Common Factors and Co-prime Numbers

Create one continuous premium Grade 6 mathematics animation titled “The Sieve of Eratosthenes”. Integrate narration and visual directions in sequence. Use a large, perfectly aligned number grid from 1 to 100. Cross-outs and circles must remain readable; never cross out a prime number. SEQUENCE 1 — START WITH 1 Visual: display grid 1–100. Cross out 1 in a distinct colour and label “1 is neither prime nor composite.” Narration: “Start with the numbers from one to one hundred. First, cross out one. It is neither prime nor composite.” SEQUENCE 2 — CIRCLE 2 Visual: circle 2 as the first prime. Cross out every other multiple of 2: 4, 6, 8, 10 and onward to 100. Keep 2 circled and untouched. Narration: “The first uncrossed number is two. Circle it: two is prime. Now cross out the other multiples of two, because they have two as a factor.” SEQUENCE 3 — NEXT UNCROSSED NUMBER Visual: circle 3. Cross out multiples of 3 that are not already crossed out: 9, 15, 21, 27, and onward. Do not cross out 3. Narration: “The next uncrossed number is three. Circle it. Cross out the multiples of three that are still uncrossed.” SEQUENCE 4 — CONTINUE THE SIEVE Visual: next uncrossed number 5: circle it and cross out remaining multiples of 5. Then circle 7 and cross out its remaining multiples. Continue the sieve correctly through the grid; only prime numbers remain circled. Show each new prime chosen as the next uncrossed number, without needing to narrate every crossed-out value. Narration: “Continue with the next uncrossed number. Circle it, then cross out its multiples that remain. Repeat the process. The circled numbers are prime; the crossed-out numbers greater than one are composite.” SEQUENCE 5 — REVEAL THE PRIMES Visual: show the correctly completed sieve and highlight the primes up to 100: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97. Narration: “Here are the prime numbers up to one hundred. Each has exactly two factors: one and itself.” SEQUENCE 6 — THINK AND CHECK Visual: ask “Why is 91 crossed out?” Pause, then reveal 91 = 7 × 13. Ask “Why is 97 circled?” Reveal that no smaller prime number divides it exactly; keep explanation at Grade 6 level. Narration: “Why is ninety-one crossed out? It is seven times thirteen, so it is composite. Ninety-seven remains circled because it has no factor other than one and itself.” End memory card: “Sieve: circle the next uncrossed number; cross out its other multiples; repeat.” Do not teach prime factorisation.Create one continuous premium Grade 6 mathematics animation titled “Common Factors and Co-prime Numbers”. Integrate the visuals and narration. Use accurate number-line jumps, factor lists and clean comparison cards. Let learners see the pattern before revealing the term CO-PRIME. Arin is the only character if a character appears in the core. SEQUENCE 1 — TEST 12 AND 26 Visual: two aligned number lines, 0–12 and 0–26. Animate jump size 2: 0→2→4→6→8→10→12 and 0→2→4→…→24→26. Both land exactly. Narration: “Can the same jump size reach both treasures? Try jumps of two. Two reaches twelve exactly, and it reaches twenty-six exactly too.” SEQUENCE 2 — CONNECT TO COMMON FACTORS Visual: show 12 ÷ 2 = 6 and 26 ÷ 2 = 13. Highlight 2 in both factor lists. Narration: “Because two divides both numbers exactly, two is a common factor of twelve and twenty-six. So this pair is not safe.” SEQUENCE 3 — TEST 4 AND 9 Visual: reveal treasure pair 4 and 9. Try jump size 2: it reaches 4 but passes 9. Try jump size 3: it reaches 9 but passes 4. Show the failed landings clearly. Narration: “Now try four and nine. A jump of two reaches four, but not nine. A jump of three reaches nine, but not four. No jump size greater than one reaches both.” SEQUENCE 4 — COMPARE FACTOR LISTS Visual: FACTORS OF 4: 1, 2, 4. FACTORS OF 9: 1, 3, 9. Highlight only 1 in common. Narration: “Look at the factors. Four has one, two and four. Nine has one, three and nine. Their only common factor is one.” SEQUENCE 5 — NAME CO-PRIME Visual: reveal definition: “Two numbers are co-prime if their only common factor is 1.” Show 4 and 9 → CO-PRIME; 12 and 26 → NOT CO-PRIME. Narration: “When two numbers have no common factor other than one, they are called co-prime numbers. Four and nine are co-prime. Twelve and twenty-six are not.” SEQUENCE 6 — QUICK THINK Visual: ask which pairs are co-prime: 15 and 39; 4 and 15; 18 and 29; 20 and 55. Pause, then reveal answers with short common-factor reasoning: 15 & 39 share 3 → not co-prime. 4 & 15 share only 1 → co-prime. 18 & 29 share only 1 → co-prime. 20 & 55 share 5 → not co-prime. Narration: “Pause and check each pair. Fifteen and thirty-nine share three, so they are not co-prime. Four and fifteen are co-prime. Eighteen and twenty-nine are co-prime. Twenty and fifty-five share five, so they are not co-prime.” SEQUENCE 7 — THREAD-ART CHALLENGE Visual: show a circular peg board. Demonstrate a thread that moves from peg to peg using a fixed gap. Ask learners to predict whether the thread visits every peg before returning to the start. Do not state an unsupported universal rule; show the supplied examples as investigation and invite learners to compare peg count and gap. Narration: “Now look at the thread art. The thread moves by a fixed gap around the pegs. Will it visit every peg before returning to the start? Compare the number of pegs with the thread gap, and explain what you notice.” End memory card: “Co-prime = the only common factor is 1.” Do not teach HCF/GCF, prime factorisation or a formal LCM algorithm.