# Mathematical vocabulary

# Mathematical vocabulary by categories with grade levels

Words are the message, but emotions energize them.

Howard Rankin

*Overview*

- Introduction
- Algebra & patterns
- Calculator
- Data analysis & probability
- Fractions
- Geometry & spatial
- Measurement - linear, area, volume, capacity, weight, mass, time, money, & temperature
- Measurement outcomes by level
- Number values
- Problem solving
- Reasoning & proof

## 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

### Kindergarten - Third Grade

- 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

### Grade 4 - grade 6

- 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

### Grade 7 - 8

- binary operation
- cube
- function
- root,

### Grade 9+

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
- quadrant
- 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*

*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.

**Three**

- trey, triad, trio

- Two and one

*Two*, **Many**, **More**

*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,

#### Fractional values

See fractions

**Operations**

Kindergarten - Third Grade

- add, addition, addend, all, amount (cardinality), Arabic numeral, attribute
- 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
- identify, increase , instead
- 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

### **Operations**

Grade 4 - grade 6

- 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,

**Operations**

Grade 7^{+}

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

### Calculator

#### Kindergarten - Third Grade

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

#### Grade 4 -grade 6

- 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

#### Grade 7 +

- 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)

#### Kindergarten - Third Grade

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

#### Grade 4 -grade 6

- 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

### Kindergarten - grade 3

- 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

### Grade 4 - grade 6

- 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)
- quadrilateral (kite, rhombus, parallelogram)
- 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)

### Grade 7 -

- 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

See also measurement outcomes by grade level

### 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

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

### Grade 4 - 6

#### Measurement

- acre
- baker's dozen
- capacity
- decade
- estimate
- graduated, gross
- 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

#### Money

- currency
- deposit
- withdraw

### Grades 7 - 9

#### Measurement

- avoirdupois
- pi, precision

#### Time

#### Money

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

## Measurement Outcomes by grade level

PreK grade measurement outcomes | |
---|---|

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 |

First grade measurement outcomes | |
---|---|

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 |

Second grade measurement outcomes | |
---|---|

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 |

Third grade measurement outcomes | |
---|---|

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 |

Fourth grade measurement outcomes | |
---|---|

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 |

### Fifth Grade

Fifth grade measurement outcomes | |
---|---|

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 |

### Sixth Grade

Sixth grade measurement outcomes | |
---|---|

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

#### Kindergarten - grade 3

- add, addition, addend, all, amount
- base ten blocks, basic facts, between, both
- column, combine
- difference, digit, division, double
- equal, equivalent, estimate, exact
- fact, fewer
- greater than, given information, group
- identify, increase, instead
- 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

#### Grade 4 -grade 6

- 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

### Kindergarten - grade 5

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

#### Grade 6+

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

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