Exercise_A
stringlengths
8
63
Exercise_B
stringlengths
6
63
Similarity_avg
float64
1
9
Similarity_raw
stringlengths
9
29
Difficulty_avg
float64
1
8.45
Difficulty_raw
stringlengths
9
29
Prerequisite_avg
float64
1.17
8.8
Prerequisite_raw
stringlengths
9
29
judging_axis_of_symmetry
parabola_intuition_3
2.75
1_1_1_1_6_8_2_2
7.625
9_9_8_9_8_2_8_8
2.375
1_1_1_1_4_8_2_1
judging_axis_of_symmetry
similar_triangles_1
3.5
9_3_1_1_4_4_3_3
6.5
5_6_7_7_7_9_5_6
2.625
7_2_1_1_3_1_4_2
square_roots_2
exponents_2
3.153846
4_2_3_3_3_7_2_2_2_3_2_2_6
5.846154
6_8_8_6_9_4_8_7_5_4_2_2_7
3.615385
4_2_5_3_3_6_1_2_4_3_8_4_2
square_roots_2
exponents_1
3.615385
3_2_5_2_3_8_1_2_3_2_3_6_7
3.076923
2_1_8_2_7_3_1_1_3_3_4_4_1
4.076923
7_2_3_2_3_7_2_4_6_2_6_6_3
square_roots_2
simplifying_radicals
6.923077
5_9_7_6_9_6_7_9_6_6_5_7_8
4.538462
6_5_7_4_5_4_2_3_5_4_3_7_4
6.153846
3_9_3_6_8_6_7_8_7_7_6_3_7
square_roots_2
square_roots
7.230769
7_9_8_7_9_9_9_9_5_4_4_7_7
3.230769
2_3_1_6_7_3_3_1_6_4_1_1_4
7.384615
7_8_8_7_3_9_8_9_6_6_9_8_8
factoring_polynomials_by_grouping_1
writing_fractions_1
3
3_5_1_6_3_1_1_3_3_6_3_3_1
1.615385
2_4_1_1_1_2_1_1_2_1_2_2_1
3.846154
7_6_2_4_6_2_1_2_4_8_3_4_1
factoring_polynomials_by_grouping_1
factoring_polynomials_1
7.846154
9_8_8_7_9_7_7_8_8_9_7_7_8
4.461538
4_5_5_2_5_6_3_2_5_5_6_5_5
6.769231
8_6_7_8_9_7_7_3_8_6_3_7_9
factoring_polynomials_by_grouping_1
factoring_polynomials_2
7.846154
9_8_8_7_9_7_7_7_9_8_7_8_8
4.846154
5_5_5_2_5_6_3_7_5_5_5_5_5
6.230769
6_6_7_8_6_4_7_4_8_6_3_7_9
factoring_difference_of_squares_1
multiplying_expressions_1
6.454545
4_8_7_6_8_5_7_8_4_7_7
5.181818
5_5_3_7_4_6_6_4_2_8_7
5.454545
6_7_7_6_8_4_7_9_2_1_3
factoring_difference_of_squares_1
factoring_difference_of_squares_2
8.272727
8_9_8_9_9_6_7_9_9_9_8
6.363636
7_5_7_5_6_6_8_5_6_9_6
5.363636
3_4_8_5_8_4_9_6_7_1_4
factoring_difference_of_squares_1
factoring_polynomials_1
7.454545
7_8_8_7_8_7_8_9_5_7_8
6.454545
5_5_6_7_6_6_7_7_8_9_5
5.818182
7_6_8_6_8_4_5_5_5_1_9
factoring_difference_of_squares_1
multiplying_expressions_0.5
7.090909
4_8_6_7_8_6_7_9_8_7_8
5.636364
4_5_8_6_4_4_5_5_6_9_6
6.636364
