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# Math Dictionary For Kids: The Essential Guide To Math Terms For Parents, Teachers And Kids

Bet you never thought you’d need a math dictionary for kids when your child started school or when you started teaching! But as parents and teachers, the math words that children have to contend with in school may be quite different from those you learned and used in your education- even the basic math.

Throughout their time studying math in school, in elementary school, middle school and beyond, children will be introduced to a huge amount of math vocabulary, much of which may seem baffling – both to them and to you.

This online math dictionary for kids, teachers and parents is, we hope, the solution to questions and confusion and can serve as a quick reference guide. It’s an A to Z math glossary of meanings in simple language for all those words and phrases you’re not sure about, from acute angles through to word problems.

It is by no means a comprehensive list of every mathematical term that could come up throughout a child’s school life (as that would be too overwhelming), but it includes the key ones they will need to form solid foundations in elementary school and middle school math so they are ready to move onto high school math.

This blog is part of our series of blogs designed for teachers, schools and parents supporting home learning.

Click on the letter to find the maths dictionary definition you need

### The importance of spoken mathematical language

When children struggle to articulate their thoughts, it is usually a sign that they do not understand the topic they are discussing in great depth and this can often be the case in math.

This quote taken from What Works Clearinghouse (WWC) reflects the importance of mathematical language amongst children:

If children hear math vocabulary in context and then practice using it, they may be better able to understand the underlying math concepts. The panel believes there is evidence of a positive relationship between math-related talk and children’s math knowledge.”

What Works Clearinghouse, 2013

When children use spoken language in math in a productive manner, it allows them to evaluate their learning, support their peers, challenge the status quo, justify their own answers and most importantly ask questions!

Using a wide range of math vocabulary can help children to make links across not only different areas of math, but also throughout real life situations. One example of this could be in the supermarket when they would realize, thanks to their range of vocabulary, that a 50% off sticker means the same as half price. These connections in turn support students’ problem solving skills for reasoning questions in math.

Mathematical vocabulary appears in more places than you would think, and that is why it is very important that children are confident in their ability to articulate about all things mathematical!

### How you can encourage a wider range of mathematical language in your students

There are a number of ways you can encourage your students to enhance their mathematical vocabulary and they include:

• Getting them to read and test themselves with our math dictionary;
• Asking them open ended questions. No more “Do you know the answer to this question?” and more “What do you think the answer to this question is?”;
• Playing some word based math games;
• Reading outside the world of math as many children’s books will incorporate elements of math in a fun and engaging way. ‘One is a Snail, Ten is a Crab’ is a great example of this.

## #

### < and >

< and > are symbols representing one number being ‘greater than’ or ‘less than’ another.

For example 16 > 8 or 8 < 16 says that 16 is greater than 8 and 8 is less than 16.

### 12-hour and 24-hour clock

The 12-hour clock goes from 1 am in the morning to 12 noon and from 1 pm in the afternoon to 12 midnight. This is known as ‘analog’ time.

The 24-hour clock goes from 00:00 (midnight) to 23:59 (one minute to midnight). This is known as ‘digital’ time.

Read more: What is the 12 hour and 24 hour clock

### 2D shapes

A 2D shape is any flat or ‘two-dimensional’ shape, such as a square, circle or triangle.

### 3D shapes

A 3D shape is ‘three-dimensional’ and has volume, for an example a cube (cardboard box), pyramid or cylinder (tube).

Read more: 2D shapes, 3D shapes and properties of shapes

## A

### Acute angle

An acute angle is any angle less than 90°.

An addend is a number that is added to another number. For example, in the equation 7 + 5 = 12, 7 and 5 are addends.

### Algebra

In algebra, letters and symbols are used to represent numbers in equations or formulae.

For example, if w = 3, what is 6w + 7?

### Analog and digital clocks

An analogue clock is a clock with the numbers 1 to 12 around the outside and two hands, one short hand that represents hours and one long hand that represents minutes.

