 # Mathematical vocabulary by categories with grade levels

Words are the message, but emotions energize them.

Howard Rankin

## Introduction

This collection of mathematical vocabulary started as a suggestion from a lead math teacher who wanted to provide continuity across classes and grades in an elementary school. At first, it seemed a list wouldn't include all that many words, however, our initial list has grown to include many more words than we initially envisioned. Hopefully, it is a good source for you to create your own lists for your grade levels.

## Algebra & patterns & functions

• conjecture
• element, empty set, equation, even number, expanded numeral, expressions
• input
• mathematical
• open sentence, output
• rename
• sentence, sequence, similar, solution, symbol, subset
• unequal, unknown, unnamed
• variable

• absolute value, additive, arithmetic mean,
• dependent variable, distributive property
• exponent
• formula
• identify, independent variable, inequality, integer, intersection of sets, inverse
• linear
• negative
• opposite
• parentheses, prime, property
• notation
• reciprocal
• square root
• union of sets

• binary operation
• cube
• function
• root,

Derivative - an expression that represents the rate of change of a function with respect to an independent variable. Velocity is the first derivative of an object's motion. Acceleration is its second.

## Data analysis

### K - 3

• average
• bar graph
• data
• grid
• picture graph
• table, tally, trial

### 4 - 6

• broken line graph
• descriptive statistics
• equally likely events
• frequency, factor tree
• generalization
• histogram
• inference, interpret, interpolate
• line graph, line plot
• mean, media, midway, mode
• ordered pair, outcome
• probability
• random range, ratio
• sample, scale drawing, simple event, statistics

### 7 - 9

• box plot
• compound event, circle graph
• error of measurement, extrapolate
• mutually exclusive
• outlier
• quartile
• scatter plot, skew lines, stem and leaf plot
• whisker

## Number sense: number values, operations, calculator, & fractions

### Names for numbers, values, cardinality, ordinality, ...

Obviously before a number value can be assigned to something, there needs to be a name to communicate the value assigned the number value. Assigning a number value isn't the same as counting as a number value or cardinality can be determined without counting (subitize).

#### Things to count

Things to count can be singular, alone, solitary, sole, separate, exclusive, whole, complete, overlapping, and combined.

• Objects, things, items, artifacts, properties, attributes, borders, edges, surfaces, shapes ...

#### Vocabulary for number values

##### One
• ace, alone, complete, digit, exclusive, first, isolated, lone, object, one, only, particular, self, separate, set, single, singular, sole, solitary, solo, thing, unique, unit, unitary, whole,
• Names that imply singular: A specific name of something, object, image, person, space.
• Smallest whole number. One and zero.
• Pronouns - each, I, me, you, it, this, that, here, there,
##### Two
• binary, copy, couple, deuce, double, duet, duo, dual, duo, duplicate, dyad, har, match, mate, pair, twin, replica, second,
• Pronouns - them, they, us
• Together brother sister identical, plural, repeat, similar, same,
• One and one.
• Two and one
##### Two, Many, More
• additional, all, a lot, also, bounty, bountiful, bunch, countless, covey, crowd, extra, few, flock, finite, gaggle, group, handful, heaps, herd, horde, infinite, innumerable, people, piles, pride, quantity, lots, many, most, much, multiple, multitude, myriad, numerous, scattering, several, some, sprinkling, tons, umpteen,
• Pronouns - us, they, them, those, others, more,
• Animal names: ox, oxen; goose, geese;
##### Zero
• aught, cipher, empty, goose egg, nada, nil, nix, none, not, nothing, nought, null, vacant, zilch, zip
Starting point, rock bottom, least,

#### Sequence

• First, second, third, fourth, fifth, sixth, seventh, eighty, ninth, tenth
• fewest
• average, center, median, middle,
• majority
• nearly all
• all,
• greatest, maximum,

See fractions

### Operations Kindergarten - Third Grade

• base ten blocks, basic facts, between, both
• cardinality / cardinal value, a number used to indicate value (how many) , classify, column, combine, commutative property, compare, compute, count, combining a spoken number word with the actual or conceptualized objects cardinal value
• difference, digit, division, double
• each, element, eleven, twelve, thirteen… , equal, equivalent, estimate, exact, expanded, extra(neous) information
• fact, fewer, first, second, third…
• given information, greater than, group
• hundred
• least, left overs, less
• many, match, middle, minuend, minus, missing, model, more, multiplication,
• number, a written or stated symbol that represents the value / cardinality of a set , number line, numeral, a written or stated symbol that represents a number , numeration, one, two, three…ten
• operations
• place value (ones, tens…)
• plus, product
• regroup, related facts, Roman Numerals, rounding
• same, sign, skip counting, solve, standard numeral, subtract, subtraction, sum,
• total
• whole number
• zero

