Mathematical vocabulary by dimensional categories and 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

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

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

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

It is important to consider how learning and logic is developed by different learners at diiferent times of their development.

PreK grade measurement outcomes
General outcomes demonstrated with Linear measurement	Identify what (property or attribute) is being measured. Objects measurements are conserved when they are moved. Moving an object does not change the measurement of its properties or its attributes (length). Compare longer, shorter, with direct measurement of objects for linear measurement. Demonstrate iteration of units, which can be copied, arranged, and repeated to measure with a single unit being reused. Measure the entire length by iterating objects (snap cubes, strings of paper clips, strips of paper, yarn along the entire distance without gaps or overlaps (continuous). Estimate by visualizing a non-standard unit compared to what you don't know book is so many (blocks, paper clips ... )
Area	Solve tiling problems (how many tiles to cover this paper? How many cards are needed to cover the desk?)
Volume & Capacity	Demonstrate which container can hold more (i.e. compare two trash cans, containers of water and sand.)
Weight & Mass	Use a balance to compare weight and mass.
Time	Guess at the 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. Objects measurements are conserved when they are moved. Moving an object does not change the measurement of its properties or its attributes (length). Use nonstandard units to measure Identify tools of measurement (clock, calendar, balance, ruler) and use of tools Recognize units can be partitioned into fractional amounts smaller than the nonstandard unit.
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	Solve tiling problems like how many tiles to cover this paper? How many to cover the desk?)
Volume & Capacity	Solve volume problems like 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	zIdentify temperature as hot (swimming weather or warmer) medium (room temperature) cold (Winter jackets snow, ice, refrigerator) Explain that temperature relates to the season.

Second grade measurement outcomes
General	Objects measurements are conserved when they are moved. Moving an object does not change the measurement of its properties or attributes (length, area, volume). Identify an appropriate standard unit of measure for all categories below. Measure to the nearest whole standard and non standard unit. Visualize lengths of objects and explain how they visualize its iteration to measure. Recognize units can be partitioned into fractional amounts smaller than the standard unit. Recognize a standard unit facilitates conmmunication. Explain what is counted and what numbers represent on clocks and rulers.
Linear	Identify an appropriate standard unit of measure forlength: centimeters, foot, meter to measure length. Measure to the nearest foot, inch, centimeter, and meter. Visualize lengths of objects and explain how they visualize its iteration to measure. Like there are about ten inches across the cover of a book with their fingers. Recognize linear units can be partitioned into fractional amounts smaller than the standard unit.
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 objects 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	Identify temperatures as hot warm cool cold.

Third grade measurement outcomes
General	Identify appropriate standard units of measure for all categories below. Measure to the nearest whole standard and non standard unit. Visualize units of measurement and explain how they can be iterated to measure. Recognize units can be partitioned into fractional amounts smaller than the standard unit. Identify that standard units help communicate measurements better than non standard. Each measurement tool has a conventional zero point, but any point can be used as an unconventinal zero point. Explain what is counted and what numbers represent on different measurement tools. (rulers, clock, protractor). Explain how measuring tools are more efficient than using multiple single units.
Linear	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. Determine perimeter.
Area	Placing square cards within a large shape drawn on the floor. 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	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	Identify temperatures as hot warm cool cold freezing boiling Celsius Fahrenheit
Estimate	Estimate by visualizing a non-standard unit compared to what you don't know by iteration. A book is so many blocks or paper clips long.

Fourth grade measurement outcomes
General	Objects measurements are conserved when they are moved. Moving an object does not change the measurement of its properties or attributes (length, area, volume, angle). Identify appropriate standard units of measure for all categories below. Measure to the nearest whole standard and non standard unit. Visualize units of measurement and explain how they can be iterated to measure. Recognize units can be partitioned into fractional amounts smaller than the standard unit. Identify that standard units help communicate measurements better than non standard. Use measurement in problem solving . Explore advantages of the metric system. Measure using nonstandard and standard units. Explain how measuring tools are more efficient than using multiple single 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
Estimation	Estimate by visualizing a non-standard unit compared to what you don't know by iteration.

