Don't just just the formula; learn how the formula came to be! What better way to do that than by watching an animation that helps you visualize where the algebraic formula for finding the area of a trapezoid comes from?
Deriving the Formula for Volume of a Triangular PrismKyle Pearce
The document discusses the volume formula for a triangular prism. It begins by reviewing the volume formula for a rectangular prism, which is length times width times height. It then derives the volume formula for a triangular prism, which is (1/2) times the base times height times length. The document works through various representations of the area of the triangular base and confirms the volume formula for a triangular prism is (1/2) times the base times height times length.
Pythagorean triples are sets of three whole numbers that satisfy the Pythagorean theorem. A primitive Pythagorean triple has no common factors between the three numbers. Euclid developed a formula to generate primitive Pythagorean triples using two integers where one is odd and they are relatively prime. The document discusses using Euclid's formula to find primitive Pythagorean triples and prove the formula, as well as properties of primitive Pythagorean triples.
This document discusses Pythagorean triples, which are sets of three positive integers a, b, and c that satisfy the Pythagorean theorem a2 + b2 = c2. It provides examples of Pythagorean triples like (3, 4, 5) and explains Euclid's proof that there are infinitely many such triples. The document also describes properties of Pythagorean triples and how to construct them using formulas involving positive integers m and n. Finally, it mentions that the list provided only includes the first or "primitive" Pythagorean triple for each unique combination and not their multiples.
Pythagoras’s theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. The document provides examples of Pythagorean triples, which are sets of three integers that satisfy the Pythagorean theorem, such as 3, 4, 5. It also lists several other common Pythagorean triples and provides a method for calculating additional triples using basic algebra. Finally, the document includes one person's opinion that while Pythagorean's theorem can be useful in situations like artillery firing, they rarely find it useful in everyday life.
The document discusses Pythagorean triples and the Pythagorean theorem. It provides:
1) A brief history of the Pythagorean theorem, which was discovered by Pythagoras and is also known to have been used in ancient India and Maya civilizations.
2) An explanation that Pythagorean triples are sets of integers that satisfy the Pythagorean theorem relationship a2 + b2 = c2.
3) Examples of the 3-4-5 triangle as the simplest Pythagorean triple and the non-Pythagorean triple of 3-7-9.
Pythagorean triples are whole number sets that satisfy the Pythagorean theorem, where a2 + b2 = c2. The document discusses properties of Pythagorean triples and how they relate to rational points on the unit circle. It presents theorems showing that every basic Pythagorean triple corresponds to a rational point on the unit circle, and vice versa. Formulas are derived for generating Pythagorean triples from a given rational slope of a line passing through (-1,0) and a point on the unit circle. The document also briefly discusses 60-degree triangles, whose sides satisfy the equation c2 = a2 + b2 - ab, relating to an ellipse rather than a circle.
Fourier Series of Music by Robert FusteroRobertFustero
The document discusses the Fourier series expansion of a mathematical function that describes musical harmony and the Pythagorean tuning system. It shows that the ratios between notes in the Pythagorean scale can be expressed as a linear sequence of powers of 2 and 3. This allows the ratios to be written as terms of a Fourier series expansion, with a periodic nature where the exponential resets every time the integer value increases by the period. The Fourier coefficients are then calculated through integration to express the function in its Fourier form.
Deriving the Formula for Volume of a Triangular PrismKyle Pearce
The document discusses the volume formula for a triangular prism. It begins by reviewing the volume formula for a rectangular prism, which is length times width times height. It then derives the volume formula for a triangular prism, which is (1/2) times the base times height times length. The document works through various representations of the area of the triangular base and confirms the volume formula for a triangular prism is (1/2) times the base times height times length.
Pythagorean triples are sets of three whole numbers that satisfy the Pythagorean theorem. A primitive Pythagorean triple has no common factors between the three numbers. Euclid developed a formula to generate primitive Pythagorean triples using two integers where one is odd and they are relatively prime. The document discusses using Euclid's formula to find primitive Pythagorean triples and prove the formula, as well as properties of primitive Pythagorean triples.
This document discusses Pythagorean triples, which are sets of three positive integers a, b, and c that satisfy the Pythagorean theorem a2 + b2 = c2. It provides examples of Pythagorean triples like (3, 4, 5) and explains Euclid's proof that there are infinitely many such triples. The document also describes properties of Pythagorean triples and how to construct them using formulas involving positive integers m and n. Finally, it mentions that the list provided only includes the first or "primitive" Pythagorean triple for each unique combination and not their multiples.
