Nivan Investigates Triangle Areas on a Grid

Create one continuous premium Grade 6 mathematics animation titled “Nivan Investigates Triangle Areas on a Grid”. Follow the grid-based reasoning shown in Section 6.3. Keep grid lines visible and show how triangle areas can be related to halves of rectangles. Use the supplied textbook diagram for the blue triangle BAD and red triangle ABE where possible. SEQUENCE 1 — READ THE GRID Visual: show a clear square grid and identify the rectangle ABCD. Label the corners only where they are legible and consistent with the textbook diagram. Narration: “A grid helps us see the area inside a figure. We can use the rectangles in the grid to reason about a triangle.” SEQUENCE 2 — BLUE TRIANGLE BAD Visual: highlight triangle BAD in blue inside rectangle ABCD. Show that the diagonal divides the rectangle into two equal-area triangles. Display “Area of triangle BAD = half the area of rectangle ABCD.” SEQUENCE 3 — RED TRIANGLE ABE Visual: highlight triangle ABE in red. Divide the triangle visually into two smaller triangles, AEF and BEF, using the textbook's construction. Show that triangle AEF is half of rectangle AFED and triangle BEF is half of rectangle BFEC. Then connect the two rectangle regions to the whole rectangle ABCD. SEQUENCE 4 — COMPARE WITHOUT GUESSING Visual: place the blue and red triangle outlines side by side while retaining the grid. Narration: “The triangles look different, but the grid and rectangle relationships help us reason about their areas instead of judging by appearance alone.” SEQUENCE 5 — STUDENT CHALLENGE Show a simple triangle on a square grid. Ask learners to explain which rectangle or rectangles could help them find its area. Pause before displaying the key idea: use the rectangle-half relationship and keep track of the square units.