Concepts to Manipulatives to References

Algorithms -- algebra tiles, calculators/graphing calculators, games/puzzles/toys, geoboards, money, dice/number cubes, computers/Internet/software/spreadsheets

Amplitude -- protractors, calculators/graphing calculators, rulers/tape measures/trundle wheels/callipers

Angles -- protractors, compasses, geoboards, miras/mirrors/reflective material, rulers/tape measures/trundle wheels/callipers, computers/Internet/software/spreadsheets, measures/trundle wheels/callipers, pattern blocks, calculators/graphing calculators, clinometer/transit

Area/surface area -- geoboards, base-ten blocks, cubes/Unifix cubes, pattern blocks, rulers/tape measures/trundle wheels/callipers, geometric shapes, paper/origami/stencil patterns/graph paper/geometric solids/polyhedra/nets

Calculus - calculators/graphing calculators, dice/number cubes, candy/food, models/simulation, computers/Internet/software/spreadsheets, paper/origami/stencil patterns/graph paper, books/journals/newspapers/portfolios

Circular functions -- calculators/graphing calculators, computers/Internet/software

Classification/sorting/making sets -- cubes/Unifix cubes, pattern blocks, money, base-ten blocks, geometric solids/polyhedra/nets, geoboards, computers/Internet/software/spreadsheets, money, maps/projections/globe, calculators/graphing calculators, models/simulation, candy/food, tower of Hanoi/Atlantis, paper/origami/stencil patterns/graph paper, games/puzzles/toys, building blocks/Lego, geometric shapes

Coordinate/analytic geometry -- computers/Internet/software/spreadsheets, geoboards, calculators/graphing calculators, books/journals/newspapers/portfolios, paper/origami/stencil patterns/graph paper

Conic sections -- computers/Internet/software/spreadsheets, calculators/graphing calculators, paper/origami/stencil patterns/graph paper, models/simulation

Constructions -- computers/Internet/software/spreadsheets, miras/mirrors/reflective material, rulers/tape measures/trundle wheels/callipers, compasses, protractors

Counting/skip-counting/one-to-one correspondence -- cubes/Unifix cubes, geoboards, games/puzzles/toys, spinners, dice/number cubes, money, calculators/graphing calculators, computers/Internet/software/spreadsheets, compasses, video technology/multi-media

Decimals -- base-ten blocks, money, calculators/graphing calculators, dice/number cubes, spinners, computers/Internet/software/spreadsheets, candy/food

Dimensionality/3D/2D -- building blocks, geometric shapes, geometric solids/polyhedra/nets, computers/Internet/software/spreadsheets, cubes/Unifix cubes, paper/origami/stencil patterns/graph paper, pattern blocks, fractal cards, models/simulation, knitting needles, rulers/tape measures/trundle wheels/callipers, maps/projections/globe, candy/food, calculators/graphing calculators

Discrete mathematics -- computers/Internet/software/spreadsheets, calculators/graphing calculators

Dow Jones industrial average -- computers/Internet/software/spreadsheets, books/journals/newspapers/portfolios

Dynamic geometry/mathematics -- models/simulation, paper/origami/stencil patterns/graph paper, calculators/graphing calculators, computers/Internet/software/spreadsheets, books/journals/newspapers/portfolios

Equality/equivalence/inequality/equations -- algebra tiles, calculators/graphing calculators, games/puzzles/toys, money, cubes/Unifix cubes, clocks/stopwatches/calendars, rollers, protractors, compasses, telephone, computers/Internet/software/spreadsheets, geoboards, building blocks/Lego, geometric shapes, video technology/multi-media, rulers/tape measures/trundle wheels/callipers, paper/origami/stencil patterns/graph paper, games/puzzles/toys, balance scale/weights/scales, models/simulation, candy/food, books/journals/newspapers/portfolios

Estimation -- geoboards, balance scale/weights/scales, rulers/tape measures/trundle wheels/callipers, computers/Internet/software/spreadsheets, calculators/graphing calculators, games/puzzles/toys

Euclidean geometry -- compasses, calculators/graphing calculators, games/puzzles/toys, computers/Internet/software/spreadsheets, pattern blocks, paper/origami/stencil patterns/graph paper, rulers/tape measures/trundle wheels/callipers