5_7_6_7_8_6_9_9_8_1_7
factoring_difference_of_squares_1
multiplying_polynomials
5.818182
4_7_4_5_7_6_5_9_4_6_7
6.181818
4_7_8_7_7_5_7_5_2_9_7
3.909091
4_3_7_6_4_6_4_3_2_1_3
factoring_difference_of_squares_3
factoring_difference_of_squares_1
7.714286
7_8_9_9_8_8_6_7_8_5_8_8_9_8
3.642857
1_6_1_4_6_3_4_5_2_4_2_4_5_4
7.571429
9_8_8_9_9_8_8_6_8_6_4_7_7_9
factoring_difference_of_squares_3
factoring_difference_of_squares_2
7.785714
8_9_9_9_8_9_7_7_6_4_8_8_9_8
3.857143
5_4_2_5_4_3_4_4_2_3_5_4_5_4
7.428571
7_7_9_9_6_9_9_7_3_6_8_7_8_9
factoring_difference_of_squares_3
multiplying_expressions_0.5
5.5
4_6_7_6_5_6_4_5_7_4_4_4_7_8
3.428571
5_2_1_4_5_2_4_3_3_2_3_5_5_4
5.785714
6_6_4_7_7_5_6_4_8_6_5_4_7_6
herons_formula
areas_of_circles_and_sectors
3
1_4_2_3_6_3_2_3
4.125
6_4_3_4_3_4_4_5
4.125
1_2_3_5_7_3_7_5
herons_formula
shaded_areas
3.5
1_5_3_2_6_2_2_7
4.25
4_3_4_2_7_5_3_6
4.125
1_5_4_5_3_5_6_4
herons_formula
angles_2
2
1_1_2_1_4_3_2_2
3.5
6_3_2_2_2_7_3_3
3.375
1_1_3_1_8_3_7_3
multiplying_expressions_0.5
multiplying_polynomials
7.166667
7_8_9_8_4_7
6.666667
7_7_7_6_6_7
4.5
4_7_3_7_3_3
multiplying_expressions_0.5
multiplying_expressions_1
8.5
9_8_9_9_8_8
5.666667
6_4_5_6_7_6
7
7_9_7_9_6_4
multiplying_expressions_0.5
adding_and_subtracting_polynomials
4.5
3_6_7_1_3_7
3.833333
4_3_1_6_6_3
5.166667
5_6_7_2_4_7
multiplying_expressions_0.5
recognizing_conic_sections
1.666667
1_1_3_1_2_2
1.666667
1_2_3_1_1_2
2
1_1_3_1_5_1
reading_stem_and_leaf_plots
divisibility
2
2_1_1_4_1_2_4_1
7
5_8_6_6_9_9_6_7
2.375
2_1_1_3_1_2_5_4
reading_stem_and_leaf_plots
simplifying_radicals
1.25
1_1_1_1_1_1_2_2
6.25
1_7_7_7_8_6_7_7
1.625
2_1_1_2_1_1_3_2
reading_stem_and_leaf_plots
reading_tables_1
6.625
6_2_8_9_5_6_9_8
3.625
3_1_4_3_5_3_5_5
6.5
6_3_8_9_7_7_7_5
reading_stem_and_leaf_plots
reading_tables_2
5
4_2_8_8_1_4_9_4
4.5
5_6_4_5_5_2_6_3
5.125
3_3_8_8_1_6_4_8
reading_stem_and_leaf_plots
reading_bar_charts_1
6.375
6_2_8_9_5_7_9_5
4.25
6_5_4_3_5_2_5_4
7
6_5_8_8_6_6_9_8
reading_stem_and_leaf_plots
telling_time_0.5
3.25
3_1_1_6_1_8_5_1
2.75
6_1_3_3_3_4_1_1
3.5
3_1_1_7_1_7_7_1
absolute_value_of_complex_numbers
