1. TO USE THE SIEVE OF ERATOSTHENES & USE NUMBER PATTERNS
(Copy this today and
everyday.)
TO USE THE SIEVE OF ERATOSTHENES & USE NUMBER PATTERNS
He was born in 276 BC in Shahhat, Libya
He is best known for being the first person to calculate the circumference of the earth. (Yes, he knew the earth was round—unlike
Europeans, who centuries later thought the
earth was flat!)
In number theory, he introduced the SIEVE OF ERATOSTHENES , an efficient method of identifying prime numbers.
He was the founder of scientific Chronology (the arrangement of events or dates in the order of their occurrence.)
He died in 194 BC in Alexandria, Egypt.

2. LESSON:
Refer to the handout that you just got.
We will start with recognizing that “1” is not a prime number! Surprise! It is considered the trivial prime.
We will start marking out numbers using colored pencils and making designs to differentiate the multiples.
Soooooo, that means that we will start with 2. We will mark out all the numbers that are multiples of 2 (NOT INCLUDING 2—BECAUSE IT’S PRIME.)
The next unmarked number is three. Changing color and pattern, mark out all the numbers that are multiples of 3.

3. The next unmarked number is three
The next unmarked number is three. Changing color and pattern, mark out all the numbers that are multiples of 3. (NOT INCLUDING 3—BECAUSE IT’S PRIME.)
Since 4 is already marked out, the next unmarked number is 5. Repeat the procedure until you run out of numbers that have not been marked out.
Every number that is left un-marked is a prime number!
Notice the patterns the numbers make. What do you see with the 2’s? The 3’s? etc.
How does this help you? Understanding the relationships and patterns between the numbers helps you to gain number sense.

4. Let’s look at some other number patterns:
Find 3 sets of numbers that add to get 7.
= _________ or _________ or _________
10 = _________ or _________ or _________
16 = _________ or _________ or _________
Will everyone get the same answers every time?
Try 6 sets:
24 = _________ or _________ or _________ _________ or _________ or _________

5. What about multiplication?
Find 3 sets of numbers that multiply to get 12.
= _________ or _________ or _________
30 = _________ or _________ or _________
54 = _________ or _________ or _________
Will everyone get the same answers every time?
Try 6 sets:
60 = _________ or _________ or _________ _________ or _________ or _________

6. What about a combination of addition or multiplication
What about a combination of addition or multiplication? (Hint: it is the distributive property.)
Find 3 sets of numbers that add, then multiply to get 12.
12 = _________ or _________ or _________
32 = _________ or _________ or _________
75 = _________ or _________ or _________
Will everyone get the same answers every time?
Try 6 sets:
64 = _________ or _________ or _________ _________ or _________ or _________

7. Assignment: Finish these three slides:
Find 3 sets of numbers that add to get 9.
9 = _________ or _________ or _________
11 = _________ or _________ or _________
27 = _________ or _________ or _________
Will everyone get the same answers every time?
Try 6 sets:
40 = _________ or _________ or _________ _________ or _________ or _________

8. What about multiplication?
Find 3 sets of numbers that multiply to get 28.
28 = _________ or _________ or _________
36 = _________ or _________ or _________
75 = _________ or _________ or _________
Will everyone get the same answers every time?
Try 6 sets:
100 = _________ or _________ or _________ _________ or _________ or _________

9. What about a combination of addition or multiplication
What about a combination of addition or multiplication? (Hint: it is the distributive property.)
Find 3 sets of numbers that add, then multiply to get 18.
12 = _________ or _________ or _________
45 = _________ or _________ or _________
88 = _________ or _________ or _________
Will everyone get the same answers every time?
Try 6 sets:
96 = _________ or _________ or _________ _________ or _________ or _________

10. How can the distributive property possibly help
How can the distributive property possibly help? If you want to multiply, say 8 x 37, we can split it into 8 (30 + 7). It is easy to understand that:
8 * 30 = and 8 * 7 = 56. then just add to get the final answer of 296!
Let’s use the distributive property to simplify:
5 * 42 = _____________ = ____________ = _____
Try: (How would you tackle the last one?)
4 * 33 = _____________ = ____________ = _____
7 * 22 = _____________ = ____________ = _____
9 * 42 = _____________ = ____________ = _____
6 * 228 = _____________ = ____________ = _____