Grammar:
I learned about the two parts of a sentence. There is a subject, which is what the sentence is about, and the predicate, which is what we are saying about the subject. My mom wrote out sentences that I had to cut where the subect ends and the predicate starts. You need to be careful because a subject isn't the first word or so. It can be be really long, about half of the sentence sometimes. I got them all right!
PreAlgebra:
I moved into harder exponents after learning squares. I learned to add, subtract, multiply, and divide integers with exponents. Here are the rules I learned:
Definition: Let a be any number and let n be a positive integer. The power a^n, pronounced “a to the n,” is defined by the equation
A^n = a * a * … * a.

V
N copies of a
For example, a^5 = a * a * a * a * a
Important: let a and b be numbers. Let n be a positive integer
Power of product: (a*b)^n = a^n*b^n
Power of reciprocal: if b is nonzero, then (1/b)^n = 1/b^n
Power of quotient: If b is nonzero, then (a divided by b)^n = a^n divided by b^n
WARNING!! Suppose a and b are nonzero numbers, and n is an integer greater than 2. Just as (a + b)^2 is not equal to a^2 + b^2, the expression (a + b)^n is not necessarily equal to a^n + b^n.
Important: Cube of negation: Let a b any number. Then
(a)^3 = a^3
Important: Power of negation: Let a be any number. Let n be a positive integer. If n is even, then (a)^n = a^n if n is odd, then (a)^n = a^n.
Important: Product of powers (same base): Let a be any number. Let m and n be positive integers. Then
A^m · a^n = a^m+n.
Quotent of powers (same base): Let a be a nonzero number. Let m and n be positive integers such that m is greater than n. then
A^m divided by a^n = a^m–n
Important: Power of power: Let a be any number. Let m and n be positive integers. Then
(a^m)^n = a^mn
Ancient Civilization:
I learned how to make peasant girdle bread this time. I thought it was pretty good with butter. Grama Tina liked hers with jam. Here is the recipe for you to try:
Ingredients
 a cup of warmed ale
 wholemeal flour
 an egg
 Bolt the flour through a cloth, to make the flour white (this makes manchet (white) bread)
 Add the warmed ale – the yeast in this will make the bread rise. Mix to make a dough
 Into the centre of the dough, add the egg and fold this into the dough
 On a floured board, knead half of the dough into a flat circle
 Repeat with the rest of the dough
 Set a griddle pan on the fire to heat. When it is hot put a piece of fat in and coat the pan
 Place one bread in at a time a cook. The bread will need to be turned from time to time to stop it burning
 Wrap the cooked breads in a clean cloth to keep warm while the rest cook
 When they are all cooked, serve hot
love your pictures!! The bread didn’t look as yummy as the soup! So glad we have sliced bread now:)
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i must admit I lost you on all the n^s and a*s and putting it all together to make a problem! I forgot, and tHis reminded me, That algebra is really a language rather than a math in many ways! Good job on all your work! I must remember not to play “Are You Smarter Than a Fifth Grader” with you, because I know I have forgotten all of that and know I am not! God job Sage! I am impressed! And you can cook too! Chemistry should be right up your ally!
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Sage, you won’t remember me but I want to tell you that you are so far ahead of your years. I know everyone is so proud of you. Keep learning all you can. God Bless you. You are such a handsome young man.
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