Math and learning glossary
Short, plain definitions of the math words students meet from elementary school through Algebra II, and of the testing and privacy terms California schools use.
Numbers and operations
- Absolute value
- A number's distance from zero, which is never negative. The absolute value of −6 is 6.
- Factor
- A whole number that divides another with no remainder. The factors of 12 are 1, 2, 3, 4, 6, and 12.
- Greatest common factor (GCF)
- The largest factor two numbers share. The GCF of 12 and 18 is 6.
- Least common multiple (LCM)
- The smallest number that is a multiple of both. The LCM of 4 and 6 is 12, which is why 12 works as a common denominator for fourths and sixths.
- Integer
- A whole number or its negative, such as −3, 0, or 8.
- Rational number
- Any number that can be written as a fraction of two integers, such as 3/4, −2, or 0.5.
- Irrational number
- A number that cannot be written as a fraction of two integers, such as the square root of 2 or pi. Its decimal never ends or repeats.
- Exponent
- A small raised number that says how many times the base is used as a factor. 2 to the 5th power is 2 × 2 × 2 × 2 × 2, which is 32.
- Square root
- A number that multiplies by itself to give the original. The square root of 49 is 7.
- Scientific notation
- A way to write very large or small numbers as a number at least 1 and less than 10, times a power of ten. 4,500,000 is 4.5 × 10⁶.
- Order of operations
- The agreed order for simplifying expressions: parentheses, exponents, multiplication and division from left to right, then addition and subtraction from left to right.
Fractions, ratios, and percents
- Numerator and denominator
- The top and bottom of a fraction. The denominator says how many equal parts make a whole, and the numerator says how many of those parts you have.
- Equivalent fractions
- Fractions that name the same amount, such as 3/4 and 6/8.
- Common denominator
- A shared denominator that lets you add or subtract fractions. 2/3 + 1/4 becomes 8/12 + 3/12, which is 11/12.
- Ratio
- A comparison of two quantities, such as 3 cups of flour to 2 cups of sugar.
- Unit rate
- A rate for one unit of something, such as 60 miles per hour or $2 per pound.
- Proportional relationship
- Two quantities that always have the same ratio, so one is a constant multiple of the other. Its graph is a straight line through the origin.
- Percent
- A ratio out of 100. 15% of 40 is 6.
Algebra and functions
- Variable
- A letter that stands for a number you do not know yet or that can change, such as x.
- Coefficient
- The number multiplying a variable. In 7x, the coefficient is 7.
- Expression
- Numbers, variables, and operations without an equals sign, such as 3x + 12.
- Equation
- A statement that two expressions are equal, such as 3x + 7 = 22. Solving it means finding x = 5.
- Inequality
- A statement that one side is greater or less than the other, such as x > 4. Its solutions are usually a range of numbers.
- Distributive property
- Multiplying a sum by multiplying each part. 3(x + 4) = 3x + 12.
- Like terms
- Terms with the same variable part, such as 4x and −2x, which can be combined to 2x.
- Function
- A rule that gives exactly one output for each input. Written f(x), read "f of x."
- Domain and range
- The inputs a function accepts and the outputs it produces.
- Slope
- How steep a line is, found as rise over run. The line through (1, 2) and (3, 8) has slope 6/2, which is 3.
- Y-intercept
- Where a graph crosses the y-axis, the b in y = mx + b.
- System of equations
- Two or more equations solved together. The solution is the point that makes all of them true.
- Quadratic equation
- An equation with a squared variable as its highest power, such as x² − 5x + 6 = 0.
- Parabola
- The U-shaped graph of a quadratic function.
- Discriminant
- The expression b² − 4ac in the quadratic formula. Its sign tells you whether there are two, one, or no real solutions.
Geometry and measurement
- Area
- The amount of flat space inside a shape, measured in square units.
- Perimeter
- The distance around a shape.
- Volume
- The amount of space inside a solid, measured in cubic units.
- Pythagorean theorem
- In a right triangle, the squares of the two shorter sides add up to the square of the longest side. A triangle with sides 3, 4, and 5 is a right triangle because 9 + 16 = 25.
- Transformation
- A move of a shape on the plane, such as a translation (slide), reflection (flip), rotation (turn), or dilation (resize).
- Congruent
- The same size and shape.
- Similar
- The same shape but possibly a different size, with all side lengths scaled by the same factor.
Statistics and probability
- Mean
- The average, found by adding the values and dividing by how many there are. For 2, 3, 3, 5, 7, the mean is 4.
- Median
- The middle value when the data are in order. For 2, 3, 3, 5, 7, the median is 3.
- Mode
- The most frequent value. For 2, 3, 3, 5, 7, the mode is 3.
- Range (in statistics)
- The largest value minus the smallest. For 2, 3, 3, 5, 7, it is 5.
- Probability
- How likely something is, from 0 (impossible) to 1 (certain).
- Scatter plot
- A graph of paired data points used to look for a relationship between two quantities.
Learning, testing, and privacy terms
- Standards
- The statements of what students should know and be able to do by the end of each grade. California uses the California Common Core State Standards for Mathematics and the California Next Generation Science Standards (CA NGSS).
- CAASPP
- The California Assessment of Student Performance and Progress, the state testing system. It includes the Smarter Balanced tests in math and English and the California Science Test (CAST).
- Formative assessment
- Checking understanding during learning, such as an exit ticket or a quick question, so teaching can adjust.
- Scaffolding
- Temporary support, like a hint or a simpler related problem, that is removed as a student gains confidence.
- Productive struggle
- Working through a problem that is hard but reachable, rather than being shown the answer right away.
- Fluency
- Being able to do a skill accurately and efficiently, such as recalling multiplication facts, without heavy effort.
- Intervention
- Extra, targeted instruction for students who need more support on specific skills.
- FERPA
- The Family Educational Rights and Privacy Act, a federal law that protects the privacy of student education records.
- COPPA
- The Children's Online Privacy Protection Act, a federal law that requires websites and online services aimed at children under 13, or that knowingly collect data from them, to get verifiable parental consent before collecting a child's personal information.
- SOPIPA
- California's Student Online Personal Information Protection Act, which limits how education technology companies may use student data, including a ban on targeted advertising to students.
Questions
What is the difference between an expression and an equation?
An expression, like 3x + 12, has no equals sign and can only be simplified or evaluated. An equation, like 3x + 7 = 22, says two things are equal and can be solved.
What is the difference between a rational and an irrational number?
A rational number can be written as a fraction of two integers, so its decimal ends or repeats. An irrational number, like pi or the square root of 2, cannot, and its decimal goes on forever without repeating.
Is range in statistics the same as range of a function?
No. In statistics, range is the largest value minus the smallest. For a function, range is the set of all outputs it can produce.
What does CAASPP measure?
CAASPP is California's statewide testing system. It measures progress on the state standards in English language arts and math in grades 3 to 8 and 11, and in science through CAST.