Interactive Algebra Plan

Overall summary

  1. Variables and Formulas *
  2. Fractions*
  3. Equations*
  4. Word Problems*
  5. Logic*
  6. Primes*
  7. Decimals
  8. Graphs*
  9. Combinatorics*
  10. Logarithms and Exponentials
  11. Complex Numbers
  12. Factoring Polynomials*
  13. Trigonometry and Trigonometric Identities*
  14. Inequalities
  15. Matrices
  16. Determinants
  17. Statistics
  18. Asymptotics
  19. Advanced Polynomials
  20. Multivariate Polynomials
  21. Introduction to Calculus
  22. More Calculus
  23. More Advanced Polynomials

1. Variables and Formulas *

  1. Intro
  2. variables [slider]
  3. several variables [slider]
  4. variables as boxes [draggable numbers to boxes and text display]
  5. values as bars and dots [bars and dots]
  6. addition of values [double bars and double dots]
  7. multiplication of values [dot arrays, grid arrays]
  8. simple binary expressions
  9. +-and-* pocket calculator
  10. results as inputs to other oerators
  11. +-and-* spreadsheet
  12. picture of spreadsheet as graph [graph layout]
  13. algebraic expressions
  14. subtraction
  15. +,-,and * pocket calculator
  16. +,-,and ms* spreadsheet
  17. division

2. Fractions*

  1. k/m is measured as part of a rug; by dividing into m columns and any number of rows, and taking k of the m columns
  2. comparison of fractions
  3. equality of fractions
  4. fractions in lowest terms
  5. cross multiplication as comparison and equality test
  6. addition of fractions - take parts, put together
  7. multiplication of fractions - take part of parts
  8. +-and-* fraction pocket calculator
  9. +-and-* fraction spreadsheet
  10. subtraction of fractions

3. Equations*

4. Word Problems*

5. Logic*

6. Primes*

7. Decimals

8. Graphs*

9. Combinatorics*

10. Logarithms and Exponentials

11. Complex Numbers

12. Factoring Polynomials*

13. Trigonometry and Trigonometric Identities*

14. Inequalities

15. Matrices

16. Determinants

17. Statistics

18. Asymptotics

19. Advanced Polynomials

20. Multivariate Polynomials

21. Introduction to Calculus

22. More Calculus

23. More Advanced Polynomials

Estimate is about 5,400 screens

Materials developed so far, including materials for elementary grades


counting_1.stlelem counting: items -> box   • 1st Grade
counting_2.stlelem counting: items in box   • 1st Grade
counting_3.stlelem counting: kinds in box   • 1st Grade

(Note: develop more categories: big and little things, attange as 2 + 3, take away, leave)


building_prod_groups.stlmultiplying by forming groups   • 1st Grade
dividing_into_groups.stldividing by forming groups   • 1st Grade
dividing_into_groups2.stldividing by forming groups   • 1st Grade
building_prod_groups2.stlcreating equal groups    • 1st Grade
find_n_more.stlk more than n   • 1st Grade
find_n_less.stlk less than n   • 1st Grade
how_many_more.stlhow many more are there    • 1st Grade
how_many_less.stlhow many more are there    • 1st Grade

which_has_more.stlvisual comparison   • 1st Grade

numbers_4_ways.stlgenerator    • 1st Grade
numb_4_ways_equal.stl expressing same number    • 1st Grade
numb_4_ways_more_by_1.stlexpressing number one more   • 1st Grade
numb_4_ways_more_by_10.stlexpressing number ten more   • 1st Grade
numb_4_ways_less_by_1.stlexpressing number one less   • 1st Grade
numb_4_ways_less_by_10.stlexpressing number ten less   • 1st Grade

wds_4_ways.stlgenerator, numbs verbally   • 1st Grade
wds_4_ways_equal.stl expressing same number    • 1st Grade
wds_4_ways_more_by_1.stlexpressing number one more   • 1st Grade
wds_4_ways_more_by_10.stlexpressing number ten more   • 1st Grade
wds_4_ways_less_by_1.stlexpressing number one less   • 1st Grade
wds_4_ways_less_by_10.stlexpressing number ten less   • 1st Grade

