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Long Descriptions for Chapter Eleven

Long descriptions for complex figures and tables in Chapter Eleven of the Mathematics Framework for California Public Schools, Kindergarten through Grade Twelve.
Figure 11.1: Technological Pedagogical Content Knowledge Model

A three-circle Venn diagram. Technological Knowledge (TK), Content Knowledge (CK), and Pedagogical Knowledge (PK) overlap to create Pedagogical Content Knowledge (PCK), Technological Pedagogical Knowledge (TPK), Technological Content Knowledge (TCK), and Technological Pedagogical Content Knowledge (TPACK).

Figure 11.2: “Land the Plane”

Coordinate plane with a line indicated, with equation y = 1/2x – 7. The line crosses the y-axis at (0,–7) and x-axis at (14,0). There is an airplane runway drawn on the line, extending from roughly (7,–4) to (16,1). Text on the right includes instructions: “Change one number in the equation below to safely hold the plane. Press ‘Submit’ to see if the plan lands safely.”

Figure 11.3: Class Gallery for “Land the Plane”

Desmos snapshot tool titled, “Class Gallery, Make My Challenge.” “Other students’ challenges” are presented as twelve graphs containing proposed runways for aircraft at varying degrees. Graph 1: Henri Poincaré, includes a runway in quadrants I and IV. Graph 2: Christiaan Hu..., includes a runway in quadrant III. Graph 3: Joseph Fourier, includes a runway in quadrant II and III. Graph 4: Leonard Euler, includes a runway in quadrants I and IV. Graph 5: Maria Agnesi, includes a runway in quadrant I. Graph 6: Emmy Noether, includes a runway in quadrants IV and I. Graph 7: Grigory Marg..., includes a runway in quadrants III and IV. Graph 8: Girolamo Car..., includes a runway in quadrants I, II, and IV. Graph 9: Frances Kirwan, includes a runway in quadrant I. Graph 10: Euclid, includes a runway in quadrants II and III. Graph 11: Georg Cantor, includes a runway in quadrants III and IV. Graph 12: Martin Gardner, includes a runway in quadrants I and II.

Questions:   Curriculum Frameworks and Instructional Resources Division | cfird@cde.ca.gov | 916-319-0881
Last Reviewed: Wednesday, June 04, 2025
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