A digital clock can use 24-hour or 12-hour time and always has four digits.

For example, 15:30 is half-past three in the afternoon on a digital clock.

### Area

The area of a shape, surface, piece of land etc. means the amount of space it takes up.

For example, a rectangular soccer field has an area of 64m² or 64 squared meters.

### Array

An array is a visual representation of a calculation, using rows of dots, to help children understand multiplication and times tables.

An array can also help show repeated addition. For example, the array shown below can represent 3 + 3 + 3 + 3 or 4 + 4 + 4.

### Arrow cards

Arrow cards are a math tool useful for explaining place value and how to partition numbers (separate them into ones, tens, hundreds etc).

### Ascending order

To ascend means to go up, so numbers given in ascending order are going from smallest to largest or least to greatest.

For example, 1, 2, 3, 4, 5, 6 are numbers in ascending order.

### Associative property

The associative property says that when we add or multiply numbers, it doesn’t matter how we group them (which we calculate first).

For example, (7 + 5) + 3 = 7 + (5 + 3) or (4 x 5) x 2 = 4 x (5 x 2)

### Average

The average of a set of numbers is found by adding all the numbers together and dividing by how many numbers there are.

For example, the average of 12, 10, 8 and 6 is 9 because (12 + 10 + 8 + 6 = 36 ÷ 4).

### Axes

The axes of a graph or chart are the horizontal and vertical lines that create it, often known as the x-axis and y-axis.

## B

### Bar graph

A bar graph is a form of graph that displays information using rectangular bars of different heights, according to their numerical value.

### Bar model

A bar model is a method that uses diagrams of rectangular bars to represent math problems in a visual way, making it easier for children to see which operation to use to work out a calculation. Younger children may use cubes to physically represent this.

Read more: What is a bar model

### Block graph

A block graph is a simpler version of a bar graph, but using blocks to represent the data, with each block worth 1 unit.

### BODMAS

BODMAS is a rule for the order to work out calculations with mixed operations. It stands for Brackets, Orders, Division, Multiplication, Addition, Subtraction and is sometimes seen as BIDMAS (Brackets, Indices, Division, Multiplication, Addition, Subtraction). In the US, it is more commonly referred to as PEMDAS (Parentheses, Exponents, Multiplication, Division, Addition, Subtraction)

### Bridging through 10

For example, to add 8 + 7, you add 2 (from the 7) to get 10, then add the remaining 5 to get 15.

### Bus stop method

The ‘bus stop’ method or short division is a way of dividing numbers with two or more digits by one or two digit numbers.

Read more: What is bus stop method

## C

### Capacity

The capacity of a container is how much that container can hold, measured using units such as litres, millilitres, pints etc.

### Cardinal numbers

A cardinal number tells you how many of something there are; they refer to a set of objects. For example, there are three marbles in my hand. This is in contrast to an ordinal number which tells you the position of something in a list, for example, first, second, third.

### Carroll diagram

More often referred to as a simple table, a Carroll diagram is more than this and is a way of organizing information and grouping according to what criteria it fits into.

For example, which shape has 6 sides and 1 line of symmetry?

Read more: What Is A Carroll Diagram

### Circle

A circle is a simple curved 2D shape, with 1 edge, no corners and infinite lines of symmetry.

### Circumference

The circumference is the length around the edge of a circle.

### Clockwise and anti-clockwise

To move in a clockwise direction means moving in the same direction as the hands on a clock. If something moves in the opposite direction to the hands of a clock, it is moving in a counterclockwise direction.

### Coordinates

The coordinates of a shape or object refer to where on a map or graph they are, by looking at the two axes and recording the numbers they are at. These can be taught with the phrase “along the corridor and up/down the stairs” to refer to looking at the x-axis first then looking at the y-axis.

### Column method

The column method is a way to solve addition and subtraction calculations that sometimes involve ‘exchanging’ or ‘regrouping’ amounts from one column to the next (which in the past has been called ‘carrying’ and ‘borrowing’).