reading_graphs.stlreading dot graphs   • 1st Grade
make_a_graph.stlbuilding dot graphs   • 1st Grade

animated_time.stlanimated analog clock    • 1st Grade+
telling_time.stlpractice telling time    • 1st Grade+
setting_time.stlpractice setting time    • 1st Grade+

shopping.stldollar-constrained shopping   • 2nd Grade
shopping2.stldollar-constrained shopping   • 2nd Grade


reading_rave.stlillustrative: elem. reading    • 1st Grade
death_by_fractions.stl fractions rave    • 5th Grade
numroll.stl integer arithmetic rave    • 4th Grade

class_overview_rave.stl simulation of teacher's 'class progress' window


(Note: develop more versions, emphasizing rearrangement)

what_adding_means.stl addition as 'counting up'   • 1st Grade
what_subtracting_means.stlsubtraction as 'counting down'   • 1st Grade
what_subtracting_means2.stlsubtraction as 'throwing away'   • 1st Grade
alg_dem_grouping_assoc.stldemonstration of assoc. law   • 2nd Grade
alg_dem_grouping_fordiv.stlgrouping into specified piles   • 2nd Grade
multiplication_experiment.stl1-digit slider driven exps.   • 2nd Grade


arranging_numbs_2_sm.stlcomparing single digits    • 1st Grade
arranging_numbs_2_smrev.stlcomp. single digits - reversed   • 1st Grade
arranging_numbs_2.stl comparing double digits    • 1st Grade
arranging_numbs_2_rev.stlcomp. double digits - reversed   • 1st Grade
arranging_numbs_2big.stlcomparing 4 digits   • 2nd Grade
arranging_numbs_2bigrev.stlcomp. 4 digits - reversed   • 2nd Grade
arranging_numbs_10.stl sorting double digits    • 2nd Grade
arranging_numbs_10_rev.stlsorting double digits - rev.   • 2nd Grade
arranging_numbs_10big.stlsorting 4 digits   • 2nd Grade
arranging_numbs_10bigrev.stlsorting 4 digits- reversed   • 2nd Grade
arranging_numbers.stl generator


arranging_dishes_3num.stlarranging 3 grps., tot. no   • 2nd Grade
arranging_dishes_3round.stlarranging 3 grps., no. of rnd.   • 2nd Grade
arranging_dishes_3diff.stlarranging 3 grps., no. of diff   • 2nd Grade+

arranging_dishes_6num.stlarranging 6 grps., tot. no   • 3rd Grade
arranging_dishes_6round.stlarranging 6 grps., no. of rnd.   • 3rd Grade
arranging_dishes_6diff.stlarranging 6 grps., no. of diff   • 3rd Grade+



number_problems_mi_let_28.stl- eqns, 1-let vars to 28   • 3rd Grade
number_problems_mi_let_9.stl- eqns, 1-let vars to 9    • 2nd Grade+
number_problems_mi_lwd_9.stl- eqns, sm. name vars to 9   • 2nd Grade
number_problems_mi_swd_9.stl- eqns, lng name vars to 9   • 2nd Grade
number_problems_pl_let_28.stl+ eqns, 1-let vars to 28   • 3rd Grade
number_problems_pl_let_9.stl+ eqns, 1-let vars to 9    • 2nd Grade
number_problems_pl_lwd_9.stl+ eqns, lng name vars to 9   • 2nd Grade
number_problems_pl_swd_9.stl+ eqns, sm. name vars to 9   • 2nd Grade
number_problems_ti_let_28.stl* eqns, 1-let vars to 28   • 3rd Grade+
number_problems_ti_let_9.stl* eqns, 1-let vars to 9    • 3rd Grade
number_problems_ti_lwd_9.stl* eqns, lng name vars to 9   • 3rd Grade
number_problems_ti_swd_9.stl* eqns, sm. name vars to 9   • 3rd Grade

