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This is a picture of the problem (which is similar to the Snack Bag problem): And this is what the solution looks like:
Prime Time Study Guide Test-Monday, Sept. 21 and Tuesday, September 22
It is a BIG test. It is worth 100 points. You need to know your multiplication facts, know a prime number, and you must know the difference between factors of a number (factors are always smaller than the number, factors are what you multiply to get that product) and multiples of a number (multiples are that number or larger, they are what you get when you multiply the number by 1, 2, 3, 4, etc.). You must be able to:
5. If you eat oatmeal every 5 days, a hamburger every 7 days, and yogurt every 3 days, if you had all three today, how many days until you have all three again (you must find the LCM of 3 numbers). 35 days. Show how you work. I would list multiples of the numbers. 5 7 3 5 7 3 10 14 6 15 21 9 20 28 12 25 35 15 30 42 18 35 49 21 40 56 24 45 63 27 30 33 35 7. 32 42 2 x 16 2 x 21 2 x 8 3 x 7 2 x 4 2 x 2 Remember, in real class, you ALWAYS circle the prime numbers. Here I had to highlight them. So the factor string for 32 is 2 x 2 x 2 x 2 x 2 42 is 2 x 3 x 7 I CAN’T GET MY VENN DIAGRAM TO WORK. YOU HAVE EXAMPLES IN YOUR BINDER. So a 2 is in both factor strings and one 2 would go into the exclusive GCF club (Greatest Common Factor Club), or shared part of the circles. Four 2s would go into the circle for 32 only. 3 and 7 would go into the circle for 42. The GFC is everything inside the shared part multiplied, this time it is only 2. The GCF of 32 and 42 is 2. The LCM (Least Common Multiple) is found by multiplying ALL the digits in both circles (including the shared portion), or 2x2x2x2(from the 32 circle only)x2(from the shared part)x3x7(from the 42 circle only) (which is 32 x 3 x 7 = 672). So the LCM of 32 and 42 is 672. 8. Remember: Parenthesis Exponent Multiplication Division Addition Subtraction - I’ll highlight each step I’m doing 6 (3+2) - 4 4 + (2-1) x (2+2) 6 x 3 - 4(2) / 2 6(5) - 4 4 + 1 x (2+2) 18 - 4(2) / 2 30 - 4 4 + 1 x 4 18 - 8 / 2 26 4 + 4 18 - 4 8 14 Always do ONE step at a time. Prime factorization (and factor strings) are all about breaking a number down into the prime numbers (or for factor strings, any combination of possible factors to create a product) that make up a number. An example: 30 is a composite number. It can be made in any number of ways 1 x 30, 2 x 15, 3 x 10, 5 x 6 OR 2 x 3 x 5. With larger composite numbers (like 240), there are many more possibilities (like 2 x 120, 2 x 12 x 10). I told them prime factorization is like taking a Lego model apart into all its little pieces.
The picture below shows what they are doing for bellwork this week. It is practicing Order of Operation skills. Since they will be moving into Algebra within a few years, I make them show all the steps they use (GOOD HABITS START EARLY). |
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September 2015
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