Ganita Prakash, period by period — fitted to your timetable.
Tell Meyy your periods and their length; it plans every chapter of Ganita Prakash to fit, and you tick off sections as you teach.
Why the Diagonal Doubles the Square
Doubling a Square · Inductive
Watch for students who confuse doubling the side with doubling the area — stress repeatedly that doubling the side yields four times the area. The diagonal-and-triangle argument (four triangles fitting exactly into the tilted square, two into the original) is the core reasoning to consolidate before moving on. If time permits, ask students to extend the sequence: what square on the diagonal of the doubled square would give area 4 times the original?
0–10Pose Baudhāyana's opening question: how do you construct a square with exactly double the area of a given square? Students sketch a unit square and its diagonal, and predict what shape a tilted square on the diagonal might be and how large.
10–22Guide the geometric reasoning: draw horizontal and vertical lines through the tilted square to see that the original square contains two small triangles while the new tilted square contains four congruent triangles, establishing the doubling relationship. Discuss Math Talk, section 2.1, p.34 ("Why should the extension of the vertical and horizontal sides of the original square pass through the vertices of the dotted (doubled) square?...") with student pairs.
22–45Students carry out Activity 1 (Doubling a Square Using Paper), p.35 ("Cut two identical squares of paper; cut Square 1 along diagonals into 4 triangular pieces...."), arranging the triangular pieces around an intact square to confirm the area doubling physically. Groups share what they notice about the areas of the triangles and the whole.
Math Talk, section 2.1, p.34 — Why should the extension of the vertical and horizontal sides of the original square pass through the vertices of the dotted (doubled) square?
A square has side length s. Its diagonal is drawn and a new square is constructed with the diagonal as one side. Explain, using the triangle-counting argument, why the new square has exactly double the area of the original square.
The original square can be divided into 2 congruent right triangles by its diagonal. The new tilted square, constructed on that diagonal, can be divided into 4 congruent right triangles of the same size (by drawing horizontal and vertical lines through the tilted square). Since the new square contains 4 such triangles and the original contains 2, the new square has exactly double the area of the original.
Also saved as 8 periods or 11 periods.
- 2The Midpoint Square and Its Hidden Area
Halving a Square - 3From Diagonal to Hypotenuse: Defining c² = 2a²
Hypotenuse of an Isosceles Right Triangle - 4Computing Hypotenuses and Bounding √2
Hypotenuse of an Isosceles Right Triangle - 5Baudhāyana's Verse: Why a² + b² = c²
Combining Two Different Squares - 6Applying the Theorem to Find Missing Sides
Combining Two Different Squares - 7Generating Baudhāyana Triples: Pattern and Proof
Right-Triangles Having Integer Sidelengths - 8Primitive vs. Non-Primitive: Reasoning About All Triples
Right-Triangles Having Integer Sidelengths - 9Fermat's Last Theorem: A 300-Year Story
A Long-Standing Open Problem - 10Lotuses and Diagonals: The Theorem at Work
Further Applications of the Baudhāyana-Pythagoras Theorem - 11Rhombuses, Rectangles, and Grid Squares
Further Applications of the Baudhāyana-Pythagoras Theorem - 12Grid Squares, Equilateral Triangles, and Integer Areas
Further Applications of the Baudhāyana-Pythagoras Theorem - 13Mixed Application Problems: Consolidating the Theorem
Further Applications of the Baudhāyana-Pythagoras Theorem - 14Four Problems, One Theorem: Putting the Chapter to Work
Synthesis
- 1. A Square and A Cube
- 2. Power Play
- 3. A Story of Numbers
- 4. Quadrilaterals
- 5. Number Play
- 6. We Distribute, Yet Things Multiply
- 7. Proportional Reasoning-1
- 8. Fractions in Disguise
- 9. The Baudhāyana-Pythagoras Theorem
- 10. Proportional Reasoning–2
- 11. Exploring Some Geometric Themes
- 12. Tales by Dots and Lines
- 13. Algebra Play
- 14. Area
Any 3 chapters free · no payment details · then introductory offer ₹499 per subject-stage, per year.