adding_and_subtracting_complex_numbers
5.444444
4_3_4_3_7_7_8_6_7
2.666667
1_1_2_2_4_2_6_2_4
5.444444
4_2_4_5_8_8_3_7_8
absolute_value_of_complex_numbers
imaginary_unit_powers
4.888889
3_2_2_2_6_8_6_7_8
3
5_1_3_3_5_1_2_3_4
5.333333
3_1_4_5_8_9_4_7_7
absolute_value_of_complex_numbers
pythagorean_theorem_1
5
7_5_7_6_2_6_1_3_8
3
1_3_3_6_4_3_2_3_2
3.333333
6_2_3_1_2_7_1_6_2
absolute_value_of_complex_numbers
the_complex_plane
5.555556
8_1_3_2_7_8_6_7_8
2.777778
1_1_2_2_3_3_6_5_2
5.222222
9_1_3_3_7_7_4_6_7
order_of_operations
perimeter_1
3.3
1_3_3_5_2_3_3_3_4_6
2.3
2_1_1_1_2_4_1_6_2_3
4.6
1_1_7_8_2_1_9_5_7_5
order_of_operations
properties_of_numbers_1
4.6
6_3_8_5_5_3_4_3_4_5
3.2
3_1_1_8_3_2_1_6_3_4
5.7
6_6_7_1_7_5_8_4_7_6
order_of_operations
properties_of_numbers_2
5.1
6_3_3_7_6_5_2_5_7_7
2
1_1_1_3_2_1_1_7_1_2
6.4
3_5_7_8_6_7_8_6_8_6
order_of_operations
multiplying_and_dividing_negative_numbers
4.4
6_4_4_2_3_2_2_8_7_6
4.5
5_2_1_6_4_4_7_5_5_6
4.8
6_6_6_2_6_3_3_6_6_4
lhopitals_rule
limits_2
6.888889
7_6_7_5_7_8_6_8_8
5
4_5_9_8_3_3_5_4_4
6.111111
7_5_3_2_8_9_6_7_8
lhopitals_rule
derivatives_1
5.888889
7_7_7_5_6_6_1_8_6
6.222222
4_5_9_7_6_3_9_7_6
5.333333
7_5_7_4_4_7_1_8_5
time_word_problem_4
subtraction_3
5.75
6_6_6_7_3_5_6_5_3_9_6_7
2.833333
3_1_3_4_2_1_2_5_2_5_3_3
5.083333
3_5_7_7_4_5_6_5_1_6_6_6
time_word_problem_4
time_units_transformation_1
6.333333
4_7_6_6_4_6_4_8_8_8_7_8
3.5
2_1_3_5_6_1_4_5_2_6_4_3
6.5
3_8_7_5_7_7_6_7_7_6_8_7
time_word_problem_4
telling_time_2
5.166667
4_6_4_4_2_3_6_7_6_6_7_7
2
1_1_3_4_4_1_1_3_1_2_2_1
5.25
4_3_7_6_6_2_8_8_3_7_7_2
time_word_problem_4
time_word_problem_2
7.916667
8_9_6_6_8_8_9_9_9_7_8_8
5
5_5_5_5_6_3_5_5_5_7_5_4
6.75
8_9_5_5_7_9_6_8_9_3_5_7
inscribed_angles_3
inscribed_angles_2
8.1
6_9_9_9_9_8_8_7_8_8
4.5
3_5_3_5_5_6_4_5_5_4
7.6
6_9_9_8_9_4_9_5_8_9
inscribed_angles_3
inscribed_angles_1
8
6_9_8_9_9_8_7_7_8_9
4
4_5_1_5_5_3_3_6_5_3
7.5
6_9_8_8_9_7_8_4_8_8
inscribed_angles_3
circles_and_arcs
3.7
4_3_1_4_4_4_1_6_3_7
6
6_7_6_8_8_3_6_5_4_7
3.3
4_2_1_2_3_6_1_5_6_3
vertical_angles
complementary_and_supplementary_angles
6.583333
