Breaking news from around the world Get the Bing + MSN extension. trates some typical shapes and Areas of ponds which are almost sizes of ponds. solution to the above exercise width x = 125 mm and length y = 125 mm. A square is a rectangle with all sides of equal length, so the diagonal's length. A rhombus is a parallelogram with four congruent sides. A rectangle of blue and hazy light was framed by the dark wall. Therefore, finding the area is pretty easy! Since the area of a square or rectangle is length x width, we can just square the length of the side!. Spiraling Golden Rectangles. Rectangle Shape. If you know side lengths of the rectangle, you can easily find the length of the diagonal using the Pythagorean Theorem, since a diagonal divides a rectangle into two right triangles. The area of a square is equal to the length of one side to the power of two (length squared). A = 48 square units or 48 units 2 A special type of rectangle, called a square , has four equal sides. Define rectangle. One side is the height of the can, the other side is the perimeter of the circle, since the label wraps once around the can. Area of a Square or a Rectangle - Area of a plane figure is the measure of space inside the figure and is two dimensional. This means that the area of rectangle B is 12 x 16 square centimeters or 192 square centimeters. The lengths of the sides will be given as a,b or you can use l and w for "length" and "width". that give us 2*3 = 6 squares. Therefor a square cannot be a rectangle unless the rules of a rectangle are overridden. find the perimeter of each figure Let S be the side of the square and l,b be the dimensions of rectangle. 75 or 120 3/4 or 120 3 4 In the diagram, if the diagonal is. This tool is used to define rectangular or square selections. If you know side lengths of the rectangle, you can easily find the length of the diagonal using the Pythagorean Theorem, since a diagonal divides a rectangle into two right triangles. The fifth triangle number is half of that rectangle: 30/2 = 15. Areas of rectangles with the same perimeter. Also opposite sides are parallel and of equal length. A rectangle is a parallelogram with 4 right angles. The area is measured in units units such as square centimeters $(cm^2)$, square meters $(m^2)$, square kilometers $(km^2)$ etc. What is the length of this rectangle? cm 11. 4s, where s is the length of one side of the square. C Program for Beginners : Area of Square Shape : Square Formula : side * side Definition : A plane rectangle with four equal sides and four right angles A four-sided regular polygon You can compute the area of a square if you know the length of its sides Program : [crayon-5dbbb22e88e54888435067/] Output : […]. Probably the tangram pieces are developed from cutting a 4x4-square in pieces. Even a complete beginner can. Each rectangle is one higher than it is wide, so the rectangle for the fifth triangle number is 5 by 6. Review quadrilaterals (trapezoid, parallelogram, rhombus, rectangle, kite, and square) with your child. Rectangle trampolines differ from other shapes because of the even bounce they provide. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice. Really clear math lessons (pre-algebra, algebra, precalculus), cool math games, online graphing calculators, geometry art, fractals, polyhedra, parents and teachers areas too. Some origami models start with a hexagon instead of a square sheet of paper. A500 is a standard specification for cold-formed carbon steel structural tubing and is commonly used in construction projects and structural supports. You'd have to watch the Info palette's W and H values as you draw it. Rectangle border calculator provide you with a simple way of determining the square footage area for a rectangle shape with border. A rectangle MUST have the following: Four sidesFour angles that are right angles (90 degrees), so that the. 5 inch circles inside a 10 inch x 10 inch square. It can also be defined as an equiangular quadrilateral, since equiangular means that all of its angles are equal (360°/4 = 90°). The tank will be partially underground, the grade level is 10′ below the top of the tank. 4 km Area of a Rectangle Find the area of each rectangle. A rectangle of blue and hazy light was framed by the dark wall. A rectangle has four straight sides with four right angles, but the sides can be different lengths. com *** This page is dedicated to the Hungarian mathematicians who are the pioneers in this discipline. Each of the. Log in for more information. The Rectangle tool places a rectangular markup on the document. How to calculate square footage for rectangular, round and bordered areas. Input the rectangle inside dimensions - height and width and the circles outside diameters. A rectangle is a parallelogram with 4 right angles. Note that the second and third methods require that you first show (or be given) that the quadrilateral in question is a parallelogram: If all angles in a quadrilateral are right angles, then it’s a rectangle (reverse of the. Using a small ruler such as a 6 ½″ or 5 ½″ square repeat the same process above to square off this small block. 10 cm 8 cm a. The Properties of a Square - Cool Math has free online cool math lessons, cool math games and fun math activities. Forgot Password Instructions have been sent. Anyway, the whole business is not really worth arguing about once it is seen that of all the four sided figures with four right angles, there is a special one which also has four equal sides. Make a Rectangle Paper to a Square Paper : Things you need for Making a rectangle paper to a square paper. First, we know that rectangles are parallelograms, so - The opposite sides are parallel and congruent. Square is a parallelogram with right angles and equal sides ( Fig. The two-sided square is a symbol which is constantly found in the Book of the Dead, also in various Egyptian papyrii. The area of the square is 12 × 12 or 144 square centimeters. A Rectangle's Perimeter. Find the perimeter of a rectangle when l = 5 cm and w = 3 cm P = 2 × 5 + 2 × 3 P = 10 + 6 P = 16 Notice that it is perfectly ok to do P = 5 + 3 + 5 + 3 = 8 + 8 = 16 However, it is usually easier and quicker to multiply each dimenssion by 2 and adding the result. The rectangle can occur over a protracted period of time or form quickly amid a relatively wide-ranging series of bounded fluctuations. A rectangle that is not a square is colloquially known as an oblong. Property 1: In a square, every angle is a right angle. The area of the square is 12 × 12 or 144 square centimeters. Rectangle can have incongruent adjacent sides, but square must have congruent adjacent sides. show equal sides. The area of the rectangle is 15 × 12 or 180 square centimeters. You will measure this from the inside of the room. In the figure above, drag any orange dot to resize the rectangle. A rectangular piece is cut from the sheet as shown in Fig. Area of a Square or a Rectangle - Area of a plane figure is the measure of space inside the figure and is two dimensional. If the measurements are equal then the corners are square. When modelling squares and rectangles in object-oriented programming languages, defining this relationship can lead to unexpected bugs. A cube and a square prism are both special types of a rectangular prism. Find its dimensions. More trigonometric functions and relations For centroid, moments of inertia, polar moments of inertia, and radius of gyration, click the following icon:. Each rectangle is one higher than it is wide, so the rectangle for the fifth triangle number is 5 by 6. Square a number in Excel using the formula =N^2, where N is a number or the cell you want to square. Explain why every square is a polygon. Choose the correct answer below. Photoshop Marquee Select Tools. A rectangle does not NECESSARILY meet the criteria for a square. A square is a rectangle with equal sides. Is it possible in AS3 to draw a rectangle with both square and round corners? I am trying to draw a square, that has rounded corners on the top right and bottom left and square corners for the remaining ones. A rectangular house must also be a "square" rectangle, meaning each set of two sides are equal. Each face is a square. Founded on its mission to connect families one bounce at a time, Skywalker Trampolines and Skywalker Sports offers quality trampolines, playground equipment, and sports equipment for all. Is a rectangle a square? Well, no. For more discussion on the properties of rectangles, see this sheet. and 4 right angles, no more and no less. With products such as Aluminium Square / Rectangular Tube available, have a look at what we can offer!. Calculator Use. This doesn't work though because in the square class i would still be able to change the hight and width if it truly IS a rectangle. Trapezoid is a quadrangle, two opposite sides of which are parallel (Fig. To find the area of the rectangle, we find out how many one-centimetre squares we can fit into the rectangle. Rectangle – In Euclidean geometry, a rectangle is also a quadrilateral and as with the square, has four equal angles at 90°. Citation from "Chapter 12", Eastbound & Down (TV), Season 2 Episode 6 (2010) blacked out to resolve Google's penalty against this site. If a figure is both a rectangle (right angles) and a rhombus (equal edge lengths), then it is a square. This calculator is really intended to deal with oblongs, and needs 2 entries. A square has equal sides and every angle is a right angle (90°) Also opposite sides are parallel. A diagonal is a straight line that connects one corner of a rectangle to the opposite corner. It can also be defined as an equiangular quadrilateral, since equiangular means that all of its angles are equal (360°/4 = 90°). Both have 4 90 degree (right) angles. Therefore, a square is a special rectangle. This means that for a rectangle to be a rhombus, its sides must be equal. Splash Math is an award winning math learning program used by more than 30 Million kids for fun math practice. Calculator Use. A square is a rectangle that has four sides of equal length. So a square is a special kind of rectangle, it is one where all the sides have the same length. A square is a type of equiangular parallelogram and square properties include congruent diagonals and diagonals that bisect each other. When connecting the consecutive midpoints on each of these separate