xnumber_problems_mmm_9.stlmult eqns, --- to 9 (calc)   • 4th Grade
xnumber_problems_ppp_9.stlmult eqns, +++ to 9 (calc)   • 4th Grade
xnumber_problems_ptm_9.stlmult eqns, +*- to 9 (calc)   • 4th Grade
xnumber_problems_ttt_9.stlmult eqns, +*- to 9 (calc)   • 4th Grade
xnumber_probs_ptpmt_lwd_9.stlmult eqns, +*+-*, nmd. vars   • 4th Grade
xnumber_problems_ptpmt_9.stlmult eqns, +*+-* to 9 (calc)
xnumber_problems.stl generator

adding_signed_integers.stladding 1-D vectors   • 4th Grade
making_signed_integers.stldrag vector to show signed int
multi_digit_multiply.stlmultiplication using pickwidget


number_words_laboratory.stlwords for numbs to trillions   • 3rd Grade+
numbers_to_words_practice.stlnaming numbers to trillions   • 3rd Grade+
words_to_numbers_practice.stlreading number names    • 3rd Grade+
single_digit_add.stl adding hundred, thousand, etc   • 3rd Grade+
single_digit_add2.stl adding n-hundred, thousand, etc   • 3rd Grade+
single_digit_subtract.stlsubtract hundred, thousand, etc   • 3rd Grade+
single_digit_subtract2.stlsubtr n-hundred, thousand, etc   • 3rd Grade+

digit_meaning_practice.stldigit meaning by position   • 3rd Grade+
multi_digit_addition.stladdition using pickwidget   • 3rd Grade+
multi_digit_addition_setup.stladdition using pickwidget   • 3rd Grade+
multi_digit_subtraction.stlsubtraction using pickwidget   • 3rd Grade+
multiplying_lead_digits.stlmultiplying tens, hundreds,..   • 3rd Grade+
multiplying_lead_digits2.stlmultiplying tens, hundreds,..   • 3rd Grade+

rounding_numbers.stl rounding by posn and dirn   • 3rd Grade+

ruler_experiments.stl reading a ruler: practice   • 3rd Grade+
ruler_practice1.stlfinding ruler positions    • 3rd Grade+
ruler_practice2.stlreading ruler positions    • 3rd Grade+
decimal_ruler_experiments.stldrag line, thus showing decimal   • 3rd Grade+
decimal_ruler_practice1.stldrag line to show decimal   • 3rd Grade+
decimal_ruler_practice2.stlread posn.on ruler   • 3rd Grade+


ruler_practice.stlpractice using ruler    • 3rd Grade
ruler_eights_practice.stlpractice using finer ruler   • 4th Grade
ruler_deceighths_practice.stlfiner ruler,result in decimal    • 5th Grade
ruler_periphery_practice.stlmeasuring periphery   • 5th Grade
protractor_practice.stlusing a protractor   • 5th Grade


add_3_digits.stlmultidigit addition (Ocken)   • 2rd Grade
alg_dem_1_group_by_10s multidigit counting - dots form   • 3rd Grade
alg_dem_2_multid_addn.stlmultidigit addition - dots form   • 3rd Grade
alg_dem_3_mult_table.stlfilling out mult table    • 3rd Grade
alg_dem_4_columnadd.stl double digit addn - carries   • 3rd Grade
alg_dem_5_rowtimes_digit.stlrow times digit - carries   • 3rd Grade

multi_digit_addition.stlmultidigit addition (popup)   • 3rd Grade
multi_digit_multiply.stlmultidigit subtraction (popup)    • 3rd Grade
multi_digit_subtraction.stlmultidig. multipl, (popup)   • 3rd Grade+

