Equation · Graph · Table · Function

Integrated Algebra

Study relationships by moving between symbolic, visual, numerical, and functional representations. The representation changes; the relationship stays connected.

Representation workbench

One linear relationship, four coordinated views.

symbol ↔ graph ↔ table ↔ language
Symbolic form
y = 2x + 0
Verbal rule

Start at 0 on the y-axis, then change y by 2 for every 1 unit increase in x.

Graph
y = mx + b
gold points = table window
Table window
Scroll here or move the sampled x-values.
x ≈ 0
x
y
-3
-6
-2
-4
-1
-2
0
0
1
2
2
4
3
6
step
What changes together?
Sloperises left → right
Y-interceptcrosses at (0, 0)
Functionone output for every input
Integrated map

Eleven core topics, with deeper lessons nested beneath the topic they extend.

describe → rewrite → generalize