The numbers are written on top of each other, with the correct digits in each column (e.g. hundreds, tens, ones). This is also known as standard algorithm subtraction and standard algorithm addition.

### Commutative property

The commutative property states that addition and multiplication calculations can be carried out with the numbers in any order, whereas for subtraction and division, the numbers must be in a particular order.

For example, 8 x 9 = 72 or 9 x 8 = 72

### Complementary addition (subtraction on a number line or the jump strategy)

Complementary addition is a method for subtraction that involves using a number line to jump from the smaller number to the bigger number and counting the number of jumps. This method is useful in kindergarten and first grade for teaching children to ‘find the difference’ between two numbers.

### Concrete Representational Abstract approach (CRA)

The concrete, representational, abstract approach is a way of teaching mathematical concepts and theories in various stages, in order to help children fully understand and master what they are learning.

The concrete stage involves using items, models and objects, giving children a chance to be ‘hands-on.’

For example, children may solve a problem by adding groups of toys together using real toys, or they may manipulate buttons, Legos, etc when working out fractions of amounts. At school, there are a variety of concrete resources specially designed for math, such as place value counters, base ten blocks, and ten frames.

The representational stage uses visual representations of concrete objects to model problems, encouraging children to make connections between the physical object and the picture that represents the object.

For example, children may use drawings of toys to solve a problem adding toys.

The abstract stage uses symbols, such as numbers or mathematical symbols (+, -, x, =) to model problems. Children will need to master the concrete and representational stages before moving onto the abstract stage.

### Converting into same units

When you convert measurements into the same units, you understand that the same length, weight or capacity can be shown in different units of measurement.

For example, a bottle of water can be measured in cups or pints and there are 2 cups in 1 pint.

### Cube numbers

A cube number is the result when a number is multiplied by itself three times. When writing cube numbers, we write a small three above the number, e.g. 3 x 3 x 3 or 3³ = 27. We would read this as ‘3 cubed.’

Read more: What are cube numbers?

## D

### Data handling

Data handling is another term for statistics, meaning how we collect, display and interpret data or information, such as the most popular flavor of ice cream in a class, using tables, tally charts, pictograms, block diagrams, bar graphs, line graphs and pie charts.

### Decimal

A decimal is a number that contains tenths, hundredths, thousandths etc, with a decimal point between the ones and tenths. Money is often used to teach decimals.

### Perimeter

The perimeter is the distance around a 2D shape and is often taught using the example of fences around a field or garden.

Read more: What is the perimeter?

### Perpendicular

Perpendicular lines are two lines that meet to create a right angle, often seen in shapes.

### Pictogram

A pictogram, or pictograph, is a type of graph that uses pictures to represent information. These are often taught early in elementary school before moving onto block charts and bar graphs.

### Pie chart

A pie chart is a circular chart divided into sections, representing different values, which can be fractions, decimals, percentages or angles.

### Place value

The place value of a number is how much each digit in the number represents.

For example, the place value of 157 is 1 hundred, 5 tens and 7 ones.

Read more: What is place value?

Try this: Place value grid to make at home

### Polygon

A polygon is any 2D shape with straight, closed sides. Any shapes with open or curved sides are not polygons. For example, triangles, squares and parallelograms are polygons, but circles and ovals are not.

### Prime number

A prime number is any number greater than 1 that can only be divided equally by itself and 1. For example, 5, 7, 11 and 13 are prime numbers.

### Prism

A prism is a 3D shape with two identical flat sides and ends. Cubes and cuboids are examples of prisms.

### Probability, chance and likelihood

Probability is the study of how likely or how big a chance there is that something will happen. It can be described in words, fractions, percentages or ratios. For example, there is a 20% chance of rain tomorrow.

### Product

A product of two numbers is the name for the answer to a multiplication calculation.

For example, 35 is the product of 5 x 7.

### Proportion

A proportion is a portion or part of a whole, and is often taught alongside ratio.

### Protractor

A protractor is an instrument used to measure angles.