spiral_game.stlgame: advance by choosing digits   • 4thGrade+


fractions_main.stlnarrative account of fractions   • 4th Grade
fractions_main_rev.stl revised narrative    • 4th Grade
fractions_writing.stl numerator/denominator practice   • 4th Grade
fractions_lowterms1.stlrecognizing lowest terms   • 4th Grade
fractions_lowterms2.stlreducing to lowest terms   • 4th Grade
fractions_lowterms3.stltest equality by lowest terms   • 4th Grade
fractions_adding.stl adding fractions   •4th Grade
fractions_subtracting.stlsubtracting fractions    • 4th Grade
fractions_multiplying.stlmultiplying fractions    • 4th Grade
fractions_dividing.stldividing fractions   • 4th Grade

fractions_redimp.stl reduce improper fractions   • 4th Grade
fractions_expimp.stl expand improper fractions   • 4th Grade
fractions_addimp.stl adding improper fractions   • 4th Grade
fractions_subtractimp.stlsubtracting improper fractions   • 4th Grade
fractions_multiplyimp.stlmultiplying improper fractions   • 4th Grade
fractions_divideimp.stldividing improper fractions   • 4th Grade
fractions_addneg.stl adding negative fractions   • 4th Grade+
fractions_subtractneg.stlsubtracting negative fractions   • 4th Grade+
fractions_multiplyneg.stlmultiplying negative fractions   • 4th Grade+
fractions_divideneg.stldividing negative fractions   • 4th Grade+

fractions_addnegi.stl adding negimp fractions    • 4th Grade+
fractions_subtractnegi.stlsubtracting negimp fractions   • 4th Grade+
fractions_multiplynegi.stlmultiplying negimp fractions   • 4th Grade+
fractions_dividenegi.stldividing negimp fractions   • 4th Grade+

common_factor_practice.stlfinding a common factor    • 4th Grade+
lowest_terms_practice.stlfinding fracts in lowest terms   • 4th Grade+
fraction_equality_expers.stlvisualizing equal fractions   • 4th Grade+
converting_imprope_practice.stlconv to num + fract   • 4th Grade+
dollar_fractions_image.stlfractions in coins   • 4th Grade+
nickel_dime_quarter.stl image of coin values    • 4th Grade+
showing_fractions_practice.stlshow given fracs graphically   • 4th Grade+

fractions: ancillaries

arithmetic_laws.stlbasic laws of arithmentic   • 4th Grade+
converting_imprope_practice.stlconverting improper fractions   • 4th Grade+
crossmultiply_practice.stlfraction ops by crossmultiply   • 4th Grade+
fraction_addition_diagram.stldiagram of fraction addition   • 4th Grade+
fraction_arith_practice.stlgenerator for various pactice modules
history_of_fractions.stlmaterial on fractions history   • 4th Grade+


smallest_factor.stlprime factorization of a number   • 4th Grade+


units_and_proport.stl master account: word problems   • 5th Grade
units_practice_1.stl unit conversion problems   • 5th Grade
units_practice_2.stl unit conversion problems (from mults.)   • 5th Grade


sets_main.stlmain narrative account of sets   • 5th Grade+
set_equality_practice.stlrecognizing set equality   • 5th Grade+
set_inclusion_practice.stlrecognizing set inclusion   • 5th Grade+


ruler_practice.stlcoarse ruler practice    • 5th Grade+
ruler_eighths_practice.stlfiner ruler practice    • 5th Grade+
ruler_deceighths_practice.stldecimal ruler measurements   • 5th Grade+
ruler_periphery_practice.stlperiphery measurement    • 6th Grade+
protractor_practice.stl use of protractor   • 6th Grade+

graphing.stlsimple graphing laboratory   • 6th Grade+
point_by_point_graphing.stlindividual function values   • 5th Grade+


decimals_main.stlnarrative account of decimals   • 5th Grade+

decimal_addition_practice.stladdition practice   • 5th Grade+
decimal_subtr_practice.stlsubtraction practice    • 5th Grade+
decimal_multip_practice.stlmultiplication practice    • 5th Grade+
decimal_display.stldecimal place value by sliders   • 5th Grade+
decimal_point_practice.stlnaming decimal position    • 4th Grade+
decimal_point_practice2.stldrag digit to named position   • 4th Grade+
decimal_words_lab2.stl viewing alternative decm. names   • 5th Grade+
decimal_words_laboratory.stlviewing decimal names    • 5th Grade+
one_digit_decimals.stl decimals with denom 1    • 4th Grade+
trailing_zeroes_in_decimalkeep and suppress (sliders)   • 5th Grade+
number_line.stldirectly draggable number line   • 5th Grade+
number_line_turned.stl'zoom-in' draggable number line   • 5th Grade+
zooming_real.stldecimal ruler pract. w. zoom   • 5th Grade+


