Presenation originally wrtten to support the teaching of OCR GCSE Mathematics Module 6, chapter 1: Using a calculator effectively.
BIDMAS/BODMAS (PEMDAS) and negative numbers.
The document discusses subtracting integers using number lines, algebra tiles, and the rule for subtracting integers. It provides examples of subtracting integers with each method and asks students to practice subtracting integers using the different approaches. The document also includes a section connecting subtracting integers to concepts of poverty, hunger, and righteousness from the Beatitudes in the Gospel of Matthew.
This document provides information and examples about integer operations:
- Addition of integers follows the same rules as normal addition, such as 20 + 10 = 30 and -40 + -60 = -100.
- Subtraction of integers is performed similarly to addition, such as -3 - 7 = -10 and 15 - 9 = 6.
- When multiplying integers, the product is positive if the signs are the same and negative if the signs are different, exemplified as -2 ร 6 = -12 and 2 ร -3 = -6.
- For division of integers, the quotient is positive if the signs are the same and negative if the signs are different, with examples like 12 รท -4 =
This document provides a lesson on decimals, place value, and operations with decimals. It includes examples of writing decimals in word form, filling in place value charts, writing numbers given place value positions, and ordering and comparing decimal numbers. Students are asked to perform operations like addition and multiplication with decimals. The document aims to build mastery of decimals, place value, and related skills.
The document discusses properties of real numbers. It defines real numbers and distinguishes between rational and irrational numbers. Rational numbers can be expressed as ratios of integers, while irrational numbers have non-terminating, non-repeating decimals. It also outlines relationships between subsets of real numbers and properties that real number operations satisfy, such as commutativity, associativity, identities, inverses, and distribution.
The document provides step-by-step instructions for solving basic addition and subtraction equations. It begins by explaining how to isolate the variable by performing the inverse operation to both sides of the equation. Several examples are worked through, showing how to draw a line to separate the equation, perform the operation to both sides, then check the solution. It emphasizes the importance of checking work and provides additional tips for eliminating double signs when variables are combined with addition or subtraction.
This document provides an overview of fractions, decimals, and percentages. It explains how to convert between the different representations and compare their values. Key points covered include:
- Fractions represent a part over a whole
- To convert a fraction to a percentage, express it with a denominator of 100
- To convert a percentage to a fraction, write it as a fraction over 100
- To write a decimal as a percentage, multiply it by 100 and add the percent sign
- Fractions, decimals, and percentages can be compared by first converting them to the same representation (e.g. fractions over 100) and then comparing their values.
This document discusses addition and subtraction of integers using two-colored counters. It provides examples of representing integer addition and subtraction problems using red and yellow counters to model positive and negative numbers. Rules for adding and subtracting integers with the same sign or different signs are explained. An example problem about the distance between a submarine and airplane is worked out to demonstrate subtracting a negative number by adding its additive inverse. Finally, an evaluation activity called FACEing MATH is described that has students answer math questions to complete drawings of faces.
The document discusses subtracting integers using number lines, algebra tiles, and the rule for subtracting integers. It provides examples of subtracting integers with each method and asks students to practice subtracting integers using the different approaches. The document also includes a section connecting subtracting integers to concepts of poverty, hunger, and righteousness from the Beatitudes in the Gospel of Matthew.
This document provides information and examples about integer operations:
- Addition of integers follows the same rules as normal addition, such as 20 + 10 = 30 and -40 + -60 = -100.
- Subtraction of integers is performed similarly to addition, such as -3 - 7 = -10 and 15 - 9 = 6.
- When multiplying integers, the product is positive if the signs are the same and negative if the signs are different, exemplified as -2 ร 6 = -12 and 2 ร -3 = -6.
- For division of integers, the quotient is positive if the signs are the same and negative if the signs are different, with examples like 12 รท -4 =
This document provides a lesson on decimals, place value, and operations with decimals. It includes examples of writing decimals in word form, filling in place value charts, writing numbers given place value positions, and ordering and comparing decimal numbers. Students are asked to perform operations like addition and multiplication with decimals. The document aims to build mastery of decimals, place value, and related skills.
The document discusses properties of real numbers. It defines real numbers and distinguishes between rational and irrational numbers. Rational numbers can be expressed as ratios of integers, while irrational numbers have non-terminating, non-repeating decimals. It also outlines relationships between subsets of real numbers and properties that real number operations satisfy, such as commutativity, associativity, identities, inverses, and distribution.