Fibonacci sequences/numbers -- computers/Internet/software/spreadsheets, calculators/graphing calculators

Fractal geometry/chaos theory -- fractal cards, calculators/graphing calculators, pattern blocks

Fractions -- computers/Internet/software/spreadsheets, pattern blocks, base-ten blocks, geoboards, clocks/stopwatches/calendars, cubes/Unifix cubes, money, calculators/graphing calculators, dice/number cubes, spinners, games/puzzles/toys

Functions -- calculators/graphing calculators, computers/Internet/software/spreadsheets, compasses, geoboards, video technology/multi-media, protractors, rulers/tape measures/trundle wheels/callipers, paper/origami/stencil patterns/graph paper, games/puzzles/toys, candy/food, telephone, models/simulation, rollers, books/journals/newspapers/portfolios

Geometry -- calculators/graphing calculators, cubes/Unifix cubes, compasses, geoboards, geometric shapes, games/puzzles/toys, geometric solids/polyhedra/nets, miras/mirrors/reflective material, protractors, paper/origami/stencil patterns/graph paper, models/simulation, video technology/multi-media, balloons, rollers, maps/projections/globes, knitting needles, math tables/number lines/100s charts/10x10 grid/circle chart, dice/number cubes, pattern blocks, books/journals/newspapers/portfolios, candy/food, computers/Internet/software/spreadsheets, building blocks/Lego, rulers/tape measures/trundle wheels/callipers

Hamiltonian circuit -- maps/projections/globe

Horsepower -- clocks/stopwatches/calendars, balance scale/weights/scales, calculators/graphing calculators, rulers/tape measures/trundle wheels/callipers

Hyperbolic geometry/functions -- computers/Internet/software/spreadsheets

Integers -- computers/Internet/software/spreadsheets, calculators/graphing calculators, base-ten blocks, games/puzzles/toys, video technology/multi-media, algebra tiles, candy/food

Iteration/recursion -- calculators/graphing calculators, computers/Internet/software/spreadsheets, building blocks/Lego, pattern blocks, books/journals/newspapers/portfolios

Latitude/longitude -- rulers/tape measures/trundle wheels/callipers, clinometer/transit, knitting needles, maps/projections/globe, candy/food, calculators/graphing calculators, compasses, protractors

Linear algebra/matrices/determinants/vectors -- calculators/graphing calculators, spinners, computers/Internet/software/spreadsheets, games/puzzles/toys, dice/number cubes

Logistic growth model -- calculators/graphing calculators, models/simulation

Maps &emdash; geometric shapes, geometric solids/polyhedra/nets, paper/origami/stencil patterns/graph computers/Internet/software/spreadsheets, games/puzzles/toys, miras/mirrors/reflective material, video technology/multi-media, calculators/graphing calculators, rulers/tape measures/trundle wheels/callipers, maps/projections/globe, paper, balloons

Markov process model -- computers/Internet/software/spreadsheets, games/puzzles/toys, spinners, dice/number cubes

Measurement/scale -- rollers, protractors, clinometer/transit, compasses, maps/projections, clocks/stopwatches/calendars, computers/Internet/software/spreadsheets, springs, balance scale/weights/scales, geometric solids/polyhedra/nets, calculators/graphing calculators, knitting needles, models/simulation, candy/food, rulers/tape measures/trundle wheels/callipers, graduated cylinder, base-ten blocks, paper/origami/stencil patterns/graph paper, video technology/multi-media, telephone, clocks/stopwatches/calendars, clinometer/transit, maps/projections/globe

Mental math -- games/puzzles/toys, dice/number cubes, spinners

Modular arithmetic -- computers/Internet/software/spreadsheets, games/puzzles/toys, calculators/graphing calculators, video technology/multi-media

Money management -- computers/Internet/software/spreadsheets, money, calculators/graphing calculators, paper/origami/stencil patterns/graph paper

Number concepts/operations -- cubes/Unifix cubes, spinners, dice/number cubes, candy/food, calculators/graphing calculators, base-ten blocks, money, balance scale/weights/scales, models/simulation, protractors, building blocks, rulers/tape measures/trundle wheels/callipers, geoboards, clocks/stopwatches/calendars, paper/origami/stencil patterns/graph paper, arithmetic-mean machine, games/puzzles/toys, compasses, computers/Internet/software/spreadsheets, math tables/number lines/100’s chart/10x10 grid/circle chart, video technology/multi-media, fractal cards, nomographs, slide rules

