comes new vocabulary terms. Help your child stay on top of their math vocabulary by reviewing the suggestions, vocabulary terms and definitions below.

How Can I Help My 7th Grader Learn Math Vocabulary?

Familiarity with vocabulary terms can make learning math easier. If students know math vocabulary, they will be more likely to understand what their teacher is talking about. Unlike vocabulary in language arts, students have probably never heard math vocabulary terms before and are unlikely to use them outside of math class. You can help your child learn math by helping him create a math dictionary in the back of his notebook. The definitions should be written in your child's own words and include examples.

Repetition is one of the key ways that students remember terms, so practice at home with flashcards before a test. Also, make sure your child has frequent exposure to these terms. For instance, encourage her to label the relevant terms while solving math problems. For the problem 5x=4, she can label the coefficient (which is 5 in this example), variable (x) and solution. This repeated practice will help your child learn math vocabulary words without spending a lot of extra time on review.

7th Grade Math Vocabulary

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5 Actionable Strategies That Can Help You Grow Your Student’s Mathematical Vocabulary

Math concepts and vocabulary are not easy to understand for every student. Mathematical vocabulary can be tricky because some general English language words have different meanings in math. Therefore, teaching mathematics vocabulary is another important task for teachers to perform while teaching math.

Math vocabulary is a set of words used in math subjects, just like English words. Math vocabulary includes words like decimal , reciprocal , fraction , determinant , quotient and dividend , and many others. Teachers need to strengthen students’ mathematical vocabulary along with teaching concepts.

• Actionable Strategies For Teaching Mathematical Vocabulary:

1. Play A Vocabulary Game

2. use math journals, 3. math word wall, 4. increase the child’s exposure to math words, 5. make math vocabulary song, final thought:.

Math vocabulary is vital for understanding mathematics and its importance in the subject cannot be underestimated. However, students generally get confused with some words in math vocabulary; therefore, teaching and explaining such words to students becomes necessary. There are many strategies that educators can use while teaching math vocabulary to students to make it easier for students.

100+ Free Math Worksheets, Practice Tests & Quizzes

Playing a math vocabulary game can be the best way to teach students mathematical vocabulary. There are many games that students can play in the classroom—learning something while playing is the best way to learn and explore.

Even the student can understand the concept easily while playing. A teacher can find many vocabulary games online which can be played in the class.

One game is for teachers to write one vocabulary word on the board, divide the students into pairs of two, and call them one by one.

Then, make the student stand so that one student’s face should be towards the board, and the other person’s back should be towards the board; he should not see what is written on the board.

Next, the person seeing the board will try to explain the word to another partner by expression and gesture, and that person has to guess what is written on the board without seeing it.

This way, students can quickly learn the vocabulary words for mathematics.

Journaling is the best way to learn vocabulary and words. A person who writes journals has an excellent command of the words and the language, as he practises writing differently.

Writing strategies can also be used for math vocabulary. As a teacher, you can ask your child to write a journal every day after every math class. Ask them to write what they have studied in the whole class.

They can start writing like, “Today we have completed this topic or concept and did this, many questions and found 2 to 3 ways to find a solution to the problem, etc.”

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While writing the journal, students can find different math words they can use daily to help improve their understanding of math vocabulary.

To make teaching mathematics vocabulary easier, the teacher can create a math vocabulary wall in the classroom.

To prepare this wall teacher needs to create many cards which each word on each card with its meaning, definition, and pictures related to that word. It is good to add those words from the unit in class.

In this way, students see these words daily on the wall they can remember them easily.

Some games can also be played from the words written on the wall. For example, a teacher can give some clue to students to which they have to find the solution, and the solution is among the world on the wall, students have to figure out which word could be the answer.

Or a teacher can also give the fill-in-the-blanks to students in which blanks should be filled from the word on the board according to the given clue.

Teachers can also ask children to find pictures related to the word on the board and ask them to make a collage of all the pictures.

Or they can ask children to choose any of the two words from the wall and find the relation between them.

Teachers first divide them into pairs of two in which one student will draw a picture related to a word on the wall, and the other student will guess that it could be the word.

Through this method, students can use the word on the way to have some fun and learn some math vocabulary words in this fun.

When teachers teach students a new word in language classes, they pronounce it, tell students in which context it is used, or show them an image or definition related to it. All this is done to increase the exposure of students to that word.

The same can be done to teaching mathematical vocabulary. Math teachers can use the same method while teaching math vocabulary to students.

When teachers start any new chapter in the class, they can follow the following steps to teach math vocabulary.

• Pre-teaching : In this stage, teachers can introduce all the vocabulary words to students from the chapter by showing some pictures related to that word or telling the definition of the word and explaining them. In this stage, they must explain the vocabulary related to that topic. It might be possible that the student cannot understand the vocabulary at this stage, but it is just beginning.
• Teaching mathematics vocabulary: At this stage, the teacher can explain the exact meaning of the word with the use of the word in actual context, or they can also conduct a discussion on the word and encourage the student to ask any doubt about the word. Teachers can also use the word wall and can conduct various activities related to the word to give a greater understanding of the topic. This way, students can understand the importance and application of math vocabulary.
• Review: At this stage, students should be tested whether they understood the meaning of the words or not. To test children, the teacher can ask the student a question, explain the meaning of the word to another student, or draw an image of the picture related to the word.

It is the best way of teaching mathematics vocabulary to the student by explaining the context in which it is used. It can help to understand better where the words are used. Using examples to explain something is essential as it gives a clearer and deeper understanding of the topic.

It is the most interesting strategy for teaching mathematics vocabulary to the student.

In this strategy, students have to sing the song with the math vocabulary in its lyrics. If you do not find such songs, you can search for them on google or YouTube, or even if you are not finding any songs, students can create some songs themselves.

To create the song, the student has to select a song or melody and do minor edits in the song by adding the math vocabulary to the lyrics of the song, and it should be in such a way that melody or tune of the song should be the same as it was earlier.

Composing a mathematical song is a creative task as it widens the mind and can give a deeper understanding of the word because when they will use any word, they should know the meaning.

Singing the song daily can improve the brain’s retaining power and make it easier for students to learn and understand complex math vocabulary words.

We cannot make mathematical vocabulary easy, but we can make a way to learn it quickly.

This strategy can help the student enjoy the learning process while having fun. This activity can also enhance the creative thinking of the students.

You may also like to read- 15 Back To School Math Activities For 6th Grade

These are all the strategies educators can use while teaching mathematics vocabulary. It isn’t elementary but can be made easy by simple steps to make learning easier. Math vocabulary is an essential part of the subject and should not be ignored.

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Edexcel GCSE Maths Complete Keywords sheets

Subject: Mathematics

Age range: 14-16

Resource type: Assessment and revision

Last updated

26 December 2020

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These keywords sheets cover most, if not all of the keywords studied within the Edexcel Maths GCSE. They perfectly align with the chapters from the higher textbook and are therefore suitable for both higher and foundation students. These sheets are great to use for terminology tests or to revise from for end of topic tests!

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jamiecroll2006

Overall is a great piece of material to have for GCSE maths, gives multiple definitions on a variety of different topics creating a better understanding for the content and maths as a whole. Great to have to have a look back in case you have forgotten a word.

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