The document provides step-by-step instructions for solving basic addition and subtraction equations. It begins by explaining how to isolate the variable by performing the inverse operation to both sides of the equation. Several examples are worked through, showing how to draw a line to separate the equation, perform the operation to both sides, then check the solution. It emphasizes the importance of checking work and provides additional tips for eliminating double signs when variables are combined with addition or subtraction.
This document provides an overview of fractions, decimals, and percentages. It explains how to convert between the different representations and compare their values. Key points covered include:
- Fractions represent a part over a whole
- To convert a fraction to a percentage, express it with a denominator of 100
- To convert a percentage to a fraction, write it as a fraction over 100
- To write a decimal as a percentage, multiply it by 100 and add the percent sign
- Fractions, decimals, and percentages can be compared by first converting them to the same representation (e.g. fractions over 100) and then comparing their values.
This document discusses addition and subtraction of integers using two-colored counters. It provides examples of representing integer addition and subtraction problems using red and yellow counters to model positive and negative numbers. Rules for adding and subtracting integers with the same sign or different signs are explained. An example problem about the distance between a submarine and airplane is worked out to demonstrate subtracting a negative number by adding its additive inverse. Finally, an evaluation activity called FACEing MATH is described that has students answer math questions to complete drawings of faces.
- The document discusses proportional relationships between distance and time when speed is constant. It provides examples of using ratios, proportions, and linear equations to solve problems about distance and time given average or constant speed.
- Key concepts covered include defining average speed, identifying when constant speed can be assumed to use proportions, and writing linear equations relating distance and time under conditions of constant speed.
- Students are encouraged to practice basic ratio and proportion skills in preparation for working on proportional relationship word problems over two class periods.
The document discusses square roots and how to estimate them to varying degrees of precision. It defines the principal root as the positive square root of a number. It provides examples of perfect squares and their roots. It explains that irrational numbers are those that cannot be expressed as a ratio of integers, like ฯ. The document then gives steps to estimate square roots to the nearest tenths or hundredths place by considering the closest perfect squares before and after the given number.
Multiplying Polynomials: Two BinomialsJoey Valdriz
ย
This document contains notes from a mathematics lesson on multiplying polynomials. The key points covered are:
1. The learner recalls the laws of exponents and multiplies two binomials.
2. Examples are provided of multiplying polynomials using algebra tiles, the distributive property, the box method, and FOIL (First, Outer, Inner, Last).
3. Practice problems are given for students to multiply different binomial expressions.
The document discusses ratios and provides examples using Lucky Charms cereal. It states there are 287 marshmallow pieces and 2,583 oat pieces in one box of Lucky Charms. This ratio of marshmallows to oats can be written in three ways: as a fraction, using the word "to", or using a colon. The document also discusses writing ratios in simplest form and explaining their meanings.
Lesson plan on Linear inequalities in two variablesLorie Jane Letada
ย
This document contains a semi-detailed lesson plan for a math class on linear inequalities in two variables. The lesson plan outlines intended learning outcomes, learning content including subject matter and reference materials, learning experiences including sample math word problems and explanations of key concepts, an evaluation through an online quiz, and an assignment for students to create a budget proposal applying their understanding of linear inequalities.
Adding and subtracting rational expressionsDawn Adams2
ย
Using rules for fractions, rational expressions can be added and subtracted by finding common denominators. To find the common denominator, we find the least common multiple (LCM) of the denominators. With polynomials, the LCM will contain all factors of each denominator. We can then convert the fractions to equivalent forms using the LCM as the new denominator before combining like terms to evaluate the expression. Special cases may involve fractions with understood denominators of 1 or similar but non-equal denominators that can be made equal through factoring.
The document discusses the method of mathematical induction. It is used to verify infinitely many related statements without checking each one individually. As an example, it examines the statement that the sum of the first n odd numbers equals n^2 for all natural numbers n. It shows the base case of this statement is true, and if the statement is true for an arbitrary n, it must also be true for n+1. Therefore, by the principle of mathematical induction, the statement is true for all natural numbers n.
This document provides an introduction to decimals for students. It begins with an overview of decimals and then discusses how to write, read, and compare decimal values. Examples are provided such as writing amounts of money in decimal form. The document explains place value of decimals and how to use symbols like tenths, hundredths and thousandths. Students are given opportunities to practice writing, reading and comparing decimal values through interactive exercises.
