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"A tray strewn with dust or sand, used in ancient times for calculating. A contrivance for calculating, consisting of beads or balls strung on wires or rods set in a frame."—Wright, 1902

Abacus

"A tray strewn with dust or sand, used in ancient times for calculating. A contrivance for calculating,…

"Abacus is a Latin term applied to an apparatus used by the Chinese for facilitating arithmetical operations, consisting of a number of parallel cords or wires, upon which balls or beads are strung, the uppermost wire being appropriated to units, the next to tens, &c.-In classic architecture it denotes the tablet forming the upper member of a column, and supporting the entablature. In Gothic architecture the upper member of a column from which the arch springs."—(Charles Leonard-Stuart, 1911)

Abacus

"Abacus is a Latin term applied to an apparatus used by the Chinese for facilitating arithmetical operations,…

Two Chinese men use the abacus to calculate for their business. "The abacus was one of the earliest aids to calculation." -Hill, 1921

Chinese Abacus

Two Chinese men use the abacus to calculate for their business. "The abacus was one of the earliest…

"That point in which a right line drawn from the eye parallel to another given right line cuts the picture of plane."-Whitney, 1902

Accidental Point

"That point in which a right line drawn from the eye parallel to another given right line cuts the picture…

Used in businesses and bookkeeping, the adding machine was a device used for calculations. "One of the first successful adding and listing machines (courtesy of the Burroughs Adding Machine Company)." -Hill, 1921

Adding Machine

Used in businesses and bookkeeping, the adding machine was a device used for calculations. "One of the…

"It is found that the cord covering the curved surface is twice as long as the one covering the flat surface. So the area of the entire curved surface of a sphere is equal to the area of the surface of 4 circles like the one measured." -Foster, 1921

Area of Sphere

"It is found that the cord covering the curved surface is twice as long as the one covering the flat…

"The bases of the pyramids are considered as forming the surface of the sphere, while the altitude of the pyramids is the radius of the sphere." -Foster, 1921

Area of Sphere

"The bases of the pyramids are considered as forming the surface of the sphere, while the altitude of…

Illustration of the three bears with three chairs that can be used to write mathematics story problems involving comparison, taller, shorter, highest, lowest, etc..

Three Bears and Chairs

Illustration of the three bears with three chairs that can be used to write mathematics story problems…

Illustration of children sitting on a bench and standing that can be used to write mathematics story problems involving comparison, taller, shorter, highest, lowest, counting, etc.

Children On A Bench

Illustration of children sitting on a bench and standing that can be used to write mathematics story…

Illustration of a child holding blocks that can be used to write mathematics story problems involving addition, subtraction, and counting.

Child Counting Blocks

Illustration of a child holding blocks that can be used to write mathematics story problems involving…

Illustration of a child counting books by twos that can be used to write mathematics story problems involving addition, subtraction, and counting.

Child Counting Books

Illustration of a child counting books by twos that can be used to write mathematics story problems…

The bushel, a unit of dry measure.

Bushel

The bushel, a unit of dry measure.

A calculating machine

Calculating

A calculating machine

Illustration of 20 chicks that can be counted by twos. It can be used to write mathematics story problems involving addition, subtraction, and counting.

Counting Chicks by Twos

Illustration of 20 chicks that can be counted by twos. It can be used to write mathematics story problems…

Illustration of children playing darts that can be used to write mathematics story problems involving addition, subtraction, and comparison.

Children Playing Darts

Illustration of children playing darts that can be used to write mathematics story problems involving…

Illustration of a child buying doll clothes. It can be used to write mathematics story problems involving addition, subtraction, money, and counting.

Child Buying Doll Clothes

Illustration of a child buying doll clothes. It can be used to write mathematics story problems involving…

Illustration of a child buying doll toys. It can be used to write mathematics story problems involving addition, subtraction, money, and counting.

Child Buying Doll Toys

Illustration of a child buying doll toys. It can be used to write mathematics story problems involving…

Illustration of woman selling food in dozens that can be used to write mathematics story problems involving addition, subtraction, and counting.

Woman Selling Dozens of Items

Illustration of woman selling food in dozens that can be used to write mathematics story problems involving…

Illustration of a 6 toy elephants and a toy man that can be used to write mathematics story problems involving addition, subtraction, and counting.