• actual, adjacent, alternative, approximately, array, associative property, at least, at most
• calculate, cardinal, common multiple, composite number
• decimal, decimal point, determine, distributive property, dividend, divisor
• extrapolate
• factor
• geometric pattern
• if….then, infinite set, insufficient information
• magic square , multiple , multiplication, member, multiplier
• natural number, natural order
• place value, prime, prime factorization, problem, property, proportion,
• quotient
• ratio, remainder, repeating decimal, rule
• score, statement
• terminate, times
• value,

• generalization
• scientific notation, square root, system
• universal set, upper limit

### Calculator

• calculator display, clear key, constant feature
• equals key
• keystrokes
• minus key, multiplication key
• plus key
• suppressed zero

• clear entry key
• decimal key, division key
• E error sign,
• memory and the functions of the keys: memory plus, memory minus, clear memory, recall memory,
• order of operations sequence

• opposite of key, overflow
• percent key, percent of increase, percent of decrease
• square root key
• underflow

### Fractions

Fractional parts without specific quantity

part, piece, portion, portion, share, slice, chunk, fraction, section, member, region, territory, bit, hunk, morsel, crumb, shred, cut, )

Fractional parts with a quantity other than half: thirds, fourths, fifths,

(Also Fraction concepts)

• 16 ths, 8 ths, 4 ths, 3rds
• fraction
• half, one-half, twin
• less than
• more than
• one - fourth, one - third
• unit

• 10 ths, 100 ths, 12 ths, 18 ths, 20 ths, 50 ths, 6ths, 9 ths
• common denominator, convert
• decimal, denominator
• equivalent decimals, equivalent fractions
• greatest common factor
• higher term fraction
• improper
• least common fraction, lowest term fraction
• mixed numeral
• numerator
• percent, proportion
• rate, ratio, reciprocal
• simplest terms, simplify

## Geometry and spatial relationships

• alike, angle, area, attribute blocks
• box
• carton, center, circle, closed, cone, congruent, connect, construct, contain, corner, corresponding, crooked, cube, curve, curved, cylinder
• edge, end point
• face, figure, flip, flat
• geometry
• hexagon, horizontal
• inside
• on, open, outside
• parallelogram, pattern block, pentagon, point
• rectangle, room, rotate, round, ruler
• same shape, same size, segment, side, size, solid, sphere, square, stairs, straight, straightedge, symmetry: line of symmetry, folding symmetry, mirror symmetry
• Tangrams, tessellation, tile, tilt, triangle, tube, turn
• vertical
• whole, width

• altitude, angle (acute, obtuse, right), arc, axis
• base
• circle (center, diameter, radius, semicircle), compass, construction, coordinates
• diagonal, diagram
• hemisphere
• image, intersect
• line, line of symmetry, line segment
• parallel, perimeter, perpendicular, pi , plane, polygon, population density, prism (square, triangular), pyramid (square, triangular)
• radius, ray, reallotment, reflections, rotations (half - turn, quarter - turn)
• scale drawing, semi - circle, similar, surface area, symmetrical, symmetry
• translation, trapezoid, triangle (equilateral, right, isosceles, scalene),
• vertex, view (front, side, top)

• central, chord, circumscribe, closed curve, complimentary, coordinate system, cross section
• enlargement
• interior
• median, midpoint, n - gon
• prism with any base, pyramid with any base, Pythagorean
• relation, radian, reduction, regular n - gon
• scalene triangle, secant, sectors, size transform, supplementary
• tangent, theorem

## Measurement, time, money

### K - 3

#### Measurement

• apart, area
• box
• Celsius, centimeter, cm, cubic unit
• decimeter dm, degree, dimension, distance, dozen
• empty
• Fahrenheit, foot, feet
• gallon, gram, g
• height
• inch
• kiloliter, kl, kilogram, kg, kilometer km
• length, linear unit, liter, l
• measure, measurement, meter, m, meter stick, metric unit, mile , milligram, mg, millimeter, mm, milliliter, ml
• ounce
• pint, pound
• quart
• rectangular, ruler
• scale
• tablespoon, teaspoon , thermometer, temperature
• volume
• weight, width
• yard , yardstick

