From Manipulatives to Concepts

The following is a listing of some of the concepts that can be effectively taught using the given manipulatives. The list is recommended by the National Council of Supervisors of Mathematics, Supporting Leaders in Mathematics Education: A Source Book of Essential Information, 1994.

Algebra tiles

integers, equations, inequalities, polynomials, similar terms, factoring, estimation

Attribute blocks

sorting, classification, investigation of size, shape, color, logical reasoning, sequencing, patterns, symmetry, similarity, congruence, thinking skills, geometry, organization of data

Balance scale

Weight, mass, equality, inequality, equations, operations on whole numbers, estimation, measurement

Base-ten blocks

place value, operations on whole numbers, decimals, decimal-fractional-percent equivalencies, comparing, ordering, classification, sorting, number concepts, square & cubic numbers, area, perimeter, metric measurement, polynomials

Calculators

problems with large numbers, problem solving, interdisciplinary problems, real-life problems, patterns, counting, number concepts, estimation, equality, inequality, fact strategies, operations on whole numbers, decimals, fractions

Capacity containers

Measurement, capacity, volume, estimation

Clocks

times, multiplication, fractions, modular arithmetic, measurement

Color tiles

color, shape, patterns, estimations, counting, number concepts, equality, inequality, operations on whole numbers and fractions, probability, measurement, area, perimeter, surface area, even and odd numbers, prime and composite numbers, ratio, proportion, percent, integers, square and cubic numbers, spatial visualization

Compasses

constructions, angle measurement

Cubes

number concepts, counting, place value, fact strategies - especially turnaround facts, classification, sorting, colors, patterns, square and cubic numbers, equality, inequalities, averages, ratio, proportion, percent, symmetry, spatial visualization, area, perimeter, volume, surface area, transformational geometry, operations on whole numbers and fractions, even and odd numbers, prime and composite numbers, probability

Cuisenaire rods

classification, sorting, ordering, counting, number concepts, comparisons, fractions, ratio, proportion, place value, patterns, even and odd numbers, prime and composite numbers, logical reasoning, estimation, operations on whole numbers

Decimal Squares

decimals - place value, comparing, ordering, operations, classification, sorting, number concepts, equality, inequality, percent, perimeter, area

Dominoes

counting, number concepts, fact strategies, classification, sorting, patterns, logical reasoning, equality, inequality, mental math, operations on whole numbers

Fraction models

fractions—meaning, recognition, classification, sorting, comparing, ordering, number concepts, equivalence, operations, perimeter, area, percent, probability

Geoboards

size, shape, counting, area, perimeter, circumference, symmetry, fractions, coordinate geometry, slopes, angles, Pythagorean Theorem, estimation, percent, similarity, congruence, rotations, reflections, translations, classification, sorting, square numbers, polygons, spatial visualization, logical reasoning

Geometric solids

shape, size, relationships between area and volume, volume, classification, sorting, measurement, spatial visualization

Math balance; Invicta, number

equality, inequality, operations on whole numbers, open sentences, equations, place value, fact strategies, measurement, logical reasoning

Miras

symmetry, similarity, congruence, reflections, rotations, translations, angles, parallel & perpendicular lines, constructions

Money

money, change, comparisons, counting, classification, sorting, equality, inequality, operations on whole numbers, decimals, fractions, probability, fact strategies, number concepts

Number cubes

counting, number concepts, fact strategies, mental math, operations on whole numbers, fractions, decimals, probability, generation of problems, logical reasoning

Numeral cards

counting, classification, sorting, comparisons, equality, inequality, order, fact strategies, number concepts, operations on whole numbers, fractions, decimals, logical reasoning, patterns, odd and even numbers, prime and composite numbers

Pattern blocks

patterns, one-to one correspondence, sorting, classification, size, shape, color, geometric relationships, symmetry, similarity, congruence, area, perimeter, reflections, rotations, translations, problem solving, logical reasoning, fractions, spatial visualization, tessellations, angles, ratio, proportions

Polyhedra models

shape, size, classification, sorting, polyhedra, spatial visualization

Protractors

constructions, angle measurement

Rulers; Tape measures

measurement, area, perimeter, constructions, estimation, operations on whole numbers, volume

Spinners

counting, number concepts, operations on whole numbers, decimals, fractions, fact strategies, mental math, logical reasoning, probability, generation of problems

Tangrams

geometric concepts, spatial visualization, logical reasoning, fractions, similarity, congruence, area, perimeter, ratio, proportion, angles, classification, sorting, patterns, symmetry, reflections, translations, rotations

Ten-frames

fact strategies, mental math, number concepts, counting, equality, inequality, place value, patterns, operations on whole numbers

Thermometers

temperature, integers, measurement

Two-color counters

counting, comparing, sorting, classification, number concepts, fact strategies, even and odd numbers, equality, inequality, operations, ratio, proportions, probability, integers