Download Essential Math Vocabulary—Elementary

Essential Math Vocabulary
This partial list of essential math concepts was compiled for educational purposes. It does not
necessarily reflect the policy or position of the California After School Resource Center (CASRC) or
the California Department of Education (CDE). Intended as a quick reference or tool for supporting
mathematics, the list provides key terms, corresponding symbols, customary abbreviations,
examples, related terms (“must-know” vocabulary), and instructional tips. (It is not a glossary).
Educators are advised to seek more comprehensive resources (e.g., curricula and professional
materials), such as those available from the CASRC library, to support students in after school
programs.
Key Term
add
Symbols, Abbreviations,
or Examples
+ (plus)
Related Terms & Instructional Tips
addend, addition, sum, total, combine
Tip: Young students starting school benefit from using
manipulatives, such as counters, to practice addition.
algebraic
expression
9x
(An expression for nine
times a number)
amount
angle
numbers, symbols, variables, unknown, operations
Tip: Algebra is essential to real-life problem-solving in
science, engineering and design, architecture, and
routine tasks. Understanding the properties of addition
and multiplication will help students to solve algebraic
expressions.
amt.
quantity
∠
ray, vertex, intersect, point, trigonometry (the study of
angles, triangles, and their functions), sine, cosine
An Acute Angle
Types of angles:
right angle (equal to 90º)
obtuse angle (greater than 90º)
acute angle (less than 90º)
complementary angles (add up to 90º)
supplementary angles (add up to 180º)
bisector (a ray dividing an angle into two equal parts)
Tip: Use protractors to help elementary students measure
a variety of angles, which are found in just about every
corner of objects and places.
Associative
Property
Associative Property of
Addition
(5+3)+9 = 5+(3+9)
Associative Property of
Multiplication
(4x7)2 = 4(7x2)
In addition, the sum (total) is not affected by the grouping
of the addends.
In multiplication, the product (answer) is not affected by
the grouping of the factors.
Tip: Help students understand this property by explaining
that numbers “associate” with different “friends” inside the
parenthesis, but the outcome is the same.
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average
avg.
mean (the sum of a set of numbers divided by the number
of elements in the set)
Tip: Use real-life examples, such as sports statistics or
class data, to help students compute averages.
calendar
Sun. (Sunday)
Mon. (Monday)
Tues. (Tuesday)
Wed. (Wednesday)
Thurs. (Thursday)
Fri. (Friday)
Sat. (Saturday)
day, week/ly, month/ly,
annual, yearly
Seasons: spring, summer, fall/autumn, and winter
Tip: Help young students develop their sense of time by
having a daily calendar activity and talking about when
different activities occur throughout the day. Discuss
holidays and other special days as appropriate.
Jan. (January)
Feb. (February)
Aug. (August)
Sept. (Sept.)
Oct. (October)
Nov. (November)
Dec. (December)
cardinal
numbers
morning, noon/afternoon, midnight, evening, night
0, 1, 2, 3 …
counting numbers
Digits include 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9.
Tip: Do your students know how to hyphenate numbers
from 21 to 99 (e.g., seventy-three)? Use a math journal,
word hunts and puzzles, and other fun ways to help
students learn how to spell numbers.
cent
¢
clock
A.M.
P.M.
change (money left over after buying something)
coins:
penny (singular), pennies (plural)
nickel, dime, quarter, half dollar, silver dollar
Tip: Ask parents and school members to donate items for
a class sale. Engage students in running the sale and
counting the profit, if any. Use the money toward a worthy
cause (e.g., a field trip or a charity donation).
o’clock, watch, wristwatch
half, quarter to, past, until
Tip: Do your students know how to skip count by fives? If
they do not, they may have a difficult time telling time on
a clock. Lots of examples and practice telling time should
help.
Commutative
Property
Commutative Property
of Addition
25+79 = 79+25
Commutative Property
of Multiplication
11x3 = 3x11
In addition, the sum (total) is not affected by the order of
the addends.
In multiplication, the product (answer) is not affected by
the order of the factors.
Tip: Help students understand this property by explaining
that numbers “commute” or travel back and forth, but the
outcome is the same.
