Kategoriak: All - comparison - identity - subtraction - measurement

arabera Stephanie Munguia 12 years ago

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MAT 156 Math for Elementary Teachers

The principles of subtraction and addition are foundational for elementary mathematics. Subtraction is framed as the inverse of addition and can be understood through various methods such as comparison, take-away, and missing addend.

MAT 156 Math for Elementary Teachers

Cartesian Product

Characterized by finding all possible pairings between 2 or more sets of objects.

Continuous

Characterized by repeatedly adding a quantity of continuous quantities. A specified number of times.

MEAUREMENTS

ex. 50mph for 3 hours.

Area Model

Characterized by a product of two numbers representing the sides of a rectangular region such that the product represents the number of unit sized squares within the rectangular region.

Discreet

As repeated addition

There are 3 rows on a bus, there are 4 children in each row. How many children are there in the bus?

Different ways to Add

Left-to-Right

Scratch Method

Low Stress

Any Column First

Speaks for itself.

Lattice Method

Properties of Subtraction?

If a is an element of w then a-0=a=0-a

Counter Example

a-0=a Let a=1 then 1-0=1

but 0-a doesn not equal a because 0-1=-1

Commutaive Property

If a is an element of w and b is an element of w

then a-b=b-a

Counter example

Let a=1 and b=3

a-b=-2 b-a=2

so a-b does not equal b-a

Closure Property

If a is an element of w and b is an element of w,

then (a-b) is an element of w

Counter example

Let a=1 b=3 then 1-3 is not an element of w

MAT 156 Math for Elementary Teachers

Multiplication

Zero Property

a is an element of w

0 x a= 0

Distributive Property

a is an element of w

b is an element of w

c is an element of w

a(b+c) = ab+ac

Identity Property

a is an element of w

1 x a= a

1 is the identity element

Associative Property

a is an element of w

b is an element of w

c is an element of w

(a x b) x c = a x (b x c)

Commutative Property

a is an element of w

b is an element of w

ab is an element of ba

Closure Property

a is an element of w

b is an element of w

ab is an element of w

Subtraction

Subtraction is inverse operation of addition.

Four fact families

3+7=10

7+3=10

10-3=7

10-7=3

Missing addend

Characterized by the need to determine what quantity must be added to a specified number to reach some targeted amount.

ex. Tim has 1 ipod. After christmas Tim has 3 ipods. How many ipods did he get for christmas?

Comparison

Characterized by a comparison of the relative sizes of two quantities and determing either how much larger or how much smaller one quantity is compared to the other.

ex. Jonny has 3 baseball cards. Steve has 5 baseball cards. How many more baseball cards does Steve have than Jonny?

Take-away

Characterized by starting with some initial quantity and removing/taking away a specified amount.

ex. Sally had 4 apples, she eats 2 apples. How many apples does sally have now?

Sequences

Sequence: Ordered list of objects, events, or numbers.

Recurrence Relationship Sequences

Current term is dependent on previous term(s)

Geometric Sequences

We can write a rule if we know -The first term (a1) and -The common ratio ( r )

Arithmetic Sequences

We can write a rule if we know -The first term (a1) and -The common difference(d)

Problem Solving

The 4 Steps"How to solve a Problem"
Check your Answer
Implement your Strategy
Devise a Plan

What Strategy are you going to use?

Examples

-Act it out -Draw it out

-Look for a pattern -Guess & check

Understanding the Problem

Division

Measurement (repeated subtraction)

Characterized by using a given quantity to create groups (partitions) of a specified size (amount) and determining the number of groups (partitions) that are formed.

KNOW

-Quantity starting with

-Size of each group

FIND

-Number of groups

*Twenty-five students must be grouped into groups of 5. How many groups of students can be made?

Partition (equal sharing)

Characterized by distributing a given quantity among a specified number of groups (partition) and determing the size (amount) in each group.

KNOW

-The quantity we're starting with

-Number of groups

FIND

-Size of each group

*Twenty-four pieces are to be shared among 6 students. How many pieces of candy will each student get?

Addition

Identity Property of Addition of Whole Numbers (w)

If a is an element of w then a+0=a=0+a The identity element for addition is 0.

Associative Property of Whole Numbers (w)

If a is an element of w, b is an element of w and c is an element of w, then (a+b)+c=a+(b+c)=(a+c)+b

Commutative Property of addition on whole numbers (w)

If a is an element of w and b is an element of w, then a+b=b+a

Closure Property of Additive

If a is an element of x and b is an element of x, the a+b is an element of x.

Models/Context

Continuous (Numberline) Model
Measured Quantities

Time, Distance, Area, Volume

Characterized by the combining of two continuous quantities.

Discreet (set) Model
Counted Quantity

Markers, Feet, Chairs, Desks

Characterized by combing two sets of discreet objects.

Discreet- Indidually seperate and distinct objects.

Ways of Recording Numbers

0 is not a counting number.

Hindu-Arabic

Usage of digits/numerals and place value.

Roman System
Babylonions
Mayan
Egyptian
Tally System

Works for smaller amounts