#### Time

• after, afternoon, alarm, a.m.
• before, birthday, breakfast
• calendar, clock (long hand, short hand)
• daily, date, day (school day, vacation day, week day), days, days of the week (Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, Sunday) during
• early, evening
• half hour, holiday, holidays, hour
• late
• midday, minute, minutes, month, months (January, February, March, April, May, June, July, August, September, October, November, December), morning
• night, noon,
• p.m.
• quarter hour
• season, seasons, second. seconds
• time, today, tomorrow, tonight
• watch, week
• year, yesterday

#### Money

• cent, change, cost
• dime, dollar
• half - dollar
• monetary value, money
• nickel
• pay, penny
• quarter
• save, sell, spend

#### Measurement

• acre
• baker's dozen
• capacity
• estimate
• perimeter, protractor
• quart
• scale, squared foot, square inch, square meter, square mile
• ton
• yearly

#### Time

• century
• Earth rotation - day, Earth orbit - year
• month - mo0n
• seasons

• currency
• deposit
• withdraw

#### Measurement

• avoirdupois
• pi, precision

#### Money

• discount
• interest: rates, compound, simple
• mark up
• profit
• rate

## Measurement Outcomes by grade level

Linear Longer, shorter, compare objects linear measures
Measurement with continuous objects (snap cubes, strings of paper clips, strips of paper, yarn ...)
Estimation: visualize non-standard unit compared to what you don't know (blocks, paper clips)
Area Tiling problems (how many tiles to cover this paper? How many cards are needed to cover the desk?)
Volume & Capacity Volume: which container can hold more (i.e. compare two trash cans)
Weight & Mass Use a balance
Time Duration of a minute, second
Identify different events as occurring during the day: morning, noon, or night
Identify numerals on a clock

General Identify objects as larger, smaller, more, equal, less
Use nonstandard units to measure
Identify tools of measurement (clock, calendar, balance, ruler) and use of tools
Linear Longer, shorter, compare objects linear measures
Measurement with continuous objects (snap cubes, strings of paper clips, strips of paper, yarn ...)
Estimation: visualize non-standard unit compared to what you don't know (blocks, paper clips)
Area Tiling problems (how many tiles to cover this paper? How many to cover the desk?)
Volume & Capacity Volume: which container can hold more (i.e. compare two trash cans)
Weight & Mass Put objects on a balance and identify the heavier or lighter
Use nonstandard comparisons
Time Identifying past, present, and future
Duration of a minute, second, weeks, months, years
Identify different events as occurring during the day: morning, (AM) noon, or night (PM)
Tell time to the half hour(**)
Money Identify penny, nickel, dime, quarter, dollar
Temperature Hot (swimming weather or warmer) medium (room temperature) cold (Winter jackets snow, ice, refrigerator)
Temperature relates to the season

Linear Vocabulary: centimeters, length, foot, meter Measure to the nearest foot, inch, estimating lengths of objects
Area Tiling problems (hexagons on a triangle, desk area)
Volume & Capacity Recognize cup, pint, quart, gallon
Compare capacities of different containers.
Weight & Mass Identify ounces, pounds,
Weigh using a scale
Time Tell time on digital and analog clocks
Solve problems using a calendar that involve days, weeks, months, and holidays
Classify events as past, present, and future
Huge clocks with numbers, add something to represent every minute (dots, cubes, cut out dots with a paper punch and glue them around the clock model) Elapsed time
Temperature Read a thermometer (should be one-to-one correspondence, 0-100 showing each increment)
Money Identify penny, nickel, dime, quarter, dollar
Solve for equivalent values of different collections of money.
Temperature Hot warm cool cold

Linear Tell that standard units help communicate measurements better than non standard.
Identify standard units (inches, feet, meters)
Figuring out how many "large steps" or "baby steps" from one place to another.
Using various objects to measure lengths (toothpicks, straws, cards, pieces of paper)
Estimate to the nearest inch using a measuring device (or meter, centimeter, etc.) what a particular measurement is. Perimeter
Area Placing square cards within a large shape drawn on the floor. Students count the number of squares within the shape to estimate the area of the shape.
Draw a floor plan of bedroom and estimate the area the objects in the room take up. Use graph paper to help estimate (make a "bird's eye view plan").
Volume & Capacity Arrange a group of different sized containers from least volume to most volume. Estimate volumes of irregular shapes.
Weight & Mass Students estimate the weights of two objects, then place the objects on a two-pan balance and find each object mass/weight.
Time Complete a time line of the student's day. Listing activities done and at what time.
Create a clock showing hours and minutes.
Estimate ages of family members, closest to a century old, decade old, year old.
Money Identify penny, nickel, dime, quarter, dollar
Solve for equivalent values of different collections of money.
Count money
Count change by counting up
Solve money problems
Temperature Hot warm cool cold freezing boiling Celsius Fahrenheit
Estimate