Pythagoras’s theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. The document provides examples of Pythagorean triples, which are sets of three integers that satisfy the Pythagorean theorem, such as 3, 4, 5. It also lists several other common Pythagorean triples and provides a method for calculating additional triples using basic algebra. Finally, the document includes one person's opinion that while Pythagorean's theorem can be useful in situations like artillery firing, they rarely find it useful in everyday life.
The document discusses Pythagorean triples and the Pythagorean theorem. It provides:
1) A brief history of the Pythagorean theorem, which was discovered by Pythagoras and is also known to have been used in ancient India and Maya civilizations.
2) An explanation that Pythagorean triples are sets of integers that satisfy the Pythagorean theorem relationship a2 + b2 = c2.
3) Examples of the 3-4-5 triangle as the simplest Pythagorean triple and the non-Pythagorean triple of 3-7-9.
Pythagorean triples are whole number sets that satisfy the Pythagorean theorem, where a2 + b2 = c2. The document discusses properties of Pythagorean triples and how they relate to rational points on the unit circle. It presents theorems showing that every basic Pythagorean triple corresponds to a rational point on the unit circle, and vice versa. Formulas are derived for generating Pythagorean triples from a given rational slope of a line passing through (-1,0) and a point on the unit circle. The document also briefly discusses 60-degree triangles, whose sides satisfy the equation c2 = a2 + b2 - ab, relating to an ellipse rather than a circle.
Fourier Series of Music by Robert FusteroRobertFustero
The document discusses the Fourier series expansion of a mathematical function that describes musical harmony and the Pythagorean tuning system. It shows that the ratios between notes in the Pythagorean scale can be expressed as a linear sequence of powers of 2 and 3. This allows the ratios to be written as terms of a Fourier series expansion, with a periodic nature where the exponential resets every time the integer value increases by the period. The Fourier coefficients are then calculated through integration to express the function in its Fourier form.
The document discusses the Pythagorean theorem and distance formula. The Pythagorean theorem states that for any right triangle, the sum of the squares of the two sides equals the square of the hypotenuse. The distance formula allows you to calculate the distance between two points in the xy-plane by taking the square root of the sum of the squared differences between the x-coordinates and y-coordinates. An example using points (2,4) and (7,13) demonstrates applying the distance formula to get a distance of 10.3 units between the two points.
This document describes how to find the resulting amplitude when two waves with the same wavelength, frequency and direction interfere. It provides an equation that calculates the resulting amplitude based on the phase difference between the two waves. It then works through an example problem, finding that the resulting amplitude of two interfering waves - one described by a graph and one by an equation - is 5.543m.
The document discusses using the Pythagorean theorem and distance formula to solve for variables in right triangles. It explains that the Pythagorean theorem uses the lengths of the sides of a right triangle to find the length of the hypotenuse. The distance formula is used to find the distance between two points by taking the square root of the sum of the squares of the differences between the x-coordinates and y-coordinates.
The document discusses algorithms for heap data structures. It describes methods for deleting the minimum item from a heap, percolating an item down the heap to maintain the heap property, and getting the minimum item. It also proves that building a heap from an array can be done in linear time by showing the sum of node heights is linear in the number of nodes.
This document contains formulas for calculating trigonometric functions of the sum or difference of two angles. It provides formulas for sin(α+β), sin(α-β), cos(α+β), cos(α-β), tan(α+β), tan(α-β), cot(α+β), and cot(α-β) in terms of the trigonometric functions of the individual angles α and β.
The Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. The document explains the Pythagorean theorem and provides examples of using it to determine if a triangle is a right triangle or to find the length of a missing side.
This document provides instructions on how to find the secant of an angle and uses trigonometric addition formulas to solve problems involving adding angles. It contains two examples where values for cosine and sine are given for angles in different quadrants and asks to find other trig functions of the sum of the angles, including sine, cosine, coordinates, quadrants, tangent, and cosecant of the sum.
RABIN KARP algorithm with hash function and hash collision, analysis, algorithm and code for implementation. Besides it contains applications of RABIN KARP algorithm also
The significance of higher-order ... procedures is that they enable us to represent procedural abstractions explicitly as elements in our programming language, so that they can be handled just like other computational elements.
