Problem Solving- Melody

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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