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Numbers, Operations and Proportional Reasoning for K-8 Teaching - Coggle…
Numbers, Operations and Proportional Reasoning for K-8 Teaching
Week 1
We went over the syllabus, class expectations, and goals of the class.
Introduction to Base Ten: We were introduced to the base-ten counting system and how to apply manipulative within the lesson.
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Numerical Systems: We discussed other numerical systems like roman numerals and the tally mark system.
Roman numerals: I = one
V = five
X = ten
L = fifty
C = one hundred
D = five hundred
M = one thousand
Tally Marks;
Shown by I and then a slash through 4 to show 5
Week 2
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Base-two and Base-five: We discussed base-five and base-two systems in order to understand how to show students to apply this to multiple different numbers.
Base numbers: counts how many sets of a number we can fill up from a certain number. Broken down division
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Week 3
The Four Main Properties: We learned the 4 main properties; closure, communitive, associative and identity.
Closure: Whole number (+,-,x,/) whole number = unique whole number
Communitive: can be able to commute
Associative: able to switch around parenthesis
Identity: number + 0 = number
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Addition: We discussed vocabulary, how to show, and properties of addition.
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Week 4
Different Algorithms: We discussed the different algorithms to show students how to tackle a product like expanded, partial and standard.
Expanded: Really broken down to help see smaller numbers that we do know into the bigger numbers
Partial: Working towards bigger numbers, middle point between expanded and standard
Standard: Minimally broken down, using bigger numbers that we know.
Subtraction: We learned the basics of subtraction like vocabulary, how to show, and properties of subtraction.
Subtraction: the difference between two numbers
Minuend: part that is started with
Subtrahend: part being taken away
Difference: result of subtraction
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Week 5
Division: We discussed the basics of division like properties, vocabulary and how to show students.
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Multiplication: We discussed the basics of multiplication, such as vocabulary, properties and how to show.
Multiplication: same size groups of things being repeated
Factors; the number being repeated
Product: the result
Week 6
Exponents: We were introduced to exponents, how to show them, PEMDAS and how to apply them throughout our lessons.
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Week 8
Odds and Evens with Prime and Composite: We tied in even and odd numbers while also discussing prime and composite numbers. We were show how to show it and what ways would click in the students minds.
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Week 7
Odd and Even Numbers: We learned how to show and differentiate odd and even numbers and used methods with visuals.
Factors: We were given and introduction on how factors contribute to other numbers while understanding them in combination with multiplication.
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Week 9
Integers and LCM/GCF: Following factors and prime/composite numbers, we applied this knowledge to integers and LCM/GCF. We understood how these play a role into one another.
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Week 10
Fractions: This week was tricky as we learned how to understand and show fractions, add, subtract and overall the general concept of fractions.
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Week 11
Fractions: We continued learning about fractions and how to multiply them. We were also shown how to show students in multiple different ways
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Week 13
We built upon the ideas of multiplying and dividing fractions further. We discussed more methods and ways to show students.
Mentions of ideas like KCF (Keep, Change, Flip) and why it is important to know how to explain that to students.
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Week 14
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We reviewed the importance of knowing why and how things work, and why it's important for students to know how to do something. This process is essential for teachers to know how to do in order for students to really understand and engage.
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