The Rabin-Karp string matching algorithm calculates a hash value for the pattern and for each substring of the text to compare values efficiently. If hash values match, it performs a character-by-character comparison, otherwise it skips to the next substring. This reduces the number of costly comparisons from O(MN) in brute force to O(N) on average by filtering out non-matching substrings in one comparison each using hash values. Choosing a large prime number when calculating hash values further decreases collisions and false positives.
The document provides an introduction to continuity and differentiation in quantitative techniques. It includes:
1) Definitions of continuity, including that a function f(x) is continuous at a point x=a if f(a) = lim f(x) as x approaches a.
2) Rules for determining continuity of standard functions like sums, products, and quotients of continuous functions.
3) An explanation of derivatives as the slope of the tangent line to a curve at a point, and how to evaluate derivatives using limits.
4) Derivative rules for standard functions like polynomials, exponentials, and logarithms.
5) The Chain Rule for finding derivatives of composite functions like f
Pythagoras was a Greek mathematician born around 570 BCE in Samos, Greece. He founded a school in Croton, Italy where he studied mathematics and developed the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. Pythagoras made many contributions to mathematics and music. He discovered that the musical scale is based on string length ratios and ratios of whole numbers.
The document discusses the Pythagorean theorem and distance formula. The Pythagorean theorem states that for any right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. The distance formula calculates the distance between two points and involves taking the difference of the x-coordinates squared and the difference of the y-coordinates squared and adding those values together. Examples of using both the Pythagorean theorem and distance formula are provided.
The Pythagorean theorem states that the sum of the squares of the two shorter sides of a right triangle equals the square of the longest side or hypotenuse. It is used to calculate the length of the hypotenuse given the lengths of the other two sides. Two examples demonstrate using the Pythagorean theorem to find the length of unknown sides of right triangles.
The document discusses slope and how to find it. Slope is defined as the rise over the run between two points on a line. Slope can be found using the equation m=(y2-y1)/(x2-x1) or by looking at the incline of a line on a graph. The document provides an example of using two points, (3, -5) and (-2, 1), to find the slope is -6/5. It then shows how to create a line equation y=-6/5x-7/5 using the slope and one of the points.
The document discusses the Pythagorean theorem and distance formula. The Pythagorean theorem states that the square of the hypotenuse of a right triangle equals the sum of the squares of the other two sides. The distance formula calculates the distance between two points and is the square root of (x2 - x1)2 + (y2 - y1)2. An example problem applies the distance formula to find the distance between the points (-1,4) and (1,3).
JEE Mathematics/ Lakshmikanta Satapathy/ Quadratic Equation part 2/ Question on properties of the roots of a quadratic equation solved with the related concepts
This document summarizes and compares several string matching algorithms: the Naive Shifting Algorithm, Rabin-Karp Algorithm, Finite Automaton String Matching, and Knuth-Morris-Pratt (KMP) Algorithm. It provides high-level descriptions of each algorithm, including their time complexities, which range from O(n*m) for the Naive algorithm to O(n) for the Rabin-Karp, Finite Automaton, and KMP algorithms. It also includes examples and pseudocode to illustrate how some of the algorithms work.
The document provides information about the Pythagorean theorem including:
- Pythagoras was a famous Greek mathematician from around 2500 years ago who founded a school in southern Italy and was interested in philosophy, music, and astronomy.
- The Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
- Examples are provided to demonstrate using the Pythagorean theorem to calculate missing sides of right triangles.
The Pythagorean theorem has many applications in modern life. It can be used to calculate distances in baseball diamonds, determine ladder lengths, and compare heights and weights. Builders use it to lay floors and construct buildings by calculating missing sides of triangles. Artists also employ the theorem as a drawing tool to create mosaics and triangular shapes. The Pythagorean theorem forms the basis of trigonometry and connects algebra and geometry. It continues to be important in fields like fractal geometry, cell phone location, and the construction of 3D environments in video games.
Lp visualizing and finding the area of trapezoidDeped Tagum City
This document outlines a lesson plan for teaching 5th grade students about finding the area of trapezoids. The objectives are for students to visualize and calculate trapezoid areas. The lesson will include reviewing related concepts, demonstrating how to derive and apply the trapezoid area formula, and an activity where students estimate and calculate the areas of different trapezoids. Formative assessment questions are provided to check students' understanding of trapezoid properties and applying the area formula to word problems.