quadrilaterals, the figure formed is a square for the square and a parallelogram for the parallelogram. The length of the diagonal of any rectangle equals the square root of the sum of the squares of its length and width. Some examples could be the size of a 12-inch computer screen (77. In this example, the derived class overrides the function printArea. Square or Rectangle? The Babylonian Talmud discusses how the Luchot fit perfectly in the Ark of the Covenant together with the Torah scroll written by Moses. A square is a rectangle using all the SAME edge-lengths. If a square has a base of length 6 inches its area is 6*6=36 square inches. Be sure to look at all sides and shapes even those you can’t see. The fluid level inside. These ideas are therefore perfect for using with our other riddles about shapes. Recommended number of lines:4. Click and hold the red square. B) It is a parallelogram with perpendicular diagonals. Size of imprint: 27 x 10 mm. A triangle has 3 sides! A rectangle has 4 sides, A rectangle has 4 sides, Two are long, and Two are short. The primary difference between rhombus and parallelogram is that while rhombus can be referred as a slanting square, whose adjacent sides are equal, parallelogram is a slanting rectangle with two set of parallel opposite sides. Square from a Rectangle Method 2: If you need a square sheet without the diagonal creases, try the next method. Every square has 4 right angles, so every square is a rectangle. This term can also be used for reservoirs. The diagonal of a rectangle can be computed using the same theorem - BUT each rectangle is different. An example of a special parallelogram that is both equiangular and equilateral is the square. The springs work independently, which allow for a controlled takeoff and landing from any point on the jumping mat. We want to find the area of the shaded part. Regarding the Liskov-substitution: if you introduce constraints, you get around the pitfalls. Rectangle properties include (1) diagonals that are congruent, (2) perpendicular diagonals that bisect each other and (3) diagonals that bisect each of the angles. The area of a square that has a side-length of 1 cm is 1 square centimetre (or 1 cm 2 ). A box whose every side is a. Because ACBR is a rectangle, its diagonals bisect each other and are equal. It is also a special case of a parallelogram but with extra limitation that the angles are fixed at 90°. A rectangular piece is cut from the sheet as shown in Fig. A rhombus is a parallelogram with four congruent sides. A square must be a rectangle, but a rectangle does not have to be a square. 5708) times the area of the square. A rhombus is defined as a parallelogram with four equal sides. It has characteristics of both of these. in Homework Help. Not all rectangles are squares because they do not all have four equal sides. When you’re working with tools, if you need to. Enter 2 sides and hit Calculate to re-draw with correct diagonal. It's a popular shape for windows and record albums, among many other things. Default values are for 0. For a candy to be a lollipop, it must be on a stick. Properties of a Square. A rectangular house must also be a "square" rectangle, meaning each set of two sides are equal. However, a square is a rectangle, because it has 2 sets of parallel sides and 4 right angles. ' 'Show students how to combine rectangles and triangles to create houses. In the case of kite, of all of its sides are congruent it will become either a rhombus or a square. A square must have opposite sides parallel, all sides congruent, and four right angles. The side length of the smaller rectangle or square is called the size of the tile, and the number of different sizes of tiles determines the order of the tiling. Distance across is the same up and down and distance to one set of adjacent corners needs to be the same as it is to the other set. For a rectangle, its pair parallel sides are of equal dimension (length or width) while in a square, all the sides are of equal dimensions. Rectangle properties include (1) diagonals that are congruent, (2) perpendicular diagonals that bisect each other and (3) diagonals that bisect each of the angles. Explanation:. Example Question #5 : How To Find The Area Of A Rectangle Angela is carpeting a rectangular conference room that measures 20 feet by 30 feet. Area formulas for all geometric figures. Rectangle border calculator provide you with a simple way of determining the square footage area for a rectangle shape with border. 00 + 5 Deal Score. It follows that the lengths of the pairs of sides opposite each other must be equal. A rectangle with a width of 3m has a perimeter of 22m. 1 2 Perimeter Problems 3. Welcome to Ranflex Metals. Is it a square or a rectangle? Created Feb. By default, the first two parameters set the location of the upper-left corner, the third sets the width, and the fourth sets the height. To find the perimeter of the rectangle-P=S1 +S2 = 8 + 8=16 ft Perimeter of a circle is the circumference. However, not all rectangles are squares. Then students go back to the non-examples and give a reason they are not squares, this helps clarify/enhance the properties of the square. Area of a Square or a Rectangle - Area of a plane figure is the measure of space inside the figure and is two dimensional. 03/30/2017; 2 minutes to read +6; In this article. It's a special case of a rectangle. Referred by Bob Merrick. To setout a square or rectangle, make sure the diagonal is the correct length for the side lengths. To estimate costs, enter the price per sq. Use the Rectangle tool to create rectangle features. A T-shaped or Square - definition of square by The Free Dictionary. The trouble is that in everyday life, we usually use the word "rectangle" to refer to non-squares, because if the shape were a square, we would call it that. I am a 3D shape. Fraction Multiplication and Area. Area means number of square units. A square is transformed into a rectangle by increasing its length and decreasing its other side by the same percentage amount. (noun) An example of a rectangle is the shape of a an 8x10 picture frame. When you calculate square footage of rectangle, you're calculating its area. Once again, label the vertices of this rectangle $1$, $2$, $3$, and $4$. A square is also a parallelogram whose sides intersect at 90° angles. Example #2: Find the perimeter of a rectangle when l = 9 cm and w = 5 cm. So, to get the properties of a square just sum up all the properties you have learned so far. 10 ft 3 ft c. If l = w is true, then the rectangle is called a square, and then we have the following formulas: d = l√ 2, l = d÷√ 2 and S = l² = d²/2. This means that for a rectangle to be a rhombus, its sides must be equal. We need to tell whether those four line segments make a rectangle or not. Whether you need to know the area of a carpet, a parcel, a TV screen, rectangle pool or window, this area of a rectangle calculator will solve your problem in a blink of an eye! All you have to do is input the length and width (or diagonal), and allow this rectangle calc to find the values of P (perimeter) and A (area). That's right: a square is a parallelogram, a rectangle, and a rhombus all rolled into one. Definition: A conditional statement, symbolized by p q, is an if-then statement in which p is a hypothesis and q is a conclusion. Area formulas for all geometric figures. A rectangle has four straight sides with four right angles, but the sides can be different lengths. Rectangle Shape. A square has a perimeter of 56cm. It can also be called a cuboid. Acreage Calculator. A rectangular house must also be a "square" rectangle, meaning each set of two sides are equal. High ceiling contemporary dining room with fancy square table This style of dining room table is slightly more modern and nontraditional than round or rectangular varieties. I the case of a rectangle, opposite sides are equal in length, so the perimeter is twice its width plus twice its height. It is possible to override the functions of the base class in derived class. Is a square a rectangle? Can a rectangle be a square? Are all squares rectangles? I find that many students struggle with the very form of the question, as much as with the definitions it is asking about: Are we being asked if every square is a rectangle, or just if some particular square is a rectangle?. But the pattern can be also used for pillow decorations, trivets, chair pads and more! You can make it monochrome or use many different colors to perfectly match your taste. When I want to refer to a non-square rectangle, I might say "non-square rectangle" or "generic rectangle". The element’s width is calculated as a percentage of its parent’s width, while its height is calculated as a percentage of its parent’s height. Rectangle: A quadrilateral having four right angles. The highlighted part is the difference between a Rectangle and a Parallelogram. Square definition, a rectangle having all four sides of equal length. semicircles together, you have a whole circle. Citation from "Chapter 12", Eastbound & Down (TV), Season 2 Episode 6 (2010) blacked out to resolve Google's penalty against this site. The square is a special rectangle. If there is no information about the angles of the quadrilateral, we cannot say for certainty that it is a square. You'll also likely have a high forehead. A diagonal is a straight line that connects one corner of a rectangle to the opposite corner. And a square is a rectangle. Letting x denote the length of. has the definition of an object or plane that has the entire four sides of equal dimension, and the entire angles related to the perimeters are moreover equivalent. There are three parameters that define a rectangular pulse: its height , width in seconds, and center. Is a rectangle a square? | Yahoo Answers. What is the resultant change in area?. Rectangle Shape. Inside the square is an equilateral triangle. One face of this cube is therefore 10 × 10 cm = 100cm 2. Formally, a rectangle is a quadrilateral with four congruent angles (all 90°). Another productive structure (similar to rectangular-shaped) is adjective + noun+(e)d, e. One square centimeter can be translated as 0. A square has 4 sides that are all exactly the same size. This formulas help you answer the questions how to find the area of triangle, square, rectangle, rhombus, parallelogram, trapezium, quadrangle, circle