### Pyramid

A pyramid is a 3D shape with triangular sides that join at a point, with a polygon base.

## Q

### Q

A quadrilateral is any 2D shape with four sides, including a square, rhombus, kite and trapezium.

## R

### R

The radius is the distance from the centre of a circle to its circumference and is half the diameter.

### Range

The range of a set of numbers is the difference between the smallest and largest numbers in the set.

For example, in the set of numbers 50 to 60, the range is 10.

### Ratio

A ratio is used to compare values, showing the relative value of one to another. It is taught using real-life examples, such as comparing the number of boys to girls in class. For example, the ratio of boys to girls was 2:1, meaning there are two boys for every one girl.

### Reflection of shapes

A reflection of a shape is a drawing of a shape reflected in a line of symmetry, with the reflection on the other side of the line but facing in the opposite direction.

### Reflective symmetry

Reflective symmetry is a type of transformation, looking at when a shape or pattern is reflected in a mirror or line of symmetry. The reflected shape should be exactly the same size and distance from the line of symmetry as the original.

### Reflex angle

A reflex angle is any angle between 180° and 360°.

### Regular and irregular shapes

A regular shape is one where all the sides and interior angles are equal, whereas an irregular shape has sides and angles of different lengths and sizes.

Read more: What are regular and irregular shapes?

### Right angle

A right angle is an angle that measures 90°. It is also known as a quarter turn, as it is \frac{1}{4} of a full turn, which measures 360°.

### Right-angled triangle

A right-angled triangle is a 2D shape with three sides and one angle that measures 90°.

### Roman numerals

Roman numerals are the numbers used in ancient Rome, with letters from the Latin alphabet representing certain numbers. They are commonly taught using years. For example, V = 5, X = 10, C = 100, M = 1000, so 1066 is MLXVI.

### Rotation of shapes

A rotation of a shape is when a shape is moved around a fixed point, either clockwise or counterclockwise and by a certain number of degrees. However, the shape doesn’t change size.

### Rotational symmetry

Rotational symmetry is a type of transformation, where a shape is turned around a central point, without changing its size.

### Rounding numbers

To round a number means to adjust it up or down to a number that makes calculating with it easier. Numbers are usually rounded up to the nearest 10, 100 or 1000, with decimals being rounded to the nearest whole number, tenth or hundredth. There is a rule that if a digit is 4 or less it rounds down and if it is 5 or more it rounds up.

For example, 426 rounds to 430 to the nearest 10, but 400 to the nearest 100.

Repeated addition is a technique used to teach multiplication in elementary school, where children add ‘lots’ of numbers together.

For example, 3 ‘lots’ of 5 is 5 + 5 + 5 as well as 3 x 5.

## S

### Scale factor

A scale factor is used when we increase or decrease a 2D shape in size, so we make the shape larger or smaller depending on the scale factor. For example, this shape has been increased by a scale factor of 2.

### Scalene triangle

A scalene triangle is a 2D three-sided shape where all the sides and angles are unequal.

### Shared between

‘Shared between’ is a phrase used when introducing division, to show how a set of objects can be ‘shared’ into equal sized groups.

### Simplifying fractions

To simplify a fraction means to reduce it to its lowest form, by dividing the numerator and denominator by the same number. For example \frac{8}{10} can be simplified to \frac{4}{5} by dividing both the numerator and denominator by 2.

### Square numbers and Square roots

A square number is the result of multiplying a number by itself. When writing this, we write a small two next to and above the number. For example, 7² = 7 x 7 = 49.

Read more: What is a square number?

### Standard and non-standard units

Standard units are the units of measurement we normally use to indicate the length, mass or capacity of an object. For example, inches, yards, cups, pints, etc.

Non-standard units are used when introducing measurement early in elementary school, for example the length of a pencil or hand spans.

### Sum

A sum of two numbers is another name for the result of an addition calculation. For example, the sum of 15 and 23 is 38.