Pascal's triangle -- computers/Internet/software/spreadsheets, video technology/multi-media, candy/food

Patterns -- pattern blocks, geoboards, calculators/graphing calculators, cubes/Unifix cubes, computers/Internet/software/spreadsheets, games/puzzles/toys, compasses/spherical compass, models/simulation, building blocks/Lego, books/journals/newspapers/portfolios, protractors, rulers/tape measures/trundle wheels/callipers

Perimeter/circumference - geoboards, pattern blocks, cubes/Unifix cubes, candy/food, rulers/tape measures/trundle wheels/callipers, computers/Internet/software/spreadsheets, balloons, models/simulation, base-ten blocks

Permutations/combinations -- computers/Internet/software/spreadsheets, calculators/graphing calculators, books/journals/newspapers/portfolios, candy/food, games/puzzles/toys, algebra tiles, maps/projections/globe, geometric shapes, books/journals/newspapers/portfolios, video technology/multi-media

Physics -- calculators/graphing calculators, models/simulation, balance scale/weights/scales, springs, clocks/stopwatches/calendars

Probability -- spinners, dice/number cubes, balance scale/weights/scales, money, cubes/Unifix cubes, computers/Internet/software/spreadsheets, candy/food, springs, paper/origami/stencil patterns/graph paper, books/journals/newspapers/portfolios, rulers/tape measures/trundle wheels/callipers, geometric shapes, slide rules, nomographs, arithmetic-mean machine, compasses/spherical compass, games/puzzles/toys, video technology/multi-media, clocks/stopwatches/calendars

Problem solving/thinking skills -- calculators/graphing calculators, money, geometric shapes, video technology/multi-media, computers/Internet/software/spreadsheets, games/puzzles/toys, candy/food, spinners, building blocks/Lego, protractors, rulers/straightedge/tape measure/meter sticks/trundle wheels/callipers/spherical straightedge, models/simulation, dice/number cubes, geoboards, clinometer/transit, cubes/Unifix cubes, books/journals/newspapers/portfolios, base-ten blocks

Proofs/theorems -- geometric shapes, calculators/graphing calculators, models/simulation, computers/Internet/software/spreadsheets, compasses/spherical compass, rulers/straightedge/tape measure/meter sticks/trundle wheels/spherical straightedge, dice/number cubes, geoboards, games/puzzles/toys, graduated cylinder, paper/origami/stencil patterns/graph paper, video technology/multi-media

Pythagorean theorem -- computers/Internet/software/spreadsheets, calculators/graphing calculators, paper/origami/stencil patterns/graph paper, rulers/straightedge/tape measures/meter sticks/trundle wheels/calliper/spherical straightedge, geoboards, geometric shapes

Quadrilaterals -- computers/Internet/software/spreadsheets, geometric shapes, geometric solids/polyhedra/nets, pattern blocks, rulers/tape measures/trundle wheels/callipers, miras/mirrors/reflective material

Ratio/proportion/percent -- cubes/Unifix cubes, pattern blocks, compasses/spherical compass, geoboards, computers/Internet/software/spreadsheets, calculators/graphing calculators, dice/number cubes, candy/food, books/journals/newspapers/portfolios, graduated cylinder, rulers/tape measures/trundle wheels/callipers, paper/origami/stencil patterns/graph paper, knitting needles, maps/projections/globe

Rational/irrational numbers -- computers/Internet/software/spreadsheets, calculators/graphing calculators, paper/origami/stencil patterns/graph paper

Reasoning -- pattern blocks, dice/number cubes, video technology/multi-media, spinners, computers/Internet/software/spreadsheets, calculators/graphing calculators, candy/food, geoboards, games/puzzles/toys, base-ten blocks, protractors, paper/origami/stencil patterns/graph paper, rulers/tape measures/trundle wheels/callipers,