The document discusses functional notation and evaluating functions. Some key points:
- Functional notation f(x) represents a variable y in an equation, like writing f(x)=2x+6 for the equation y=2x+6.
- To evaluate a function, substitute the given value for x into the function. For example, if f(x)=2x+6 then f(3)=2(3)+6=12.
- Examples are given of evaluating various functions for different values of x.
This document discusses linear functions and how to represent them using equations, graphs, and tables of values. It defines a linear function as one that can be written in the form f(x) = mx + b, where m is the slope and b is the y-intercept. Examples are provided to illustrate determining the slope and y-intercept from an equation and representing a linear function using an equation, table of values, or graph. It is explained that a linear function will produce a straight line on a graph and have constant differences in x- and y-coordinates in its table of values.
To estimate square roots:
- Recall perfect square numbers like 4, 9, 16, 25, etc.
- The square root of a number is between the greatest smaller perfect square number and the smallest greater perfect square number.
- Examples show estimating the square roots of 32, 129, and 875 by identifying the closest perfect squares above and below.
Simplification of Fractions and Operations on FractionsVer Louie Gautani
ย
The document discusses various operations involving fractions, including simplifying, converting between mixed and improper fractions, multiplying, dividing, adding, and subtracting fractions. It provides examples of performing each operation step-by-step and simplifying the resulting fraction. Rules for working with fractions are reviewed and examples of applying the rules are shown.
This document discusses rational numbers and different types of fractions including mixed numbers, improper fractions, adding, subtracting, multiplying, and dividing fractions. It explains that rational numbers are numbers that can be made by dividing one integer by another. Fractions have a numerator and denominator and can be added or subtracted by finding a common denominator. To multiply fractions, you multiply the numerators and denominators. To divide fractions, you keep the first fraction the same, change the operation to divide, and flip the second fraction to its inverse.
The document discusses completing a BSN lesson, MAP testing continuing, and no live class being held that day. It also covers lessons on negative exponents, including determining patterns from tables, evaluating expressions with negative exponents, and simplifying those expressions using properties of exponents. The agenda reviews rules for exponents and evaluates expressions with negative exponents, working through an example of 35 โ 3-5 and explaining how to change a negative exponent to a positive using the reciprocal. It concludes by instructing students to complete the BSN lesson, use other resources as needed, and get help if required.
The document discusses the coordinate plane and how to plot points on it. It defines key terms like axes, quadrants, and ordered pairs. The coordinate plane uses perpendicular x and y axes to locate all points, with the origin at their intersection. Ordered pairs (x,y) indicate points by listing the x-coordinate first, followed by the y-coordinate.
This presentation is an introduction to Exponents. Students will begin with repeated multiplication. They will then be reminded about a base an exponent. They will learn the term Exponential Form.
The document defines and provides examples of dilations and scale factors. It explains that a dilation changes the size but not the shape of a figure. The scale factor is the ratio of the image to the preimage, where a scale factor greater than 1 enlarges the figure and less than 1 shrinks it. Examples are given of finding scale factors, determining new dimensions after a dilation, finding coordinates of dilated points and vertices, and dilating triangles and other figures centered at various points using different scale factors.
Scientific notation is used to express very large and very small numbers in a way that makes them easier to work with. It writes a number as the product of a coefficient and a power of 10, where the coefficient is between 1 and 10 and the exponent indicates how many places the decimal is moved. Examples show how scientific notation can be used to write the mass of a gold atom or the number of hydrogen atoms in a gram of hydrogen in a more manageable way. The document then provides steps for converting a number to scientific notation and examples of performing this conversion.
The document discusses basic rules of algebra. It recaps terms like algebraic expressions and equations from the previous class. It then explains that the rules of addition and subtraction of algebraic terms are similar to numerical addition and subtraction, but the terms must be "like" terms, meaning they have the same variables. Unlike terms, with different variables, cannot be added or subtracted. It provides several examples to illustrate how to combine like terms through addition and subtraction.
Additive and Multiplicative Inverse StrategyAndrea B.
ย
This document discusses two strategies for balancing mathematical equations: the additive inverse strategy and the multiplicative inverse strategy. The additive inverse strategy uses the opposite of addition, which is subtraction, to move a term to the other side of the equation. The multiplicative inverse strategy uses the opposite of multiplication, which is division, to move part of a term to the other side of the equation. Both strategies aim to isolate the variable on one side of the equation so that it can be solved for. Examples are provided to demonstrate how to apply each strategy.
