Factors and Multiples Part 1: Step 1: Collect the ages of 7 people of interest to you. These can be friends, family members, celebrities, historical figures, etc. Make a list of the 7 ages. (For example, I can have a list of ages of 12, 35, 37, 31, 24, 9, and 86) Part 2: (Representing Factors and Multiples) Step 2: Choose two different ages from the list of 7 that are composite numbers. Step 3: List all the factors for each composite number chosen in step 2. Step 4: Choosing one of the composite numbers from step 2, represent all the factors using the bar model. Step 5: Choosing one of the composite numbers from step 2 (it can be the same number from step 4 or you can choose your other composite number from step 2), represent all the factors of that number using the rectangular model. Part 3: (Divisibility Tests) Step 6: Create two numbers using different combinations of your 7 ages by placing them side by side to form a new number. (For example, using my 7 ages I can create the new numbers 1,235,373,124,986 and 8,692,437,311,235) Step 7: Do each of the numbers in step 6 have 2 as a factor? Explain using the divisibility test for 2. Step 8: Do each of the numbers in step 6 have 5 as a factor? Explain using the divisibility test for 5. Step 9: Do each of the numbers in step 6 have 3 as a factor? Explain using the divisibility test for 3. Step 10: Do each of the numbers in step 6 have 9 as a factor? Explain using the divisibility test for 9. Step 11: Do each of the numbers in step 6 have 6 as a factor? Explain using the divisibility test for 6. Step 12: Do each of the numbers in step 6 have 4 as a factor? Explain using the divisibility test for 4. Step 13: Do each of the numbers in step 6 have 8 as a factor? Explain using the divisibility test for 8. Part 4: (The Divisibility Properties) Step 14: Choose a number that when divided by 7 has a remainder of 1. Step 15: Choose a number that when divided by 7 has a remainder of 0. Step 16: Choose a number that when divided by 7 has a remainder of 6. Step 17: If you take the numbers from step 14 and 15 and add them together, will their sum be divisible by 7? Explain with the bar model. Is this a divisibility property? Step 18: If you take the numbers from step 14 and 16 and add them together, will their sum be divisible by 7? Explain with the bar model. Is this a divisibility property? Step 19: If I multiply the number from step 15 by 2, will that new product be divisible by 7? Explain with the bar model. Is this a divisibility property?

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