and ellipse. Due to all angles in both squares and rectangles being 90 degrees, both types of shapes share the property that opposite sides are parallel to each other and connecting sides are perpendicular. The parcel is assumed to be irregular but it could be a square, a rectangle, a triangle or an irregular shaped parcel. The area of the larger rectangle is kA square units. The calculator is generic and any kind of units can be used - as long as the same units are used for all values. Since the square is the last one in the hierarchy, therefore, it must have all the properties of a parallelogram, rectangle, and rhombus. A 4-sided flat shape with straight sides where all interior angles are right angles (90°). Refine Your Results By: Shop Bakeware Performance Pans Square Cake Pans Set, 3 Piece - 8, 12 and 16-Inch Cake Pans $39. There are three ways to prove that a quadrilateral is a rectangle. Key Vocabulary •rhombus •rectangle •square In this lesson, you will learn about three special types of parallelograms: rhombuses,rectangles, and squares. This page has several printable area worksheets. How to Square up a Frame or Large Object for Welding There are a few well known processes for squaring an object among the many different trades. Then give directions to lay the yarn on the floor and make it into a circle shape, a square, a triangle, a rectangle, an oval and a diamond. All squares and rectangles have four angles of 90 degrees. The highlighted part is the difference between a Rectangle and a Parallelogram. com and www. In this case, you need to make the six-sided shapes before you start. "A square is never a rectangle. Things you need 1 rectangle paper 2 hands 1 any thing that cuts. Citation from "Pimp Daddy", Terriers (TV, 2010), Season 1 Episode 9 blacked out to resolve Google's penalty against this site. Is a square a rectangle? Can a rectangle be a square? Are all squares rectangles? I find that many students struggle with the very form of the question, as much as with the definitions it is asking about: Are we being asked if every square is a rectangle, or just if some particular square is a rectangle?. The length of a rectangular garden is 12 metres and its breadth is 5 metres. A rectangle with a width of 7cm has an area of 84cm². It follows that the lengths of the pairs of sides opposite each other must be equal. This Demonstration illustrates the relationship between a rectangular pulse signal and its Fourier transform. Now if a square IS a rectangle then I should be able to make a Square class that extends the Rectangle class. It’s a silly example though. The square is a type of rectangle, but also a type of rhombus. ☀ Free Shipping Trampolines ☀ Kids Square/Rectangle Preschool Trampoline by Pure Fun Shop The Largest Selection Of Home Furniture And Décor Across All Styles And Price Points. The length of the diagonal of any rectangle equals the square root of the sum of the squares of its length and width. This is said as "square centimeters" or "centimeters squared". The area of a square is equal to the length of one side to the power of two (length squared). The shared rectangle, however, will be counted twice if the areas are added, so the area of the small rectangle, 6 × 7 or 42, must be subtracted from the total. This is the rate of a quadrate with a rectangle and a quadrate. In this example, the derived class overrides the function printArea. The square has the following properties: All the properties of a rhombus apply (the ones that matter here are parallel sides, diagonals are perpendicular bisectors of each other, and diagonals bisect the angles). and 4 right angles, no more and no less. 5 inch circles inside a 10 inch x 10 inch square. Area of a Square or a Rectangle - Area of a plane figure is the measure of space inside the figure and is two dimensional. But wait! Does that mean that a square is a rectangle?. When modelling squares and rectangles in object-oriented programming languages, defining this relationship can lead to unexpected bugs. The perimeter is measured in units such as centimeters, meters, kilometers, inches, feet, yards, and miles. The wall height is 17′. However, not all rectangles are squares. ro|Points 323|. The length of a rectangle is 6 inches longer than its width. Enter the following dimensions: 1. Calculator Use. Ranflex Metals was founded in 1998 as a Square Pipes / Tubes Manufacturer, now Ranflex Metals has becom ISO 9001:2008 Certified company Rectangular Pipes / Tubes Manufacturing Company in INDIA, With persistence and effort,we have become one of the leading Manufacturer of Mild Steel Hollow Sections in India. At CES, the company also showed off. Find the length of the rectangle. The area of each square is 1 cm 2. Finding the Area of a Rectangle The AREA is the space inside. When I want to refer to a non-square rectangle, I might say "non-square rectangle" or "generic rectangle". Unlike many other point of sale systems, Square does not charge any monthly fees. Mathematically, a rectangular pulse delayed by seconds is defined as and its Fourier transform or spectrum is defined as. Therefore, finding the area is pretty easy! Since the area of a square or rectangle is length x width, we can just square the length of the side!. The height is the number of squares "high. Click and hold the red square. Find the length of the diagonal of a square garden having the same area as that of the rectangular garden :. a square and a rectangle have the same perimeter. To find the perimeter of the rectangle-P=S1 +S2 = 8 + 8=16 ft Perimeter of a circle is the circumference. Enter inches as decimal or fraction with space or slash. While I don't doubt that mathematics wouldn't have a problem vectorizing an area, it seems like the entire point is so that it can be used in some physical sense. This method is a little easier than the 3,4,5 trick but requires access to all 4 corners of a rectangle or square. A square is a special case of a rectangle. 10/square foot, and the material for the top costs $. Then you add a little more egg enough to have a thin sheet and you lift up the tamagoyaki a bit and let the new egg go under it so that it will stick to each other so the rolling will continue. Area of the rectangle = 4 × 2 = 8 cm 2 We need 8 one-centimetre squares to make a rectangle 4 cm long and 2 cm wide. A square, however, has all four sides the same length, or congruent with each other, so we mark them with the same number of hash marks. The marquee tools are located at the top left of the Photoshop Toolbox. Steel Rectangular Tube is easy to fabricate and has a surface suitable for painting or plating. a square is a rectangle, but a rectangle is not a square. Rectangle definition is - a parallelogram all of whose angles are right angles; especially : one with adjacent sides of unequal length. Perimeter of a rectangle. A 4-sided flat shape with straight sides where all interior angles are right angles (90°). Alternate Solution : Let us take m = 2, n = 3; The number of squares of side 1 will be 6 as there will be two cases one as squares of 1-unit sides along the horizontal(2) and second case as squares of 1-unit sides along the vertical(3). Therefore, a square is a special rectangle. Section Modulus, Radii of Gyration Equation and Rectangular Sections Equation. It is not true when a rhombus does not have any right angles. How many rectangles do you have in your room? (Flash) Print a copy of the rectangles in the Room to color. It is also a rectangle and a parallelogram. The Rectangle tool places a rectangular markup on the document. This makes squaring up any lay out a snap. Drawing) | Microsoft Docs Skip to main content. Is a rectangle a square? | Yahoo Answers. ☀ Free Shipping Trampolines ☀ Kids Square/Rectangle Preschool Trampoline by Pure Fun Shop The Largest Selection Of Home Furniture And Décor Across All Styles And Price Points. For more discussion on the properties of rectangles, see this sheet. If you don't have any geoboards handy, dot paper can be used as an alternative, although it won't make learning quite as enjoyable for students. Cafe Astrology. A square is a special case of a rectangle. A cube and a square prism are both special types of a rectangular prism. It is true when a rhombus has 4 right angles. The length of a rectangular garden is 12 metres and its breadth is 5 metres. It is also a rectangle and a parallelogram. 9—Proving a Quadrilateral is a Rhombus, Rectangle, or a Square 7. A square must have opposite sides parallel, all sides congruent, and four right angles. If the Point (px,py) is inside the given rectangle, the sum of areas of triangles formed by joining 2 rectangle points and the given point (say in anti-clockwise or clockwise direction) would be equal to the sum of rectangle.


We recently had the opportunity to review Estimation Station from Educational Insights.
This has been a fun one for us to experiment and learn with. This is best suited for ages 5 to 9, but even our youngest was able to start on the early concepts.
We started our activity with carrots, but quickly realized the carrots we had varied in size so greatly that it was difficult to get an accurate estimate.
So we started looking around the house for a good replacement.
Given that we didn’t have anything small and uniform in the treat department (jelly beans or M&Ms would have been perfect here!), we moved to the playroom.
And came across the perfect item to experiment with… building blocks. We picked a bunch out of the bin that were uniform in size, dumped them all into Estimation Station’s larger bin. Then we filled the scoop and started counting.
Both kids were able to help with the counting, though they needed some help adding those big numbers up at the end to get our estimate.
I like that Estimation Station makes it easy (and fun) for us to work on and reinforce his math concepts at home. It also includes an activity guide with ideas for estimation, counting, place value, comparing and ordering numbers, making predictions, graphing, statistics and mathematical reasoning.
This is definitely one that will grow with the kids and we’ll be able to keep returning to it as they learn a new mathematical concept.
We might also have a leg up on all those “guess the jellybean” contests – total added bonus. 😉
WIN IT: One very lucky reader will win an Estimation Station, thanks to Educational Insights!