6 Toy Elephants

Illustration of a 6 toy elephants and a toy man that can be used to write mathematics story problems…

"In geometry, a curve generated by the motion of a point on the circumference of a circle which rolls upon the convex side of a fixed circle." -Whitney, 1911

Epicycloid

"In geometry, a curve generated by the motion of a point on the circumference of a circle which rolls…

"Epicycloidal wheel, a wheel or ring fixed to a framework, toothed on its inner side, and having in gear with it another toothed wheel, of half the diameter of the first, fitted so as to revolve about the center of the latter. It is used for converting circular into alternate motion, or alternate into circular." -Whitney, 1911

Epicycloidal Wheel

"Epicycloidal wheel, a wheel or ring fixed to a framework, toothed on its inner side, and having in…

An equilateral triangle is one having all of its sides equal.

Equilateral

An equilateral triangle is one having all of its sides equal.

"Equipotential Lines about two similarly electrified spheres, A and B, the quantities of electricity being as 2:1. The lines of force are also shown radiating from the spheres." -Whitney, 1911

Equipotential

"Equipotential Lines about two similarly electrified spheres, A and B, the quantities of electricity…

Illustration of 6 children playing a game that can be used to write mathematics story problems involving addition, subtraction, and counting.

6 Children Playing Game

Illustration of 6 children playing a game that can be used to write mathematics story problems involving…

"A piece of a parallelogram left after a similar parallelogram has been removed from a corner of it. Thus, in the figure, EFGBCD is a gnomon." -Whitney, 1911

Gnomon

"A piece of a parallelogram left after a similar parallelogram has been removed from a corner of it.…

Illustration of a child buying groceries. It can be used to write mathematics story problems involving addition, subtraction, money, and counting.

Child Buying Groceries

Illustration of a child buying groceries. It can be used to write mathematics story problems involving…

An isosceles triangle is one having two of its sides equal.

Isosceles

An isosceles triangle is one having two of its sides equal.

Illustration of a jack-in-the box and 2 dolls. It can be used to write mathematics story problems involving addition, subtraction, and counting.

Jack-in-the box And Dolls

Illustration of a jack-in-the box and 2 dolls. It can be used to write mathematics story problems involving…

Illustration of a child holding a kite that can be used to write mathematics story problems involving addition and subtraction. For example: John's kite tail was 4 feet long. 1 foot of it broke off. How many feet were left?

Child Holding A Kite

Illustration of a child holding a kite that can be used to write mathematics story problems involving…

A famous Italian artist, mathematician, and engineer.

Leonardo da Vinci

A famous Italian artist, mathematician, and engineer.

Illustration of Little Bo Peep and sheep. It can be used to write mathematics story problems involving addition, subtraction, and counting.

Little Bo Peep And Sheep

Illustration of Little Bo Peep and sheep. It can be used to write mathematics story problems involving…

Students measuring fruits and grains, converting quarts, pecks, and bushels.

Measuring Grains

Students measuring fruits and grains, converting quarts, pecks, and bushels.

Illustration of 2 children measuring liquids in pints and quarts. It can be used to write mathematics story problems involving measurement.

Children Measuring Liquid

Illustration of 2 children measuring liquids in pints and quarts. It can be used to write mathematics…

Illustration of 2 children comparing multiplication flash cards. It can be used to write mathematics story problems involving multiplication.

Children Holding Multiplication Cards

Illustration of 2 children comparing multiplication flash cards. It can be used to write mathematics…

Illustration of children holding number cards that can be used to write mathematics story problems involving addition, subtraction, and comparison.

Children Holding Number Cards

Illustration of children holding number cards that can be used to write mathematics story problems involving…

The peck, a unit of dry measure.

Peck

The peck, a unit of dry measure.

Illustration of a child with 8 quarts and 1 peck. He is using the baskets to practice measuring. It can be used to write mathematics story problems involving addition, subtraction, money, measurement, and counting.

Child Measuring Using Pecks And Quarts

Illustration of a child with 8 quarts and 1 peck. He is using the baskets to practice measuring. It…

Visualizing measurement with different containers that hold one pint and one quart.

Pints and Quarts

Visualizing measurement with different containers that hold one pint and one quart.

Three students work from using dots as counters in columns (left) to writing the symbolic number (right).

Place Value

Three students work from using dots as counters in columns (left) to writing the symbolic number (right).

Illustration of three rabbits and a carrot that can be used to write mathematics story problems involving addition and subtraction.

