## 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
20. Multivariate Polynomials
21. Introduction to Calculus
22. More Calculus

### 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
12. picture of spreadsheet as graph [graph layout]
13. algebraic expressions
14. subtraction
15. +,-,and * pocket calculator
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
10. subtraction of fractions

## Materials developed so far, including materials for elementary grades

### Learning_to_count:

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

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

### defs_of_arithmetic_ops:

(Note: develop more versions, emphasizing rearrangement)

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

### measurement:

 ruler_practice.stl practice using ruler • 3rd Grade ruler_eights_practice.stl practice using finer ruler • 4th Grade ruler_deceighths_practice.stl finer ruler,result in decimal    • 5th Grade ruler_periphery_practice.stl measuring periphery • 5th Grade protractor_practice.stl using a protractor • 5th Grade

### fractions: ancillaries

 arithmetic_laws.stl basic laws of arithmentic • 4th Grade+ converting_imprope_practice.stl converting improper fractions • 4th Grade+ crossmultiply_practice.stl fraction ops by crossmultiply • 4th Grade+ fraction_addition_diagram.stl diagram of fraction addition • 4th Grade+ fraction_arith_practice.stl generator for various pactice modules history_of_fractions.stl material on fractions history • 4th Grade+

### factorization:

 smallest_factor.stl prime factorization of a number • 4th Grade+

### units_and_proportions:

 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_and_sequences

 sets_main.stl main narrative account of sets • 5th Grade+ set_equality_practice.stl recognizing set equality • 5th Grade+ set_inclusion_practice.stl recognizing set inclusion • 5th Grade+

### Measurement:

 ruler_practice.stl coarse ruler practice • 5th Grade+ ruler_eighths_practice.stl finer ruler practice • 5th Grade+ ruler_deceighths_practice.stl decimal ruler measurements • 5th Grade+ ruler_periphery_practice.stl periphery measurement • 6th Grade+ protractor_practice.stl use of protractor • 6th Grade+

### polynomials:

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

### commutativity_associativity:

 arranging_sums_commut.stl demo of commutative law • 8th Grade

### finding_roots:

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

### Euclid_axioms

analyt. discussion of axioms    • 9th Grade+

### Geometric proofs:

 geometric_proofs.stl introduction to formal proof    • 9th Grade Euclid_axioms Euclid's take on axiomtics • 9th Grade

### geometry_lab_folder:

 geometry_lab_tk.stl main geometry lab code • 7th Grade+ Geometry_laboratory_help.stl help file • 7th Grade+ various canned geometry lab examples angle_bisector.gex circ_of_double_radius.gex convex_polygon.gex convex_polys_2.gex crossing_lines.gex finding_center.gex isoceles.gex locus_equidist_pt.gex medians_concur.gex para_perp_length.gex parallel_thru_point.gex perimeter_study.gex perp_at_point.gex tangent_to_circle.gex

### mathematical_induction:

 smallest_number.stl minimal element of set • 6th Grade+

### combinatorics:

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

### probability:

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

### statistics:

 statistics_main.stl main narrative account • 11th Grade

### calculus:

 tangent_line.stl demo 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.stl addn rule - areas over intervs • 7th Grade area_interv_small.stl diff rule - areas over interv • 7th Grade area_add.stl integral as sum of slices • 8th Grade

### asymptotics:

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

### under_development:

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