General Use measurement in problem solving Explore metric system Measuring using nonstandard and standard units
Linear Use metric units
Measure fractional parts of an inch
Explore feet, yards, miles
Area Find area in shapes with right angles
Estimate area in irregular shapes
Volume & Capacity Find capacity Quarts in a gallon
Weight & Mass Use metric units
Time Tell time to the nearest minute and second Elapsed time AM PM military time
Angles Use a protractor to measure angles Measure angles in degrees
Identify obtuse, right, and acute angles
Temperature Celsius and Fahrenheit
Money Count money
Count change by counting up
Solve money problems

Linear Know how to measure using various instruments (inches, feet, yards, miles, millimeters, centimeters, meters, kilometers) to 1/2 of a unit.
Area Find and label area in square units for linear measurements
Find area for rectangles, squares, right triangles, and other figures with right angles.
Estimate area of irregular shapes.
Volume & Capacity Find volume of cubes, rectangular prisms
Weight & Mass Use a balance Use ounces, pounds, tons, grams, kilograms, and metric tons to find the mass of objects
Time Tell time and do time problems with seconds, minutes, hours, days, months, and years
Angles Use a protractor to measure angles Measure angles in degrees
Identify obtuse, right, and acute angles
Money Count money
Count back change by counting up
Solve money problems with and without decimals

Linear Measure using various instruments (inches, feet, yards, miles, millimeters, centimeters, meters, kilometers) to 1/2 of a unit.
Find perimeter of polygons, circles,
Area know how to find and label (square units for linear units) area (rectangles, squares, parallelograms, triangles, circles)
Estimate area of irregular shapes.
Find the surface area of shapes that have faces that are (rectangles, squares, parallelograms, triangles, circles)
Volume & Capacity Cups, pints, quarts, gallons, milliliter, liter,
Know how to find and label (cubic units) volume
Compare cubic units to volume in metric system
Find volume of cubes, rectangular prisms, cylinders triangular prisms
Make three dimensional models of prisms, pyramids, cylinders
Identify properties of three dimensional shapes.
Weight & Mass Use a balance Use ounces, pounds, grams, and kilograms to find the mass of objects
Time Tell time and do time problems with seconds, minutes, hours, days, months, and years
Angles Use a protractor to measure angles Measure angles in degrees
Temperature Use a thermometer and read temperature to one degree
Metric Visual representation of mm cm m km g kg ml l
the students will know a quart is a little less than a liter, meter is a little more than a yard, Kilogram is a little more than two pounds. A Kilometer is a little more than a mile. Estimate foot and yard to meters
Money Count money
Count change by counting up
Solve money problems with and without decimals
Solve money problems involving percents.

## Problem solving

• base ten blocks, basic facts, between, both
• column, combine
• difference, digit, division, double
• equal, equivalent, estimate, exact
• fact, fewer
• greater than, given information, group
• least, left overs, less
• many, minus, minuend, missing. model, multiplication,
• number
• operation,
• place value, plus, product
• regroup, rounding
• skip count, solve, sum, subtract, subtraction, sign,
• total

• actual, adjacent, alternative, approximate, array, associative property, at least, at most,
• calculate, cardinal, common multiple, composite number
• decimal, decimal point, determine, distributive property, divide, dividend, divisor
• factor
• geometric pattern, generalization
• if, then, infinite set, insufficient information
• magic square, multiple, multiply, multiplication, member, multiplier
• natural number, natural order,
• place value, prime, prime factor, prime factorization, problem, property, proportion
• quotient
• ratio, remainder, repeating decimal, rule
• score, statement, scientific notation, square root, system,
• terminate, times
• universal set, upper limit
• value

## Reasoning & Proof

• analysis
• conjecture, counter example
• definition
• explanation
• logic
• premise, proof, properties,
• reason, representation, rigor

• Proposition: If X, then Y.
• Inverse: If ~X, then ~Y.
• Converse: If Y, then X.
• Contrapositive: If ~Y, then ~X.

Notes

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