Math for Elementry Teachers

Tessellations

Transformations

Rotation

Reflection

Translation

Composition

Dilation

Congruent Triangles

Fractals

Geoboard

Circular

Coordinate

Isometric

Platonic Solids

Duals

Slicing

Pythagorean Theorem

1. Understand the Problem

2. Devise a Plan

look for patterns

guess and check

draw a picture/model

make a table

symbols

use tools

act something out

simplify/ break it down

work backwards

find resource to assist

3. Implament a Plan

4. Look back at the answer/ reflect

Attribute Blocks amd Trains

Geoboard

Pattern Blocks

Time

Analog

Digital

What time will it be?

Fill and Pour

Tangrams

Tally System

Egyptian

Mayans

Babylonians

Roman

Hindu-Arabic

usage of digits/numerals and place value

Place Value

assigns value to a digit depending on its placement in a numeral

Numeration System

collection of properties and symbols agreed upon to represent numbers systematically

Bar Chart

Base Blocks

Addition

let A & B be two disjoint finite sets. If n(A)=a and n(B)=b; then a+b=n(A U B)

Arithmetic Sequence with each successive term from the second on obtained from the previous term by the addition or subtraction of a fixed number, the differnce

Ways to Add

Lattice Method

Scratch Method

Low Stress Method

Left-to-Right Method

Any column first

Table

diagonally numbers appear in bands all possible ways to add two numbers

Subtraction

For any whole numbers a and b such that a>b, a-b is unique whole number c such that b+c+a

Take-away

characterized by starting with some inital quantity and removing or taking away a specified amount

Comparison

characterized by a compaison of the relative sizes of two quantites and determing either how much larger or how much smaller one quanitity is than the other

Missing Addend

characterized by the need to determine what quanitity must be added to a specified number to reach some targeted amount

Inverse of addition

Fractions

multiple interpertations

part-whole (most common)

2/3 represents 2 parts of a whole that was divided into 3 parts

division

the fraction bar eventually becomes an alternate tool for indicating division

partitun (long divison)

know number of groups/partitun

find size of partitun

repeated subtraction

know size of group

find number of groups

copies of a unit fraction (accompaniement to part-whole)

2/3 is two copies of the unit fraction 1/3

ratio

comparing two separate things

2/3 the ratio of boys to girls

may look like a fraction

comaping two quantites regardless of whether the unit are the same

if units happen to be differnt this is typically referred to as a RATE

a quantitative relationship showing the number of times one vaule contains or is contained within another value

Proportion

two ratios are equal

as a analogy: a is to b as c is to d

a:b as c:d

a:b = c:d

a:b :: c:d

Proportional Reasoning

Ratio Sense

Rational numbers

Relative Thinking

multiplictive thinking

Quantities and how they change

unitizing

compare appropriate units

Rational numbers

any number that can be expressed as the quotient of two integers a/b

improper frations & mixed numbers

advantages to improper fractions

no regrouping needed of the fraction

looks like part-whole context-not distracted

process is similar to mult/div of fractions

disadvantages to improper fractions

work with larger numbers

more oppurtunity for mistake-converting between two forms

use mult/div within problem

simplified fractions

Color Patterns

Division

Partitun(equal sharing model)

characterized by distributing a given quantity among a specified number of groups (partitun) and determing the size(amount) in each group or (partitun)

Know: quantity starting with & number of groups

Find: Size of each group

Measurement(repeated subtraction)

characterized by using a given quantity to create groups (partitions) of a specifed size (amount) and determining the number of groups (partituns) that are formed

Know: quantitu starting with & size of each group

Find: number of groups

Scaffolding Method

Partial-Quotients Method

Column Division

Array Division

Venn Diagrams

Multiplication

Geometric Sequence with each successive term from the second on obtained from the previous term by the multiplication of a fixed non zero number, the ratio

Discrete

Repeated Addition

Continuous

characterized by repeatedly adding a quanity of continuous quantities a specified number of times

Area Model

characterized by a product of two numbers representing the sides od a rectanglar region such that the product represents the number of unit sized squares with in the rectangular region

Cartesian Product Context

characterized by finding all possible paring between two or more sets of objects

Properties

Communitive

Associative

Identity

Zero

Distributive

Closure

Partial Product

Lattice

Factor Tree

Money

Sets

Proper Subset

for all sets A & B, B ps of A written B C A all elemnts that are in B are in A and there is atleast on elemnt of A that is not in B

Subset

All elements that are in A are in B

Equivalent Sets

exsist in a one-to-one correspondence between the sets

Empty Set

Contains no elements, cardinal number 0

Universal Set

contains all elements being considered in a given discussion

Complement of a Set

Divisibility

b is a factor of a

a is a multiple of b

b is a divisor of a

a is divisble by b

Modular Arithmetic

closure porperty

communtative property

indentity property

inverse property

Integers

Decimals

Rational numbers

any number that can be written in the form a/b where a,b E integers

as division leads to decimals

1342.3176

one thousand threehundred forty-two and three thousand one hundred seventy six ten-thousandths

division with deciamls

multiply by 1 "whole number as divisor"

percent

perr 100

decimal fraction

terminating decimal

Algebra Tiles

Color Patterns

Pentominoes

Polyominoes

Triominoes

Manipulate the puzzle pieces to find multiple solutions

Grapher

Space Blocks

3D

Balance Scales

Positive

Negative

Factor Tree

Cuisenaire Rods

Factoring/Multiples

Greatest Common Factor

Least Common Multiple

Fractions

Function Machine

Peg Puzzle

Bar Chart

Pie Chart

Spinners

Histogram

Loan Calculator

Saving Calculator

Scatterplot

Stick or Switch with Decsions

Box Model

Box Plot

Coin Tossing