Binary numeral system The binary or base-two numeral system is a representation for numbers that uses a radix of two. It was first described by Gottfried Leibniz, and is used by most modern computers because of its ease of implementation using digital electronics--early 20th century computers were based the on/off and true/false principles of Boolean algebra. Binary can be considered the most basic practical numeral system (the Unary system is simpler, but impractical for most computation). Representation A binary number can be represented by any set of bits (binary digits), which in turn may be represented by any mechanism capable of being in two mutually exclusive states. 0101001101011 on off off on off on + - - + - + Y N N Y N Y In keeping with customary representation of numerals using decimal digits, binary numbers are commonly written using the symbols 0 and 1. 100101 binary (explicit statement of format) 100101b (a suffix indicating binary format) 1001012 (a subscript indicating base-2 notation)
Modeling integers When modeling integers, we can use colored chips to represent integers. One color can represent a positive number and another color can represent a negative number Here, a yellow chip will represent a positive integer and a red chip will represent a negative integer For example, the modeling for 4, -1, and -3 are shown below: It is extremely important to know how to model a zero. For example, all the followings represent zero pair(s) And so on... Adding and subtracting integers with modeling can be extremely helpful if you are having problems understanding integers In modeling integers, adding and subtracting are always physical actions. If a board is used with the chip, adding always mean " Add something to the board" and subtraction always mean "Remove something from the board" Here, we will use a big square to represent a board Let's start with addition of integers: Example #1: -2 + -1 Put two red chips on the board. Notice that big arrow represents the "+" sign or the action of adding
Sheppard Software: Fun free online learning games and activities for kids. Maths and Stats by Email | Why is A4 paper the size that it is? Tangrams You will need Copy of the printout Scissors Pens or pencils (optional) What to do Cut out each of the pieces. Arrange the pieces on a surface so their positions match the arrangement in the printout. The pieces make two squares that are the same size. What’s happening? To finish this puzzle you have to take two smaller squares and turn them into one large square. When you finish the puzzle, you’ll find the largest triangles have their diagonals along the edges of the square. Applications If you started out with two squares, each 1 metre across, the resulting large square would have a side length of √2 metres. √2 is an important number – when you multiply √2 by itself, you get 2. √2 is a tricky number to write down. For any square, to find its diagonal, simply multiply the side length by √2. More information Try tangram puzzles online
Problem Solving Teaching Ideas Understanding Word Problems - Use your comprehension time to discuss strategies for understanding word problems! Teaching Problems - Some advice and tips for teaching problem solving to children. Bingo Investigation - Maths investigation based around a short play (scripts and information is included). Nim! An interactive version of the popular puzzle game. Contributed by Planet Primary. Magic Squares - Can you children complete these magic squares? <A HREF=" More Resources: Standard Deviation and Variance Deviation just means how far from the normal Standard Deviation The Standard Deviation is a measure of how spread out numbers are. Its symbol is σ (the greek letter sigma) The formula is easy: it is the square root of the Variance. Variance The Variance is defined as: The average of the squared differences from the Mean. To calculate the variance follow these steps: Work out the Mean (the simple average of the numbers)Then for each number: subtract the Mean and square the result (the squared difference).Then work out the average of those squared differences. Example You and your friends have just measured the heights of your dogs (in millimeters): The heights (at the shoulders) are: 600mm, 470mm, 170mm, 430mm and 300mm. Find out the Mean, the Variance, and the Standard Deviation. Your first step is to find the Mean: Answer: Mean = 600 + 470 + 170 + 430 + 3005 = 19705 = 394 so the mean (average) height is 394 mm. Now we calculate each dog's difference from the Mean: So the Variance is 21,704 Formulas
Place Value Activities Number Line-Up This activity is designed to actively involve students in using place value concepts to build numbers. Objective: LWDAT use place value to form 3-6 digit numbers to satisfy different conditions. Materials: Demo digit cards, one set for class use Small digit cards, one set for each student Directions: Select 3-6 students and give each student one of the demo digit cards. Build a Number Identify the digits students will use by handing demo digit cards to selected students (e.g. 3, 5, 8). Decimal Build a Number: Hand out the decimal point demo card as well as several digit cards to students. Place Value Games Games provided extended place value practice for students and allow them to use their conceptual understanding to develop appropriate strategies to win the game. Online directions for High-Number Toss Game High-Number Toss Game: Decimal Version Download High-Number Toss Recording Sheet for student use in sheet protector with dry erase markers: single round version Play
How to Calculate a Square Root by Hand Edit Article CalculatorUsing Prime FactorizationFinding Square Roots Manually Edited by NatK, Maluniu, Luís Miguel Armendáriz, Webster and 44 others In the days before calculators, students and professors alike had to calculate square roots by hand. Ad Steps Method 1 of 2: Using Prime Factorization 1Divide your number into perfect square factors. Method 2 of 2: Finding Square Roots Manually Using a Long Division Algorithm 1Separate your number's digits into pairs. 9To continue to calculate digits, drop a pair of zeros on the left, and repeat steps 4, 5 and 6. Understanding the Process 1Consider the number you are calculating the square root of as the area S of a square. 11To calculate the next digit C, repeat the process. Tips
Resources Maths - Resources Maths Investigations Games Test Yourself Revise Other Stuff Resources Feedback Updates Links Source File Types PDF file. You might need to install Acrobat Reader to view and print these files. Open Document An open standard for office documents. Microsoft Office These may or may not be compatible with the version of Office you have installed. Zip archive A zip archive is a convenient way of combining and compressing several files into one single file. WWW link Link to another site. Stationery | Starters & Puzzles | Worksheets: Number | Worksheets: Geometry | Worksheets: Statistics | Miscellaneous Stationery This section contains printables that you might find useful. Links Graph paper generator (incompetech.com) Make your own graph paper! Statistical graph papers (weibull.com) More downloadable graph papers Starters & Puzzles Worksheets - Number Worksheets - Geometry Worksheets - Statistics & probability Miscellaneous
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