8_7_7_6_5_9_3_8_7_6_6_7
4.833333
3_7_7_6_5_5_2_5_5_6_5_2
5.666667
8_4_7_6_7_9_4_6_5_4_4_4
vertical_angles
angle_addition_postulate
5.333333
7_6_4_2_6_5_6_4_6_5_6_7
7
4_8_9_8_9_8_8_6_7_8_3_6
3.333333
6_3_2_1_3_3_3_3_3_2_6_5
vertical_angles
vertical_angles_2
7.166667
7_7_9_8_9_5_7_4_8_6_8_8
6.416667
5_7_8_5_7_7_5_6_6_7_6_8
4.916667
7_5_6_7_7_4_7_3_2_3_7_1
vertical_angles
angle_types
4.083333
2_7_3_2_5_8_2_3_4_3_4_6
2.666667
2_2_2_1_6_3_1_1_7_3_3_1
4.916667
1_8_1_4_9_8_3_8_7_4_5_1
vertical_angles
writing_expressions_1
1.75
1_3_1_1_1_4_1_1_3_2_2_1
5.916667
1_5_9_7_7_4_5_5_8_6_5_9
2.666667
3_5_1_1_1_3_1_5_5_4_2_1
time_word_problem_2
arithmetic_word_problems_1
6
6_7_4_9_3_9_4
2.428571
5_1_4_1_1_1_4
5.142857
4_6_2_8_4_9_3
time_word_problem_2
subtraction_3
5.714286
8_7_3_2_4_9_7
2.142857
5_1_4_1_1_1_2
5.428571
7_6_2_6_2_9_6
time_word_problem_2
time_units_transformation_1
7.428571
8_8_8_8_5_8_7
2.285714
1_2_4_1_2_1_5
7.142857
9_6_8_7_4_9_7
time_word_problem_2
telling_time_comparing
7.285714
8_9_7_8_4_7_8
5.142857
5_4_4_2_5_9_7
5.857143
8_7_8_7_6_2_3
time_word_problem_2
telling_time
7
8_9_7_3_8_8_6
1.571429
1_1_2_1_1_1_4
7.142857
7_6_8_7_7_9_6
time_word_problem_3
arithmetic_word_problems_1
5.1
2_1_5_8_7_3_6_9_6_4
3.2
2_3_2_2_7_2_3_5_3_3
4.9
1_1_3_7_8_6_3_9_5_6
time_word_problem_3
telling_time_2
5.4
6_7_6_4_3_2_4_8_6_8
2.7
1_3_1_1_9_1_1_5_3_2
5.1
3_6_5_3_8_6_2_9_6_3
time_word_problem_3
time_word_problem_1
8
9_9_9_8_5_7_7_9_9_8
3.8
5_5_4_2_4_3_2_5_5_3
7.8
8_9_9_8_6_7_7_9_7_8
dividing_fractions_word_problems
dividing_fractions
6.923077
8_9_7_3_8_4_8_6_6_8_7_7_9
4.384615
3_4_7_8_5_3_3_2_5_3_6_4_4
6.538462
7_9_7_3_9_4_9_6_5_8_3_6_9
dividing_fractions_word_problems
simplifying_fractions
4
8_6_1_3_4_3_3_3_3_2_3_6_7
2
2_1_1_1_1_2_3_1_2_5_3_2_2
3.846154
7_2_1_2_2_4_5_3_9_2_4_5_4
dividing_fractions_word_problems
dividing_fractions_0.5
7.153846
9_8_7_9_9_3_5_8_7_8_5_7_8
2.769231
2_1_2_5_5_3_3_2_2_2_3_3_3
7.538462
9_8_7_9_9_6_7_8_7_8_6_7_7
dividing_fractions_word_problems
multiplying_fractions_0.5
4.923077
9_3_2_3_8_4_6_2_4_6_6_4_7
2.461538
1_1_2_3_4_2_3_2_3_2_4_3_2
4.692308
9_3_2_3_9_4_8_2_8_2_4_4_3
