Yesterday, I went to the dentist and orthodontist. I had no cavities! I have to have four teeth pulled to make room for my molars and wisdom tooth. The orthodontist is then going to put spacers and a spacer bar inside my bottom teeth to make room for all my teeth, and then I will need braces. Right now it's like I have two sets of teeth all crammed together like a shark. Derp!

## Cub Scouts:

Saturday, I went in a four mile hike at Raven Knob with my Grama Tina. Now I've hiked over 14 miles total. It was super cold Saturday. We had a freeze.

## Minecraft Homeschool: Ancient Civilization:

I started building the outside of my castle this week. I have to do research and make sure it's like a real medieval castle. I learned that horses kick at shields to help the rider. I learned that technologies developed and a arrow was developed to go right through chain-mail. I learned that crossbows can come in different sizes.

This is the outside of my castle (the walls) and my bridge, which is a retractible model that has a redstone line to retract a piston to create a disadvantage for the enemy!

## Pre-Algebra:

This week I learned about number theory: multiples and divisibility.

**Definition**: Let a and b be numbers. We say that a is a multiple of b if a equals b times some integer. in other words, a is a multiple of b if there is an integer n such that a = b · n.

**Important**: if we start from any multiple of n and count either upward or downward by n’s, all the numbers we hit will be multiples of n.

**Important**: if a and b are multiples of c, then a + b and a – b are both multiples of c.

**Important**: if we start with a multiple of n and add (or subtract) a number that is not a multiple of n, the resulting sum (or difference) is not a multiple of n.

**WARNING**!! In this book, when we say between “1oo and 2oo,” we don’t include 100 and 200.

**Concept**: One way to approach a difficult problem is to relate the problem to an easier problem you already know how to do.

**Important**: If a is a multiple of b, then every multiple of a is also a multiple of b.

**Definition**: Let a be any number, and let b be a nonzero number. We say that a is divisible by b if a divided by b is an integer.

**Important**: Any integer that has 0 or 5 as its units digit is a multiple of 5. Any integer that does not have 0 or 5 in it is not a multiple of 5

**Important**: Any integer that has an even units digit (0, 2, 4, 6, 8) is a multiple of 2. Any integer that has an odd units digit (1, 3, 5, 7, 9) is not a multiple of 2.

**Important**: A positive integer is divisible by 4 if the number formed by the last two digits of the original integer is divisible by 4. If this number is not divisible by 4 then the original integer is not divisible by 4.

**Important**: if the sum of the digits of an integer is a multiple of 9, then the integer is divisible by 9. Otherwise, the integer is not divisible by 9.

**Important**: if the sum of the digits of an integer is a multiple of 3, then the integer is divisible by 3. Otherwise, the integer is not divisible by 3.

I love your castle, you are doing such a great job. It really looks like a fun project!

I love hiking in the woods, the leaves turning beautiful colors, the quiet and the crisp, clean air are just great for the soul!

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