Math glossary
Find a math term, see an example, and follow a related lesson.
A
Addend
An addend is a number you add to another number.
Example: In 8 + 7 = 15, the addends are 8 and 7. The answer, 15, is the sum.
Add by making 10Addition
Addition combines amounts to find a total. Its sign is +.
Example: If you have 8 points and earn 7 more, you have 15 points: 8 + 7 = 15.
Add by making 10Algebra
Algebra uses symbols, often letters, to represent numbers and describe relationships.
Example: In x + 7 = 12, the letter x stands for 5.
See how operations build an equationAmplitude
The amplitude of a wave is the distance from its middle level to a peak.
Example: For y = 3sin(x) + 2, the middle is 2 and the peak is 5, so the amplitude is 3.
Explore angles, sine and cosineAngle
An angle measures the turn between two directions.
Example: A quarter turn is 90°, and a full turn is 360°.
Explore angles, sine and cosineAxis
An axis is a reference line used to read positions on a graph.
Example: The x-axis runs horizontally, and the y-axis runs vertically.
Read a linear function and its graphB
Base
The base is the number you raise to a power. In a logarithm, it names the powers you work backwards from.
Example: 2 is the base in both 2³ and log₂(8).
Explore powers and exponential growthC
Coefficient
A coefficient is a number multiplying a variable or a power of a variable.
Example: In 3x, the coefficient of x is 3.
Read a linear function and its graphColumn vector
A column vector writes its parts in a vertical list. In two dimensions, the horizontal part goes above the vertical part.
Example: With 2 above −3, the vector moves two units right and three down.
Describe a move with a vectorCompensation
Compensation means changing a number to make a calculation easier, then adjusting the answer to undo that change.
Example: For 38 + 19, add 20 to get 58. Then take away the extra 1: 58 − 1 = 57.
Try the round and adjust strategyCoordinates
Coordinates are numbers that locate a point using a chosen reference system.
Example: On ordinary x-y axes, (3, 2) is three units right and two up from (0, 0).
Read a linear function and its graphCosine
On a unit circle, cosine gives the horizontal coordinate of a point at a chosen angle.
Example: cos(0°) = 1 and cos(90°) = 0.
Explore angles, sine and cosineD
Decimal
A decimal uses a point to separate whole-number places from parts such as tenths and hundredths.
Example: 2.35 = 2 + 3/10 + 5/100.
Add and subtract decimalsDecimal place
A decimal place is a position after the decimal point. The first three places are tenths, hundredths and thousandths.
Example: 0.375 has three decimal places: 3 tenths, 7 hundredths and 5 thousandths.
Add and subtract decimalsDecimal point
The decimal point separates the units place from the tenths place.
Example: In 12.5, the point separates 12 whole units from five tenths.
Add and subtract decimalsDegree
A degree is an angle unit equal to 1/360 of a full turn. Its symbol is °.
Example: A right angle measures 90°.
Explore angles, sine and cosineDenominator
The denominator is the bottom number of a fraction. For parts of a whole, it names how many equal parts make one whole.
Example: In 3/4, the denominator is 4, so each part is a quarter.
Explore equivalent fractionsDifference
The difference is the result of subtraction. It can tell you how far apart two numbers are.
Example: The difference between 83 and 67 is 16, because 83 − 67 = 16.
Find a difference by counting upDigit
A digit is one symbol used to write a number. Our decimal system uses the digits 0 to 9.
Example: 507 has three digits: 5, 0 and 7.
See place value in decimalsDisplacement
Displacement is the change in position from a starting point to an ending point.
Example: From (1, 2) to (4, 6), the displacement is (3, 4).
Describe a move with a vectorDivision
Division splits an amount into equal groups, or finds how many equal groups fit inside it. Its sign is ÷.
Example: Share 24 counters equally among 6 people. Each person gets 4: 24 ÷ 6 = 4.
Divide using facts you knowDivisor
The divisor is the number you divide by.
Example: In 24 ÷ 6 = 4, the divisor is 6.
Connect division and multiplicationDot product
The dot product multiplies matching parts of two vectors, then adds the results. It gives one number.
Example: (2, 1) · (3, 4) = 2 × 3 + 1 × 4 = 10.
Use dot products to compare directionsDoubling
Doubling means multiplying a number by 2. You can also add the number to itself.
Example: Double 18 is 36: 18 × 2 = 36, or 18 + 18 = 36.
Use doubling and halving to multiplyE
Equation
An equation says that two amounts are equal. The equals sign, =, separates its two sides.
Example: In x + 7 = 12, x must be 5 so both sides have the same value.
Equivalent fractions
Equivalent fractions have the same value, even when their top and bottom numbers differ.
Example: 1/2 = 2/4 = 3/6.
Explore equivalent fractionsExponent
An exponent is the small raised number in a power. For positive whole-number exponents, it counts repeated factors.
Example: In 2³ = 8, the exponent 3 means three factors of 2.
Explore powers and exponential growthExponential function
An exponential function uses a fixed positive base raised to a variable power. The base is different from 1.