adding_fractions
equivalent_fractions_2
5
8_3_5_2_3_5_5_8_4_4_8
3.181818
5_2_1_2_7_3_1_3_5_2_4
5
5_5_4_6_2_5_2_7_5_7_7
adding_fractions
converting_mixed_numbers_and_improper_fractions
5.454545
4_6_4_6_4_5_4_8_4_7_8
3
3_4_1_1_4_3_2_1_5_5_4
6.363636
7_6_3_7_5_7_4_9_5_8_9
adding_fractions
adding_fractions_with_common_denominators
7.727273
8_8_8_9_8_7_7_9_4_8_9
1.636364
2_1_1_1_3_3_1_1_2_1_2
7.545455
8_9_7_9_7_7_5_9_7_8_7
adding_fractions
adding_and_subtracting_fractions
7.636364
7_8_9_8_8_7_7_8_5_9_8
6.090909
5_6_5_9_6_6_6_8_5_5_6
4.727273
5_6_9_2_4_4_6_1_5_6_4
adding_fractions
simplifying_fractions
5.272727
6_2_5_3_6_6_5_8_4_6_7
2.727273
6_4_1_1_4_3_1_2_3_2_3
6.272727
5_6_6_8_6_6_3_8_6_7_8
simplifying_expressions_with_exponents
exponents_2
5.625
4_7_4_8_9_4_2_7
2.5
6_2_2_3_1_2_2_2
5.125
4_7_2_8_9_5_2_4
simplifying_expressions_with_exponents
scientific_notation_intuition
2.875
2_6_1_2_1_2_3_6
2.25
4_2_1_4_2_1_1_3
3.625
3_8_1_4_3_1_6_3
simplifying_expressions_with_exponents
exponent_rules
7.375
3_8_6_8_9_8_9_8
3.5
6_2_1_4_5_2_4_4
7.125
4_7_5_8_8_9_7_9
simplifying_expressions_with_exponents
exponents_1
4.625
1_7_1_3_9_2_7_7
1.75
1_2_1_1_1_1_6_1
4.75
2_8_2_6_9_2_6_3
divisibility_0.5
divisibility_intuition
6.363636
8_6_8_3_7_6_6_9_4_5_8
3.909091
2_3_7_1_2_5_6_1_8_3_5
6.272727
8_7_6_6_4_6_6_9_3_5_9
divisibility_0.5
composite_numbers
6.272727
7_6_7_2_3_6_8_8_7_7_8
4.272727
7_3_2_4_4_5_5_5_3_5_4
6.272727
4_6_8_5_3_6_8_7_6_7_9
divisibility_0.5
division_2
5.818182
7_6_7_6_4_6_4_8_3_6_7
2.545455
3_3_1_4_2_3_3_1_1_4_3
5.636364
8_6_6_7_7_7_6_8_2_3_2
divisibility_0.5
divisibility_tests
6.636364
8_4_8_6_8_7_4_8_6_6_8
4.363636
4_4_2_1_7_4_6_3_4_6_7
6.181818
8_6_7_6_8_7_5_8_6_4_3
divisibility_0.5
prime_numbers
6.727273
8_6_8_6_3_6_7_8_7_7_8
3.909091
7_3_2_1_4_5_4_5_3_5_4
5.818182
3_6_7_5_4_6_7_7_6_5_8
comparing_absolute_values
absolute_value
8.3
9_9_7_8_9_9_9_8_8_7
3.8
5_2_4_5_5_5_5_1_3_3
8.1
8_9_7_9_8_9_9_8_7_7
comparing_absolute_values
absolute_value_add_sub
6.9
8_8_6_8_8_4_6_7_6_8
7.3
7_7_7_8_7_7_9_7_7_7
4.8
4_5_7_8_4_4_2_5_6_3
comparing_absolute_values