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compare
coordinates
order, sequence, similar, different
greater than >
less than <
equal =
Tip: As a scaffold, pretend that the greater than (>) sign is
an alligator that “eats” the bigger number to help young
students compare two numbers.
The Coordinates of
Point A = 2, 3
Y
A (2, 3)
3
2
1
grid, y-axis, x-axis, abscissa, point, ordered pair, vertical,
horizontal
Tip: Create math artwork by having students locate and
connect several coordinates on a grid to reveal a hidden
design. Graph paper can be useful for this.
X
0 1 2 3
cost
Price, dollar sign
Tip: Manage the occasional behavior management
problem by implementing a “token economy,” whereby
students are “charged” a certain amount of make-believe
“cash” for misbehaving. (Adding up their “infractions” will
help them understand the concept of cost and increase
their self-control).
decimal point
.
ones, tenths, hundredths, thousandths, etc.
Tip: Help students keep track of decimal points by using
graph paper and placing each digit in a square.
degree
divide
º
÷ and /
(divided by)
double
dozen
equal
2+2, 3+3, 4+4, 5+5,
6+6, 7+7, 8+8, 9+9,
10+10, etc.
doz.
=
Tip: In math, the term “degree” can apply to measuring
temperature, as well as to angle measurements.
divisor, dividend, quotient, remainder
dividend ÷ divisor = quotient
Tip: Division requires students to know their addition,
subtraction, and multiplication facts, and to apply all of
them in a systematic manner. Using graph or lined paper
turned sideways to keep the digits lined up as they divide
may be helpful.
duplicate, two of the same, pair
Tip: Double facts help students solve operations faster
and understand other fact relationships, such as:
4+4+1=9
(If students know that 4+4=8, they will add the 1 and
arrive at 9 faster).
twelve, half-dozen (6)
Same, opposite of unequal (≠)
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equation
An Equation
number sentence or two mathematical expressions that
are equal
Tip: Present equations as a game where the object is to
find the “mystery number” (variable). Use the concept of a
scale where both sides must balance equally.
even number
Examples:
34, 80, and 126
estimate
59 + 24 is about 85
divisible by 2 or ending in 0, 2, 4, 6, or 8
(opposite of odd numbers)
Tip: Play a movement game by asking students to jump
up and down if a number you call is odd, and to clap if it is
even. Call out a few numbers, alternating between odds
and evens.
round, guess, approximation, mental math (computing in
your head)
(numbers rounded to 60
Tip: Help students develop their sense of quantity by
and 25)
estimating the number of items in a jar, or the actual cost
of things.
exponent
52
exponent
base
This problem is read as,
“Five to the second power
or five squared.”
fact family
Addition/Subtraction
9 + 3 = 12
3 + 9 = 12
12 – 3 = 9
12 – 9 = 3
Multiplication/Division
7 x 2 = 14
2 x 7 = 14
14 ÷ 7 = 2
14 ÷ 2 = 7
figure
Fig.
Flat Figures:
exponent, power, base, square, cube, expanded form,
standard form, repeated multiplication
Tip: Help students experiment with exponents by writing
out the factors in the problem. For instance,
5
9 =9x9x9x9x9
5=
9 59,049
related addition and subtraction or division and
multiplication facts
Tip: Use flash cards, repetition, educational toys, and
games to help students memorize addition and
subtraction facts. These are critical to more advanced
operations, such as multiple-digit multiplication and
division.
shape, flat/plain, three-dimensional/solid,
round, square, rectangular, polygon
trapezoid
parallelogram
octagon
Tip: Play a game of “human geometry” by asking students
to make geometric figures using their fingers, arms, legs,
or getting into small groups to position their bodies to
form shapes.
Solid Figures:
cylinder
rectangular prism
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formula
Formulas exist for:
side, base, length, width, pi, square and cubic units
• Perimeter (distance
around a figure
• Area (the square unit
measure of the
interior region of a
figure
• Circumference (the
perimeter of a circle)
• Volume (how many
cubic units it takes to
fill up a solid.
Tip: Know these three basic formulas.
Figure
Polygon
Formula
Perimeter = P
Example
P = s1 + s2 + …
(where s = side)
3cm
P = 3+3+3+3+3
P = 15 cm
Square
Perimeter = P
P = 4s
7in.