Relationships/connections -- pattern blocks, clocks/stopwatches/calendars, cubes/Unifix cubes, money, dice/number cubes, spinners, algebra tiles, calculators/graphing calculators, balance scale/weights/scales, games/puzzles/toys, geometric shapes, base-ten blocks, geoboards, books/journals/newspapers/portfolios, computers/Internet/software/spreadsheets, nomographs, slide rules, arithmetic-mean machine, geometric solids/polyhedra/nets, video technology/multi-media, building blocks/Lego, models/simulation, rulers/tape measures/trundle wheels/callipers, graduated cylinder, springs, candy/food, paper/origami/stencil patterns/graph paper

Sequences/series -- computers/Internet/software/spreadsheets, calculators/graphing calculators, fractal cards, nomographs, slide rules, arithmetic-mean machine, money, dice/number cubes

Similarity/congruence -- computers/Internet/software/spreadsheets, geoboards, pattern blocks, miras/mirrors/reflective material, fractal cards, calculators/graphing calculators, graduated cylinder, rulers/tape measures/trundle wheels/callipers, candy/food, maps/projections/globe, books/journals/newspapers/portfolios, clocks/stopwatches/calendars, paper/origami/stencil patterns/graph paper

Spatial visualization -- pattern blocks, geoboards, geometric solids/polyhedra/nets, cubes/Unifix cubes, computers/Internet/software/spreadsheets, models/simulation, maps/projections/globe, building blocks, miras/mirrors/reflective material, paper/origami/stencil patterns/graph paper

Spreadsheets -- computers/Internet/software/spreadsheets, calculators/graphing calculators, books/journals/newspapers/portfolios, paper/origami/stencil patterns, geoboards, protractors, rulers/straightedge/tape measure/meter sticks/trundle wheels/spherical straightedge

Statistics/data management -- animal/people, balance scale/weight/scales, base-ten materials, books/journals/newspapers/portfolios/learning logs, computers/Internet/software, money/coins, geoboards, graduated cylinder, clocks/stopwatches/calendars, pattern blocks, patty papers, springs, rulers/straightedge/tape measures/meter sticks/trundle wheels/callipers/spherical straightedge, computers/Internet/software/spreadsheets, building blocks/Lego, protractors, games/board games/puzzles/toys/playing cards, telephone, paper/origami/stencil patterns/graph paper, number cubes/dice, geometric shapes, candy/food, maps/projections/globe

Symmetry -- geoboards, pattern blocks, miras/mirrors/reflective material, cubes/Unifix cubes, computers/Internet/software/spreadsheets, calculators/graphing calculators, games/puzzles/toys, maps/projections/globe, games/puzzles/toys, geometric shapes, compasses/spherical compass, rulers/tape measures/trundle wheels/callipers

Tangent -- geometric shapes, rulers/tape measures/trundle wheels/callipers, protractors

Transformational geometry -- geoboards, cubes/Unifix cubes, miras/mirrors/reflective material, computers/Internet/software/spreadsheets, maps/projections/globe, paper/origami/stencil patterns/graphing paper, calculators/graphing calculators, models/simulation, pattern blocks

Trigonometry/trigonometric functions -- calculators/graphing calculators, springs, protractors, knitting needles, clocks/stopwatches/calendars, computers/Internet/software/spreadsheets, dice/number cubes, geometric shapes, clinometer/transit, games/puzzles/toys, rulers/tape measures/trundle wheels/callipers, candy/food, maps/projections/globe, models/simulation, balance scale/weights/scales

Variables/variability -- candy/food, calculators/graphing calculators, models/simulation, money, computers/Internet/software/spreadsheets, clocks/stopwatches/calendars, dice/number cubes, rulers/tape measures/trundle wheels/callipers, books/journals/newspapers/portfolios, balance scales/weights/scales

Velocity/speed/rate -- protractors, calculators/graphing calculators, rulers/tape measures/trundle wheels/callipers, video technology/multi-media, balloons, paper/origami/stencil patterns/graph paper, books/journals/newspapers/portfolios

Volume -- cubes/Unifix cubes, geometric solids/polyhedra/nets, rulers/tape measures/trundle wheels/callipers, candy/food, calculators/graphing calculators, graduated cylinder, building blocks, models/simulation, balloons, computers/Internet/software/spreadsheets

Weight/mass -- balance scale/weights/scales, building blocks, calculators/graphing calculators, computers/Internet/software/spreadsheets, geometric solids/polyhedra/nets

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