This document provides examples of calculating the area of a trapezoid using the formula Area = 1⁄2(b+B)h, where b and B are the two bases and h is the height. It demonstrates finding the height when it is not explicitly given by using properties of isosceles triangles or the Pythagorean theorem. In one example, it shows dividing the larger base into pieces to find the height of two congruent triangles formed. In another, it notes that if the base angles are 45 degrees, the triangles formed will be isosceles and the shared height can be used for the trapezoid area.
The document discusses the Pythagorean theorem and distance formula. The Pythagorean theorem states that for any right triangle, the sum of the squares of the two sides equals the square of the hypotenuse. The distance formula allows you to calculate the distance between two points in the xy-plane by taking the square root of the sum of the squared differences between the x-coordinates and y-coordinates. An example using points (2,4) and (7,13) demonstrates applying the distance formula to get a distance of 10.3 units between the two points.
This document describes how to find the resulting amplitude when two waves with the same wavelength, frequency and direction interfere. It provides an equation that calculates the resulting amplitude based on the phase difference between the two waves. It then works through an example problem, finding that the resulting amplitude of two interfering waves - one described by a graph and one by an equation - is 5.543m.
The document discusses using the Pythagorean theorem and distance formula to solve for variables in right triangles. It explains that the Pythagorean theorem uses the lengths of the sides of a right triangle to find the length of the hypotenuse. The distance formula is used to find the distance between two points by taking the square root of the sum of the squares of the differences between the x-coordinates and y-coordinates.
The document discusses algorithms for heap data structures. It describes methods for deleting the minimum item from a heap, percolating an item down the heap to maintain the heap property, and getting the minimum item. It also proves that building a heap from an array can be done in linear time by showing the sum of node heights is linear in the number of nodes.
This document contains formulas for calculating trigonometric functions of the sum or difference of two angles. It provides formulas for sin(α+β), sin(α-β), cos(α+β), cos(α-β), tan(α+β), tan(α-β), cot(α+β), and cot(α-β) in terms of the trigonometric functions of the individual angles α and β.
The Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. The document explains the Pythagorean theorem and provides examples of using it to determine if a triangle is a right triangle or to find the length of a missing side.
This document provides instructions on how to find the secant of an angle and uses trigonometric addition formulas to solve problems involving adding angles. It contains two examples where values for cosine and sine are given for angles in different quadrants and asks to find other trig functions of the sum of the angles, including sine, cosine, coordinates, quadrants, tangent, and cosecant of the sum.
RABIN KARP algorithm with hash function and hash collision, analysis, algorithm and code for implementation. Besides it contains applications of RABIN KARP algorithm also
The significance of higher-order ... procedures is that they enable us to represent procedural abstractions explicitly as elements in our programming language, so that they can be handled just like other computational elements.
The Rabin-Karp string matching algorithm calculates a hash value for the pattern and for each substring of the text to compare values efficiently. If hash values match, it performs a character-by-character comparison, otherwise it skips to the next substring. This reduces the number of costly comparisons from O(MN) in brute force to O(N) on average by filtering out non-matching substrings in one comparison each using hash values. Choosing a large prime number when calculating hash values further decreases collisions and false positives.
The document provides an introduction to continuity and differentiation in quantitative techniques. It includes:
1) Definitions of continuity, including that a function f(x) is continuous at a point x=a if f(a) = lim f(x) as x approaches a.
2) Rules for determining continuity of standard functions like sums, products, and quotients of continuous functions.
3) An explanation of derivatives as the slope of the tangent line to a curve at a point, and how to evaluate derivatives using limits.
4) Derivative rules for standard functions like polynomials, exponentials, and logarithms.
5) The Chain Rule for finding derivatives of composite functions like f
Pythagoras was a Greek mathematician born around 570 BCE in Samos, Greece. He founded a school in Croton, Italy where he studied mathematics and developed the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. Pythagoras made many contributions to mathematics and music. He discovered that the musical scale is based on string length ratios and ratios of whole numbers.
The document discusses the Pythagorean theorem and distance formula. The Pythagorean theorem states that for any right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. The distance formula calculates the distance between two points and involves taking the difference of the x-coordinates squared and the difference of the y-coordinates squared and adding those values together. Examples of using both the Pythagorean theorem and distance formula are provided.
The Pythagorean theorem states that the sum of the squares of the two shorter sides of a right triangle equals the square of the longest side or hypotenuse. It is used to calculate the length of the hypotenuse given the lengths of the other two sides. Two examples demonstrate using the Pythagorean theorem to find the length of unknown sides of right triangles.
