1 / 21

Prime Time

Prime Time. Whole Number Arithmetic. A little vocabulary. Factors are one of two or more whole numbers that are multiplied together to get a Product 5 x 7 = 35 Five and seven are factors, and thirty-five is a product. There are 2 kinds of numbers…. Prime Numbers

juro
Télécharger la présentation

Prime Time

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Prime Time Whole Number Arithmetic

  2. A little vocabulary • Factors are one of two or more whole numbers that are multiplied together to get a Product • 5 x 7 = 35 • Five and seven are factors, and thirty-five is a product

  3. There are 2 kinds of numbers… • Prime Numbers • These numbers have only two factors… One and themselves • 7 = 7 x 1 • 7: 1,7 • Composite Numbers • Have at least three factors • 10 = 5 x 2 and 10 x 1 • 10: 1,2,5,10 • 12 = 6 x 2 and 4 x 3 and 12 x 1 • 12: 1,2,3,4,6,12

  4. Factor Pairs 24: 1, 2, 3, 4, 6, 8, 12, 24 All factors have pairs

  5. Finding All of the Factors • You have to be systematic • Start with one and count up • Stop when you find two consecutive factors whose product is the number you are working on. 60: 1, 2, 3, 4, 5, 6, 10 6 x 10 = 60 so this is the central factor pair Now just match your other factors!

  6. Square Numbers • 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144 • 3 x 3 = 9. This statement could be modeled like this:

  7. Square Numbers • 16: 1, 2, 4, 8, 16 • Because we don’t repeat factors in our lists, square numbers have an odd number of factors • 4 x 4 is the middle pair • The square root of a square number is a whole number! • Numbers between square numbers have square roots between the squares…

  8. Square Roots • The numbers between 25 and 36 have square roots between 5 and 6 (non whole numbers) • Examine Factor Pair Mountain (website) • Knowing our square roots, tells us when to stop looking for factors. • 27’s square root is between 5 and 6 so I only need to count to 5 to find all of the numbers up FPM • 27: 1, 3 – and we’re ready to climb down!

  9. Divisibility • 1: All numbers have 1 as a factor • 2: All even numbers (ending in 0, 2, 4, 6, 8) have 2 as a factor • 3: If the sum of the digits is divisible by 3 so is the number itself • 81 -> 8 + 1 = 9, which is divisible by 3, so 81 is too! • 372 -> 3 + 7 + 2 = 12, so 3 is a factor • 109 -> 1 + 0 + 9 = 10, so 3 is not a factor

  10. Divisibility • 5: Numbers that end in 5 or 0 have five as a factor • 6: Numbers that have 2 & 3 as factors have 6 • 9: Same trick as for 3! • 162 -> 1 + 6 + 2 = 9 • 162 = 9 x 18 So what about the rest of the numbers? This is where it gets interesting…

  11. Stretching Numbers How do we know if 8 goes into 140? Our math facts don’t go up that high! Long division? Pick a number close to 140 that you know 8 goes into… how about 80. Look at the difference (60) If 8 goes into the difference, it goes into the number

  12. Stretching Numbers See if 8 goes into 224 You might use 8 x 3 to come up with 8 x 30 Since we know 8 goes into 240 all we have to do is check the difference – in this case 16. This means that 8 is a factor of 224. (8 x 28 = 224) Let’s practice!

  13. Primes • The Fundamental Theorem of Arithmetic • All numbers are the unique product of prime numbers • I think of this as a unique fingerprint for each number, or perhaps a number’s true name (Eragon)

  14. Factor Trees 36: 2 x 2 x 3 x 3

  15. Factor Trees 42 = 2 x 3 x 7

  16. Factor Trees • You can start any way you want, but the end result will always be the same – the order of the factors does not matter • Examine different factor trees for 100 • Practice!

  17. LCM & GCF • Knowing the prime factorization of numbers allows us to see what they have in common. • Greatest Common Factor (GCF) • ALL of the prime factors that any two (or more) numbers have in common. • INTERSECTION • Least Common Multiple (LCM) • ALL of the prime factors (without duplications) • UNION

  18. LCM & GCF 2 2 3

  19. Going Forward • Computation is probably always going to be a part of your child’s math education – have them master the facts now. • Do mental math at every opportunity with them • Not just the facts • Estimation • Divisibility tests • Large numbers

  20. Next Units • Bits and Pieces (CMP) • Fractions – representations and computation • Potential parent night? • Division (Additional Materials) • Long Division – standard algorithm • Estimation • Mental Math

  21. Thanks • There will be more group practice if time permits

More Related