Course Contents
Course Content
Unit 1: Numbers and Operations
● Counting
● Models for Addition & Subtraction with natural numbers
● Addition and Subtraction as inverse Operations
● Word problems involving addition and subtraction
● Working in the base-10 system
● Models for Multiplication with natural numbers
● Multiplication and Division as inverse operations
● Models for Division with natural numbers
● Nature of the remainder in division
● Factors, Prime and Composite Numbers
● Models of fractions (sets, number line, area, volume)
● Types of fractions (proper, improper and mixed-number)
● Decimals as fractions linked to base-10 place value
● Concept of GCF and LCM
● Operations with fractions and decimals
● Percent as related to fractions and decimals
● Ratio and Proportion
● Rates
● Integers, Operations with integers
● Venn Diagrams
Unit 2: Algebra
● Repeating patterns and growing patterns
● Generalizing a pattern and finding a rule
● Creating coordinate graphs
● Continuous, discontinuous, and discrete graphs
● Equivalent expressions
● Interpreting tables, graphs and equations of linear functions
● The concept of slope
● Order of Operations
● Interpreting tables, graphs and equations of quadratic functions
● Solving for x, the unknown
Unit 3: Geometry and Geometric Measurement
• Characteristics of Polygons with an emphasis on Triangles and Quadrilaterals,
• Point, line, line segment, ray
• Models of angles
• Benchmark angles
• Classifying angles by measurement
• Perimeter and Area formulas
• Circumference and Area formulas
• Surface Area formulas
● Volume formulas
● Squares, square numbers, square roots (surds)
● The Pythagorean Theorem
Unit 4: Information Handling
1- Graphic displays of information
● Collect & organise data via: tally marks, pictographs, line plot, bar graph, and line graphs (discrete and continuous)
● Interpret the above graphic displays of data
2- Measures of dispersion and central tendency
● Range
● Mean
● Median
Mode
Course Synopsis
This course provides opportunities for prospective elementary teachers to strengthen their mathematical knowledge and skills and to gain confidence in their understanding of mathematics. An important outcome of this course is for prospective teachers to be able to teach mathematics successfully in the elementary grades.
Research-based knowledge about good math instruction provides a solid base of information for educators to use as they identify mathematics skills students need to develop, as well as teaching strategies and instructional approaches that best support the development of these skills. The course is designed based on what research tells us about good math instruction.
The overall organization of the course is divided into four units:
1. Number and Operations
2. Algebra and Algebraic Thinking
3. Geometry and Geometric Measurement
4. Information Handling
Each unit of study has a consistent design or organization and is meant to maximize time on learning for prospective teachers.
1. Content: Most one hour sessions will begin working on a math problem. Prospective teachers will engage in solving and discussing a math problem and sharing approaches and solutions. The content has been developed to so that prospective teachers will engage in mathematics in depth to help them connect concepts within and across the four units.
2. Pedagogy: In each lesson prospective teachers will actively engage in doing mathematics in order to experience approaches to teaching and learning math that they can use when they teach. They will recognize that there are often multiple ways of approaching a problem and in some instances more than one correct answer. The instructor will present questions that stimulate curiosity and encourage prospective teachers to investigate further by themselves or with their classmates.
The course will also examine how children learn and develop mathematical understanding and skills and how the way children think influences the teaching of mathematics in the primary, elementary, and middle grades.
3. Assignments: Students are expected to continue learning about math and the teaching of math after class. There will be assignments to stretch prospective teachers content knowledge and to learn more about teaching math. Assignments will take many forms including independently solving math problems and school based tasks.
In summary, the General Mathematics course is a comprehensive effort to build and deepen maths content knowledge, to learn and use high-quality instructional practices, and to study ways in which young students approach and learn mathematics.