The document discusses slope and how to find it. Slope is defined as the rise over the run between two points on a line. Slope can be found using the equation m=(y2-y1)/(x2-x1) or by looking at the incline of a line on a graph. The document provides an example of using two points, (3, -5) and (-2, 1), to find the slope is -6/5. It then shows how to create a line equation y=-6/5x-7/5 using the slope and one of the points.
The document discusses the Pythagorean theorem and distance formula. The Pythagorean theorem states that the square of the hypotenuse of a right triangle equals the sum of the squares of the other two sides. The distance formula calculates the distance between two points and is the square root of (x2 - x1)2 + (y2 - y1)2. An example problem applies the distance formula to find the distance between the points (-1,4) and (1,3).
JEE Mathematics/ Lakshmikanta Satapathy/ Quadratic Equation part 2/ Question on properties of the roots of a quadratic equation solved with the related concepts
This document summarizes and compares several string matching algorithms: the Naive Shifting Algorithm, Rabin-Karp Algorithm, Finite Automaton String Matching, and Knuth-Morris-Pratt (KMP) Algorithm. It provides high-level descriptions of each algorithm, including their time complexities, which range from O(n*m) for the Naive algorithm to O(n) for the Rabin-Karp, Finite Automaton, and KMP algorithms. It also includes examples and pseudocode to illustrate how some of the algorithms work.
The document provides information about the Pythagorean theorem including:
- Pythagoras was a famous Greek mathematician from around 2500 years ago who founded a school in southern Italy and was interested in philosophy, music, and astronomy.
- The Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
- Examples are provided to demonstrate using the Pythagorean theorem to calculate missing sides of right triangles.
The Pythagorean theorem has many applications in modern life. It can be used to calculate distances in baseball diamonds, determine ladder lengths, and compare heights and weights. Builders use it to lay floors and construct buildings by calculating missing sides of triangles. Artists also employ the theorem as a drawing tool to create mosaics and triangular shapes. The Pythagorean theorem forms the basis of trigonometry and connects algebra and geometry. It continues to be important in fields like fractal geometry, cell phone location, and the construction of 3D environments in video games.
Lp visualizing and finding the area of trapezoidDeped Tagum City
This document outlines a lesson plan for teaching 5th grade students about finding the area of trapezoids. The objectives are for students to visualize and calculate trapezoid areas. The lesson will include reviewing related concepts, demonstrating how to derive and apply the trapezoid area formula, and an activity where students estimate and calculate the areas of different trapezoids. Formative assessment questions are provided to check students' understanding of trapezoid properties and applying the area formula to word problems.
This document provides examples of calculating the area of a trapezoid using the formula Area = 1⁄2(b+B)h, where b and B are the two bases and h is the height. It demonstrates finding the height when it is not explicitly given by using properties of isosceles triangles or the Pythagorean theorem. In one example, it shows dividing the larger base into pieces to find the height of two congruent triangles formed. In another, it notes that if the base angles are 45 degrees, the triangles formed will be isosceles and the shared height can be used for the trapezoid area.
A trapezoid is a quadrilateral with two sides parallel and two sides non-parallel, with the parallel sides called the bases and non-parallel sides called the legs. If the legs of a trapezoid are congruent, it is an isosceles trapezoid, and its properties include that the base angles are congruent and the diagonals bisect each other.
This lesson plan outlines teaching students how to calculate the area of a triangle. It includes objectives of stating the area formula, drawing triangles, and cooperating in activities. Procedures include reviewing triangles, motivating with an example of cutting paper, deriving and practicing the area formula of 1/2 base x height, and sample problems finding area, base or height when given other values. An evaluation assesses applying the formula to find area, base or height in word problems.
Detailed Lesson Plan (ENGLISH, MATH, SCIENCE, FILIPINO)Junnie Salud
Thanks everybody! The lesson plans presented were actually outdated and can still be improved. I was also a college student when I did these. There were minor errors but the important thing is, the structure and flow of activities (for an hour-long class) are included here. I appreciate all of your comments! Please like my fan page on facebook search for JUNNIE SALUD.
*The detailed LP for English is from Ms. Juliana Patricia Tenzasas. I just revised it a little.
For questions about education-related matters, you can directly email me at mr_junniesalud@yahoo.com
The document provides information about trapezoids and the formula to calculate the area of a trapezoid. Specifically, it defines a trapezoid as a quadrilateral with one pair of parallel sides. It then presents the formula for calculating the area of a trapezoid as (b1 + b2) x h / 2, where b1 and b2 are the two bases and h is the height. It provides four example problems to find the area of different trapezoids using the given dimensions.
