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Arin Solves the Perimeter Mysteries

Walking around a court's outside, how do you find a rectangle's missing length? Perimeter is the distance around the outside. With perimeter 14 cm and...

Prompt

Source idea used to generate this video.

Create one continuous premium Grade 6 mathematics animation titled “Arin Solves the Perimeter Mysteries”. Integrate the following sequences and narration in order. Keep each calculation readable and pause before challenge answers. SEQUENCE 1 — FIND THE MISSING LENGTH Visual: rectangle with perimeter 14 cm, breadth 2 cm and unknown length. Show 14 − 2 − 2 = 10, then 10 ÷ 2 = 5 cm. Add a quick final challenge: perimeter 30 cm, breadth 5 cm; reveal 30 = 2 × (L + 5), 15 = L + 5, L = 10 cm. SEQUENCE 2 — THE 36 cm STRING CHALLENGE Visual: the same 36 cm string forms three regular shapes. Square: 36 ÷ 4 = 9 cm per side. Equilateral triangle: 36 ÷ 3 = 12 cm per side. Regular hexagon: 36 ÷ 6 = 6 cm per side. Emphasise: “The perimeter stays the same, but the side length changes.” SEQUENCE 3 — THE FARMER’S FENCE Visual: rectangular field labelled length 230 m and breadth 160 m. Calculate one round: 2 × (230 + 160) = 780 m. Then show three rounds: 780 × 3 = 2,340 m of rope. SEQUENCE 4 — AKSHI AND TOSHI: WHO RAN FARTHER? Use the textbook values, not the alternative values in the supplied script. Akshi runs on the outer track 70 m × 40 m for 5 rounds: one round = 2 × (70 + 40) = 220 m; total = 5 × 220 = 1,100 m. Toshi runs on the inner track 60 m × 30 m for 7 rounds: one round = 2 × (60 + 30) = 180 m; total = 7 × 180 = 1,260 m. Conclude: Toshi ran farther by 160 m. SEQUENCE 5 — STRAIGHT AND DIAGONAL UNITS Visual: reproduce the textbook dot-grid figures. Trace the boundary and distinguish horizontal/vertical straight units from diagonal units using contrasting line styles. Demonstrate the short notation shown in the textbook: 6s + 3d units, where s represents a straight unit and d represents a diagonal unit. Ask learners to count the two types separately on a second figure. Do not assume a diagonal unit has the same length as a straight unit. SEQUENCE 6 — SPLIT AND REJOIN Visual: begin with the textbook’s 6 cm × 4 cm rectangular paper cut into two equal pieces. Animate the two pieces being joined in the different arrangements shown in the textbook. Highlight the exposed outside boundary only; edges that become internal when pieces are joined must not be counted in the perimeter. Ask learners to determine the perimeter of each arrangement. End with the textbook challenge: “Arrange the two pieces to form a figure with a perimeter of 22 cm.” Use the exact textbook arrangement diagrams for b, c and d. The supplied screenshots do not explicitly label every side length, so do not invent dimensions or claim an unverified answer. SEQUENCE 7 — MEMORY CARD Show: “Known perimeter → work backwards”; “Equal sides → divide by the number of equal sides”; “Several rounds → perimeter × rounds”; “Dot grid → count straight and diagonal units separately”; “Rearranged shapes → trace the exposed outside boundary”; “Compare runners → calculate distance per round, then multiply by rounds.”

Narration

Narration used to create this video.

Video narration

Walking around a court's outside, how do you find a rectangle's missing length? Perimeter is the distance around the outside. With perimeter 14 cm and breadth 2 cm: 14 − 2 − 2 = 10; 10 ÷ 2 = 5 cm. Subtract both breadths, then split the rest between two equal lengths. Challenge: perimeter 30 cm, breadth 5 cm. [Pause.] 30 = 2 × (L + 5); 15 = L + 5; L = 10 cm. The same 36 cm string: square, 36 ÷ 4 = 9 cm; triangle, 36 ÷ 3 = 12 cm; hexagon, 36 ÷ 6 = 6 cm. Same perimeter, different side lengths. The field: 2 × (230 + 160) = 780 m per round; three rounds, 780 × 3 = 2,340 m of rope. Akshi: 2 × (70 + 40) = 220 m per round; five rounds, 1,100 m. Toshi: 2 × (60 + 30) = 180 m per round; seven rounds, 1,260 m. Toshi ran 160 m farther. Dot grid: 6s + 3d. Count straight units and diagonal units separately; their lengths aren't established as equal. Now count both types on the next figure. Cut the 6 cm by 4 cm paper into equal pieces. When rejoined, count exposed edges, not shared inside edges. Find each perimeter. Can you arrange them for 22 cm? Memory card: known perimeter-work backwards; equal sides-divide; several rounds-perimeter times rounds; dot grid-count straight and diagonal units separately; reshaped pieces-trace exposed edges; runners-distance per round times rounds. So, the missing length is 5 cm: the two 2 cm sides leave 10 cm, shared equally by the two lengths.