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Parallelogram

Quadrilateral

Rhombus

Polygon

A quadrilateral that has both pairs of opposite sides parallel.

A four-sided polygon.

A parallelogram in which all the sides are the same length. H…

A closed figure formed by three or more line segments.

Parallelogram

A quadrilateral that has both pairs of opposite sides parallel.

Quadrilateral

A four-sided polygon.

Linear Measurement

Area Measurement

Area

Volume

The distance between two objects, a straight-line measurement…

A square unit equals unit square.

The number of square units required to cover a surface.

Amount of space occupied by an object or fluid.

Linear Measurement

The distance between two objects, a straight-line measurement…

Area Measurement

A square unit equals unit square.

Triangle Congruence

3 Properties of Congruence

Side Angle Side Congruence (SAS)

Angle Side Angle Congruence (ASA)

A set of theorems stating that if particular parts of a trian…

Side Angle Side (SAS)... Angle Side Angle (ASA)... Side Side Side (…

If two sides and the included angle of one triangle are congr…

If two angles and the included side of one triangle are congr…

Triangle Congruence

A set of theorems stating that if particular parts of a trian…

3 Properties of Congruence

Side Angle Side (SAS)... Angle Side Angle (ASA)... Side Side Side (…

Math Fluency components

Reasoning

Three types of math reasoning

Inductive

Accuracy, Automaticity, Rate, Flexibility

students' ability to hypothesis, test their theories, and dra…

Inductive, deductive, adaptive

Reasoning in which conclusions are based on observation

Math Fluency components

Accuracy, Automaticity, Rate, Flexibility

Reasoning

students' ability to hypothesis, test their theories, and dra…

acute triangle

objective assessment

alternative assessment

authentic assessment

A triangle in which all three angles measure less 90 degrees.

refers to testing that requires the selection of one item fro…

refers to the other (no traditional) options used to assess s…

is a form of alternative assessment that incorporates real-li…

acute triangle

A triangle in which all three angles measure less 90 degrees.

objective assessment

refers to testing that requires the selection of one item fro…

Math Fluency components

Reasoning

Three types of math reasoning

Inductive

Accuracy, Automaticity, Rate, Flexibility

students' ability to hypothesis, test their theories, and dra…

Inductive, deductive, adaptive

Reasoning in which conclusions are based on observation

Math Fluency components

Accuracy, Automaticity, Rate, Flexibility

Reasoning

students' ability to hypothesis, test their theories, and dra…

Whole Number

Decimal Point

Numerator

Denominator

There is no fraction, decimal or negatives.... Ex: 1,2,3,4,5...

A point used to separate the whole number from the fractional…

The top number of a fraction that tells you how many parts yo…

The bottom number of a fraction that tells you how many parts…

Whole Number

There is no fraction, decimal or negatives.... Ex: 1,2,3,4,5...

Decimal Point

A point used to separate the whole number from the fractional…

NCTM

Common Core Standards

Math Practice Standards (Common Core S…

Content Standards (Common Core Standar…

National Council of Teachers of Mathematics

1. Math Practice Standards... 2. Content Standards

How the students learn

What the students learn

NCTM

National Council of Teachers of Mathematics

Common Core Standards

1. Math Practice Standards... 2. Content Standards

word names

standard numerals

pictorial models

counting numbers

the specific names given to the concept of a specific quantit…

...

a visual representation which models the essential characteri…

the set containing numbers 1, 2, 3, ....

word names

the specific names given to the concept of a specific quantit…

standard numerals

...

prime number

composite number

factors

multiples

can be divided only by 1 and itself

can be divided by 1, itself and other numbers

numbers that when multiplied together produce a given number

the products of given factors

prime number

can be divided only by 1 and itself

composite number

can be divided by 1, itself and other numbers

National Council of Teachers of Mathem…

Quote by NCTM

Curriculum and Evaluation Standards fo…

Professional Standards for Teaching Ma…

world's largest mathematics education organization with more…

Learning mathematics is maximized when teachers focus on math…

publication which has had the most enormous effect on school…

publication which articulates a vision of teaching mathematic…

National Council of Teachers of Mathem…

world's largest mathematics education organization with more…

Quote by NCTM

Learning mathematics is maximized when teachers focus on math…

Commutative Property

Associate Property

Hexagon

Polygon is regular if...

If the operation can be performed on any two numbers from the…

...

Polygon with six sides.

all sides are congruent.

Commutative Property

If the operation can be performed on any two numbers from the…

Associate Property

...

Equity Principle

Five Content Standards

Five Process Standards

Strategies for promoting discource (RR…

All students must have the opportunity and adequate support t…

Numbers and Operation... Algebra... Geometry... Measurement... Data Analy…

Problem Solving... Reasoning and Proof... Communicate... Connections... R…

Revoicing-repeat what is said... Rephrasing-get students to use…

Equity Principle

All students must have the opportunity and adequate support t…

Five Content Standards

Numbers and Operation... Algebra... Geometry... Measurement... Data Analy…

What is an integer?

What is a prime a number?

What is a composite number?

What is an even number?