P = 4(7)
P = 28 in.
Circle
fraction
Circumference = C
C = 2Πd
(where pi
represented by Π is
about 3.14 and d
stands for
diameter)
3m
C = 2Πd
C = 2 x 3.14 x 6
C = 37.68 m
numerator, denominator, common denominator, shaded,
part, whole, equivalent, proper, improper
Tip: Help students in grades four through six compare
fractions by cross-multiplying them, such as in the
example below:
Which fraction is greater, ¾
Cross-multiply:
or ⅝?
3 x 8 = 24 and 4 x 5 = 20
3
4
frequency
f
graph
5
8
Therefore, ¾
>⅝
mean, median, mode, outlier, and histogram (a graph
used to show numerical relationships)
pictograph, bar graph, pie graph, etc.
Note: A graph is a table or pictorial device used to show
relationships between numbers.
line
Segment
Lines can extend to infinity in both directions.
Ray
Tip: Explain that lines can extend to infinity in both
directions, while rays start at a certain point along a line
and continue, and segments refer to only a part of a line.
Line
Perpendicular lines
Parallel lines
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measurement
Units of Measurement:
centimeter (cm.)
gram (g.)
inch (in.)
liter (L.)
meter (m.)
milliliter (mL.)
ounce (oz.)
multiply
x and *
(times)
unit, area, distance, length, width, perimeter, volume
Tip: Measurement may be abstract and challenging for
students. Provide ample opportunities for them to
measure real objects using various tools, including rulers,
tape measures, containers, and thermometers. Invite
them to hop, gallop, run, crawl, or skip from place to place
to figure out how fast or slow they can move across small
distances.
group, product, multiple, factor, and array
Tip: An array is a set of objects in equal rows or columns
used to show groups. Allow students to make arrays
using math unifix cubes to visually show groupings
involved in multiplication.
a 3-by-2 array of 6 stars
or
3X2=6
negative
-
number line
absolute value (the distance of a number from zero,
always a positive number, represented by (II)
Number Line with
Positive and Negative
Numbers
odd number
numbers less than zero
Examples:
21, 79, and 345
Tip: Number lines help students understand locations,
distance, intervals, and other relationships among
numbers. Using sidewalk chalk, paint a big number line
on the playground, and invite students to move back and
forth along the line to represent addition and subtraction,
negative and positive numbers, etc.
numbers ending in 1, 3, 5, 7, or 9
(opposite of even numbers)
Tip: Play a game of thumbs-up or thumbs-down by asking
students to show thumbs-up if a number you call is odd,
or thumbs-down if it is even. Call out a few numbers,
alternating between odds and evens.
one-to-one
correspondence
A Matching Game
counting, representing, matching one object to another
(critical to counting)
Tip: Invite young students to play a variety of music
instruments with distinct sounds. Have others clap or
dance to the rhythms they hear. Then ask them to count
and move simultaneously to help them understand oneto-one correspondence.
opposite
contrary, inverse (as in inverse operations, such as
addition and subtraction, as well as multiplication and
division
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ordinal numbers
first, second, third, fourth, fifth, sixth, seventh, eighth,
ninth, tenth, etc.
1st
2nd
3rd
pattern
Tip: Ask students to line up and state their position along
the line using ordinal numbers. Invite them to make signs
to have them practice the spelling and/or abbreviations
associated with ordinals.
something that repeats itself or changes in a regular way
(e.g., a design or configuration)
Tip: Use pattern blocks to have students create patterns.
Invite them to showcase their patterns and take turns
figuring out their classmates’ patterns.
percent
%
place value
Tip: A percentage is simply a comparison of a number to
100. Use a hundreds chart to help students shade in
different percentages (color 10 squares to show 10%, 25
squares to show 25%, and so on).
Tip: Digits have a value according to their place/location
within a number. Help students understand place value
by starting with small numbers, and building on that for
bigger numbers. Place mats and improvised charts are
great for helping students put the correct digits on the
correct place value location.