This document provides instructions for finding the perimeter of a triangle using the distance formula. It defines perimeter as the distance around a shape and explains it is calculated by adding the lengths of the sides. As an example, it gives the coordinates of points A, B, and C of triangle ABC and shows how to use the distance formula to calculate the lengths of sides AB and BC. It then prompts the reader to find the length of side AC and provides the steps to add the side lengths and calculate the perimeter of triangle ABC as 18.8.
This document summarizes the history and development of scientific calculators. It discusses how the first calculators used vacuum tubes and transistors in the 1940s-1950s. The first pocket calculator was introduced in 1970 and used integrated circuits. Programmable calculators appeared in the mid-1960s and the first programmable pocket calculator was the HP-65 in 1974. The document also outlines the basic functions of calculators, improvements over time including the introduction of LCD displays, applications of calculators in education, and potential future modifications like touchscreens.
- The document discusses proportional relationships between distance and time when speed is constant. It provides examples of using ratios, proportions, and linear equations to solve problems about distance and time given average or constant speed.
- Key concepts covered include defining average speed, identifying when constant speed can be assumed to use proportions, and writing linear equations relating distance and time under conditions of constant speed.
- Students are encouraged to practice basic ratio and proportion skills in preparation for working on proportional relationship word problems over two class periods.
The document discusses square roots and how to estimate them to varying degrees of precision. It defines the principal root as the positive square root of a number. It provides examples of perfect squares and their roots. It explains that irrational numbers are those that cannot be expressed as a ratio of integers, like ฯ. The document then gives steps to estimate square roots to the nearest tenths or hundredths place by considering the closest perfect squares before and after the given number.
Multiplying Polynomials: Two BinomialsJoey Valdriz
ย
This document contains notes from a mathematics lesson on multiplying polynomials. The key points covered are:
1. The learner recalls the laws of exponents and multiplies two binomials.
2. Examples are provided of multiplying polynomials using algebra tiles, the distributive property, the box method, and FOIL (First, Outer, Inner, Last).
3. Practice problems are given for students to multiply different binomial expressions.
The document discusses ratios and provides examples using Lucky Charms cereal. It states there are 287 marshmallow pieces and 2,583 oat pieces in one box of Lucky Charms. This ratio of marshmallows to oats can be written in three ways: as a fraction, using the word "to", or using a colon. The document also discusses writing ratios in simplest form and explaining their meanings.
Lesson plan on Linear inequalities in two variablesLorie Jane Letada
ย
This document contains a semi-detailed lesson plan for a math class on linear inequalities in two variables. The lesson plan outlines intended learning outcomes, learning content including subject matter and reference materials, learning experiences including sample math word problems and explanations of key concepts, an evaluation through an online quiz, and an assignment for students to create a budget proposal applying their understanding of linear inequalities.
Adding and subtracting rational expressionsDawn Adams2
ย
Using rules for fractions, rational expressions can be added and subtracted by finding common denominators. To find the common denominator, we find the least common multiple (LCM) of the denominators. With polynomials, the LCM will contain all factors of each denominator. We can then convert the fractions to equivalent forms using the LCM as the new denominator before combining like terms to evaluate the expression. Special cases may involve fractions with understood denominators of 1 or similar but non-equal denominators that can be made equal through factoring.
The document discusses the method of mathematical induction. It is used to verify infinitely many related statements without checking each one individually. As an example, it examines the statement that the sum of the first n odd numbers equals n^2 for all natural numbers n. It shows the base case of this statement is true, and if the statement is true for an arbitrary n, it must also be true for n+1. Therefore, by the principle of mathematical induction, the statement is true for all natural numbers n.
This document provides an introduction to decimals for students. It begins with an overview of decimals and then discusses how to write, read, and compare decimal values. Examples are provided such as writing amounts of money in decimal form. The document explains place value of decimals and how to use symbols like tenths, hundredths and thousandths. Students are given opportunities to practice writing, reading and comparing decimal values through interactive exercises.
The document discusses functional notation and evaluating functions. Some key points:
- Functional notation f(x) represents a variable y in an equation, like writing f(x)=2x+6 for the equation y=2x+6.
- To evaluate a function, substitute the given value for x into the function. For example, if f(x)=2x+6 then f(3)=2(3)+6=12.
- Examples are given of evaluating various functions for different values of x.