Since Kevin Mitnick coined the phrase in 2002, the cybersecurity industry has been awash with the phrase 'the human factor is the weakest link’. From vendors to researchers, engineers, hackers, and journalists, we are all fond of blaming the ‘dumb users’. In this talk I argue that when we say that the ‘human being is the weakest link in cybersecurity’, not only are we telling a lie, we are inevitably setting ourselves up for a fall.
Here is the slide-by-slide Visualizing the Maximim Area of a 3-Sided Rectangular Enclosure Keynote presentation I used to create the YouTube animation explaining this concept
Prof. DiAfonso - Elementos da Comunicação e Funções da Linguagem - QuestõesDiógenes de Oliveira
Este documento avalia a aprendizagem de estudantes sobre elementos da comunicação, funções da linguagem e acentuação gráfica. Contém três textos e oito questões que abordam esses tópicos.
5.13.2 Area of Regular Polygons and Composite Shapessmiller5
- The document discusses formulas for calculating the areas of regular polygons and composite shapes. It provides formulas for finding the area of a regular polygon, equilateral triangle, and regular hexagon.
- It also explains that to find the area of a composite shape, one divides the shape into simple shapes like triangles, rectangles, trapezoids and circles. The areas of the individual shapes are then calculated and added or subtracted to find the total area.
- Examples are provided to demonstrate using the formulas and dividing composite shapes into simple shapes to calculate their total areas.
Learn how to write and read in Nalibata (National Alibata)Daniel A. Jimenez
Learn to read and write in Nalibata (National Alibata). With the adaptation of the Alphabeto using traditional Alibata alphabet, Filipinos can now reclaim unique identity by using Nalibata Script as a re-found expression!
This document provides an introduction to social media monitoring tools. It discusses the large volume of social media content created daily and the challenges this poses for organizations. As a result, many tools have emerged to help track and analyze social media conversations. However, selecting the right tool can be difficult due to the large number and variety of options available. The document aims to help PR professionals understand the benefits of social media monitoring and provide information about different tools and pricing models to assist in selecting one that meets their needs.
The document discusses a mathematic group task involving properties of trapezoids. The group members are listed as Luthfi Arya Daksa, Alif Mirciano Farizal, Nyayu Habsyah Anggraini, Galuh Arya Pangestu, and Luthfia Sabrina. It then defines a trapezoid and discusses its properties, including that it has one pair of parallel sides (except for an isosceles trapezoid) and defining different types of trapezoids based on side lengths. Formulas are provided for calculating the perimeter and area of a trapezoid.
Mathematics 9 Lesson 1-B: Solving Quadratic Equations using Quadratic FormulaJuan Miguel Palero
This powerpoint presentation discusses or talks about the topic or lesson Solving Quadratic Equations using the Quadratic Formula. It also discusses the steps in solving quadratic equations using the method of Quadratic Formula.
This lesson plan is for a 5th grade mathematics class. It involves teaching students how to solve word problems about circumference. The lesson will have students practice sample problems mentally and on paper. It then presents two example word problems for students to work through the problem solving process. Finally, students will work in groups to solve another word problem and show their work. The lesson aims to help students learn and apply the formula for circumference.
The document provides examples and steps for performing operations with fractions, including:
1) Converting between improper fractions and mixed numbers, such as changing 12/7 to 1 5/7.
2) Adding similar fractions by adding the numerators and keeping the same denominator, and dissimilar fractions by finding a common denominator.
3) Subtracting fractions using the same steps as addition, subtracting the numerators for similar fractions.
Worked examples are provided for changing forms and adding and subtracting fractions to demonstrate the procedures.
The formula for calculating the area of a trapezoid is (b1 + b2)h/2, where b1 and b2 are the two parallel bases and h is the height or perpendicular distance between the bases. Several examples are given applying this formula to find the areas of different trapezoids where the dimensions are provided. The areas of two trapezoids are added together for problems 4 and 5.
The document provides examples and steps for multiplying and dividing decimals by 10, 100, and other decimals. It explains that when multiplying decimals by 10 or 100, you move the decimal point to the right by the number of zeros. For dividing decimals or whole numbers by decimals, you change the divisor to a whole number by moving the decimal point left, and then move the dividend's decimal point the same number of places. It includes word problems applying these concepts and an assessment with additional problems to solve.
