# Math for Educators I

Get Started. It's Free
369
478
1
535
363
566
Math for Educators I

## 1. Mathematical Processes

### 1.1. Contexts

1.1.1. 1. Handshake Problem

1.1.2. + or - (Gauss)

1.1.3. Finite Differences

1.1.4. Triangle Problem

1.1.6. Probability (Area model/ Pascal's Triangle

## 3. Sets, Numbers Operations and Properties

### 3.1. Contexts

3.1.1. Mathematicians' Survey

3.1.2. Who Took What?

3.1.3. To Pass or Not to Pass

3.1.4. How many Sandwiches?

### 3.2. Book Assignments

3.2.1. Chapter 2: Introduction

3.2.2. Section 2-1

3.2.2.1. Negation and Quantifiers

3.2.2.2. Truth tables and compound statements

3.2.2.3. Conditionals and Biconditionals

3.2.2.4. Valid Reasoning

3.2.3. Section 2-2

3.2.3.1. The Language of Sets

3.2.3.2. One-to-one correspondence

3.2.3.3. Equivalent Sets

3.2.3.4. Cardinal numbers

3.2.3.5. the empty set

3.2.3.7. the empty set as a subset

3.2.3.8. Inequalities: an application of set concepts

3.2.3.9. Number of a subset of a finite set

3.2.4. Section 2-3

3.2.4.1. Set intersection

3.2.4.2. set union

3.2.4.3. set differences

3.2.4.4. properties of set operations

3.2.4.5. using venn diagrams as a problem solving tool

3.2.4.6. cartesian products

3.2.5. Projects

3.2.5.1. Library exploration

3.2.5.2. standards review

## 4. Book assignments

### 4.1. Strategies for Problem Solving

4.1.1. Look for a pattern

4.1.2. Examine a related problem

4.1.3. Examine a simpler case;make a table

4.1.4. Identify a subgoal

4.1.5. Make a diagram

4.1.6. Use guess and check

4.1.7. Work backward

4.1.8. Write an equation

### 4.2. Section 1-2 Explorations with Patterns

4.2.1. Inductive Reasoning

4.2.2. Arithmetic Sequences

4.2.3. Fibonacci Sequences

4.2.4. Other Sequences

## 5. Numeration Systems and Whole Number Operations

### 5.1. Contexts

5.1.1. number tools

5.1.2. base 10 number line

5.1.4. number systems chart

5.1.5. other number bases chart

5.1.6. Math to learn operation explorations

5.1.8. expressions explorations

### 5.2. Book Assignments

5.2.1. 3-1

5.2.1.1. Hindu arabic numeration systems

5.2.1.2. Tally numeration system

5.2.1.3. Egyptian Numeration system

5.2.1.4. Babylonian Numeration system

5.2.1.5. Mayan Numeration system

5.2.1.6. Roman numeration system

5.2.1.7. other number base systems

5.2.2. 3-2

5.2.2.4. subtraction of whole numbers

5.2.2.5. take-away model

5.2.2.6. properties of subtraction

5.2.3. 3-3

5.2.3.2. properties of whole-number multiplication

5.2.3.3. division of whole numbers

5.2.3.4. relating multiplication and division as inverse operation

5.2.3.5. division by 0 and 1

5.2.4. 3-4

5.2.4.2. subtraction algorithms

5.2.4.4. understanding addition and subtraction in bases other than ten

5.2.4.5. mental computation and estimation for whole number addition and subtraction

5.2.4.7. mental computation: subtraction

5.2.5. 3-5

5.2.5.1. preperties of exponents

5.2.5.2. multiplication algorithms

5.2.5.3. division algorithms

5.2.5.4. division by a two digit number

5.2.5.5. multiplication and division in different bases

5.2.5.6. mental computation: multiplication

5.2.5.7. mental computation: division

### 5.3. Projects

5.3.1. web research

5.3.2. mathematical autobiography

5.3.3. useful number tools

5.3.4. notable number patterns

5.3.5. classroom observation

## 6. Integers

### 6.1. contexts

6.1.1. integer number line

6.1.2. chip model

6.1.3. charged field model

6.1.4. movement model

### 6.2. book assignments

6.2.1. 5-1

6.2.1.1. representations of integers

6.2.1.3. absolute value

6.2.1.5. integer subtraction

6.2.1.6. defining integer subtraction

6.2.2. 5-2

6.2.2.1. patterns model for multiplication of integers

6.2.2.2. integer division

6.2.2.3. order of operations on integers

6.2.2.4. ordering integers

## 7. Clever Counting: Combinations

### 7.1. contexts

7.1.1. tree diagrams

7.1.2. factorials

7.1.3. networks

7.1.4. dominoes (order)

### 7.2. book assignments

7.2.1. investigation 1: counting possibilities

7.2.2. investigation 2: opening locks

7.2.3. investigation 3: networks

7.2.4. investigation 4: deciding whether order is important

7.2.5. investigation 5: wrapping things

### 7.3. projects

7.3.1. concept map

7.3.2. assessment portfolio