Place Value Chart
polygon
Examples of Simple
Polygons
simple (one boundary), complex (intersects itself), convex
(no angles pointing inwards), concave (internal angles
greater than 180º), regular (all angles equal), and
irregular (angles vary)
Tip: Teach the meaning of prefixes associated with
polygons to help students remember the number of sides
in each figure:
Prefix
positive
prepositions
+
9, 10, 11
before between after
triquad-
Meaning/
# of Sides
3
4
pentahexaheptaoctanonadeca-
5
6
7
8
9
10
Polygon
triangle
quadrilateral (squares,
rectangles, trapezoids)
pentagon
hexagon
heptagon
octagon
nonagon
decagon
numbers greater than zero
above, after, before, below, beneath, beside, between,
next, next to, over, etc.
Tip: These words help students understand math
directions and problems. Play a game of “Simon Says” to
help students understand the meanings of prepositions.
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ratio
regroup
/
Regrouping
Tens
4
5
-3
1
Ones
17
7
9
8
ruler
comparison of two numbers using division
ones, tens, hundreds, thousands, ten thousands …
Tip: Avoid using the terms “borrow” and “carry,” as these
have been replaced with “regroup” because technically,
that is what is happening (numbers are regrouped into a
group of ten).
Tip: A device used for measuring or drawing straight lines
takes some practice for young students who are still
developing their locomotor skills. Use small rulers first,
and move bigger ones over time.
season
Tip: Discuss the look and feel of spring, summer,
fall/autumn, and winter with young students.
The Four Seasons
biggest
bigger
size
skip count
Skip Counting by
5s and 12
Tip: Adjectives, comparatives, and superlatives, such as
short(er/est), long(er/est), big(ger/est), small(er/est), are
useful to students in making math comparisons.
Tip: Skip counting helps students understand intervals,
perform operations, and remember facts (e.g., addition
and multiplication). Play a game of hopscotch to practice
skip counting outdoors.
Other ways to skip
count:
2, 4, 6, 8, 10, 12 …
5, 10, 15, 20 …
10, 20, 30, 40 …
11, 22, 33, 44, 55 …
solution
strategy
•
•
•
•
•
•
A solution of
3y = 18 is y = 6
To answer, solve, or figure out the value that makes an
equation true is to find a solution.
Math Strategy
Examples
understand, plan, solve, check, use logic
Drawing conclusions
Working backwards
Finding clue words
Find a pattern
Make a table
Draw a picture
Tip: Encourage students to use a variety of problemsolving strategies, and to share their approaches with
each other.
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square root
√
Subtract
- (minus)
Tip: Help students understand square roots as a special
value that when multiplied by itself gives the same
number. Having an understanding of exponents may
help.
difference, take away, less
Tip: Have students line up around a sheet or a parachute.
As a class, count several bean bags before adding them
to the center of the parachute or sheet. Invite everyone to
lift it, tossing the beanbags into the air. Catch as many as
possible, prompting students to subtracting those that fall
off. Repeat several times, checking or writing out the
problems on the board as needed.
symmetry
symmetrical
symmetrical (two halves match)
asymmetrical (two halves do not match exactly)
asymmetrical
temperature
Thermometer
thermometer, degrees, weather
Tip: People in many foreign countries measure how hot or
cold it is using Celsius (C) scale, while the United States
uses the Fahrenheit (F) scale. Help students understand
temperatures by calling out a few weather forecasts, and
inviting them to act out whether they will feel mild, cold, or
hot.
triangle
Types of Triangles
Equilateral: equal
sides and angles
measuring 60º
Isosceles: two equal
sides and angles
Scalene: no equal
sides or angles
Right: contains
one 90º angle
variable
Zero Property of
Multiplication
In 9n, the variable is n.
nx0=0
equilateral, isosceles, scalene, right, obtuse, acute, base,
height, arm, Pythagorean Theorem
Tip: Help students understand how to compute the area
of triangles using the formula Area = ½ bh, where b
stands for the base, and h stands for the height of the
triangle.
h = 8 cm.
A = ½ (b x h)
A = ½ (5 cm x 8 cm)
2
A = 20 cm.
b = 5 cm.
unknown, a symbol that stands for a quantity (e.g., x or y)
The product of any number and zero is zero.
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