This document contains formulas for calculating the areas, volumes, and surface areas of various 2D and 3D shapes. It includes formulas for calculating the area of triangles, parallelograms, trapezoids, circles, rhombi/kites, and regular polygons. For 3D shapes it includes formulas for calculating the volume, surface area, and lateral area of rectangular prisms, other prisms, cylinders, pyramids, and cones. It also contains the Pythagorean theorem and formulas for calculating trigonometric ratios, circumferences, and the altitude of a triangle.
Digging Deep Into Ratios and Proportional Reasoning in the Middle Grades - NC...Kyle Pearce
The document discusses proportional relationships and ratios. It provides background on a symposium hosted by the Arizona Mathematics Partnership to clarify conceptual images related to ratios and proportional relationships from the Common Core State Standards. Dick Stanley is quoted as saying the CCSS approach to proportionality through proportional relationships and the constant of proportionality is remarkable and an improvement over previous approaches using ratios and proportions.
Day 1, Session 2 - The Progression of Multiplication and DivisionKyle Pearce
The document discusses progression of multiplication and division concepts through examples of doughnuts and splitting them between classes. It uses visual representations and step-by-step working to solve word problems involving multiplying and dividing large numbers. Interactive examples are provided to reinforce concepts like area, distributive property, and setting up multi-step word problems algebraically.
Day 1, Session 1 - The Progression of Counting and Quantity - Sudbury Catholi...Kyle Pearce
Slide deck from Sudbury Catholic District School Board (SCDSB) on the Progression of Counting and Quantity during our morning of learning on August 23rd, 2017.
The Life of a Suzukian Mathematician! | Dr. D. Suzuki Public School Parent Ma...Kyle Pearce
The Life of a Suzukian Mathematician! was a morning dedicated to engaging parents in the mathematics education of their children. We spent the morning doing a presentation and visiting math classrooms at Dr. D Suzuki Public School from the GECDSB in Windsor, Ontario Canada.
Making Math Moments That Matter - OAME 2017 PresentationKyle Pearce
What makes a memorable math moment?
Is it a real world task? Is it relevant to your students? Is it media-rich or delivered in 3 acts?
We believe it is much more than that.
Join Jon Orr and Kyle Pearce to help tear apart a math lesson to uncover the components that lead to more memorable math moments during each class.
OTF Connect - Making Connections Between Proportional Thinking and Fractional...Kyle Pearce
OTF Connect - Making Connections Between Proportional Thinking and Fractional Thinking. Webinar for Ontario Teachers Federation delivered December 2016.
SERCC - Making Math Contextual, Visual and ConcreteKyle Pearce
The document discusses strategies for making math more engaging for students in grades 7-12. It notes that traditional math class focuses on procedures, examples, and homework, which can disengage students. The document advocates for a vision of math education that is contextual, visual, concrete and builds connections. It provides examples of using story problems and modeling to make math more relevant and understandable for students. The goal is to increase student engagement, confidence and success in math.
OTF Connect - Exploring The Progression of Proportional Reasoning From K-9Kyle Pearce
Ontario Teachers Federation (OTF) Connect Webinar Session - Exploring the Progression of Proportional Reasoning From K-9. Delivered on Wednesday October 26th, 2016.
GECDSB Mathematics Learning Teams (MLT) Session #1Kyle Pearce
This is the slide deck from the Greater Essex County District School Board (GECDSB) Mathematics Learning Teams (MLT) Session #1 held during the week of October 17th to 21st, 2016.
2016 05-25- HPEDSB Making Math Contextual, Visual and ConcreteKyle Pearce
Making Math Contextual, Visual and Concrete Full Day Workshop with Hastings Prince Edward District School Board in Belleville, Ontario. Presentation took place in May 2016.
2015-16 Middle Years Collaborative Inquiry (MYCI) Project Session #3Kyle Pearce
2015-16 Middle Years Collaborative Inquiry (MYCI) Project Session #3 Slide Deck for the Greater Essex County District School Board (GECDSB). Presented on Friday May 13th, 2016.
GECDSB Subject Specific PD - Gamifying Formative Assessment With Knowledgehoo...Kyle Pearce
This document discusses gamifying formative assessment with Knowledgehook gameshow. It provides information on various topics related to professional development including mathematics, student success initiatives, and educational Twitter accounts to follow. Key individuals from the school board are also listed. The rest of the document consists of slides from a presentation discussing balancing new and traditional teaching methods, conceptual vs procedural understanding in math, the school board's math vision framework, and the four stages of learning mastery.