adding_and_subtracting_negative_numbers
4.5
6_7_6_6_4_2_1_3_4_6
4.8
6_6_5_5_5_6_6_2_3_4
4.1
4_6_6_8_2_2_2_3_4_4
comparing_absolute_values
adding_negative_numbers
4.9
7_8_7_7_4_2_1_3_4_6
4.4
6_4_5_1_5_6_6_3_5_3
4.2
4_6_6_7_2_4_2_4_3_4
corresponding_angles_2
alternate_interior_angles_2
8.222222
9_7_9_8_8_8_8_9_8
5.222222
5_5_5_5_5_6_6_5_5
7.666667
6_7_9_8_9_8_8_5_9
corresponding_angles_2
congruent_angles
7.444444
4_6_7_8_9_9_7_9_8
2.555556
2_2_1_6_5_2_3_1_1
7.111111
8_7_7_8_9_8_7_9_1
corresponding_angles_2
parallel_lines_1
7.555556
8_6_7_8_8_7_8_9_7
4
4_2_1_6_5_7_5_5_1
6.666667
6_7_8_8_9_7_8_6_1
corresponding_angles_2
parallel_lines_2
7.666667
8_6_9_6_8_7_8_9_8
4.888889
5_2_5_6_5_6_5_5_5
7.555556
6_8_9_7_9_7_7_6_9
corresponding_angles_2
alternate_interior_angles
8.222222
8_8_9_8_8_8_8_9_8
4.333333
5_5_5_5_5_2_5_5_2
6.888889
5_7_9_8_9_9_9_5_1
areas_of_kites
triangle_inequality_theorem
2.166667
1_3_1_2_5_1
4.333333
6_6_2_4_4_4
2
2_3_1_1_4_1
areas_of_kites
areas_of_rhombi
8
8_8_7_9_8_8
5.166667
6_5_5_5_5_5
8.166667
8_8_8_9_7_9
areas_of_kites
angles_1
1.666667
2_1_1_1_3_2
5.5
1_9_4_8_7_4
2.166667
2_4_1_1_3_2
areas_of_kites
solid_geometry
5
7_8_1_6_3_5
5.5
7_5_6_7_2_6
4.5
5_6_1_7_5_3
areas_of_kites
angles_2
1.833333
2_1_1_1_3_3
6.166667
2_9_6_8_7_5
1.5
1_1_1_1_3_2
l_ml_time_div
subtraction_2
1.5
3_1_2_2_1_1_1_1
1.375
1_1_2_1_2_1_1_2
1.5
1_1_1_1_1_1_1_5
l_ml_time_div
expressions_with_unknown_variables
1.625
4_1_3_1_1_1_1_1
7.375
5_7_6_8_7_8_9_9
1.375
3_1_1_1_1_1_1_2
l_ml_time_div
linear_equations_4
1.375
3_1_2_1_1_1_1_1
8.125
6_7_9_9_7_9_9_9
1.25
3_1_1_1_1_1_1_1
l_ml_time_div
l_ml_word_problem
7.5
7_8_8_7_8_8_7_7
3.875
5_1_4_5_4_3_5_4
8.25
6_8_9_8_8_9_9_9
l_ml_time_div
l_ml_transform
8.125
8_8_8_8_9_8_7_9
2.875
2_1_2_3_5_2_3_5
8.25
6_8_9_8_9_9_8_9
absolute_value
comparing_absolute_values
8.3
9_8_8_8_7_8_9_9_9_8
5.3
5_5_5_6_7_3_5_5_6_6
4.8
4_9_6_4_4_6_5_3_3_4
absolute_value
negative_number_word_problems
4.1
1_1_2_4_7_5_5_3_7_6
6.9
7_9_7_7_6_6_8_5_8_6
3
2_1_1_4_4_6_2_5_2_3
absolute_value
adding_negative_numbers
4.8
3_1_1_6_6_3_8_9_6_5
5.8
6_7_5_5_5_5_6_6_7_6
3.8
3_1_2_5_6_6_5_4_3_3