This document discusses linear functions and how to represent them using equations, graphs, and tables of values. It defines a linear function as one that can be written in the form f(x) = mx + b, where m is the slope and b is the y-intercept. Examples are provided to illustrate determining the slope and y-intercept from an equation and representing a linear function using an equation, table of values, or graph. It is explained that a linear function will produce a straight line on a graph and have constant differences in x- and y-coordinates in its table of values.
To estimate square roots:
- Recall perfect square numbers like 4, 9, 16, 25, etc.
- The square root of a number is between the greatest smaller perfect square number and the smallest greater perfect square number.
- Examples show estimating the square roots of 32, 129, and 875 by identifying the closest perfect squares above and below.
Simplification of Fractions and Operations on FractionsVer Louie Gautani
ย
The document discusses various operations involving fractions, including simplifying, converting between mixed and improper fractions, multiplying, dividing, adding, and subtracting fractions. It provides examples of performing each operation step-by-step and simplifying the resulting fraction. Rules for working with fractions are reviewed and examples of applying the rules are shown.
This document discusses rational numbers and different types of fractions including mixed numbers, improper fractions, adding, subtracting, multiplying, and dividing fractions. It explains that rational numbers are numbers that can be made by dividing one integer by another. Fractions have a numerator and denominator and can be added or subtracted by finding a common denominator. To multiply fractions, you multiply the numerators and denominators. To divide fractions, you keep the first fraction the same, change the operation to divide, and flip the second fraction to its inverse.
The document discusses completing a BSN lesson, MAP testing continuing, and no live class being held that day. It also covers lessons on negative exponents, including determining patterns from tables, evaluating expressions with negative exponents, and simplifying those expressions using properties of exponents. The agenda reviews rules for exponents and evaluates expressions with negative exponents, working through an example of 35 โ 3-5 and explaining how to change a negative exponent to a positive using the reciprocal. It concludes by instructing students to complete the BSN lesson, use other resources as needed, and get help if required.
The document discusses the coordinate plane and how to plot points on it. It defines key terms like axes, quadrants, and ordered pairs. The coordinate plane uses perpendicular x and y axes to locate all points, with the origin at their intersection. Ordered pairs (x,y) indicate points by listing the x-coordinate first, followed by the y-coordinate.
This presentation is an introduction to Exponents. Students will begin with repeated multiplication. They will then be reminded about a base an exponent. They will learn the term Exponential Form.
The document defines and provides examples of dilations and scale factors. It explains that a dilation changes the size but not the shape of a figure. The scale factor is the ratio of the image to the preimage, where a scale factor greater than 1 enlarges the figure and less than 1 shrinks it. Examples are given of finding scale factors, determining new dimensions after a dilation, finding coordinates of dilated points and vertices, and dilating triangles and other figures centered at various points using different scale factors.
Scientific notation is used to express very large and very small numbers in a way that makes them easier to work with. It writes a number as the product of a coefficient and a power of 10, where the coefficient is between 1 and 10 and the exponent indicates how many places the decimal is moved. Examples show how scientific notation can be used to write the mass of a gold atom or the number of hydrogen atoms in a gram of hydrogen in a more manageable way. The document then provides steps for converting a number to scientific notation and examples of performing this conversion.
The document discusses basic rules of algebra. It recaps terms like algebraic expressions and equations from the previous class. It then explains that the rules of addition and subtraction of algebraic terms are similar to numerical addition and subtraction, but the terms must be "like" terms, meaning they have the same variables. Unlike terms, with different variables, cannot be added or subtracted. It provides several examples to illustrate how to combine like terms through addition and subtraction.
Additive and Multiplicative Inverse StrategyAndrea B.
ย
This document discusses two strategies for balancing mathematical equations: the additive inverse strategy and the multiplicative inverse strategy. The additive inverse strategy uses the opposite of addition, which is subtraction, to move a term to the other side of the equation. The multiplicative inverse strategy uses the opposite of multiplication, which is division, to move part of a term to the other side of the equation. Both strategies aim to isolate the variable on one side of the equation so that it can be solved for. Examples are provided to demonstrate how to apply each strategy.
This document provides instructions for finding the perimeter of a triangle using the distance formula. It defines perimeter as the distance around a shape and explains it is calculated by adding the lengths of the sides. As an example, it gives the coordinates of points A, B, and C of triangle ABC and shows how to use the distance formula to calculate the lengths of sides AB and BC. It then prompts the reader to find the length of side AC and provides the steps to add the side lengths and calculate the perimeter of triangle ABC as 18.8.
