Author:
Ashley Morgan, Connie Blalock, Jessica Chambers, Stefanie Holmes
Subject:
Mathematics
Material Type:
Lecture Notes
Level:
Community College / Lower Division
Tags:
  • Eduaction
  • Logic
  • Math
  • Model
  • Modeling
  • Number Theory
  • Sets
  • Tennessee Open Education
  • License:
    Creative Commons Attribution
    Language:
    English

    Math 1410 Number Concepts for Teachers

    Math 1410 Number Concepts for Teachers

    Overview

    This course is an introduction to problem solving; logic, sets, and operations on sets; and properties and operations on whole numbers, integers, rational numbers, irrational numbers, and real numbers. Modelling techniques necessary for future elementary educators will also be covered in this course.

    Getting Started

    MyOpenMath Help Video Playlist

    A YouTube playlist has been created to help instructors navigate MyOpenMath. A multitude of videos have been created to help walk new users through everything they need to use MyOpenMath in their courses. Access the playlist at:

    https://youtube.com/playlist?list=PL4DaWQ8GB98Q0VLyE9QCmrb697U8UUc4T

    Can’t find what you need? Email chambersjh@roanestate.edu to request additional video help.

    Hello and welcome to our algebra concepts course developed for teachers. In this course, students will have focus on eight different units of study. The first unit begins with a "boot camp" which allows students to review much needed math skills. The next three units will provide a focus on logic with problem solving and critical thinking, logic and reasoning, and set theory. The following three units will focus on number theory including number systems, base systems, and number theory. The course closes with a study of real numbers and modeling.

    Copying the MyOpenMath

    Math 1410: Number Concepts for Teachers Template

     

    To copy the MyOpenMath Math 1410: Number Concepts for Teachers course that is to be used in conjunction with the materials in the OER Commons, begin by visiting https://www.myopenmath.com/ and then following these three easy steps:

    Step 1: Log in to MyOpenMath by typing in the username and password you selected when creating your MyOpenMath account.

    Step 2: Once you are logged in, click the “Add a New Course” button under the section titled “Courses you’re teaching”.

    Step 3: To copy the promoted course, Math 1410: Number Concepts for Teachers, select “Copy a template or promoted course”. A box will open with all the available templates and promoted courses. Scroll down until you see Math 1410: Number Concepts for Teachers. To minimize the number of courses you have to scroll through, you can filter by level by selecting “Level” and checking Arithmetic, Prealgebra, Elementary Algebra, Non-STEM Algebra/Math Literacy, and Math for Liberal Arts/Quantitative Reasoning.

    Unit 0: Math Boot Camp

    Topic List 

    • Topic 1: Place Value, Rounding, and Operations on Whole Numbers
    • Topic 2: Integers and Absolute Value
    • Topic 3: Fractions and Mixed Numbers
    • Topic 4: Decimals
    • Topic 5: Order of Operations, Exponents, and Roots

    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

    All equations have been rendered in EquatIO: https://www.texthelp.com/products/equatio/ .


    Homework is available in the accompanying MyOpenMath course

    Unit 1: Problem Solving and Critical Thinking

    Topic List 

    • Patterns and Critical Thinking
    • Problem Solving Strategies
    • Estimating Number 

    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

    All equations have been rendered in EquatIO: https://www.texthelp.com/products/equatio/ .


    Homework is available in the accompanying MyOpenMath course

    Unit 2: Logic and Reasoning

    Topic List 

    • Statements and Simple Negations
    • Compound Statements and Negations
    • Conditional, Biconditional, and Validity of Reasoning

    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

    All equations have been rendered in EquatIO: https://www.texthelp.com/products/equatio/ .


    Homework is available in the accompanying MyOpenMath course

    Unit 4: Expanded Form, Place Value, and Roman Numerals

    Topic List 

    • Expanded Form and Place Value
    • Roman Numerals

    Additional Homework 

    • Larger Roman Numberals

    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

    All equations have been rendered in EquatIO: https://www.texthelp.com/products/equatio/ .


    Homework is available in the accompanying MyOpenMath course

    Unit 5: Other Base Systems

    Topic List 

    • Understanding Other Base Systems and Converting Between Them
    • Operations in Other Base System

    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

    All equations have been rendered in EquatIO: https://www.texthelp.com/products/equatio/ .


    Homework is available in the accompanying MyOpenMath course

    Unit 6: Number Theory

    Topic List 

    • Divisibility
    • GCD and LCM
    • Prime Numbers, Composite Numbers, and Prime Factorization

    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

    All equations have been rendered in EquatIO: https://www.texthelp.com/products/equatio/ .