Course Learning Outcomes
Students will:
● Increase their mathematical content knowledge for Number and Operations, Algebra and Algebraic Thinking, Geometry and Geometric Measurement, and Information Handling for teaching in the primary, elementary, and middle grades
● Increase their confidence, competence, interest, and enthusiasm for mathematics by exploring and doing mathematics
● Deepen an understanding of how children learn mathematics
● Build a variety of instructional techniques with clear purposes
● Enhance their use of questioning techniques to elicit children’s understanding
● Learn ways to engage students in mathematical thinking through interactive activities
Course Syllabus and Guide
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week 1 Addition and subtraction Equivalence
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week 1 Addition and subtraction Equivalence
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week 1 Addition and subtraction Equivalence
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week 1 Addition and subtraction Equivalence
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week 1 Place value
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week 1 Multiplication of whole numbers
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week 1 Multiplication of whole numbers
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week 2 Fractions and decimals
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week 1 Division of Whole number
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week 2 Fractions and decimals
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week 2 Fractions and decimals
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week 2 Fractions and decimals
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week 2 Ratio, Proportion and Percent
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week 2 Proportion
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week 2 Ratio
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week 2 Percentage
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week 3 Integers
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week 3 Integers
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week 3 Integers
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week 3 Algebra as generalized arithmetic Patterns
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week 3 Algebra as generalized arithmetic Patterns
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week 3 Algebra as generalized arithmetic Patterns
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week 3 Algebra as generalized arithmetic Patterns
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week 4 Algebraic terminology x as a variable
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week 4 Algebraic terminology x as a variable
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week 4 Algebraic terminology x as a variable
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week 4 Coordinate graphs
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week 4 Linear functions
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week 4 Orders of Operations
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week 5 Square expressions and equations
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week 5 Square expressions and equations
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week 5 Square expressions and equations
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week 5 Symbol manipulation
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week 5 Symbol manipulation
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week 5 Polygons
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week 5 Polygons
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week 6 Undefined terms in geometry
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week 6 Identification and construction of angles
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week 6 Identification and construction of angles
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week 6 area
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week 6 Perimeter
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week 7 Circumference and area of circles
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week 7 Surface area of cuboids and cylinders
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week 7 Volume of cuboids and cylinders
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week 7 Introduction to the Pythagorean theorem
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week 8 Graphic displays of information
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week 8 Measures and central tendency
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Week 3 : Veen Diagram
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Week 3 : Veen Diagram description
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Week 3 : Veen Diagram definition
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Book Title : 190 ready-to-use activities that make math fun!
Author : George Watson
Edition : 1
Publisher : Josey Bass- A Wiley Imprint
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Title : addition and subtraction of mixed numbers (week 2)
Type : Other
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Title : addition and subtraction 1 (week 1)
Type : Other
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Title : multiplication and division (week 1)
Type : Other
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Title : multiplication and division (week 1)
Type : Other
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Title : multiply divide integers fact sheet (week 1)
Type : Other
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Title : addition and subtraction of proper fraction (week 2)
Type : Other
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Title : addition and subtraction of fractions (week 2)
Type : Other
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Title : division of fractions (week 2)
Type : Other
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Title : multiplication of fractions (week 2)
Type : Other
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Title : percentage (week 2)
Type : Other
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Title : ratios,proportions and percentage
Type : Other
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Title : ratios and proportions (week 2)
Type : Other
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Title : ratios (week 2)
Type : Other
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Title : Add and subtract Integers (week 3)
Type : Other
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Title : Algebra multiplication (week 3)
Type : Other
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Title : algebra substitution (week 3)
Type : Other
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Title : Introduction to algebra (week 3)
Type : Other
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Title : whole numbers and integers (week 3)
Type : Other
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Title : introduction to inequalities (week 3)
Type : Other
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Title : algebra basic definitions (week 4)
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Title : order of operations (PM) (week 4)
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Title : order of operations (week 4)
Type : Other
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Title : completing squares (week 5)
Type : Other
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Title : equations and formulas (week 5)
Type : Other
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Title : polygon angle facts (week 5)
Type : Other
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Title : polygon basics (week 5)
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Title : polygon details (week 5)
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Title : solving equations (week 5)
Type : Other
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Title : sum of angles in polygons (week 5)
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Title : geometry notes perimeter and area
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Title : geometry notes perimeter and area (week 6)
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Title : mensuration of cubes, cuboids and cylinders (week 7)
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Title : point line plane (week 6)
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Title : point line plane 2 (week 6)
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Title : pythagoras (week 7)
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Title : intro to Pythagorean Theorem (week 7)
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Title : mean definitions (week 8)
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Title : mean median mode (week 8)
Type : Other
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Title : TASK
Type : Assignment
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Title : TASK-II
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Title : Mathematics assignment
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Title : Presentation Slides
Type : Presentation
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Title : Algebra
Type : Assignment
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