The set of positive and negative numbers, including zero. The…

A whole number greater than one that is evenly divisible only…

A whole number greater than one that has more than two factor…

An integer that can be divided by two without leaving a remai…

What is an integer?

The set of positive and negative numbers, including zero. The…

What is a prime a number?

A whole number greater than one that is evenly divisible only…

deductive reasoning

inductive reasoning

adaptive reasoning

problem analysis

conclusions are made based on prior knowledge

reasoning based on observations, not proofs.

ability to justify strategies and to analyze strengths and we…

ability to apply and adapt a variety of math strategies to so…

deductive reasoning

conclusions are made based on prior knowledge

inductive reasoning

reasoning based on observations, not proofs.

Math Fluency components

Reasoning

Three types of math reasoning

Inductive

Accuracy, Automaticity, Rate, Flexibility

students' ability to hypothesis, test their theories, and dra…

Inductive, deductive, adaptive

Reasoning in which conclusions are based on observation

Math Fluency components

Accuracy, Automaticity, Rate, Flexibility

Reasoning

students' ability to hypothesis, test their theories, and dra…

congruent

A line of symmetry

Product

estimate

figures that are the same size and shape

a line that divides a shape with 2 exactly alike parts

the answer to a multiplication problem

a number close to the exact number

congruent

figures that are the same size and shape

A line of symmetry

a line that divides a shape with 2 exactly alike parts

What is an integer?

What is a prime a number?

What is a composite number?

What is an even number?

The set of positive and negative numbers, including zero. The…

A whole number greater than one that is evenly divisible only…

A whole number greater than one that has more than two factor…

An integer that can be divided by two without leaving a remai…

What is an integer?

The set of positive and negative numbers, including zero. The…

What is a prime a number?

A whole number greater than one that is evenly divisible only…

What is an integer?

What is a prime a number?

What is a composite number?

What is an even number?

The set of positive and negative numbers, including zero. The…

A whole number greater than one that is evenly divisible only…

A whole number greater than one that has more than two factor…

An integer that can be divided by two without leaving a remai…

What is an integer?

The set of positive and negative numbers, including zero. The…

What is a prime a number?

A whole number greater than one that is evenly divisible only…

(1) Set A is contained in set B, AND s…

N

Z

Q

How do you prove that sets A and B equal each other?

What denotes the set of all positive integers (or natural num…

What denotes the set of all integers?

What denotes the set of all rational numbers?

(1) Set A is contained in set B, AND s…

How do you prove that sets A and B equal each other?

N

What denotes the set of all positive integers (or natural num…

Equity Principle

Five Content Standards

Five Process Standards

Strategies for promoting discource (RR…

All students must have the opportunity and adequate support t…

Numbers and Operation... Algebra... Geometry... Measurement... Data Analy…

Problem Solving... Reasoning and Proof... Communicate... Connections... R…

Revoicing-repeat what is said... Rephrasing-get students to use…

Equity Principle

All students must have the opportunity and adequate support t…

Five Content Standards

Numbers and Operation... Algebra... Geometry... Measurement... Data Analy…

Equity Principle

Five Content Standards

Five Process Standards

Strategies for promoting discource (RR…

All students must have the opportunity and adequate support t…

Numbers and Operation... Algebra... Geometry... Measurement... Data Analy…

Problem Solving... Reasoning and Proof... Communicate... Connections... R…

Revoicing-repeat what is said... Rephrasing-get students to use…

Equity Principle

All students must have the opportunity and adequate support t…

Five Content Standards

Numbers and Operation... Algebra... Geometry... Measurement... Data Analy…

Van Hiele Level 0

Van Hiele Level 1

Van Hiele Level 2

Van Hiele Level 3

Visual/Recognition- It's a rectangle because it looks like one"

Descriptive/Analysis- focuses on component parts of a figure.…

Abstract/Relationships- "a square is a rhombus and a rectangl…

Deduction/Proof- "Justify" High School Geometry Level

Van Hiele Level 0

Visual/Recognition- It's a rectangle because it looks like one"

Van Hiele Level 1

Descriptive/Analysis- focuses on component parts of a figure.…

Objective 1

Key to finding solutions

Guess and Check

Making a sketch or a picture

Apply a variety of approaches to interpret and solve mathemat…

Guess and check; making a sketch or a picture; make a table o…

Make your best guess, then check the answer to see whether it…

Draw an image

Objective 1

Apply a variety of approaches to interpret and solve mathemat…

Key to finding solutions

Guess and check; making a sketch or a picture; make a table o…

scientific notation

multiplication

division

11²

a method of simplifying calculations by reducing numbers to a…

if you round one number up, round the other down to compensate

if you round one number up, round the other up to compensate

121

scientific notation

a method of simplifying calculations by reducing numbers to a…

multiplication

if you round one number up, round the other down to compensate

modular arithmetic

congruent modulo 12 ... true: 2 = 14 (mod…

congruent modulo 12... true: 3 = 39 (mod12)

congruent modulo 12... true: 4 =52 (mod12)