This document summarizes the history and development of scientific calculators. It discusses how the first calculators used vacuum tubes and transistors in the 1940s-1950s. The first pocket calculator was introduced in 1970 and used integrated circuits. Programmable calculators appeared in the mid-1960s and the first programmable pocket calculator was the HP-65 in 1974. The document also outlines the basic functions of calculators, improvements over time including the introduction of LCD displays, applications of calculators in education, and potential future modifications like touchscreens.
- A scientific calculator is an invaluable tool for learning math and science that can help solve complex problems, as they provide functions like trigonometric, exponential, logarithmic, and statistical operations.
- Scientific calculators use different input methods, like algebraic notation where terms are entered in order of appearance or reverse polish notation (RPN) where values are entered before the operator.
- It is important to learn the functions and input methods of your specific scientific calculator by referring to the owner's manual. Understanding how to properly use the calculator ensures accurate results.
The document provides a 3-page summary of the operation of a scientific calculator:
- It describes the key layout, display formats, and basic arithmetic functions.
- It explains how to enter values, use trigonometric and other mathematical functions, and store values in the calculator's memory.
- Examples are provided throughout to illustrate how to perform calculations for tasks like conversions between angular units, exponential functions, permutations, and time calculations.
This document provides a summary of a scientific calculator project. It includes sections on the introduction, basic functions, proposed system description, system requirements, system design, source code, testing, and future scope. The introduction describes the calculator as a fully featured scientific calculator implemented with proper operator precedence and various mathematical functions. The basic functions section lists the addition, subtraction, multiplication, division, and other core functions included. The proposed system section outlines improving user friendliness, restricting access to data, and helping users view privileges. It also lists some key functions to be provided like viewing, adding, deleting and modifying data. The system requirements include operating system, language, processor, RAM, and hard disk needs.
The document provides 3 examples of perimeter calculations: 1) Finding the perimeter of a triangle with sides of 5, 9, and 11 cm, which equals 25 cm. 2) Calculating the perimeter of a rectangle and two similar squares shown in a diagram, which equals 34 cm. 3) Determining the cost of barbed wire to fence a 120m x 120m square garden, which is RM5280 using 480m of fencing at RM11 per meter.
The document describes the goals of a project to design a dual-core superscalar computer system. It involves:
1. Designing each core with two pipelines, buffer registers at the beginning and end of each pipeline, and a finite state machine to control the instruction cycle.
2. Duplicating the design of the first core to create a second identical core.
3. Adding a shared memory for the cores to communicate through and share data.
4. Implementing new instructions using the wait state of the pipelines that allow writing to and reading from the shared memory and a general purpose register.
5. Creating a test methodology to demonstrate the full functioning of the dual-core superscal
Este documento describe las funciones y capacidades de la herramienta Actividad Calculadora del programa Una Laptop por Niรฑo. La calculadora permite realizar cรกlculos simples y complejos, y cuenta con funciones como รกlgebra, trigonometrรญa, lรณgica booleana y constantes. El documento explica cรณmo usar, guardar y editar trabajos en la calculadora.
La calculadora de Windows es una aplicaciรณn preinstalada que permite realizar cรกlculos aritmรฉticos bรกsicos y avanzados. Existen modos estรกndar, cientรญfico y de programador, cada uno con funciones especรญficas como logaritmos, estadรญsticas y conversiones de unidades. Para acceder a la calculadora, los usuarios deben buscarla en el menรบ Inicio o escribir su nombre en la barra de bรบsqueda y seleccionarla de la lista de resultados.
Utilizando la calculadora cientifica PARTE 1Adรกn Godoy
ย
La utilizaciรณn de la calculadora cientรญfica para calcular razones trigonomรฉtricas debe enseรฑarse con mucho cuidado. Esta presentaciรณn pretende ser de utilidad para iniciar a los alumnos en el manejo de esta herramienta tecnolรณgica.
