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Suggested activities Numbers and the number system: Prime numbers 2/2a use factors and E How many factors? multiples, express What types of numbers have 2 factors? 3 factors? 4 factors? 5 factors? Other numbers of factors? numbers as products of factors - prime numbers have 2 factors, square numbers have an odd number of factors, How many factors? Fill in all the factor pairs on the last four cards, then use the cards to complete this task. Sort the cards into groups: two factors, three factors, four factors… A cube number Can you find another number to fit each group? will always have What do you know about the properties of the numbers in each group? … factors Can you make any statements about the property and the number of factors that are always true? 2 factors 3 factors 4 factors 5 factors 6 factors 7 factors 8 factors 9 factors 15 23 49 16 1 × 15 3×5 1 × 23 1 × 49 7×7 1 × 16 2 × 8 4×4 81 27 31 25 1 × 81 3 × 27 1 × 27 3×9 1 × 31 1 × 25 5×5 9×9 8 9 10 11 Suggested activities Numbers and the number system: Prime numbers 2/2a find common factors D Consecutive LCM use primes Lowest common multiples of sequences of whole numbers, plus 1. LCM {1, 2} = 2 2 + 1 = 3 ……3 is prime LCM {1, 2, 3} = 6 6 + 1 = 7…….7 is prime LCM {1, 2, 3, 4} = 12 12 + 1 = 13… 13 is prime LCM {1, 2, 3, 4, 5} = How far does this sequence work? Why does it break down? Consecutive LCM Rule: write a sequence of whole numbers, starting with 1 Find their LCM then add 1 When does this stop giving a prime number? Can you explain why it does not always work? consecutive numbers = LCM add 1 = ? prime number? 1×2 =2 2+1 =3 1×2×3 =6 6+1 =7 1 × 2 × 3 × 4 = 12 12 + 1 = 13 1×2×3×4×5 = +1 = 1×2×3×4×5×6 = +1 = Suggested activities Numbers and the number system: Prime numbers 2/2a express numbers as C Factors of powers of 10 products of primes How many factors does 10 have? 100? 1000? Is there a pattern? Why? - write each power of 10 as a product of 2, 5 - consider combinations of 2, 5 to make the various factors eg 100 = 2²5², factors are 2050, 2051, 205², 2150, 2151, 215², 2²50, 2²51, 2²5² Factors of powers of ten Use the information in the table to predict the number of factors for 1 000 000. Begin to fill in the table rows. Can you check your prediction without completing every row? power of product of number factors exploring ten primes of factors 10 2×5 1 2 5 10 4 100 2² × 5² 1 2 4 5 10 9 20 25 50 100 1000 10 000 100 000 1 000 000 Suggested activities Numbers and the number system: Prime numbers 2/2a express numbers as C Generating prime numbers products of primes x2 + x + 41 Does this expression always generate a prime number? For example 12 + 1 + 41 = 43 22 + 2 + 41 = 47….. continue! What if we replace 41 with a different prime number, e.g. x2 + x + 13; x2 + x + 23? Do these expressions generate prime numbers? n² + 1 Does n² + 1 produce an infinite number of primes? n! + 1; n! – 1 3! = 3 x 2 x 1 = 6 So 3! + 1 = 6 + 1 = 7. 7 is prime. Is 4! + 1 prime? What about 4! - 1? Generating prime numbers Does the expression x2 + x + 41 always Try changing the 41 is to a different prime generate a prime number? number. Will the new expression still always generate a prime number? trial x² + x + 41 prime? trial x² + x + … prime? 1 1² + 1 + 41 43 1 1² + 1 + … 2 2² + 2 + 41 47 2 2² + 2 + … 3 3² + 3 + 41 3 3² + 3 + … 4 4 5 5 1² + 1 = 3, 2² + 1 = 5. Does the expression n² + 1 always generate a prime number? 4! is 4 factorial, it 1! + 1 = 2, 2! + 1 = 3, 3! + 1 = 7. means 4 × 3 × 2 × 1 Does the expression n! + 1 always generate a prime number? so 4! = 12 Does the expression n! – 1 always generate a prime number? Suggested activities Numbers and the number system: Equivalent fractions 2/2c 2/2d know fraction to F Matching decimal conversion Fractions Decimals Percentages dominoes (or other matching games) for fractions where the denominator is a multiple of 10 7 14 07 69% 065 . . 100 25 sixty-nine 13 10 hundredths 20 035 20 7% 16 35 65% 75% 080 . . 20 100 three 7 14% 007 05 . . quarters 50 . 4 075 50% 056 5 35% 65 75 7 70% 80% . . . . . . 100 100 20 one 14 014 069 56% half 20 065 65% 13/20 65/100 080 80% 4/5 16/20 056 56% 14/25 007 7% 7/100 014 14%. 7/50 035 35% 7/20 35/100 075 75% 75/100 three quarters 07 70% 14/20 05 50% 10/20 one half 069 69% sixty-nine hundredths Suggested activities Numbers and the number system: Equivalent fractions 2/2c 2/2d know fraction to E decimal conversion Find the pairs of numbers that have a product which ends in zero. Which numbers are never included? for fractions where the denominator is a multiple of 2, 5, 10 Suggested activities Numbers and the number system: Equivalent fractions 2/2c 2/2d classify fractions as C recurring/terminating ATM Thinkers – On the spot generalisation using knowledge of e.g. 28/99 = 0.282828282828… what can we deduce, predict or generalise from this? the factors of their denominators

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posted: | 2/22/2010 |

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