Example: For y = 3 × 2ˣ, the output doubles whenever x rises by 1.
Explore powers and exponential growthExpression
An expression combines numbers, symbols and operations to name a value.
Example: 3x + 4 is an expression. When x = 2, its value is 10.
See how operations build an equationF
Factor
A factor divides a whole number exactly, with no remainder. When you multiply two numbers, you call each one a factor.
Example: In 4 × 6 = 24, both 4 and 6 are factors of 24.
See how factors work in doubling and halvingFraction
A fraction writes a division as one number above another. The bottom number cannot be zero.
Example: 3/4 means three of four equal parts of one whole.
Explore equivalent fractionsFunction
A function is a rule that gives exactly one output for each allowed input.
Example: The rule f(x) = 2x + 4 gives f(3) = 10.
Read a linear function and its graphG
Graph
A graph shows a relationship between values using points, lines or curves.
Example: On the graph of y = 2x, the point (3, 6) pairs x = 3 with y = 6.
Read a linear function and its graphH
Halving
Halving means dividing a number by 2, or splitting an amount into two equal parts.
Example: Half of 18 is 9, because 18 ÷ 2 = 9. The two halves add back to 18.
Use doubling and halving to multiplyI
Input
An input is a value you give to a function.
Example: In f(3) = 10, the input is 3.
Read a linear function and its graphInteger
An integer has no fractional part. Integers include zero and numbers such as 3 and −3.
Example: −3, 0 and 12 are integers. The numbers ½ and 2.5 are not integers.
Inverse operation
An inverse operation undoes another step. Adding and taking away the same amount undo each other. So do multiplying and dividing by the same non-zero number.
Example: Start at 5 and add 7 to get 12. Subtract 7 from 12 to return to 5.
Connect division and multiplicationL
Linear function
A linear function changes by a fixed amount for each equal step in its input. Its graph is a straight line.
Example: For y = 2x + 4, y rises by 2 whenever x rises by 1.
Read a linear function and its graphLogarithm
A logarithm asks which exponent gives a chosen value. The base and input must be above zero. The base cannot be 1.
Example: log₂(8) = 3 because 2³ = 8.
Work backwards with logarithmsLogarithmic scale
A logarithmic scale uses equal spacing for equal multiplying factors, instead of equal added amounts.
Example: On a base-ten logarithmic scale, 1, 10, 100 and 1,000 are equally spaced.
Work backwards with logarithmsM
Magnitude
The magnitude of a vector is its length.
Example: The vector (3, 4) has magnitude √(3² + 4²) = 5.
Find a vector’s lengthMental math
Mental math means working out an answer in your head. You can use known facts, split numbers into parts or spot patterns.
Example: For 29 + 6, think 29 + 1 = 30, then add the remaining 5 to get 35.
Start with the make 10 strategyMultiple
A multiple of a number is the result of multiplying it by an integer.
Example: The numbers 6, 12, 18 and 24 are multiples of 6. For example, 6 × 4 = 24.
Use known multiples to divideMultiplication
Multiplication can find the total in equal groups. Its sign is ×.
Example: Four groups of 6 counters contain 24 counters: 4 × 6 = 24.
Build the 4 and 8 times tablesN
Number bonds
Number bonds show how a number splits into parts that add back to the whole.
Example: The parts 3 and 7 make 10: 3 + 7 = 10. Knowing this also tells you that 10 − 3 = 7.
Use number bonds to make 10Numerator
The numerator is the top number of a fraction. It counts how many parts you have.
Example: In 3/4, the numerator is 3.
Explore equivalent fractionsO
Operator
An operator is a symbol that tells you which math action to perform.
Example: The operator + adds, while × multiplies.
See how operations build an equationOutput
An output is the value a function gives for a chosen input.
Example: In f(3) = 10, the output is 10.
Read a linear function and its graphP
Parabola
A parabola is the curve of a quadratic function. It has a turning point and can open up or down.
Example: The parabola y = x² has its lowest point at (0, 0). It is symmetric about the y-axis.
Recognise a quadratic graphPeriod
The period of a repeating function is the length of one complete repeat.
Example: sin(x) has period 2π radians. sin(2x) has period π radians.
Explore angles, sine and cosinePerpendicular
Two lines or directions are perpendicular when they meet at a right angle.
Example: The vectors (1, 0) and (0, 1) are perpendicular. Their dot product is 0.
Use dot products to compare directionsPi
Pi, written π, is a circle’s distance around its edge divided by its width through the centre.
Example: π is about 3.14159. A full turn is 2π radians.
Explore angles, sine and cosinePlace value
Place value is the value a digit has because of its position in a number.
Example: In 352, the 3 means 300, the 5 means 50 and the 2 means 2.
Use tens and ones to round and adjustPower
A power is an expression with a base and an exponent.
Example: 2³ means 2 × 2 × 2, which equals 8.
Explore powers and exponential growthProduct
The product is the result of multiplication.
Example: In 4 × 6 = 24, the product is 24. The numbers 4 and 6 are the factors.