rearrange_terms.stlpractice rearranging poly terms   • 7th Grade+
values_laboratory.stl polnomial construction by trees   • 5th Grade+

calculators: (new 'buttonless' versions)

Calculator_add_sub_pos.stladdition, subtraction pos only   • 1st Grade+
Calculator_add_sub.stl addition and subtraction only   • 1st Grade
Calculator_add_sub_prod.stladdition, subtraction mult   • 2nd Grade+

Calculator_practice1.stl'alg. by calculators' - words   • 2nd Grade+
Calculator_practice2.stl'alg. by calculators' - semiform   • 2nd Grade+
Calculator_practice3.stl'alg. by calculators' - form   • 2nd Grade+
Calculator_practice4.stl'alg. by calculators' - bigfact   • 2nd Grade+
Calculator_practice5.stl'alg. by calcs' - let times - word   • 2nd Grade+
Calculator_practice6.stl'alg. by calcs' - let times - form   • 2nd Grade+
Calculator_4_ops.stl addn, subtraction, mult, divn.   • 3rd Grade+
Calculator_5_ops_ratl.stlfractions calculator    • 4th Grade+
Calculator_5_ops.stl includes exponent   • 4th Grade+
Calculator_5_ops_decm.stldecimal calculator   • 4th Grade+
Calculator_5_ops_mod.stlmodular calculator   • 8th Grade
calculator_gen_pak.stl generator


arranging_sums_commut.stl   demo of commutative law    • 8th Grade


square_roots_1.stl   sq. root by digit guessing   • 9th Grade


cartesian_coordinates.stlcartesian coords. demo    • 6th Grade
polar_coordinates.stl polar coords. demo   • 6th Grade
similar_figures.stlexpansion/rotation demo    • 6th Grade
similar_figures2.stl angles and proportionality demo   • 7th Grade
pythagoras.stlproof of Pythagoras Thm.   • 8th Grade
similar_figures3.stl triangle similarity proof   • 9th Grade
Ptolemyhistory of Ptolemy Soter   • 9th Grade
area.stl tiling a square   • 6th Grade+
area2.stl additivity of areas   • 6th Grade+
area3.stl Cavalieri distortion    • 6th Grade+
area4.stl Cavalieri inequality    • 6th Grade+
area5.stl effect of expansion   • 6th Grade+
convexity1.stlintro to convexity   • 2nd Grade+
convexity2.stlconvex hull    • 3rd Grade+
polygons.stlpolygon play   • 3rd Grade+
convexity3.stloutward normals of convex figs.    • 6th Grade+
convexity4.stlformal def. of convexity    • 7th Grade+


analyt. discussion of axioms    • 9th Grade+

3D_basics.stlmechanisms for 3-D figures
glassless_stereo.stl mechs. for glassless viewing
pick_rotation.stlrotation pick-widget
parallel_lines.stlparallel lines illustration   • 4th Grade+
parallelogram.stlplay with parallelogram area    • 6th Grade+
periphery_accordion.stl large periphery of small fig.   • 7th Grade+
periphery_polygon.stl periphery by pull-off    • 5th Grade+
symmetry.stlproofs by symmetry
perp_same_line.stllines perp to same line (exmp)    • 6th Grade+

skyscraper.stl play with skyscraper figures    • 3rd Grade+
helix.stlhelical 3-D curve   • 4th Grade+
sphere.stlsphere   • 4th Grade+
torus.stltorus   • 4th Grade+
icosahedron.stlicosahedron    • 4th Grade+
octahedron.stloctahedron    • 4th Grade+
pyramids.stlvariable pyramids   • 4th Grade+
line_intersecting_plane.stlnormal in plane to a line    • 9th Grade+
plane_thru_3_pts.stlplane thru 3 pts    • 9th Grade+
xyz_axes.stldiagram of axes    • 9th Grade+
stereo_vision_geometry.stlgeometry of stereo vision