OTF Connect Webinar - Exploring Proportional Reasoning Through a 4-Part Math ...Kyle Pearce
Ontario Teachers Federation (OTF) Connect Webinar - Exploring Proportional Reasoning Through a 4-Part Math Lesson Slide Deck.
Delivered on February 2nd, 2015 via webinar.
OTF Connect Webinar - Exploring Measurement and the 4-Part Math LessonKyle Pearce
Ontario Teachers Federation (OTF) Connect Webinar Session: Exploring Measurement and the 4-Part Math Lesson Slide Deck. Delivered via webinar on March 9th, 2015.
OTF Connect Webinar - Connecting the 4-Part Math Lesson to Number Sense and A...Kyle Pearce
The document outlines a 4-part math lesson on number sense and algebra. It begins by introducing the concept of distributing multiplication with unknown variables. Examples are shown of distributing terms like 14x and 6x. The goal is to rewrite expressions in fully distributed form, like 6(x)(4) + 6(x)(4). This helps demonstrate how to manipulate algebraic expressions before students encounter more complex problems.
OTF Connect Webinar - Making Math Student Centred Through Inquiry-Based Inter...Kyle Pearce
The document discusses making math education more student-centered through the use of inquiry-based interactive tasks. It promotes using visual and concrete examples to build understanding and connections between math concepts. Tasks should spark student inquiry and lead to consolidation of learning. Resources like 3 Act Math tasks on iTunes U and interactive books created with iBooks Author can support this approach.
Andreas Schleicher presents PISA 2022 Volume III - Creative Thinking - 18 Jun...EduSkills OECD
Andreas Schleicher, Director of Education and Skills at the OECD presents at the launch of PISA 2022 Volume III - Creative Minds, Creative Schools on 18 June 2024.
Information and Communication Technology in EducationMJDuyan
(𝐓𝐋𝐄 𝟏𝟎𝟎) (𝐋𝐞𝐬𝐬𝐨𝐧 2)-𝐏𝐫𝐞𝐥𝐢𝐦𝐬
𝐄𝐱𝐩𝐥𝐚𝐢𝐧 𝐭𝐡𝐞 𝐈𝐂𝐓 𝐢𝐧 𝐞𝐝𝐮𝐜𝐚𝐭𝐢𝐨𝐧:
Students will be able to explain the role and impact of Information and Communication Technology (ICT) in education. They will understand how ICT tools, such as computers, the internet, and educational software, enhance learning and teaching processes. By exploring various ICT applications, students will recognize how these technologies facilitate access to information, improve communication, support collaboration, and enable personalized learning experiences.
𝐃𝐢𝐬𝐜𝐮𝐬𝐬 𝐭𝐡𝐞 𝐫𝐞𝐥𝐢𝐚𝐛𝐥𝐞 𝐬𝐨𝐮𝐫𝐜𝐞𝐬 𝐨𝐧 𝐭𝐡𝐞 𝐢𝐧𝐭𝐞𝐫𝐧𝐞𝐭:
-Students will be able to discuss what constitutes reliable sources on the internet. They will learn to identify key characteristics of trustworthy information, such as credibility, accuracy, and authority. By examining different types of online sources, students will develop skills to evaluate the reliability of websites and content, ensuring they can distinguish between reputable information and misinformation.
Creative Restart 2024: Mike Martin - Finding a way around “no”Taste
Ideas that are good for business and good for the world that we live in, are what I’m passionate about.
Some ideas take a year to make, some take 8 years. I want to share two projects that best illustrate this and why it is never good to stop at “no”.
Brand Guideline of Bashundhara A4 Paper - 2024khabri85
It outlines the basic identity elements such as symbol, logotype, colors, and typefaces. It provides examples of applying the identity to materials like letterhead, business cards, reports, folders, and websites.
How to Download & Install Module From the Odoo App Store in Odoo 17Celine George
Custom modules offer the flexibility to extend Odoo's capabilities, address unique requirements, and optimize workflows to align seamlessly with your organization's processes. By leveraging custom modules, businesses can unlock greater efficiency, productivity, and innovation, empowering them to stay competitive in today's dynamic market landscape. In this tutorial, we'll guide you step by step on how to easily download and install modules from the Odoo App Store.