Keep the same product by doubling and halvingPythagoras’ theorem
In a right triangle, square each side length. The two shorter sides' squares add up to the longest side's square.
Example: For sides 3, 4 and 5: 3² + 4² = 5².
Find a vector’s lengthQ
Quadratic function
A quadratic function has the form y = ax² + bx + c, where a is not zero.
Example: For y = x² − 1, both x = 2 and x = −2 give y = 3.
Recognise a quadratic graphQuotient
The quotient is the result of division.
Example: In 24 ÷ 6 = 4, the quotient is 4. It tells you how many groups of 6 fit into 24.
Build a quotient from easy partsR
Radian
A radian measures angle using a circle. One radian traces a distance along its edge equal to its radius.
Example: A full turn is 2π radians, and a half turn is π radians.
Explore angles, sine and cosineRadius
The radius is the distance from a circle’s centre to its edge.
Example: A circle centred at (0, 0) and passing through (3, 0) has radius 3.
Explore angles, sine and cosineRatio
A ratio compares quantities by division.
Example: A mix with two red counters for every three blue counters has a red-to-blue ratio of 2:3.
See a ratio in tangentReciprocal
The reciprocal of a non-zero number is 1 divided by that number. Multiplying a number by its reciprocal gives 1.
Example: The reciprocal of 3/4 is 4/3, because (3/4) × (4/3) = 1.
Use reciprocals to divide fractionsRemainder
A remainder is the amount left over when a number does not split exactly into whole groups of a chosen size.
Example: Share 17 counters among 5 people. Each gets 3, with 2 left over: 17 = 5 × 3 + 2.
Right angle
A right angle is a quarter turn, equal to 90°.
Example: Two adjacent sides of a square meet at a right angle.
Find a vector’s lengthRight triangle
A right triangle has one angle of 90°.
Example: A triangle with side lengths 3, 4 and 5 is a right triangle.
Find a vector’s lengthRounding
Rounding replaces a number with a nearby value at a chosen place, such as the nearest ten.
Example: To the nearest ten, 38 rounds to 40. To the nearest hundred, 352 rounds to 400.
Round, then adjust to find the exact answerS
Scalar
A scalar is a single number used to measure or scale a quantity.
Example: In 3 × (2, −1) = (6, −3), the number 3 is the scalar.
Scale a vector with a scalarSine
On a unit circle, sine gives the vertical coordinate of a point at a chosen angle.
Example: sin(90°) = 1 and sin(0°) = 0.
Explore angles, sine and cosineSlope
Slope measures how much y changes compared with a change in x along a line.
Example: If y rises by 6 as x rises by 3, the slope is 6 ÷ 3 = 2.
Read a linear function and its graphSquare root
A square root of a number gives that number when multiplied by itself. The symbol √ asks for the non-negative root.
Example: √25 = 5 because 5 × 5 = 25. Both 5 and −5 square to 25.
Find a vector’s lengthSubtraction
Subtraction finds the amount left after you take something away. It can also find the gap between two amounts. Its sign is −.
Example: You need 83 points and have 67. You need 16 more, because 83 − 67 = 16.
Subtract by counting upSum
The sum is the result of addition.
Example: In 8 + 7 = 15, the sum is 15. The numbers 8 and 7 are the addends.
Find sums by making 10T
Tangent
The tangent of an angle is its sine divided by its cosine. It is undefined where cosine is zero.
Example: tan(45°) = 1, while tan(90°) is undefined.
Understand tangent and its gapsTimes table
A times table lists multiplication facts for one number.
Example: The 4 times table includes 1 × 4 = 4, 2 × 4 = 8 and 3 × 4 = 12.
Build the 4 and 8 times tablesTrigonometry
Trigonometry studies relationships between angles and lengths. Sine, cosine and tangent are three of its main functions.
Example: On a unit circle, sine gives height and cosine gives horizontal position.
Explore angles, sine and cosineU
Unit circle
The unit circle has radius 1 and centre (0, 0). Positive angles start at (1, 0) and turn anticlockwise.
Example: The point at a quarter turn is (0, 1): cosine is 0 and sine is 1.
Explore angles, sine and cosineUnit vector
A unit vector has length 1 and can represent a direction.
Example: The vector (0, 1) is a unit vector pointing up.
Use dot products to compare directionsV
Variable
A variable is a symbol that can stand for a number or take different values.
Example: In y = 2x + 4, x and y are variables.
Read a linear function and its graphVector
A vector describes a size and direction. We write it here as two parts. The zero vector has no direction.
Example: The vector (2, −3) describes a move two units right and three down.
Describe a move with a vectorVector component
A vector component gives one part of a vector along a chosen axis.
Example: In (2, −3), the horizontal component is 2 and the vertical component is −3.
Describe a move with a vectorW
Whole number
A whole number is zero or a positive number with no fractional part.
Example: The whole numbers start 0, 1, 2, 3 and continue upward. Neither −3 nor ½ is a whole number.
Y
Y-intercept
The y-intercept is where a graph crosses the y-axis, at x = 0.
Example: The graph of y = 2x + 4 crosses the y-axis at (0, 4).
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