Problem Solving- Melody
The basic method for solving simple problems that most of us were taught isn't necessarily the best.
can be very difficult to solve problmes in your head using this method
Math: All about relationships, that's why you can always find an answer.
That's why you can ALWAYS find an answer
Using number lines, or a visual ALWAYS easier than algebra (for most people)
Properties of Addition
Identity Property of Zero
number stays the same value (itself) when you add zero
a+0=a
Associative Property
can use multiple properties to move or "group" terms to make more sense
(8+7)+3=8+(7+3)
Commutative Property
numbers in problems are movable to make problems
"more friendly"
8+7=7+8
Number Relationships
Spatial Relationships
Part-Part Whole
to conceptualize a number as being made up of 2 or more parts is the MOST important relationship to develop
Benchmarks of 5 and 10
10 is an essential numbers, must know how any given number relates to ten
One and Two More, One and Two Less
knowing which numbers are one more or two less than any given number
recognizing how many of something there are w/out counting, by seeing the visual pattern
5 Methods of Addition
34
+28
=
12(4+8)
+50 (30+20)
=62
Give and Take
Partial Sums/Instructional Algorithm
Working With Different Bases (Subtraction)
Essentially the same as addition, just have to remember how much much to carry over
(Base 7) 62-35+24-When adding to the one place of 62 just have to remember to add seven instead of ten
Working With Different Bases (Addition)
Examples
(Base 7) 46+31=110-can't go over 6 because the base is 7
(Base 3) 22+12=322-can't go over 2, just like you can't go over 9 with a base of 10
Learning when to carry over when working with bases other than 10
Time
Base of 60 Instead of typical base of 10
5:15-3:45=1:30 (base is 60, have to carry enough over from other place values to have enough minutes)
Methods For Subtraction
Holy Shift
When you subtract using a number line
if you shift the numbers to a friendlier
position (ie. from 37 and 55 to 40 and 55)
it's easier to solve the problem.
Adding/Finding the Distance
52-37
37+3=40
40+10=50
50+2=52
(3+10+2)=15
Compensating
Decomposing
Partial Sums/Differences
Traditional
Addition and Subtraction With Time and Money
easiest way is to use a number line
Visual hands on learning (drawing pictures, using manipulatives, number line)=good
Drawing a picture isn't immature or childish, but one of the best ways to understand problems, even "simple" ones.
Different methods of problem solving work for different people as long as you can explain your method, and have the correct answer it's not "wrong" the most essential thing is that you understand the problem.
Addition and Subtraction
Number lines can be essential for children to understand problems.
allows for conceptual understanding, which is essential for learning
Most commonly showed with "sets" or Venn diagrams
Venn diagram
Models for Addition (story problems)
Subtopic
MEASUREMENT/LINE/ACTIVE: some sort of action occurs
SET Model: no action performed in the problem, 2 seperate pieces