The rules: Open to U.S. residents only. Giveaway runs through October 17. Winner will be chosen with Random.org and will be notified by e-mail. Winner will have 48 hours to respond before a new winner is chosen. Good luck!
Disclosure: I was not compensated for this review. I received a product to facilitate my review. As always, all thoughts and opinions are my own.
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I'm currently a PhD student at MAP5 - Université Paris Descartes.
My advisors are Servane Gey (MAP5), Pierre Latouche (MAP5), Benjamin Guedj (INRIA - MODAL) , and Jean-François Toussaint(IRMES).
I studied maths at University of La Rochelle where I obtained my bachelor degree and at University of Rennes 1 for my master degree.
I've always been passionate about sport and thus decided to work on this field, by writing a PhD project about application of statistical methods on sport. I played rugby for 10 years, table tennis for 11 years, and recently started playing American football.
My current research focus on statistical learning methods applied to sport. I work with functional data on which I try
to perform clustering and make predictions.
The main purpose of these methods is to help sport federations to deal with the detection of their young athletes, by analyzing their performance progression curves.
Besides, I work on several other research projects in the sports field with my co-workers of IRMES. I deal with mathematical and algorithmic issues of the studies.
45 rue des Saints Pères • Bureau 725A1
75006 Paris • France
- +33(0) 7 70 34 52 84


Arc Oakbridge School Curriculum
In Key Stages 2 and 3, students will follow an adapted National Curriculum aimed at meeting their individual needs. This will include English, Maths, Science, Humanities, Physical Education and PSCHE. Practical sessions such as Food Technology, Drama and extensive opportunities to develop social skills will also form a fundamental part of the curriculum. This will involve frequent off-site activities to promote learning outside the classroom, as well as regular educational visits.
In Key Stage 4 students will work towards formal qualifications. These qualifications will be based on the individual needs of each student. The range offered will include Functional Skills, BTECs and GCSEs. We offer a core curriculum of English, Maths and Science at various levels, and will also include qualifications such as Land-Based Studies and Home Cooking Skills aimed at greater independence.
The curriculum will evolve as the school and its students evolve – the focus will remain student-centred, allowing the curriculum to be adapted to meet the needs of individual students.


A digital signature is a mathematical function that can demonstrate that a digital message or file is authentic or from a particular person.
- Alice selects the file to be digitally signed or clicks on ‘sign’ in her email application
- The hash value of the file content or the message is calculated by Alice’s computer
- This hash value is encrypted with Alice’s Signing Key (which is a Private Key) to create the Digital Signature.
- Now, the original file or email message along with its Digital Signature are sent to Bob.
- After Bob receives the signed message, the associated application (such as email application) identifies that the message has been signed. Bob’s computer then proceeds to:
- Decrypt the Digital Signature using Alice’s Public Key
- Calculate the hash of the original message
- Compare the (a) hash it has computed from the received message with the (b) decrypted hash received with Alice’s message.
- Any difference in the hash values would reveal tampering of the message
Digital signatures are very handy for sending encrypted messages that prove a person’s ownership of a message or identity.


What is Stochastic Optimization?
Stochastic optimization is the process of maximizing or minimizing the value of a mathematical or statistical function when one or more of the input parameters is subject to randomness. The word stochastic means involving chance or probability.
Stochastic optimization plays an important role in the analysis, design, and performance of modern systems. Stochastic optimization usually looks at problems from two perspectives: through the objective functions (cost functions) or through limitations.
The common example for stochastic optimization is the traveling salesman problem which states “Given a list of cities and the distances between each pair of cities, what is the shortest possible route that visits each city exactly once and returns to the origin city?”
We can solve this problem by using a stochastic optimization algorithm called ant colony optimization.
Ant Colony Optimization
This algorithm is inspired by the ant colonies, how ant travel from nest to the food source and then get back to their nest. Ants initially go out randomly to find the food source and each ant leaves a trail of pheromone on the ground and comes back with the food.
Consider an example here, let's suppose that two ants go out to search for food and reach the same food source using different paths.
One path is shorter than the other so ant following the shorter path will reach the food source first.
And it will get back to the nest first with the food source. Remember each ant leaves a trail of pheromones on the ground. So when the first ant reaches the nest with the food the other ants follow its pheromone trail to reach the food source.
By the time the ant following the longer path returned to the nest, more ants already had followed the path with higher pheromone levels.
And it also starts to follow the trail with higher pheromone levels, leaving the longer path.In this way all ants start to follow the shortest path.
And for some reason if ants face blockage in their path then they again follow the same approach. They start to move randomly until they find the pheromone trail again with the shortest path.
What is Ant Colony Optimization?
Ant colony optimization (ACO) is a population-based metaheuristic that can be used to find approximate solutions to difficult optimization problems.
In ACO, a set of software agents called artificial ants search for good solutions to a given optimization problem. To apply ACO, the optimization problem is transformed into the problem of finding the best path on a weighted graph. The artificial ants (hereafter ants) incrementally build solutions by moving on the graph. The solution construction process is stochastic and is biased by a pheromone model, that is, a set of parameters associated with graph components (either nodes or edges) whose values are modified at runtime by the ants.
Metaheuristic algorithms are algorithms which, in order to escape from local optima, drive some basic heuristic: either a constructive heuristic starting from a null solution and adding elements to build a good complete one, or a local search heuristic starting from a complete solution and iteratively modifying some of its elements in order to achieve a better one. The metaheuristic part permits the low-level heuristic to obtain solutions better than those it could have achieved alone, even if iterated.
How does ant colony optimization work?
Ant Colony optimization is a class of algorithms whose first member is called Ant System. The main idea is that of a parallel search over several computational constructive threads based on local problem data.
Consider the following graph with four nodes and initially the pheromone level is the same for each edge.
Ant is a simple computational agent you place on a node of a graph randomly
Each ant can visit each need only once. The probability of visiting a certain node is calculated by the following formula.
It is explained like this: pheromone level for the concerned edge into the heuristic value or cost for visiting that edge divided by the sum of pheromone level and heuristic value of other edges that can be visited. For the edges that cannot be visited its value is 0. where α and β are user-defined parameters (0 ≤ α,β ≤ 1) that control the relative importance of the pheromone versus the heuristic information ηij=1/dij where dij is the length of the visiting edge.
When all the ants have completed their tours then the pheromone level is calculated for all the edges and the heuristic values are also calculated. Pheromones are updated using
It is explained like this: sum of one 1 minus evaporation rate ρ of pheromone level into the current pheromone level and sum of pheromone level calculated by the other ants for that particular edge.
The pheromone level laid by particular ant on that specific edge is calculated by
Where L is the length of the total path traveled by k ant after the whole iteration.
This whole process is repeated until an optimal solution is found.
Ant Colony System
Major improvement in this was the ant colony system which instead of using probabilistic rule for visiting certain edge, pseudorandom proportional rule was used. In this a random variable is used which is uniformly distributed between 0 and 1. We calculate the probabilities in the same previous way but there is an extra step involved . We divide those probabilities between 0 and 1 and then generate a random number, ant will choose the path in which that number lies.
This rather greedy rule, which favors exploitation of the pheromone information, is counterbalanced by the introduction of a diversifying component: the local pheromone update. The local pheromone update is performed by all ants after each construction step. Each ant applies it only to the last edge traversed:
Where φ∈(0,1] is the pheromone decay coefficient, and τ0 is the initial value of the pheromone.
The main goal of the local update is to diversify the search performed by subsequent ants during one iteration. In fact, decreasing the pheromone concentration on the edges as they are traversed during one iteration encourages subsequent ants to choose other edges and hence to produce different solutions. This makes it less likely that several ants produce identical solutions during one iteration. Additionally, because of the local pheromone update in ACS, the minimum values of the pheromone are limited.
Let us know if you have already applied above mentioned optimization processes and how it helped you to solve your problem. We would also love to know if you are a newbie and this blog helped you in any way.


|The State Education Department The University of the State of New York|
converted for web delivery by EduTech
Acknowledgments (back to Table of Contents)
The State Education Department acknowledges the assistance of teachers and school administrators from across New York State as well as resources from other states and countries in the development of the Mathematics Core Curriculum.
Preface (back to Table of Contents)
The Mathematics Resource Guide with Core Curriculum is one of four documents recently developed by the New York State Education Department. These documents were designed to provide guidance to districts and schools in New York State for development of local curricula, instruction, and assessment that meets local needs and resources and aids their students in achieving the mathematics standards for New York State.