### Symmetry

When a picture or shape is the same on both sides, we call it ‘symmetrical’, and this can be shown by drawing a line of symmetry through the center and seeing if both sides are the same.

Read this: What is a line of symmetry?

## T

### Tally chart

A tally chart uses marks instead of numbers to represent information. One vertical mark is used to represent each one unit, with five being shown as a fifth line crossed through the first four lines.

### Tessellation

When shapes fit together exactly with no gaps, we call this tessellation. An example of this in real life are floor tiles.

### Time intervals

A time interval is the length of time between two times. For example, the time interval between 1:15 and 1:45 is 30 minutes.

### Translation of shapes

Translation is a type of transformation, where a shape is moved into a new position, without being changed in any way.

### Triangle

A triangle is a 2D shape with three sides, angles and corners.

### Triangular number

A triangular number is a number that can make a triangular dot pattern. For example, 1 + 2 = 3, 2 + 3 = 5, 3 + 5 = 8, 5 + 8 = 13 etc.

### Turns

Turns are a movement in a circle, with a quarter turn being the same as 90°, a half turn as 180° and a full turn as 360°, either clockwise or anticlockwise.

### Two-step and multi-step problems

A two-step problem is a word problem which needs two calculations to solve it. A multi-step problem requires more than two calculations to solve it.

## U

### Unit and non-unit fractions

A unit fraction is any fraction with 1 as the numerator, whereas a non-unit fraction is any fraction with a number greater than 1 as the numerator. For example, ⅙ is a unit fraction, whereas 2/6 is a non-unit fraction.

Read this: What is a unit fraction?

Read more: What is a non-unit fraction?

## V

### Venn diagram

A Venn diagram is a visual way of sorting different objects or numbers into overlapping circles with different rules, with anything in the overlapping part sharing both rules.

Read this: What Is A Venn Diagram?

### Variation

In elementary school level math, there are two types of variation, conceptual and procedural variation.

Conceptual variation means looking at a math idea in various representations. For example, showing a number using multilink, base ten block, 100 square or partitioned, to explain place value.

Procedural variation is used to support a child’s deeper understanding of a math process by extending a problem by varying the number, varying the processes to solve a problem or varying the problems by applying the same method to a group of similar problems.

### Vertex/vertices

Vertex is another name for a corner of a 2D shape or the points where edges in a 3D shape meet.

### Vertical

A vertical line runs up and down, from top to bottom.

### Volume

The volume is the amount of space an object occupies, especially 3D shapes. Children will learn the formula for finding the volume of a shape, which is the length x width x height, with the answer having units with a cube number, for example cm³.

## W

### Word problem or story problem

A word problem or a story problem is a real-life situation where a math calculation is needed to solve a problem. For example, ‘If half a class of children have pets and there are 36 children in the class, how many have pets?’

## X

### X-axis

The x-axis is the horizontal axis on a graph, along which we find the x-coordinate (by going ‘along the corridor’).

## Y

### Y-axis

The y-axis is the vertical axis on a graph, along which we find the y-coordinate (by going ‘up the stairs’).

## Z

### Zero

Zero is a placeholder between +1 and -1, it has no value but changes the value of other numbers. For example, in the number 703 it changes the number 73 to the much larger 703.

In our math dictionary for kids, teachers and parents, we’ve tried to include as much of the math terminology your child will be learning in elementary and middle school as possible, but we know that we may have missed something!

If that is the case, then let us know which numeracy based terms we have missed, and we’ll be more than happy to add them to this A to Z math dictionary!

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##### Sophie Bartlett
Year 6 Teacher
Sophie teaches mixed age classes at a small school in central England. She is a self confessed grammar pedant and number nerd so we've welcomed her as a regular author and editor for Third Space Learning.
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#### [FREE] Fun Math Games and Activities Packs for Kindergarten to Grade 5

Individual packs for Kindergarten to Grade 5 containing fun math games and activities to complete independently or with a partner.

The activities are designed to be fun, flexible and suitable for a range of abilities.