A Computers Architecture project on Barrel shifterssvrohith 9
ย
A Barrel Shifter is a logic component that perform shift or rotate operations. Barrel shifters are applicable for digital signal processors and processors, here we designed 16-bit barrel shifter using 2X1 MUXs in Logisim simulation
El documento proporciona una breve historia del desarrollo de la calculadora y los mรฉtodos de cรกlculo a travรฉs de los aรฑos, desde el uso de dedos y รกbacos en la antigรผedad hasta el desarrollo de la calculadora electrรณnica moderna en el siglo XX. Tambiรฉn discute algunos pros y contras del uso de calculadoras, como la creaciรณn de dependencia y pรฉrdida del cรกlculo mental frente a su capacidad de facilitar cรกlculos complejos. Finalmente, presenta algunos ejemplos y problemas de cรกlculo para demostrar el uso de
Este documento proporciona instrucciones sobre el uso de la calculadora Casio fx-350 ES. Explica las operaciones bรกsicas como suma, resta, multiplicaciรณn y divisiรณn, asรญ como funciones mรกs avanzadas como potencias, raรญces, fracciones, notaciรณn cientรญfica, logaritmos, exponenciales y funciones trigonomรฉtricas directas e inversas. El documento contiene ejemplos detallados de cรณmo realizar cada tipo de cรกlculo utilizando las teclas de la calculadora.
Password protected personal diary reportMoueed Ahmed
ย
The document is a password protected personal diary program code written in C. It includes functions for adding, viewing, editing, and deleting records from the diary. The main function acts as the driver code and displays a menu for the user to select these options. Additional functions handle password validation, reading/writing data to binary files, and performing the necessary operations for each diary record option. Header files like stdio.h, string.h are included for input/output and string handling functionality.
Presentaciรณn bรกsica del uso de Calculadora Cientรญfica para la aplicaciรณn de cรกlculos de estadรญstica descriptiva bรกsica: media, desviaciรณn estรกndar. Me acabo de dar cuenta que en la presentaciรณn no estรกn funcionando los .gif, por lo tanto no se reproduce la animaciรณn en la calculadora. Favor me avisan si estรกn interesados les puedo enviar el archivo.
Este documento describe el uso bรกsico de una calculadora, incluyendo los modos, botones AC y DEL/C, y provee ejercicios para practicar operaciones matemรกticas usando una calculadora. Los ejercicios incluyen dividir manzanas entre niรฑos y resolver preguntas sobre datos demogrรกficos usando la calculadora para sumas, restas y divisiones.
Este documento resume la historia y el uso de las calculadoras. Comenzรณ con รกbacos en la antigua China y Egipto, luego evolucionรณ a reglas de cรกlculo en el siglo XVII. La primera calculadora digital fue inventada por Blaise Pascal en 1642 llamada Pascalina. Hoy en dรญa, las calculadoras cientรญficas pueden realizar funciones avanzadas, mientras que las de bolsillo son pequeรฑas y portรกtiles. Aunque inicialmente hubo resistencia, ahora las calculadoras se usan comรบnmente como recursos educativos.
Este documento presenta el desarrollo de un proyecto de una calculadora simple realizado por dos estudiantes. Incluye la introducciรณn del proyecto, definiciรณn del tema, planteamiento del problema, justificaciรณn, objetivos, marco teรณrico, metodologรญa, encuestas realizadas, creaciรณn de la aplicaciรณn, cronograma y conclusiรณn.
Charles Roady has experience in programming, teaching technical skills, and working in food service. He has a Bachelor's degree in Physics from the University of California Berkeley with a minor in Computer Science. He is proficient in Python, Java, C, C++, C#, HTML, SQL and other languages. His most recent role was as a Technical Trainer at Kibo where he taught software engineering and client development skills. He is looking for an engaging position in the software industry applying his programming and analytical skills.
Este documento presenta las declaraciones de variables necesarias para crear una calculadora bรกsica. Primero, se crean botones para las operaciones fundamentales (suma, resta, multiplicaciรณn, divisiรณn) convirtiendo la variable "nรบmero1" a tipo double. Luego, se agregan funcionalidades adicionales como raรญz cuadrada, potencia y multiplicaciรณn por ฯ a travรฉs de mรกs botones y cรณdigo. Finalmente, se explican las variables y cรณdigo utilizados para mostrar nรบmeros, realizar cรกlculos con el botรณn "=" y borrar valores.
This document provides instructions for using the power and root keys on a scientific calculator. It explains that the x^2 key is used to calculate squares, the y^x key is used to calculate powers or exponents, and the โ key is used to calculate square roots. The document includes examples of calculations and tests the reader's understanding by having them calculate various powers and roots.
The document discusses the order of operations in mathematics. It explains that the order of operations (PEMDAS) - Parentheses, Exponents, Multiplication, Division, Addition, Subtraction - provides rules for which operations to perform first in a mathematical expression without changing the result. It provides examples of evaluating expressions using the proper order of operations and also provides links to online games for practicing order of operations skills.