The first document of the series, The Learning Standards for Mathematics, Science, and Technology (1996), introduced standards and benchmark performances in mathematics, science, and technology for grades four, eight, and high school. The Mathematics, Science, and Technology Resource Guide (1997), which is periodically updated, extended the standards into classroom practice. The Resource Guide contains lesson plans for mathematics, science, or technology classes as well as lessons that integrate them. The Mathematics Test Samplers for grades 4 and 8 were distributed in February 1998 and for Math A in May 1998. They provide a variety of assessment items similar to those which will be used in the New York State Testing Program.
Core Curriculum (back to Table of Contents)
The Mathematics Resource Guide with Core Curriculum elaborates upon the standards document and provides connections among the other three documents mentioned above. The Core Curriculum is not intended to be the mathematics curriculum for school districts but instead an outline of curriculum to be used to aid districts in developing local curriculum that is reasonable for their local resources and needs.
Although the Core Curriculum addresses only Standard 3 of the Learning Standards for Mathematics, Science, and Technology, a comprehensive mathematics curriculum would also include Standard 1 (inquiry, mathematical analysis, design), Standard 2 (information systems), Standard 6 (interconnectedness), and Standard 7 (interdisciplinary problem solving). The curriculum would also have connections with English language arts through the use of childrens literature, reading, and writing as well as with social studies, which provides many opportunities to examine and analyze data.
The Core Curriculum extends the key ideas and performance indicators of Standard 3 to additional grade-level blocks of prekindergarten to kindergarten, grades 1 to 2, grades 3 to 4, grades 4 to 5, grades 7 to 8, and Math A. A draft of Math B is also included. Suggestions for grade-level content are given for each performance indicator. Suggestions of relevant assessment items or classroom activities are provided for each performance indicator. More examples of assessment items can be found in the Test Samplers and pilot tests. More examples of classroom activities can be found in the Mathematics, Science, and Technology Resource Guide. None of the documents just described are meant to stand alone. They should be used together.
The Core Curriculum is divided into three sections: Overview, Core Curriculum (Elementary, Intermediate, High School), and Reference List.
The Overview presents a discussion on processes that students use and the roles of manipulatives, technology, and assessment. Suggestions of effective instructional strategies will be discussed and each key idea of the standards will be listed and explained.
The Core Curriculum section is divided into three parts: Elementary, Intermediate, and High School. In the beginning of each part are suggestions for manipulatives. This is followed by suggestions of content for each performance indicator. Examples of assessment items are included for grade levels in which there will be State assessments. There will be suggestions for classroom activities or problems for each performance indicator for which an appropriate assessment item is not available. The assessment items and classroom activities are found at the end of each grade-level block and are listed by performance indicator (e.g., 1A. would be the first performance indicator given for Key Idea 1, which is mathematical reasoning).
The Reference List at the end of this document includes all sources used for examples of assessment items, classroom activities, and problems. Teachers may wish to refer to them for more ideas.
I. Overview (back to Table of Contents)
Standard 3: Mathematics (back to Table of Contents)
Students will understand mathematics and become mathematically confident by communicating and reasoning mathematically, by applying mathematics in real-world settings, and by solving problems through the integrated study of number systems, geometry, algebra, data analysis, probability, and trigonometry.
Mathematics curriculum and assessment of mathematical proficiency based on the mathematics standard of the Learning Standards for Mathematics, Science, and Technology revolve around the seven key ideas. The mathematics standard describes the seven key ideas listed below. Classification of mathematical content into these key ideas inevitably involves some overlap. In addition, many key ideas involve students in synthesizing knowledge across mathematical topics. A mathematics program that includes New York States standards and reflects the revised assessments will continue to emphasize the fundamental mathematical skills and knowledge that have been traditionally expected. Students are still expected to master basic skills of arithmetic, geometry, algebra, trigonometry, probability, and statistics. The State Education Department will continue to assess these skills and concepts with tests that will be given in secure settings, and the results of these tests will be made public each year.
The seven key ideas of the learning standards are a mixture of content and process goals. They speak to the mathematics content that a student should know and, at the same time, describe the ways in which the student ought to be able to use that content in meaningful contexts. This is possible by considering the key ideas as guides for selecting appropriate content. The following brief description of each key idea may help in that selection.
1. Mathematical Reasoning
Students use mathematical reasoning to analyze mathematical situations, make conjectures, gather evidence, and construct an argument.
Mathematical analysis is an integral part of problem solving. As a result, this key idea cuts across the content in all the other key ideas. At the elementary level, it includes the concept of pattern and at the high school level includes the concepts of logical terms such as and, or, not, if. . .then, as well as to what constitutes a valid argument.
2. Number and Numeration
Students use number sense and numeration to develop an understanding of the multiple uses of numbers in the real world, the use of numbers to communicate mathematically, and the use of numbers in the development of mathematical ideas.
Although number and numeration deal heavily with number concepts of whole numbers, fractions, decimal fractions, ratios, percents, integers, and irrational numbers, this key idea also includes procedures for ordering numbers and applying them to real-world situations.
Students use mathematical operations and relationships among them to understand mathematics.
Often considered to be primarily procedural, operations includes the expectation that students understand the concepts of addition, subtraction, multiplication, and division in order to be successful with problem solving. Problem solving often requires the selection of appropriate computational or operational methods. The concepts of ratio and proportion must be understood in order to recognize and solve problems that are proportional in nature.
4. Modeling/Multiple Representation
Students use mathematical modeling/multiple representation to provide a means of presenting, interpreting, communicating, and connecting mathematical information, and relationships.
Most geometry concepts are included in modeling/multiple representation but the key idea also includes procedures for geometric constructions and producing graphs and tables. Modeling/multiple representation deals with many aspects of mathematical communication. As a result, it includes the use of variables, modeling relationships both algebraically and graphically, and appropriate use of functions.
Students use measurement in both metric and English measure to provide a major link between the abstractions of mathematics and the real world in order to describe and compare objects and data.
Measuring is a procedure that includes the concepts of area, volume, perimeter, and circumference. It also includes the formulas that may be applied to calculate them. Much of the content of trigonometry and statistics is included in this key idea. Measurement is a major mathematics key idea that connects with science, technology, and social studies.
Students use ideas of uncertainty to illustrate that mathematics involves more than exactness when dealing with everyday situations.
Estimation and probability are the major topics found in the key idea of uncertainty. Most probability concepts are found in this key idea as well as procedures for calculating probabilities. Although estimation includes number sense, estimating can be used as a problem-solving strategy. This key idea includes estimation of quantity, estimation of computations, and estimation of measurements.
Students use patterns and functions to develop mathematical power, appreciate the true beauty of mathematics, and construct generalizations that describe patterns simply and efficiently.
The study of patterns and functions is one of the central themes of mathematics. Patterns are a major part of mathematics study in the elementary grades. A study of patterns requires the conceptual understanding of recognizing, describing, and generalizing patterns.
The study of function helps the student to build mathematical models that can be used to predict the behavior of real-world phenomena that have observable patterns. The widespread occurrence of regular and chaotic pattern behavior can make a study of patterns and functions interesting and valuable.
Patterning and the manipulation of functions (algebraically and graphically) have procedural aspects, but pattern seeking and function finding are strategies used in problem solving. As in the key idea of mathematical reasoning, which includes looking for patterns, key idea 7 cuts across the other key ideas.
Cognitive Categories (back to Table of Contents)
Meaningful curriculum and assessment take into consideration the three categories of cognitive functioning that have served in shaping the National Assessment of Educational Progress (NAEP) and many other state frameworks and large-scale assessments of student learning in mathematics. These categories are procedural knowledge, conceptual understanding, and problem solving. Procedural knowledge involves knowing when and how. Conceptual understanding involves knowing about. They are joined together by problem solving, which involves the merging of conceptual understanding with procedural knowledge to bring students knowledge into use in solving problems in abstract or contextual settings.#1
Students use procedural knowledge when they:
select and apply appropriate procedures correctly;
verify or justify the correctness of a procedure, using concrete models or symbolic methods;
extend or modify the procedures to deal with factors inherent in problem settings;
use various numerical algorithms;
read and interpret graphs and tables;
execute geometric constructions; and
perform non-computational skills such as rounding and ordering numbers.
Students use conceptual understanding of mathematics when they:
recognize, label, and generate examples with a concept and without a concept;
use and interrelate models, diagrams, manipulatives, and varied representations of concepts;
identify and apply principles (i.e., valid statements generalizing relationships among concepts in conditional form);
know and apply facts and definitions;
compare, contrast, and integrate related concepts;
recognize, interpret, and apply the signs, symbols, and terms used to represent concepts;
interpret the assumptions and relations involving concepts in mathematical settings; and
reason in settings involving the careful application of concept definitions, relations, or representations of definitions or relations.
