Christmas Puzzles

Christmas Puzzles with solutions
http://eldermathshare.blogspot.com/2012/12/christmas-puzzles.html#!/2012/12/christmas-puzzles.html

BLOG CONTENT

The meaning of DENOMINATOR and NUMERATOR
http://kidscanlearnalgebra.blogspot.com/2012/09/denominator-vs-numerator.html

SUBTRACTION is ADDING the OPPOSITE
http://kidscanlearnalgebra.blogspot.com/2012/05/at-least-once-in-algebra-class-students.html

ADDING POSITIVE and NEGATIVE NUMBERS
http://kidscanlearnalgebra.blogspot.com/2012/05/adding-positive-and-negatives.html

ORDER of OPERATIONS
http://kidscanlearnalgebra.blogspot.com/2012/04/which-operation-should-we-do-first.html

FIRST GRADE ALGEBRA
http://kidscanlearnalgebra.blogspot.com/2012/04/first-grade-algebra.html

Denominator vs. Numerator

Suppose someone offered you some pizza.
Your answer will determine how much you get.
"Do you want a pizza?"
1) " Yes, one " - will get you a whole pizza.
2) " one-half " = "1/2" will get you a half of pizza.

3) " two-thirds " = "2/3"
might need a picture to represent.
First the pizza will be cut into
3 equal parts and then you will
get 2 of those parts.

4) What would 5/8 get you.

The denominator says to cut it (the pizza) into 8 equal parts.
and then
you get the number of these that is in the numerator, 5.
Thus, the conclusion about a fraction:
The DENOMINATOR (Bottom) represents
the number of equal
parts in which the WHOLE (PIZZA) is to be cut.
The NUMERATOR (Top)
the number of these parts that you
want to have.

SUBTRACTION is ADDING THE OPPOSITE

At least once in an Algebra Class the students should
see the "WHY" 
in SUBTRACTION becoming ADDING THE OPPOSITE
 in 7 - (-3) becoming 7 + (+3)
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Adding Positive and Negatives

Before starting a new topic try
the review question at the LEFT.

The answers are at the end of this blog!

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****ADDING POSITIVE AND NEGATIVES*****

**************ADDITION OF NUMBERS***********
When we ADD two POSITIVES it is just
our basic ADDITION and the ANSWER IS POSITIVE.
When we ADD two NEGATIVES
(Loss plus another Loss is a LOSS)
just ADD the two numbers and the ANSWER IS NEGATIVE.
so the obvious is just plain OBVIOUS:

(-) plus (-) is = (-)
(+) plus (+) is = (+)

A decision about "LARGER in SIZE"
is necessary when ADDING OPPOSITE SIGNS
(we actually subtract the SIZE):

(+) plus (-) is = (+) as long as the (+BIGGER)

(-) plus (+) is = (+) as long as the (+BIGGER)

(-) plus (+) is = (-) as long as the (-BIGGER)

(+) plus (-) is = (-) as long as the (-BIGGER)

***********try the sample problems below******

*************ANSWERS**************

*****ANSWERS TO PMDAS REVIEW*****

Which operation should we do first?

When we are faced with an EXPRESSION to be simplified, sometimes there are many operations (+, - , *, /)
within the expression.
For example how do we handle:   "2 PLUS 3 TIMES 4"
Without commas we do not know which operation to perform first.
---Do we Add 2 and 3 and then multiply by 4?
---OR should we multiplying 3 times 4 and then adding 2?
Mathematicians have come to an agreement that we will
MULTIPLY first and then ADD in this kind of problem.

First Grade Algebra

*****I*LOVE*MATH*****
Ever since you learned
how to ADD in the
first grade you have
been doing Algebra.

Remember those pages
where you had to write
a number into an
empty square with a
to make
the equation "TRUE"?

That was ALGEBRA!


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When you are finished trying these problems,
I will put the correct answers here:
5) x = 4
6) y = 3
7) z = 8
8) w = 5
9) A = 4
10) B = 7

If #10) was written as
3 times B = 21
the solution would be the same.
We will find out later that
B+B+B is 3 times B or 3B