Geometric proofs:

geometric_proofs.stlintroduction to formal proof    • 9th Grade
Euclid_axiomsEuclid's take on axiomtics   • 9th Grade


geometry_lab_tk.stl main geometry lab code    • 7th Grade+
Geometry_laboratory_help.stlhelp file   • 7th Grade+
various canned geometry lab examples


smallest_number.stlminimal element of set    • 6th Grade+


combinatorics_1.stlelements chosen by 1 slider   • 9th Grade+
combinatorics_2.stlelements chosen by 2 sliders   • 9th Grade+
combinatorics_3.stlelements chosen by 3 sliders   • 9th Grade+
combinatorics_4.stlelements chosen by 10 sliders   • 9th Grade+
combinatorics_5.stlelts chosen by 2 diff. sliders   • 9th Grade+
combinatorics_6.stldivision into equal groups   • 9th Grade+
combinatorics_7.stlcounting lists of 2   • 9th Grade+
combinatorics_8.stlcounting lists of 3   • 9th Grade+
combinatorics_9.stlcounting lists of 10    • 9th Grade+
combinatorics_10.stl counting general lists of 3   • 9th Grade+


sin_cos_addn_law.stl derivation of addition law   • 10th Grade
sines_and_cosines.stl sines, cosines values & graph   • 10th Grade


markov_processes.stl Intro to transition processes   • 11th Grade
markov_processes_xtra.stlTransition processes, 10 states   • 11th Grade
Gaussian_0.stlbell crv - phys model & intro   • 11th Grade
gaussian.stlbell curve - experiments   • 11th Grade+
gamblers_ruin.stlpossib. unit - gamblers ruin prob.   • 12th Grade


statistics_main.stl   main narrative account    • 11th Grade


tangent_line.stldemo of the tangent_line notion   • 6th Grade
max_min_principle.stl slope is zero at extrema    • 6th Grade
area_under_curve.stl figure - area under curve    • 6th Grade
area_interv_addition.stladdn rule - areas over intervs    • 7th Grade
area_interv_small.stl diff rule - areas over interv   • 7th Grade
area_add.stlintegral as sum of slices   • 8th Grade


factorials.stlgrowth of factorial (slider)   • 9th Grade+
powers_of_two.stlgrowth of 2**n (slider)    • 9th Grade+
two_2_n.stl growth of 2**(2**n) (slider)   • 9th Grade+


spelling_numbers.stl English forms of numbers   • 1st Grade+
arranging_sums_assoc.stlassociative law for addition   • 2nd Grade
geometry_lab_tk.stl major geometry exploration tool   • 6th Grade+
square_roots_2.stlsq. root by iterative method   • 9th Grade+


   • 1st Grade
phonetics_ack.stlphonetics group '..ack'    • 1st Grade
phonetics_at.stlphonetics group ''    • 1st Grade
phonetics_at_ock.stl phonetics group ''    • 1st Grade
phonetics_ock.stlphonetics group ''    • 1st Grade
phonetics_take_ack.stl phonetics group ''    • 1st Grade
phonetics_take_at_ock.stlphonetics group ''    • 1st Grade
phonetics_take_ock.stl phonetics group ''    • 1st Grade
phonetics_take_ug.stl phonetics group ''    • 1st Grade
phonetics_ug.stl phonetics group ''    • 1st Grade
reading_game.stlminimal vocabulary reading game


cognitive_principles Discussion of underlying issues
reading_vocabularyVarious initial reading vocablularies
singapore_curriculum Info on Singapore curriculum
algebra_planOlder project plan
reading_elem_wdsSorted list of standard elementary vocabulary