In problem solving students are required to use their accumulated knowledge of mathematics in new situations when they:
recognize and formulate problems;
determine the sufficiency and consistency of data;
use strategies, data, models, and relevant mathematics;
generate, extend, and modify procedures;
use reasoning (i.e., spatial, inductive, deductive, statistical, or proportional) in new settings; and
judge the reasonableness and correctness of solutions.
Problem solving is the connecting thread through the seven key ideas of mathematics and the grade levels. Content which may require procedural knowledge for an older student may be a problem-solving task for a younger student. For example, a fourth grader can easily multiply two numbers by using a taught algorithm, but a first grader who may be unfamiliar with multiplication would have to devise a strategy to find the product, perhaps by making equal-sized groups of counters.
The Role of Assessment (back to Table of Contents)
Assessment is an ongoing process and not an end in itself. A combination of individual student work, student projects, and teacher observations can be used to assess student achievement.
School districts may use assessment data to adjust curriculum and instruction. Teachers may use assessment data to strengthen the teaching and learning process in the classroom, monitor students work and progress, and identify students strengths and areas in need of improvement. Students may evaluate their own learning by using assessment data. Parents may be partners in assessment and receive specific information about their childs progress.
New York State Testing Program
The seven key ideas mentioned previously are one of three dimensions that are considered in the construction of State assessments. The three categories of cognitive functioning are another dimension. The third dimension of the model for specifying the nature of State mathematics assessments is the type of questions and tasks that students would be expected to complete when illustrating their competence in the key ideas and categories of cognitive functioning. These formats include multiple choice questions, short constructed response problems, and extended constructed response problems.
Multiple choice questions provide a highly reliable and efficient way of assessing students ability to select correct answers and interpretations from a listing of possible alternatives.
Short constructed response problems provide much of the same information, but the student must develop the response. The student is also expected to create the answer, or sketch a drawing, among other possible actions. Such problems can be scored with a rubric that allows for partial credit.
Extended constructed response problems require students to develop a written description of the solution to a problem or to answer a series of subquestions. This requires the student to demonstrate greater knowledge and a necessity to communicate, in some depth, about the problem and its solution. Such tasks are usually scored with the use of a scoring rubric that also allows for partial credit.
Examples of each type of question can be found in the Core Curriculum section at the grade levels for which State pilot assessments have been administered (grades 4, 8, and Math A). There will be a mixture of question types on all the mathematics assessments. Specified percentages of items will assess each of the seven key ideas and three categories of cognitive functions.
Effective Instructional Strategies (back to Table of Contents)
Students develop their own meanings of mathematical concepts and procedures when given the opportunity to become actively involved in learning. Teachers who use instructional strategies guided by this principle act as facilitators for childrens active development of mathematics. They do not act merely as dispensers of rules and algorithms for students to memorize. Some of the instructional strategies they incorporate are the use of manipulative materials, student discussion of mathematical ideas, and small group learning. Active involvement on the part of the learner has the potential to deepen understanding of mathematics.
Research concerning cooperative learning has indicated that students in classes using this learning model do at least as well and often better on standardized tests. Students from minority and low-income groups are frequently those who show the most improved scores. Other advantages of cooperative learning that have been found include development of thinking skills, improved self-esteem, improvement of attitudes toward minorities, and acceptance of mainstreamed students. Cooperative learning models have been shown to work well in heterogeneous classes. It must be pointed out that all small group work is not cooperative learning. The key elements of the cooperative learning model are that each student in the group is accountable for the final result and the students in the group must work together as a team in order to succeed.
Instruction that employs a wide range of representations and contextual environments enhance student growth in both affective and cognitive dimensions. The study of mathematics focuses on the representation and communication of numerical, spatial, and data-related relationships. Many classroom activities can support that focus; for example, students may translate their mental conceptions into symbolic forms and then provide a verbal description of the same situation. Other activities might include selecting the best model to physically explain a relationship; using technology in innovative ways to explore a problem; and writing paragraphs, letters, or journals to explain observations about mathematics.
Developmentally appropriate instruction takes advantage of what students are ready to learn. It provides classroom discourse that stimulates cognitive growth. It does not require students to memorize material that is beyond their current understanding. To make use of the notion of developmental stages, teachers observe their students closely and provide them with activities for which they are ready. Hands-on activities, as well as paired, group, and class discussions in which students develop and debate their ideas, contribute to the development of cognitive growth.
Mathematics environments that are embedded in real-world situations engage students in authentic problems that require creativity and demonstrate its uses in everyday life and careers, as well as play. When school mathematics builds on the mathematics that children developed on their own before they came to school, it becomes practical and relevant.
Role of Manipulatives (back to Table of Contents)
Manipulatives are physical objects that students can move around, group, sort, and use to measure as they model mathematical concepts and problems. Manipulative-rich environments may enhance understanding and achievement across a variety of mathematics topics if they are explicitly connected with the mathematical concepts and procedures they represent. Students do not automatically make connections between concrete representations of concepts or procedures and their written or symbolic forms. It is necessary for the teacher to help students make the connection.
Teachers of the early grades commonly use manipulatives but even when studying calculus, students can benefit from manipulating a physical model. Manipulatives can be elaborate and expensive, teacher-made, or simple items from home. Commercial materials often include books, games, and lessons when purchased in classroom sets. Suggestions for commonly used manipulatives will be given at the beginning of each level in the Core Curriculum section.
Role of Technology (back to Table of Contents)
Classroom technology includes calculators, computers, videos, and multimedia. Each of these can be a valuable part of the mathematics program if used when appropriate.
Appropriate grade-level calculators should be made available to students in the classroom. They may be used to assist students in their understanding of concepts and procedures. The use of calculators should not be a substitute for a students understanding of quantitative concepts and relationships or proficiency in basic computations. Research has shown that appropriate use of calculators in the classroom does not interfere with student knowledge of number factsor with their ability to perform calculations. The classroom use of calculators has been shown to contribute to improved student attitudes toward mathematics and their problem-solving ability.
Four-function calculators are appropriate for instruction with elementary students although they are not permitted on the grade 4 State assessment at the present time. They might be used at this level in the role of skip counting. Skip counting by ones, using the calculator, can help young students relate counting to the symbols. For older students skip counting by 2s, 5s, or other numbers can relate repeated addition and multiplication. Integers may be explored through skip counting numbers less than zero.
Calculators that compute fractions are appropriate for the intermediate grades. Fraction calculators that simplify fractions through a series of stages, for example, may be used to help students speculate on the algorithm the calculator uses to put fractions in simplest form. The discussion may include concepts of common factors that are prime numbers and may lead to prime factoring as an algorithm for determining the simplest form of a fraction. Calculators will not be permitted on the multiple choice portion of the grade 8 State assessment but will be required for the rest of the test.
Scientific and graphing calculators are appropriate for secondary mathematics students. Graphing calculators demonstrate multiple ways of representing functions: graphically, symbolically, and in tabular form. Calculators that combine geometric sketching programs and symbolic manipulator software may be appropriate for high school students. Calculators will be required on the Math A and Math B assessments. (See calculator requirements at the beginning of High School: Math A and Math B.)
Computer software that allows students to create mathematics, as well as to explore, conjecture, and investigate mathematics, provides unique opportunities for students learning mathematics. Teachers should take full advantage of this resource, if available.
Young students can benefit from computer explorations that model manipulatives. The graphics, color, and sound capabilities of the microcomputer make for a dynamic model of the manipulative on the screen. Students may explore a concept, make mistakes for concept clarification, and even pose problems. The computer program often provides the student with instant help and feedback that are not possible when the student is working only with a manipulative. Studies concerning students using geometry construction software demonstrate that students develop a deeper understanding of explored concepts and, with proper instruction, develop independent inquiry skills associated with mathematical thinking.
More recent developments in microcomputer capabilities have increased its ability to aid students in the study of real-world data. Internet capacity allows students to communicate across vast distances and provides a whole other dimension to mathematics experiments and data collection. Handheld computer-based laboratory systems which include probes facilitate the collection and analysis of real-world data and can be used to connect mathematics, science, and technology.


Differentiating Mathematics for Gifted Children: A Professional Development Project for In-Service Teachers
Volume 8 Issue 4 (October 2023)
Deniz Özen Ünal Ahmet BildirenPages: 966-980 Download Count : 200 View Count: 222 DOI Number 10.24331/ijere.1342291
Gifted children should receive education that is appropriate to their potential, but the question is whether this is possible without a great deal of teacher competence. This project aims to increase the professional competence of mathematics teachers who were provided with training on the appropriate strategies for gifted students. In this study the knowledge and views of the teachers about the giftedness and the information used in gifted education is investigated. In the training process, seminars were provided regarding the teaching strategies used in gifted education, challenging mathematical tasks to be used to reveal and develop potential, and the differentiation of teaching with the help of technology. The participants of the study were 25 middle/high school in-service mathematics teachers from 17 provinces throughout the country. The teachers learned the teaching strategies for the gifted, and they provided enrichment using challenging mathematical tasks and technological tools.