Three Rabbits With Carrot

Illustration of three rabbits and a carrot that can be used to write mathematics story problems involving…

Illustration of two rabbits and 8 carrots that can be used to write mathematics story problems involving addition and subtraction.

Two Rabbits With 8 Carrots

Illustration of two rabbits and 8 carrots that can be used to write mathematics story problems involving…

A rectangle is a parallelogram whose angles are all right angles.

Rectangle

A rectangle is a parallelogram whose angles are all right angles.

A rhomboid is a parallelogam whose opposite sides are equal, and whose angles are not right angles.

Rhomboid

A rhomboid is a parallelogam whose opposite sides are equal, and whose angles are not right angles.

A rhombus is a rhomboid having equal sides.

Rhombus

A rhombus is a rhomboid having equal sides.

A right-angled triangle is any triangle having one right angle. The side opposite the right angle is called the hypotenuse. A right-angled riangle may be isosceles or scalene.

Right-Angled

A right-angled triangle is any triangle having one right angle. The side opposite the right angle is…

Illustration of 12 books labeled with Roman Numerals.

Books With Roman Numerals

Illustration of 12 books labeled with Roman Numerals.

Illustration of cards that can be used for a matching game with Roman numerals, English numerals, and words.

Matching Game With Roman Numerals

Illustration of cards that can be used for a matching game with Roman numerals, English numerals, and…

"In geometry, certain transcendental curves having, in polar coordinates, equations of the form ρ = a cos b θ. A, three-leaved rose of equation ρ = a sin 3 θ." -Whitney, 1911

Rose

"In geometry, certain transcendental curves having, in polar coordinates, equations of the form ρ…

"In geometry, certain transcendental curves having, in polar coordinates, equations of the form ρ = a cos b &theta. B, three-leaved rose of equation ρ = a cos 3 &theta." -Whitney, 1911

Rose

"In geometry, certain transcendental curves having, in polar coordinates, equations of the form ρ…

"In geometry, certain transcendental curves having, in polar coordinates, equations of the form ρ = a cos b &theta. C, four-leaved rose of equation ρ = a sin 2 &theta." -Whitney, 1911

Rose

"In geometry, certain transcendental curves having, in polar coordinates, equations of the form ρ…

"In geometry, certain transcendental curves having, in polar coordinates, equations of the form ρ = a cos b &theta. D, four-leaved rose of equation ρ = a cos 2 &theta." -Whitney, 1911

Rose

"In geometry, certain transcendental curves having, in polar coordinates, equations of the form ρ…

Illustration of a child measuring with rulers that can be used to write mathematics story problems involving comparison, measurement, etc.

Child Holding Rulers

Illustration of a child measuring with rulers that can be used to write mathematics story problems involving…

Illustration of two children holding rulers that can be used to write mathematics story problems involving comparison, taller, shorter, highest, lowest, etc.

Children Holding Rulers

Illustration of two children holding rulers that can be used to write mathematics story problems involving…

Illustration of children holding rulers that can be used to write mathematics story problems involving comparison, taller, shorter, highest, lowest, etc.

Children Holding Rulers

Illustration of children holding rulers that can be used to write mathematics story problems involving…

"Nodal Cubic, with four primary lines and their satellite. In the diagram, ABC is the satellite line. From its intersections with the cubic curve tangents are drawn to the latter, AD, AE, BF, BG, CH, CI. The points of tangency lie three by three on four primary lines, FDH, DGI, EGH, FEI." -Whitney, 1911

Satellite

"Nodal Cubic, with four primary lines and their satellite. In the diagram, ABC is the satellite line.…

A scalene triangle is one having no two of its sides equal.

Scalene

A scalene triangle is one having no two of its sides equal.

"In geometry: (a) A plane figure inclosed between the arc of a circle, ellipse, or other central curve and two radii to its extremities from the center. Thus, in the figure, CDB is a sector of a circle." -Whitney, 1911

Sector

"In geometry: (a) A plane figure inclosed between the arc of a circle, ellipse, or other central curve…

The curve of a sine wave.

Curves of sines

The curve of a sine wave.

A square is a rectangle whose sides are all of the same length.

Square

A square is a rectangle whose sides are all of the same length.

Illustration of a child reading at school at 10:00. It can be used to write mathematics story problems involving telling time and roman numerals.

Telling Time 10:00 Story Problem

Illustration of a child reading at school at 10:00. It can be used to write mathematics story problems…