Fifth Grade

Fifth grade measurement outcomes
General	Identify appropriate standard units of measure for all categories below. Measure to the nearest whole standard and non standard unit. Visualize units of measurement and explain how they can be iterated to measure. Recognize units can be partitioned into fractional amounts smaller than the standard unit. Identify that standard units help communicate measurements better than non standard. Use measurement in problem solving . Explore advantages of the metric system. Measure using nonstandard and standard units. Units can be used as additive. They can be composed and decomposed. (ten can be used as a composition of six units and four units or ten units of one group). Explain how measuring tools are more efficient than using multiple single units.
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 to determine mass and weight. Solve problems with 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
Estimation	Estimate by visualizing a non-standard unit compared to what you don't know by iteration.

Sixth Grade

Sixth grade measurement outcomes
General	Identify appropriate standard units of measure for all categories below. Measure to the nearest whole standard and non standard unit. Visualize units of measurement and explain how they can be iterated to measure. Recognize units can be partitioned into fractional amounts smaller than the standard unit. Identify that standard units help communicate measurements better than non standard. Use measurement in problem solving . Explore advantages of the metric system. Measure using nonstandard and standard units. Explain how measuring tools are more efficient than using multiple single units. Units can be used as additive. They can be composed and decomposed. (ten can be used as a composition of six units and four units or ten units of one group). The same property or attribute of an object can be measured with different units, and the resulting measurements are inversely proportional to the size of the unit. Different standard units can be converted to other units of the same type of measurement. All measurement is a approximate. The choice of unit in relation to the object determines the precision. Measures are transitive. ( if A > B and B > C, then A > C).
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	Solve measurement problems 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 ni degrees.
Temperature	Use a thermometer and read temperature to one degree
Metric	Visual representation of mm cm m km g kg ml l Know a quart is a little less than a liter. Know a meter is a little more than a yard, Know a kilogram is a little more than two pounds. Know a kilometer is a little more than a mile. Estimate feet and yards to meters
Money	Count money. Count change by counting up. Solve money problems with and without decimals. Solve money problems involving percents.
Estimation	Estimate by visualizing a non-standard unit compared to what you don't know by iteration.

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
- Objects can be compared;
- Individually - holistically, numerically, shape, length, perspective, symmetry, attributes, equivalence, mass, volume, arbitrary units, standard units, angle, parallel, coordiantes,
- As sets - pairs, attributes, similarity, sort by attribute, sort by attributes, ordering, inclusion, order size, mass, volume, length, linear, unions, area, perimeter,
- Operations addition, subtraction, multiplication, division
- Place value, bases, modular,
- Formal operational
- Integers,
- Fractions
- ermutations
- Combinations
- Ratio
- Similarity
- Continuity
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.

Notes

Mathematical vocabulary by categories & grade levels

Introduction

Algebra & patterns & functions

Kindergarten - Third Grade

Grade 4 - grade 6

Grade 7 - 8

Grade 9+

Data analysis

K - 3

4 - 6

7 - 9

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

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

Things to count

Vocabulary for number values

One

Two

Three

Two, Many, More

Zero

Sequence

Fractional values

Operations Kindergarten - Third Grade

Operations Grade 4 - grade 6

Operations Grade 7+

Calculator

Kindergarten - Third Grade

Grade 4 -grade 6

Grade 7 +

Fractions

Kindergarten - Third Grade

Grade 4 -grade 6

Geometry and spatial relationships

Kindergarten - grade 3

Grade 4 - grade 6

Grade 7 -

Measurement, time, money

K - 3

Measurement

Time

Money

Grade 4 - 6

Measurement

Time

Money

Grades 7 - 9

Measurement

Time

Money

Measurement Outcomes by grade level

Fifth Grade

Sixth Grade

Problem solving

Kindergarten - grade 3

Grade 4 -grade 6

Reasoning & Proof

Kindergarten - grade 5

Grade 6+

Operations
Kindergarten - Third Grade

Operations
Grade 4 - grade 6

Operations
Grade 7⁺