- gifted children
- teacher education


Bayesian estimation of within-between modelsSource:
A near-equivalent of
wbm() that instead uses Stan,
via rstan and brms.
wbm_stan( formula, data, id = NULL, wave = NULL, model = "w-b", detrend = FALSE, use.wave = FALSE, wave.factor = FALSE, min.waves = 2, model.cor = FALSE, family = gaussian, fit_model = TRUE, balance.correction = FALSE, dt.random = TRUE, dt.order = 1, chains = 3, iter = 2000, scale = FALSE, save_ranef = FALSE, interaction.style = c("double-demean", "demean", "raw"), weights = NULL, offset = NULL, ... )
Model formula. See details for crucial info on
panelr's formula syntax.
The data, either a
datais not a
panel_dataobject, then the name of the individual id column as a string. Otherwise, leave as NULL, the default.
datais not a
panel_dataobject, then the name of the panel wave column as a string. Otherwise, leave as NULL, the default.
"contextual". See details for more on these options.
Adjust within-subject effects for trends in the predictors? Default is FALSE, but some research suggests this is a better idea (see Curran and Bauer (2011) reference).
Should the wave be included as a predictor? Default is FALSE.
Should the wave variable be treated as an unordered factor instead of continuous? Default is FALSE.
What is the minimum number of waves an individual must have participated in to be included in the analysis? Default is
2and any valid number is accepted.
"all"is also acceptable if you want to include only complete panelists.
Do you want to model residual autocorrelation? This is often appropriate for linear models (
family = gaussian). Default is FALSE to be consistent with
wbm(), reduce runtime, and avoid warnings for non-linear models.
Use this to specify GLM link families. Default is
gaussian, the linear model.
Fit the model? Default is TRUE. If FALSE, only the model code is returned.
Correct between-subject effects for unbalanced panels following the procedure in Curran and Bauer (2011)? Default is FALSE.
Should the detrending procedure be performed with a random slope for each entity? Default is TRUE but for short panels FALSE may be better, fitting a trend for all entities.
If detrending using
detrend, what order polynomial would you like to specify for the relationship between time and the predictors? Default is 1, a linear model.
How many Markov chains should be used? Default is 3, to leave you with one unused thread if you're on a typical dual-core machine.
How many iterations, including warmup? Default is 2000, leaving 1000 per chain after warmup. For some models and data, you may need quite a few more.
Standardize predictors? This can speed up model fit. Default is FALSE.
Save random effect estimates? This can be crucial for predicting from the model and for certain post-estimation procedures. On the other hand, it drastically increases the size of the resulting model. Default is FALSE.
The best way to calculate interactions in within models is in some dispute. The conventional way (
"demean") is to first calculate the product of the variables involved in the interaction before those variables have their means subtracted and then subtract the mean of the product from the product term (see Schunk and Perales (2017)). Giesselmann and Schmidt-Catran (2020) show this method carries between-entity differences that within models are designed to model out. They suggest an alternate method (
"double-demean") in which the product term is first calculated using the de-meaned lower-order variables and then the subject means are subtracted from this product term. Another option is to simply use the product term of the de-meaned variables (
"raw"), but Giesselmann and Schmidt-Catran (2020) show this method biases the results towards zero effect. The default is
"double-demean"but if emulating other software is the goal,
"demean"might be preferred.
If using weights, either the name of the column in the data that contains the weights or a vector of the weights.
this can be used to specify an a priori known component to be included in the linear predictor during fitting. This should be
NULLor a numeric vector of length equal to the number of cases. One or more
offsetterms can be included in the formula instead or as well, and if more than one is specified their sum is used. See
Additional arguments passed on to
brms::brm(). This can include specification of priors.
wbm_stan object, which is a list containing a
brm model and a
stan_code object with the model code.
fit_model = FALSE, instead a list is returned containing a
object and a
stan_data object, leaving you with the tools you need to
run the model yourself using
wbm() for details on the formula syntax, model types,
and some other stuff.


Tapped Bulk Density Calculator
The tapped bulk density of a powder is a key component to being able to determine its suitability to being used in a tablet press or capsule filling machine.
The process for calculating the taped bulk density of a product is quite simple.
100g of powder is loaded into a measuring tube. This is then taped a set number of times to allow the powder to settle into its most compact form. The volume of the powder is then recorded in mL. You then divide 100 (the amount of powder first added to the tube in grams) by the volume in mL that the powder takes up in the tube to get the g/mL or the Taped Bulk Density.
There are two ways to do this. The most consistent and the one recognised by the EU, US and JP Pharmacopeias is to use a special device to drop the powder 3mm-14mm 250-300 times in a row in a vertical motion.
It is also possible to do it without the special apparatus by simply taping the measuring jug agents the side of padded table 100 times. While this will give you slightly less consistent results it is not overly important as the Tamped Bulk Density is predominantly used to calculate the Hausner Ratio for tableting and capsule filling and this in itself is not an exact science. It is used to calculate how much of a powder can fit in to empty capsules.
LFA has developed a Tapped Bulk Density Calculator to help you calculate the density of your products:
Tapped Bulk Density g/m -
Tapped Bulk Density mg/mL -


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In a game of texas holdem, what are the odds that with a deck of 52 cards and 9 players are all playing at the table ( thats 2 cards each = 18The prob that is has a royal flush of spades 48C14 / 52C18. This would be the same for each of the other suites too. So you could just multiply this by 4. texas holdem odds royal flush products for android |… The Texas Hold Em Odds calculator will tell you your odds of having the best. Getting Familiar with the Texas Holdem Poker Hands The Royal Flush, as the name suggests, is the best possible hand in Texas Holdem. This hand combination is made up of the five highest cards in a deck – the Ace, King, Queen, Jack and the number 10. The royal flush must have all these characters of the same suit. Texas holdem odds royal flush | TOP Games online Royal Flush Odds (Hold Em). Assume you're given 2 cards of the same suit, and the next three cards flop are also the same suit as your hole cards.Everything I know about Texas Holdem I learnt in PokerStretegy portal, you can find the link below, in Sources and related links section
Dec 27, 2018 · If you have 2 of the 5 cards needed in a royal flush… the odds of getting dealt a royal flush on the flop (first 3 cards) is 1 in 649,740. out of the 5 on the board and 2 in your hand I believe it’s 1 in 30,940. I’ve gotten a royal flush twice in my life… you’ve got to play many hands to get it. lol
These Are The Odds Of Being Dealt a Royal Flush in Poker These Are The Odds Of Being Dealt a Royal Flush in Poker. This brings the odds of getting a royal flush down to four in 2,598,960, or roughly one in 650,000. That's shockingly low compared to the odds of winning an Academy Award, otherwise known as an Oscar, which the Las Vegas Review-Journal reports as 1 in 11,500. What are the odds of making a royal flush after the flop ...
What Are the Odds? A List of Long-Shot Odds in Texas Holdem
How Likely Is Getting a Royal Flush in Poker? The Probability of Being Dealt a Royal Flush in Poker. Search. ... A royal flush is the highest ranked hand in the ... What Are Bad Poker Hands in Texas Hold'em?
Texas Holdem Royal Flush Odds - medcao.com Texas Holdem Royal Flush Odds. My road to beating ultimate texas holdem - Other Gambling Games Forum - Discuss Other Gambling Games


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Since 1950 there is has been a pattern, that gives you a preview of how the stock market may go for the next year. It is called the January Barometer.
Basic, you look the the S and P 500 (SPX), and see what it does in January. Both the first 5 days of trading and the whole month of trading. And see what that correlates too in the the past.
The first 5 days of trading, give you about an 85% correlation, and 90 percent plus for the month.
Therefore, if the SPX goes up in the first 5 days, 85 % chance that will be the direction for the year. If we watch the whole month and it goes sideways, then a 90 percent chance the market will go sideways for the year.
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Conversion math problems
Converting units: examples process when you get to physics or chemistry and have to do conversion problems k12 math 5th grade math 6th grade math. Quizlet provides conversions math metric hesi a2 activities, flashcards and games start learning today for free. A lesson on math word problems that involve units of measurement time, distance, volume etc includes a warm up and pre and post assessment worksheets. Welcome to the measurement worksheets page at math allows students to use their estimation skills to help them solve problems in converting between. Fun math practice improve your skills with free problems in 'convert rates and measurements: metric units' and thousands of other practice lessons.
