📖 Math Glossary

Combining two groups to make a whole (+)

Identifying circles, squares, triangles, rectangles

Days of week, months, seasons

Counting objects, comparing quantities

Longer/shorter, heavier/lighter concepts

Comparing quantities using more, less, equal

Identifying numerals 0–20

Writing numerals correctly, number formation

First, second, third positions

Recognizing and extending patterns

Above, below, beside, next to, in front, behind

Visual addition word problems within 5 (+)

Sorting and categorizing objects

Categorizing objects by attributes

Taking away from a whole (-)

Defining and composing shapes

Identifying penny, nickel, dime, quarter

Greater than, less than, equal to (>, <, =)

Simple graphs and charts

Introduction to halves and fourths

Relating addition and subtraction

Using comparison symbols correctly (<, >, =)

Reading clocks at half-past

Non-standard and standard units

Finding unknown in equations (5 + ? = 8) (+)

Part-part-whole relationships for numbers to 10

Using number lines for addition and subtraction (+, -)

Understanding base-ten system (Decomposition by 10s)

Counting and organizing with tallies

Reading clocks to hour and half-hour

Adding three numbers together (+)

Adding numbers up to 100 (+)

Subtracting numbers up to 100 (-)

Real-world applications

Equal groups in rows and columns

Creating and interpreting data

Mixed coins (calculating totals)

Division concept introduction (÷)

Reasonable estimates for small numbers

Classifying numbers

Organizing measurement data on line plots

Using rulers to measure length

Standard units of length (in, ft, cm, m)

Adding 10, 100; subtracting 10 mentally (+, -)

Coins, dollars, and counting money ($, ¢)

Patterns in 100s chart

Understanding 3-digit place value deeply

Time to 15-minute intervals

Carrying and borrowing

Foundation for multiplication (+)

Understanding sides, vertices, angles

Counting by multiples

Reading, writing, and comparing

Reading analog and digital clocks

Measuring rectangles and squares (P=2l+2w, A=lw)

Reading and creating scaled graphs

Repeated subtraction (÷)

Understanding and calculating remainders (÷)

Time intervals and duration

Finding factors of numbers up to 100

Comparing fractions to determine which is larger (<, >, =)

Part-to-whole relationships (a/b)

Organizing categorical data

Cups, pints, quarts, gallons

Converting within same system

Repeated addition (×)

Fluency with 0-12 multiplication tables (×)

Finding perimeter of various shapes (P = sum of all sides)

Understanding multiplication properties

To nearest 10 and 100

Interpreting scales on bar graphs

Each symbol represents multiple units

Reading clocks and elapsed time

Reading thermometers, Fahrenheit/Celsius

Understanding 1/2, 1/3, 1/4, etc. (1/n)

Ounces, pounds, grams, kilograms

Measuring angles with protractor (°)

By angles (acute, right, obtuse) and sides (equilateral, isosceles, scalene)

Plotting points in first quadrant ((x, y))

Comparing decimal values (<, >, =)

Understanding tenths and hundredths

Relationship to fractions

Simplifying fractions (a/b = c/d)

Divisibility rules and factor pairs

Visual representations (number lines, area)

Ordering multiple fractions (<, >, =)

Finding greatest common factor (GCF)

Creating and interpreting data

Multi-digit divisors (÷)

Whole + fractional parts (a b/c)

2-digit × 2-digit multiplication (×)

Finding least common multiple (LCM)

Measuring angles with protractor

Approximation to nearest place (≈)

Lines of symmetry in figures

Properties of quadrilaterals and triangles

Plotting in first quadrant ((x,y))

Understanding volume units (units³)

Histograms, line graphs, stem-and-leaf plots

Operations with decimals (+, -, ×, ÷)

Dividing with decimal divisors (÷)

Powers of 10 and basic exponent notation (10ⁿ)

Writing and evaluating numerical expressions

Adding and subtracting unlike denominators (a/b ± c/d)

Multiplying and dividing fractions ((a/b) × (c/d), (a/b) ÷ (c/d))

Converting between fractions and decimals (÷)

Solving real-world problems with fractions

Creating and interpreting trends over time

Calculating and interpreting mean (sum ÷ count)

Converting between different units

Identifying rules and sequences

Sequence of operations (PEMDAS)

Parentheses, exponents, multiplication/division, addition/subtraction (PEMDAS)

Understanding percent as per hundred (%)

Multiplying/dividing by powers of 10 (10^n)

Numbers divisible only by 1 and itself

Identifying prisms, pyramids, cylinders, cones, spheres

Three-dimensional measurement (V = l × w × h)

Distance from zero (|x|)

Area of triangles and composite shapes (A = ½bh)

Reading and creating box-and-whisker plots

Plotting points ((x,y))

Using reciprocals to divide fractions (÷, reciprocal)

Visual representation for ratios and proportions

Writing and evaluating algebraic expressions

Using GCF to simplify fractions (GCF)

Frequency distributions with intervals

Positive and negative numbers

Understanding spread in data (Q3 - Q1)

Using LCM for adding fractions (LCM)

