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Quit Home Sample Answers 1. a) 1, 5, 25; 5 b) 1, 2, 3, 5, 6, 10, 15, 30; 2, 3, 5 c) 1, 2, 3, 4, 6, 12; 2, 3 d) 1, 2, 5, 10, 25, 50; 2, 5 e) 1, 2, 4, 7, 14, 28; 2, 7 f) 1, 2, 4, 5, 10, 20, 25, 50, 100; 2, 5 g) 1, 2, 4, 5, 10, 20; 2, 5 h) 1, 3, 7, 9, 21, 63; 3, 7 2. a) 31, 37, 41, 47 b) 32, 40, 48 3. 10, 26, 35 4. b) 3 31 d) 3 29 f) 5 3 3 a) Prime d) Composite b) Composite e) Prime c) Prime f) Composite 5. 6. 7. 8. 9. 23 students 71, 73, 79 Read through the last 2 bullets in Connect. Introduce the terms prime factors, prime factorization, common factors, and greatest common factor. Refer students back to Explore. Then ask: • What numbers between 2 and 20 are prime? (2, 3, 5, 7, 11, 13, 17, 19) Composite? (4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20) In pairs, have students write the prime numbers and prime factorization of each composite number. Encourage students to check the prime factorization of each number by multiplying the factors. Invite volunteers to share their answers and the strategies they used with the class. The prime numbers have only 2 factors. The composite numbers have more than 2 factors. a) 1, 5; 5 b) 1, 2, 4, 8; 8 c) 1, 2, 3, 6; 6 d) 1, 5; 5 a) 2 3 3 b) 5 7 c) 2 2 3 3 d) 2 5 5 I found the factors for numbers 20 to 28. The only number that doesn’t have a factor of 2, 3, 4, or 5 is 23. 23 is also the only prime number between 20 and 28. Each has only 1 and itself as factors. 2, 3, 5, 7, 11, 13, 17, 19, 23, and 29 are prime numbers. So, there are 10 days in September with prime number dates. 1 is neither prime nor composite. 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28, and 30 are composite numbers. So, there are 19 days in September with composite number dates. Practice Have Colour Tiles or congruent squares available for students to use. Assessment Focus: Question 7 Students realize that the number in question is not divisible by 2, 3, 4, or 5. Some students may systematically test each number from 20 to 28 for divisibility by these numbers. Other students may use Colour Tiles to model rectangles for each number, looking for a number that does not have 2, 3, 4, or 5 as a factor. To reinforce the concepts of common factors and greatest common factor, choose a pair of factors and have students find the common factors and the greatest common factor. For example, 12 and 18. (Common factors: 1, 2, 3, 6; Greatest common factor: 6) Unit 2 • Lesson 5 • Student page 47 19 Home Quit 10. All even numbers are divisible by 2. 32 is even. Any number with 0 or 5 for a ones digit is divisible by 5. 95 is divisible by 5. 11. The spinner has 3 prime numbers (47, 13, and 59) and 3 composite numbers (55, 39, and 26). Each player has an equal chance of winning. 12. a) There could be 1, 2, or 4 buns in one package. b) There could be 1, 3, or 9 buns in one package. 13. No; 9 and 25 are odd numbers and each has more than 2 factors. So they are composite. 14. Yes Composite Prime Even 2 Odd 3, 5, 7, 11, 13, 17, 19, 23, 29 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30 9, 15, 21, 25, 27 REFLECT: You can make only a 1 by 1 rectangle with 1 tile. So, 1 has only 1 factor. Jamie is right. Numbers Every Day Students should use the same strategies to round to hundred thousands and millions as they do to round to lesser place values. • • • • 46 10 10 52 200 000 000 100 000; 000; 000; 000; 46 10 10 52 000 000 000 000 000 000 000 000 ASSESSMENT FOR LEARNING What to Look For What to Do Reasoning; Applying concepts ✔ Students understand that a prime number has only 1 and itself as factors. ✔ Students understand that a composite number has more than two factors. Extra Support: To complete question 14, suggest that students first sort the numbers into 2 groups, prime and composite, and then re-sort each group into even and odd. Students can use Step-by-Step 5 (Master 2.13) to complete question 7. Extra Practice: Have students write the dates of their family Accuracy of procedures members’ birthdays, then determine whether each person’s ✔ Students can determine whether birthday is in a prime or composite month and on a prime or a number is prime or composite. composite date within the month. ✔ Students can write prime numbers and Students can complete Extra Practice 3 (Master 2.24). the prime factorization of composite numbers to 100. Extension: Challenge students to research and use the Sieve of ✔ Students can find common factors and Eratosthenes method for finding the prime numbers less than 100. the greatest common factor of a pair Students should be able to explain why this method works. of numbers. Recording and Reporting Master 2.2 Ongoing Observations: Whole Numbers 20 Unit 2 • Lesson 5 • Student page 48