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Conversion math problems
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Direct and inverse variation graphs worksheet
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Similar to direct variation word problems, those dealing with inverse variation may be solved using the following steps: 1) Recognizing the word problem consists of inverse variation as exemplified by presence of verbiage listed above;
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Direct Variation Graph Worksheets - showing all 8 printables. Some of the worksheets displayed are Direct variation, Direct variation work, Direct and inverse variation 1, Chapter 2 you will need a direct variation, Direct and inverse variation, Inverse variation, Algebra 1 slope intercept direct...
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x and y show direct variation are “y varies directly with x” and “x and y are directly proportional.” Tell whether x and y show direct variation. Explain your reasoning. a. y + 1 = 2x b. 1 — 2 y = x y = 2x − 1 Solve for y. y = 2x Solve for y. The equation cannot be The equation can be written as y = kx. So, x and y written as y = kx ...
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Inverse Variation Frayer Model Sample.png. Inverse and Direct Variation power point.ppt. I like this worksheet because it provides students an opportunity to practice all of the different representations of Direct and Inverse Variation that I have presented to them over the two days of...
! Direct/Inverse Proportion. Examples Workout 1. Inverse Proportion. Question 1: A is directly proportional to B. When A = 12, B = 3 (a) Find a formula for A in terms of (c) Calculate the value of x, when y is twice as big as x. Question 5: These graphs represent four different types of proportionality.How is the graph of an inverse variation different from the graph of direct variation? Draw an example of an inverse variation graph. If I am looking at an inverse relation, if y increases what happens to x? Explain what happens to y as x decreases. Use the following table to answer questions 4 - 6. X Y 15 2 10 3 5 6 3 10 Does this show an ...
Showing top 8 worksheets in the category - Variation Graphing. Some of the worksheets displayed are Direct inverse and joint variation work, Direct variation, Direct variation work, Direct and inverse variation, Direct and inverse variation, Consider each power determine the power and, Work the theory of natural selection, Function inverses date period.
Does the following equation represent direct. or inverse variation? Inverse Variation. Direct Variation. y =-16x. If y varies directly as x and y = 15 when x = 3, Welcome to The Inverse Relationships -- Multiplication and Division All Inverse Relationships -- Range 2 to 9 (A) Math Worksheet from the Algebra Worksheets Page at Math-Drills.com. This math worksheet was created on 2013-02-14 and has been viewed 35 times this week and 820 times this month. It may be printed, downloaded or saved and used in ...
Algebra 2 – Lesson 10A Worksheet Direct, Inverse, and Joint Variation Solve each of the following problems using the direct, inverse and joint variation equations. Make sure to show all work on a separate sheet of paper. 1. y varies directly as x. x = 3 when y = 12. Find y when x = 12. 2. a varies directly as b. b = 1 when a = 5. Find b when ... www.justmaths.co.uk Direct & Inverse Proportion (H) - Version 2 January 2016 3. Sketch a graph on the axes below that shows that y is directly proportional to x.  4. At a constant temperature, the volume of a gas V is inversely proportional to its pressure p. By what percentage will the pressure of a gas change if its volume increases by 25%?
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Srinivasa Ramanujan was one of India’s mathematical geniuses. He made
wonderful contributions to the field of advanced mathematics.
Even today, his fascinating results and mathematical theories, and a number of unpublished notebooks filled with theorems, continue to baffle and enthrall mathematicians.
Ramanujan was born in his grandmother’s house in Erode, a small village near Chennai in Tamil Nadu. While he was still a baby, his mother took him to Kumbakonam, near Chennai, where his father worked as a clerk in a cloth merchant’s shop.
He joined the Town High School there in January 1898 and was a very good student. But his real aptitude lay in mathematics. He read GS Carr’s Synopsis of elementary results in pure mathematics to teach himself mathematics.
He got a scholarship for his first year at the Government College in Kumbakonam. But he devoted more time to mathematics and neglected his other subjects.
In 1906, Ramanujan joined Pachaiyappa’s College at Chennai. He passed in math, but flunked all his other subjects. In the following years, he worked on developing his own ideas in mathematics, without having a real idea of the research topics then. All he had were the topics in Carr’s book.
On 14 July 1909, he married a nine-year-old girl his mother arranged for him. However, Ramanujan did not live with his wife until she was 12-years-old.
During this period, he published many papers and was becoming well known in Chennai as a mathematical genius. In 1913, while he worked as a clerk in the Indian Mathematical Society, Ramanujan wrote to Cambridge mathematician, GH Hardy, and told him about his work. He had read Hardy’s 1910 book Orders of Infinity.
Soon a regular correspondence developed between the two. And in 1914 Ramanujan enrolled at Trinity College, Cambridge. There, Hardy and Ramanujan began collaborating.
But Ramanujan did not keep well. Being an orthodox Brahmin, he was a strict vegetarian. During World War I, when food was already scarce, it got harder for him to get special food and Ramanujan began having health problems. But, with Hardy’s encouragement, he continued to publish papers which were very well-received in the academic community.
In 1916, Ramanujan graduated from Cambridge with a Bachelor of Science by Research. (This degree was recognised as a Ph.D. after 1920). But a year later he fell seriously ill and his doctors feared that he would die.
Ramanujan was elected as fellow of the Cambridge Philosophical Society in 1918. At the same time, he was elected as fellow of the Royal Society of London. This was a great honour to him and his health seemed to improve.
But when Ramanujan arrived in India on 13 March that year, he was dying. Despite medical treatment, he died in 1920.


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In probability theory and statistics, the hypergeometric distribution is a discrete probability distribution that describes the probability of (exactly) k successes in n draws from a finite population (of size N) without replacement.(1)
Above you see the mathematical formula for the hypergeometric distribution (i.e. the probability mass function), where
- N is the population size
- m is the number of potential successes in the population
- n is the number of draws
- k is the number of successes
- N is the size of deck
- m is number of cards I want to draw
- n is the number of draws (the number of cards of our opening hand)
- k is the number of cards I want to draw
Oh wait, that last number for k is not entirely right! Actually we do not want to calculate the probability of having exactly one card in our opening hand (X=1), but having at least 1 card in our opening hand (X=1). Now we have two ways of solving this:
- Add the two probabilities for X=1 and X=2 (see generalized formula below), or
- Take 1 and then subtract the probability for X=0 from it.
So there's a 17.9% chance that we have at least one Information Highway in our opening hand (with 2 copies in out 75 card deck). Now the next question would be how does our chances change for drawing at least one copy of the card, if either change the decksize or if we change the number of copies (of Information Highways) in our deck.
As you can see above the calculations become tedious fast, if you want to calculate the resulting percentages over and over again for different parameters (different values of k, n, M or N). Luckily modern spreadsheet programs(2) have built-in functions for these type of calculations:
- In Microsoft Excel you can use the function "hypgeomdist" for calculation a certain probability. In general the looks like this, when you enter it:= HYPGEOMDIST(successes_in_sample, sample_size, number_of_successes, population; culmulative)(3)= HYPGEOMDIST(k; n; M; N; TRUE|FALSE)When entering the parameters from our example above, it would look like this:= 1-HYPGEOMDIST(0; 7; 2; 75; FALSE)
- A similar function (with the same name) exists in Apache OpenOffice:= HYPGEOMDIST(k; n; M; N)When entering the parameters from our example above, it would look like this:= 1-HYPGEOMDIST(0; 7; 2; 75)
As you can see it makes a huge difference how large your deck is. For the 60 card deck the probability is as high as 22,15%, and for the 90 card deck as low as 15,03%. This is one of reasons for playing smaller sized decks, especially if you're playing a number of cards that you only have one or two copies of in your deck.
What happens if now vary the number of copies of the card we want to have in our opening hand (in a deck of 75 cards).
As you can see again there's a dramatic change of the probabilities we're having when we increase the number of copies in our deck. I am not postulating to add seven Information Highway to your deck, but if you want to have a 50% chance of having some sort of crypt acceleration in your crypt you could something like 2 Information Highway, 2 Dreams of the Sphinx and 3 Zillah's Valley to your deck (for example).
Of course I'm aware, that all of you know, that increasing the number of copies in your deck or decreasing your decksize, increases the chances of drawing a particular card, but I wanted to give you exact numbers instead of an educated guess.
Varying decksize and the number of cards in the deck, the final chart looks like this:
Next time: more fun with multivariate hypergeometric distribution!
- Hypergeometric Distribution (on Wikipedia)
- Hypergeometric Calculator
- Probability: Drawing Cards from Decks (in "The Mathematics of Magic The Gathering")
(1) cf. the binomial distribution, which describes the probability of k successes in n draws with replacement.
(2) In Perl you can use the module Math-GSL-0.26 (Math::GSL::CDF).
(3) Only Excel 2010 (or higher) have the 5th parameter (cumulative).