The goal of this mind map is to explain the basic concepts of numeration and computation in the elementary grades. The audience is pre-service teachers.
Algorithms for Adding and Subtracting Whole Numbers
Use of Manipulative Devices
r
Here are three examples of manipulatives that can be used for adding and subtracting whole numbers.
Understanding of positional notation and place value
Instructional algorithms
Exchanging
r
This type of algorithm allows students to exchange pieces of manipulatives in order to represent the same number but with the smallest number of pieces.
Algorithms for Multiplication and Division of Whole Numbers
Multiplication
r
Otherwise known as "repeated addition"
Multiplication in nondecimal bases such as base five or base six
r
This video will show an example of multiplying in "base 7"
Division
r
Otherwise known as "repeated subtraction"
Short-division algorithm
r
This video shows an example of the short division algorithm.
Mental Arithmetic and Estimation
Easy Combinations
r
Typically regrouping numbers to find multiples of 10.
Adjustment
r
This term means that at the beginning of a calculation, we modify the numbers to minimize the mental effort required by adding "0".
Work from Left to Right
r
The reason for this tip is that it tends to reduce the amount a person has to remember.
Estimation
r
The site attached has ideas and examples of estimation and is geared towards the elementary grades.
Rounding
r
The site attached has information on rounding for the elementary grades.
Numeration Systems Past and Present
r
Follow the link to find information on Egyptian Numerals, Roman Numerals and the Indo-Arabic System.
Egyptian System
r
Egyptian Numeral System
Roman System
r
Roman Numeral System
Babylonian System
r
Babylonian Numeral System
Mayan System
r
Mayan System
Indo-Arabic, or decimal system
r
See hyperlink on main topic for information regarding Indo-Arabic System.
Nondecimal Positional Systems
Positional Systems
Converting from base ten to another base
r
This video shows you how to convert from base 10 to other bases.
Converting from other bases to base ten
r
This video shows you how to convert from other bases back to base 10
