Moving with Algebra Sampler

19 Lesson Plans 20 ©MathTeachersPress, Inc. Reproduction by anymeans is strictly prohibited. 14 Number Number ofSquares ofArrays Factors PorC 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. Prime and Composite Numbers Use square tiles to find the number of arrays and the factors of eachnumber from 1 to 20.Write P if the number is prime and C if the number is composite. Number Number ofSquares ofArrays Factors PorC 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. How do you know if a number is prime? 7 is a prime number. The factors of the number 7 are: 1 and 7 A prime number has only two unique factors:the number itself and the number 1. The factors of the number 6 are: 1, 2, 3, and 6 A composite number has more than two unique factors. 7 1 3 1 6 2 A composite number has more than one array. A prime number has only one array. 6 is a composite number. 1 N/A P P C P C P C C C 1 1 2 1 2 1 2 2 2 1 1,2 1,3 1,2,4 1,5 1,2,3,6 1,7 1,2,4,8 1,3,9 1,2,5,10 1 P C P C C C P C P C 3 1 2 2 3 1 3 1 3 1,11 1,2,3,4,6,12 1,13 1,2,7,14 1,3,5,15 1,2,4,8,16 1,17 1,2,3,6,9,18 1,19 1,2,4,5,10,20 It will have only 2 unique factors, 1 and itself. Objective: To find a pattern for prime and composite numbers. Materials: Cubes or squares cut from Inch Graph Paper (Master 5), index cards, playing cards Vocabulary: array, prime number, composite number, factor Prime Numbers Each group will need cubes or square tiles cut from Inch Graph Paper (Master 5). Count out 8 tiles and arrange them to show how they might be packed into rectangular shaped boxes with only one layer. Draw a picture of the different ways you could arrange the 8 tiles. Display or draw a sketch of the two possible rectangles: a 1 8 and a 2 4. Rotate each rectangle to several positions to establish that the shape of the rectangle is the same, regardless of the position. These rectangles are also called arrays. The numbers on the side of each box are related to the multiplication facts equal to 8. What are the two multiplication facts shown? (1 8 = 8 and 2 4 = 8) The numbers on each side are the factors of 8. Write on the board: The factors of 8 are: 1, 8, 2, and 4. Numbers that have more than one array are called composite numbers. Now select 11 cubes. Find all the different arrays that can be made using exactly 11 cubes. (There will be only one array, a 1 11.) Write on the board: The factors of 11 are: 1 and 11. Numbers that have only one array also have only two different or unique factors. We call these numbers prime numbers. Direct attention to the factors for 8 and 11 on the board. Is 8 prime or composite? (composite) Is 11 prime or composite? (prime) Distribute a set of index cards numbered from 1 to 20 to each small group. Each student selects an index card and builds all the different arrays that can be found for the number shown on the card. Students write the number of arrays and the sides (or factors) of each array on the back of each card. Continue until all the cards have been selected. Ask each small group to select the cards with numbers having only one array. List these numbers on the board: 1, 2, 3, 5, 7, 11, 13, 17, 19. Which 2 4 1 8 array does not have unique factors? (1) So, the number 1 is not prime. All the other numbers with only 1 array are called prime numbers. How do you know if a number is prime? (A prime number can have only 1 array made from 2 unique numbers.) Students may complete the page from the activities they have already done. Prime Card Have the class separate into groups of 3 with a deck of 52 playing cards (tens and face cards included ). Deal 5 cards to each player and turn the remaining cards face down in a pile. Players take turns discarding one card with a prime number on it or drawing cards from the deck until it is possible to discard a prime card. The person with the fewest cards at the end of the round wins. The winner receives 1 point for each card in the opponents’ hands after subtracting the points in her hand. Play several rounds as time permits. Aces = 1, jacks = 11, queens = 12, kings = 13. Prime numbers: 2, 3, 5, 7, 11 (jacks) and 13 (kings). Skill Builders pp.15–16 Prime and Composite Numbers Number Sense Finding a pattern for prime and composite numbers Sample Lesson Sample Scripting (Bold Type) Lesson Plans 20 ©MathTeachersPr Reproduction by anymeans is 14 Number Number ofSquares ofArrays Factors PorC 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. Prime and Composite Numbers Use square tiles to find the number of arrays from 1 to 20.Write P if the number is prime an Nu ofS 21. How do you know if a number is pri 7 is a prime number. The factors of the number 7 are: 1 and 7 A prime number has only two unique factors:the number itself and the number 1. 7 1 A prime number has only one array. 1 N/A P P C P C P C C C 1 1 2 1 2 1 2 2 2 1 1,2 1,3 1,2,4 1,5 1,2,3,6 1,7 1,2,4,8 1,3,9 1,2,5,10 It will have only 2 unique factor Objective: To find a pattern for prime and composite numbers. Materials: Cubes or squares cut from Inch Graph Paper (Master 5), index cards, playing cards Vocabulary: array, prime number, composite number, factor Prime Numbers Each group will need cubes or square tiles cut from Inch Graph Paper (Master 5). Count out 8 tiles and arrange them to show how they might be packed into rectangular shaped boxes with only one layer. Draw a picture of the different ways you could arrange the 8 tiles. Display or draw a sketch of the two possible rectangles: a 1 8 and a 2 4. Rotate each rectangle to several positions to establish that the shape of the rectangle is the same, regardless of the position. These rectangles are also called arrays. The numbers n the side of each box are related to the multiplication facts equal to 8. What are the two m ltiplication facts shown? (1 8 = 8 and 2 4 = 8) The numbers on each side are the factors of 8. Write on the board: The factors of 8 are: 1, 8, 2, and 4. Numbers that have more than one array are called composite numbers. Now select 11 cub s. Find ll the different arrays that can be made using exactly 11 cubes. (There will be only one array, a 1 11.) Write on the board: The factors of 11 are: 1 and 11. Numbers that have only one array also have only two different or un que factors. We call these numbers prime numbers. Direct tte tion to the factors for 8 and 11 on the board. Is 8 prime or composite? (composite) Is 11 prime or composite? (prime) Distribute a set of index cards numbered from 1 to 20 to each small group. Each student selects an index card and builds all the different arrays that can be found for the number shown on the card. Students write the number of arrays and the sides (or factors) of each array on the back of each card. Continue until all the cards have been selected. Ask each small group to select the cards with numbers having only one array. List these numbers on the board: 1, 2, 3, 5, 7, 11, 13, 17, 19. Which 2 4 1 8 array does not have unique number 1 is not prime. All with only 1 array are calle How do you know if a (A prime number can have from 2 unique numbers.) Students may complete t activities they have already Prime Card Have the cl into groups of 52 playing car included ). Deal and turn the remaining car Players take turns discardin prime number on it or dra deck until it is possible to d The person with the fewest round wins. The winner rec card in the opponents’ han points in her hand. Play sev permits. Aces = 1, jacks = 1 kings = 13. Prime numbers: and 13 (kings). Skill Builders pp.15–16 Number Sense Unit 1 F