Additional measures of center

Number line with negative values

Solving simple equations (x + a = b, ax = b)

All four operations with positive and negative numbers (+, -, ×, ÷)

Finding percentages of quantities (% × n)

Per hundred relationships (% = part/whole × 100)

Speed, cost per unit, unit conversion (rate = distance/time)

Equivalent ratios in table format (a:b)

Comparing quantities (a:b = c:d)

Analyzing data distributions (mean, median, mode, range)

Nets and surface area of prisms (SA = 2lw + 2lh + 2wh)

Triangle properties and angle relationships (Sum of angles = 180°)

2D measurement (A=lw, A=πr²)

Circumference and area (C=2πr, A=πr²)

Simplifying expressions by combining terms

Angle relationships and pairs (90°, 180°)

Expanding expressions using distribution (a(b + c) = ab + ac)

Using variables (y = mx + b)

Comparing values (x > y)

Solving complex algebraic equations with multiple operations

Tax, tip, discount, markup

Percent increase and decrease ((new - old)/old × 100%)

Simple probability concepts (P(A) = favorable/total)

Direct proportion and constant of proportionality (y = kx)

Listing all possible outcomes

Proportional reasoning (scale factor)

Principal, rate, time calculations (I = PRT)

Solving multi-step equations (ax + b = c)

Circular base volume calculations (V = πr²h)

Two-variable relationships and correlation

Finding distance between two points (d = √[(x₂-x₁)² + (y₂-y₁)²])

Repeated multiplication (aⁿ)

Categorical data with two variables

Linear vs non-linear functions (y = f(x))

Identifying function types from tables/graphs

Right triangle relationships (a²+b²=c²)

Number classification and properties

Cube roots and higher-order roots (³√, ⁴√)

Correlation and trend lines

Working with very large and small numbers (a × 10ⁿ)

Visual solution method for systems

Rate of change (m=(y₂−y₁)/(x₂−x₁))

Solving linear systems (y = mx + b)

Translations, rotations, reflections, dilations

3D measurement (V=lwh)

Advanced 3D geometry volume (V = (1/3)πr²h, V = (4/3)πr³)

Solving equations with absolute value (|x| = a)

Quadratic solving method (x² + bx + (b/2)²)

Real-world exponential problems (y = a(1±r)ᵗ)

Breaking down expressions (x²+bx+c=(x+m)(x+n))

Shifts, stretches, reflections of functions (f(x) + k, f(x + h), af(x))

Input-output mapping (f(x))

Substitution, elimination, graphing methods

Basic function families (linear, quadratic, etc.)

Combining like terms (ax²+bx+c)

Parabolic relationships (ax²+bx+c=0)

Using formula to solve quadratics (x = [-b ± √(b²-4ac)]/2a)

Simplifying and operations with radicals (√x, ∛x)

Simplifying rational expressions (a/b)

Graphing and properties (y = √x)

Inscribed angles and tangent lines

Arcs, sectors, circle theorems (arc length, sector area)

Counting principles (nCr, nPr)

Probability given conditions (P(A|B) = P(A∩B)/P(B))

Probability and expected outcomes (E(X) = Σ(x·P(x)))

Bell curves and standard scores (z-score)

Chance of events (P(A)=favorable/total)

Line of best fit for data (y = mx + b)

Converting between linear equation forms (Ax + By = C → y = mx + b)

Analyzing data sets (mean, median, mode)

Graphing and solving (y > mx + b)

Ratios of sides in right triangles (sinθ, cosθ, tanθ)

Circle calculations with radians (s = rθ, A = (1/2)r²θ)

Operations with imaginary unit i (a + bi)

Equations of conic sections (parabola, ellipse, hyperbola)

Growth and decay (y=a·bˣ)

Finding and graphing inverses (f⁻¹(x))

Non-right triangles (c²=a²+b²−2abcosC)

Triangle relationships (a/sinA=b/sinB)

Inverse of exponents (logₐx=y ↔ aʸ=x)

Long division and synthetic division

Fractional exponents and radical form (x^(m/n) = ⁿ√(xᵐ))

nth term and recursive formulas (aₙ = a₁ + (n-1)d, aₙ = a₁rⁿ⁻¹)

Arithmetic and geometric series (Σ, Sₙ)

Pythagorean and reciprocal identities (sin²θ + cos²θ = 1)

Trigonometry on the unit circle (x² + y² = 1)

Vertical, horizontal, and oblique asymptotes

Composite function derivatives (dy/dx = dy/du × du/dx)

Function continuity concepts and definitions

Instantaneous rate of change (dy/dx)

Area under a curve (∫f(x)dx)

Evaluating limits of indeterminate forms (lim f/g = lim f'/g')

Approaching values in calculus (lim(x→a) f(x))

Array operations ([a b; c d])

Parametric curves and eliminating parameters (x = f(t), y = g(t))

Converting between polar and rectangular (r, θ)

Asymptotes and graphing (f(x) = p(x)/q(x))

Sum of patterns (Σaₙ)

Measure of spread (σ=√Σ(x−μ)²/n)

Vector operations and applications (⟨x,y,z⟩)