A set of numbers that wraps around on itself like the numbers…

yes because the difference between 2 and 14 = 12 and 12 is di…

yes because the difference between 3 and 39 = 36 and 36 is di…

yes because the difference between 4 and 52 =48 and 48 is div…

modular arithmetic

A set of numbers that wraps around on itself like the numbers…

congruent modulo 12 ... true: 2 = 14 (mod…

yes because the difference between 2 and 14 = 12 and 12 is di…

Equity Principle

Five Content Standards

Five Process Standards

Strategies for promoting discource (RR…

All students must have the opportunity and adequate support t…

Numbers and Operation... Algebra... Geometry... Measurement... Data Analy…

Problem Solving... Reasoning and Proof... Communicate... Connections... R…

Revoicing-repeat what is said... Rephrasing-get students to use…

Equity Principle

All students must have the opportunity and adequate support t…

Five Content Standards

Numbers and Operation... Algebra... Geometry... Measurement... Data Analy…

Arithmetic Sequence

Constant value of Arithmetic sequence

Geometric Sequence

Constant value of Geometric Sequence

each term after the first is obtained by adding a constant va…

common difference

each term is obtained by multiplying the preceding term by a…

common ratio

Arithmetic Sequence

each term after the first is obtained by adding a constant va…

Constant value of Arithmetic sequence

common difference

deductive reasoning

inductive reasoning

adaptive reasoning

problem analysis

conclusions are made based on prior knowledge

reasoning based on observations, not proofs.

ability to justify strategies and to analyze strengths and we…

ability to apply and adapt a variety of math strategies to so…

deductive reasoning

conclusions are made based on prior knowledge

inductive reasoning

reasoning based on observations, not proofs.

Variable

Term

Constant Term

Coefficient

A letter or symbol used to represent an unknown number.

A number or a variable or a product or quotient of numbers an…

If an expression has a term that is a number (without a varia…

The number in front of each term.

Variable

A letter or symbol used to represent an unknown number.

Term

A number or a variable or a product or quotient of numbers an…

Integers

Prime numbers

Composite number

Even number

The set of whole positive and negative numbers, including zero

a Whole number greater than 1 that has only two factors, itse…

A whole number greater than 1 that has more than two differen…

any integer that can be divided by 2 without leaving a remain…

Integers

The set of whole positive and negative numbers, including zero

Prime numbers

a Whole number greater than 1 that has only two factors, itse…

Commutative Property of Addition

Commutative Property of Multiplication

Associative Property of Addition

Associative Property of Multiplication

Add numbers in any order equals the same sum

Multiplying numbers in any order equals the same product

Grouping the numbers differently doesn't change the sum

Grouping the numbers differently doesn't change the product

Commutative Property of Addition

Add numbers in any order equals the same sum

Commutative Property of Multiplication

Multiplying numbers in any order equals the same product

Objective assessment

Alternative assessments

Authentic assessment

Performance assessment (often use inte…

The first two testing that require selection of one item from…

Uses non-traditional options to assess students learning. Whe…

A form of alternative assessment that incorporates real life…

Requires the completion of a task, project, or investigation;…

Objective assessment

The first two testing that require selection of one item from…

Alternative assessments

Uses non-traditional options to assess students learning. Whe…

up, down

up, up

log A + log B

log A - B

Multiplication: If you round one number ____, round the other…

Division: If you round one number ____, round the other ____…

up, down

Multiplication: If you round one number ____, round the other…

up, up

Division: If you round one number ____, round the other ____…

Place Value

Closure

Commutative property

Associative property

expanding a number by powers of ten... ex. 456=4**10^2+5**10+6*1

If you add (multiply) two numbers of a set then the sum (prod…

changes the order of the numbers... ex. 3+4=4+3

changes the groups (what is inside the parenthesis)... ex 3+(4+5…

Place Value

expanding a number by powers of ten... ex. 456=4**10^2+5**10+6*1

Closure

If you add (multiply) two numbers of a set then the sum (prod…

Rote memorization

One-to-one correspondence

Cardinality principle

Subitize

Knowing the list of counting words in order

Children understand each item gets its own number

The last number said in counting is the final number of the set

Ability to recognize the exact quantity without counting

Rote memorization

Knowing the list of counting words in order

One-to-one correspondence

Children understand each item gets its own number

Census

Sample

Simple Random Sample

Systematic Random Sample

Asking everyone in the populaton

A few of the population that is supposed to represent the who…

Each item or person in the population is as likely to be chos…

The items or people are chosen according to a specific item o…

Census

Asking everyone in the populaton

Sample

A few of the population that is supposed to represent the who…

Addition

Closure Property

Subtraction

Types of Subtraction

set A with a elements and B with b elements which are disjoin…

If you add two whole #s you will always get a whole # because…

Inverse of addition

Take Away... Comparison... Missing Part

Addition

set A with a elements and B with b elements which are disjoin…

Closure Property

If you add two whole #s you will always get a whole # because…

Addition

Subtraction

Multiply

Divide

bringing two or more numbers (or things) together to make a n…

taking one number away from another.

The basic idea of multiplying is repeated addition.

To divide is to split into equal parts or groups. It is "fair…

Addition

bringing two or more numbers (or things) together to make a n…

Subtraction

taking one number away from another.