    Homework is available in the accompanying MyOpenMath course

    Unit 7: Real Numbers and Their Properties

    Topic List

    • Exploring Decimals
    • Exploring Factions and Mixed Numbers
    • Converting between Percent, Decimals, and Fractions
    • Exponents and Scientific Notation
    • Exploring Radicals
    • Types of Numbers and their Relationships
    • Properties of Real Numbers

    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

    All equations have been rendered in EquatIO: https://www.texthelp.com/products/equatio/ .


    Homework is available in the accompanying MyOpenMath course

    Unit 8: Modeling

    Suggest Videos for Modeling Assignments:

    Modeling whole numbers: https://www.youtube.com/watch?v=gBQV4LttpBI

    Modeling decimals numbers: https://www.youtube.com/watch?v=ibR_iBxnITE and https://www.youtube.com/watch?v=yDa0ytNgbJI

    Count - on (10 frame) model: https://www.youtube.com/watch?v=8f8bDaxe-Ls

    Partial Sums Addition:  https://youtu.be/dP2ISPW1aoE

    or https://www.youtube.com/watch?v=yzdUIOJAEpI

    Opposite-Change Algorithm:

     https://youtu.be/omd10DWd6y0

    Base 10-blocks: https://www.youtube.com/watch?v=7FIwPGoaMzg

    Chip Model: https://youtu.be/KQwvjE7eypE

    Area Model: https://youtu.be/wv8GxBcmd40

     and https://youtu.be/x33Xylme2_Y

    Number line: https://youtu.be/0Y7XD2-0sYQ

    Addition Decimals:

                100’s Grids https://youtu.be/U7TNcp-T1CQ

                Base 10 Blocks https://youtu.be/Ov9ky123rBU or https://www.youtube.com/watch?v=jjvyB4zj_lQ&t=99s

    Missing Addends Method:https://youtu.be/UPJruYaFnG8

    Comparison Model: https://youtu.be/AtwNV7M19PE

    Base 10 Blocks for Whole Numbers: https://www.youtube.com/watch?v=vQC9DXmoKt4

    Chip Model: https://www.youtube.com/watch?v=_77vO0uzBfA

    Number line Model for Integers: https://www.youtube.com/watch?v=Dfytkh_lYME

    Number line Model for Fractions: https://youtu.be/c8uVU6QzKGM

                                                    https://youtu.be/MCULak8ARgQ

                                                    https://youtu.be/R34J7nBKCMY

    Area model for Mixed Numbers: https://youtu.be/SuSat5kkamA

                                        https://youtu.be/MHr1DL-2qrk

    100's grid: https://www.youtube.com/watch?v=9yI45amCNNE

    Base 10 Blocks for Decimals: https://youtu.be/VfkgHq4jmyA

                                        https://youtu.be/H53LIKN6bII

    Multiplying Whole Numbers: https://youtu.be/6fvIRlgEoUo

                Area Model https://youtu.be/zujhbT5deoA

                Partial Products Algorithm https://youtu.be/4QXfymhSQzA

                Distributive Property:  https://www.youtube.com/watch?v=Q3wfb0CPhIY

    Multiplying Integers: https://youtu.be/I2I0Nd_X_RA

                Chip Model https://www.youtube.com/watch?v=yVwbaEPedys&t=10s

                Number Line Model https://www.youtube.com/watch?v=fW3FWuLfpFc

    Multiplying Fractions and Mixed Numbers

                Area Model https://youtu.be/B366S2aYgzU

                Number Line Model https://youtu.be/sENA3Wc6c18

                                                    https://youtu.be/luTn_H8P1GQ

                Area Model https://youtu.be/K_Uv7tvYu9g

                                        https://youtu.be/lvQM0A0PsRo

    Multiplying Decimals

                Grids https://youtu.be/IWTC4hYAz7M

    Dividing Whole Numbers: https://youtu.be/aIJ-Eg9lW5Y

                Repeated-Subtraction Model https://youtu.be/M0YHpVigG8M

                Set Model https://youtu.be/dcisBh8zZ8E

                Chip Model https://youtu.be/OoIMagblT5Q 

    Dividing Integers: https://youtu.be/QGWkw0Z5Ulg

                Chip Model https://youtu.be/sk0hmctyUJ8

    Dividing Decimals:

                100’s Grids https://youtu.be/pyQf8uaSirw

    https://www.youtube.com/watch?v=RDkvKI0AD5s

       Base 10 Blocks https://youtu.be/LmWzhGvDt58

                                        https://youtu.be/MAV9I6hO7pM

    Homework List 

    • Modeling Whole Number and Decimals Homework
    • Modeling Addition Homework
    • Modeling Subtraction Homework
    • Modeling Multiplication Homework
    • Modeling Division Homework

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    All equations have been rendered in EquatIO: https://www.texthelp.com/products/equatio/ .


     

    Group Activities and Capstone Project

    Projects and Group Activities

    • Capstone Project
    • Group Modeling

    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

    All equations have been rendered in EquatIO: https://www.texthelp.com/products/equatio/ .