Posted by David Wetzel
Number Classifications
We use numbers everyday of our lifes. Based on their characteristics, they are classified in groups.
Real Numbers – All kinds of numbers that you usually think of – from bus route numbers, to your weight, to pi and even the square root of pi! In short almost everything!!
Imaginary Numbers – Have you ever tried finding the square root of -1? If you haven’t, try it on your calculator. It might show an error (if it is a dumb calc) or it might show an ‘i’. That little ‘i’ is called an imaginary number. In short square roots of negative numbers make imaginary numbers.
Complex Numbers – It’s rather simple! Make a combination of Real and Imaginary numbers and voila! You get a Complex number. Stuff like 3+2i or 3/4i make up complex
numbers. Just think of it when you mix a real number with an imaginary one, things do get a bit complex!
Rational Numbers – Any number that can be written as a fraction is a rational number. So numbers like ½, ¾, even 22/7 and all integers are also rational numbers.
Irrational Numbers – Simply the opposite of rational numbers i.e. numbers that cannot be written as fraction, like square roots of prime numbers, the golden ratio, the real value
of pi (22/7 is a mere approximation not the real value of pi) are irrational numbers Integers – Any number that is not a fraction and does not have a tail after the decimal point is an integer. This includes both negative as well as positive numbers as well as zero.
Fractions – Numbers that are expressed in a ratio are called fractions. This classification is based on the number arrangement and not the number value. Remember that even
integers can be expressed as fractions – 3 = 6/2 so 6/2 is a fraction but 3 is not.
Proper Fractions – Whenever the value of the numerator in a fraction is less than the value of the denominator, it is called a proper fraction. i.e. it’s bottom heavy.
Improper Fractions - Whenever the value of the denominator in a fraction is less than the value of the numerator, it is called a proper fraction. i.e. it’s top heavy.
Mixed Fractions – All improper fractions can be converted into an integer with a proper fraction. This combination of an integer with a proper fraction is called a mixed fraction.
Natural Numbers – All positive integers (not including the zero) are Natural numbers. Simply put, whatever you can count in Nature uses a natural number.
Whole Numbers – All positive integers inclusive of the zero are Whole numbers. Not a big deal different from Natural numbers.
Even Numbers – All integers that end with a 0, 2, 4, 6, or 8 (including the numbers 0, 2, 4, 6 & 8 themselves) are even numbers. Note that ‘0’ itself is an even number. Also note
that negative numbers can also be even so long as they can be integrally divided by 2.
Odd Numbers – All integers that are not even numbers are odd number.
Prime Numbers - A natural number, more than one, which has exactly two distinct natural number divisors: 1 and itself - is called a Prime number. There can be infinite
prime numbers.
Composite Numbers – A positive integer which has a positive divisor other than one or itself is a composite number. In other words, all numbers that are not prime are
composite.
Source
Adapted from LazyMaths
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Filed Under: Math
Posted by David Wetzel
Writing in Math
Writing in math is an excellent way to determine if students’ understand or do not understand the math they are learning about.
Allowing students to explain how they solved a math problem, how they developed a formula to solve a problem, or how they applied a math concept requires critical thinking.
Students must use the minds as they formulate a logical explanation of how they solved a math problem. Because there is always the lingering idea regarding did a student solve a math problem by rote memorization of facts or does the student truly understand the math concept.
When students write how they solved the problem using sentences or a short story, their true understanding and misconceptions become readily apparent. This is why writing in math is a useful strategy for assessing understanding of math concepts.
Checklist
Using this checklist as overall guidance will help students grasp the fundamentals of how writing in math is different than other subjects.
- Clearly restate the problem.
- State the answer in a complete sentence which stands on its own.
- Clearly state the assumptions which underlie the formulas.
- Provide a paragraph which explains how the problem will be solved.
- Clearly label diagrams, tables, graphs, or other visual representations.
Writing Prompts
Often the best way to assess students’ prior knowledge and experiences with math is to provide a situation in which they must explain a math concept or math situation. The following are a few examples of writing prompts that can be used to stimulate student thinking:
- Tips I would give a friend to solve this problem are____________, ____________, and ____________.
- Where else could you use this type of problem solving?
- What other strategies could you use to solve this problem?
- The most important part of solving a problem is____________.
- You know several ways to____________(solve an equation, add fractions, etc.) Which method is your favorite? Why?
- Write instructions for a (insert grade level here) grader to follow when (adding fractions, finding percentages, calculating averages, etc.)
- Give two examples of situations in which you have used, seen or can find the concept of ____________. OUTSIDE of this classroom.
- Write a definition in your own words of a ____________.
- Compare and contrast the terms ____________.
Resources
Writing in Math
Math Problem Solving Stories and Case Studies
Comments:
Filed Under: Math
Posted by David Wetzel
Teachers work in the solitude of their classrooms, interrupted with occasional chances to talk with other teachers during the day. Twitter is an online technological tool which can break down the rigid classroom schedule barriers and allow teachers and students to collaborate.
Twitter has evolved into something beyond a trendy technology tool, avoiding the worry many teachers have about getting caught in a new flash-in-the-pan idea.
Strategy for Using Twitter in Math Class
Collecting Data for Geometric Analysis
- Students collect information from students located in other schools regarding the dimensions of their classroom, desks, number of students, and other objects in the room which take up floor space.
- Then students develop geometric representations of these classrooms, to determine which classroom has the greatest and least amount of square footage per student.
- Students then share their results with all participants.
Strategy for Using Twitter in Science Class
Where in the World are You?
- Introduce your class to the features of Google Earth by asking your Twitter network for a small amount of location specific information.
- Challenge your class to find the teachers who have replied with location information.
- Try to gather some evidence that you have found them - name on football field, distinct shape of building, or other features to prove they have been found.
- Reply with this information.
- Use different Google Earth layers of information to help with the search.
Allows students to have a concrete experience with the power of Twitter & Google Earth for finding information.
Resources
Using Twitter to Break Down Classroom Isolation
Science Investigations Using Google Earth
Middle School Google Earth Projects
Google Earth
Twitter Handbook for Teachers
Twit Poll
Twitter Group - Math Teachers (one of many to select from)
Twitter Group - Science Teachers (one of many to select from)