1. The document provides instructions for a multi-step math problem involving picking numbers, operations, and years. It has the reader choose numbers and perform calculations like multiplication, addition, subtraction on them.
2. Key steps include: picking a number 2-9, multiplying by 2 and adding 5, then multiplying the result by 50 and adding or subtracting based on whether the reader's birthday has passed for the current year.
3. The final step is to subtract the 4 digit number from the year the reader was born. The document then has some other random math questions and word problems involving indices.
This document outlines instructional strategies for teaching multiplication and division of whole numbers, decimals, and fractions using the concrete-representational-abstract (CRA) approach. It provides examples of using physical objects, drawings, and standard algorithms to develop conceptual understanding at each stage. The CRA approach is demonstrated for topics like multiplying large whole numbers, dividing with decimals, and solving word problems involving fractions.
1. The document provides instructions on how to use a non-programmable Casio fx-991MS scientific calculator to perform various mathematical calculations and operations on matrices.
2. It describes how to enter values and solve systems of linear equations with 2 or 3 unknowns, as well as how to solve polynomial equations up to degree 3.
3. The document also explains how to perform basic matrix operations like addition, subtraction, multiplication, determinant and inverse using the calculator's matrix mode.
Two 3rd grade geometry tasks are presented that involve patterns of squares or tiles. The first task simply asks students to determine the number of squares in the 25th arrangement, while the revised version asks students to investigate and report on the pattern. The document suggests questions teachers could ask themselves in examining student work, including the mathematical ideas explored, surprises, and implications for practice. A sample of student work is also included that provides observations about the pattern, a sketch of larger figures, methods for determining the total number of tiles, and how to convince others of the solution.
The document provides information about order of operations in math. It explains that order of operations is important to get the correct answer when a math problem contains multiple operations. It presents the mnemonic "PEMDAS" (Parentheses, Exponents, Multiplication, Division, Addition, Subtraction) as the standard order of operations. Several examples of applying order of operations to evaluate expressions are shown. The document is intended to teach students the proper order for solving expressions with multiple operations.
Objectives:
Counts the number of occurrences of an outcome in an experiment: (a) table; (b) tree diagram; (c) systematic listing; and (d) fundamental counting principle.(M8GE-IVf-g-1)
The document provides strategies for the ACT math section. It discusses pacing yourself to focus on easier questions first if running short on time. It also recommends classifying each question to determine the best approach, such as using a calculator, working backwards from answers, drawing a picture, or substituting numbers. Word problems should be solved by identifying what is given, what is asked for, and what math is required. Finally, the document advises doing a "reality check" by evaluating whether answer choices seem reasonable before selecting your answer.
The document discusses the proper order of mathematical operations known as PEMDAS. It covers absolute values, addition and subtraction of signed numbers, multiplication and division of signed numbers, and the order of operations using PEMDAS. Examples are provided to illustrate how to use PEMDAS to simplify expressions involving multiple operations. Exercises with answers are included to help readers practice applying these concepts.
This document provides an introduction and tips for working through 501 algebra questions. It begins with an introduction explaining how to use the book, which provides 501 algebra problems with step-by-step explanations. The document then provides tips for working with integers, including rules for addition, subtraction, multiplication, and division of integers. It also provides a mnemonic for the order of operations. The remainder of the document contains 20 sample algebra questions with step-by-step explanations of the solutions.
Stanford Splash Spring 2016 Basic Programming lecture introduces Yu-Sheng Chen, the instructor. Chen provides an overview of basic programming concepts like control flows, functions, and data structures. The lecture also solves sample coding problems like calculating trailing zeros in a factorial and validating parentheses to demonstrate these concepts. Complexity analysis is discussed to evaluate algorithm efficiency based on operation counts.
The document provides information about various mathematical concepts including the mean, median, mode, and range. It defines the mean as the average, which is calculated by adding all numbers in a data set and dividing by the total count. The median is defined as the middle value when the data is arranged in order. The mode is the value that occurs most frequently. The range is the difference between the highest and lowest values. Examples are given for calculating the mean of a data set.
The document describes the guess-and-check algorithm for division. It involves estimating how many times the divisor goes into the dividend and recording estimates in a side column. The estimates are then added to find the quotient. Even students with limited math facts knowledge can use this intuitive approach to find correct answers. The document also provides guidance for teachers to help students understand the process.
The document discusses significant figures and measurement uncertainty in science. It explains that only digits that are meaningful based on the precision of the measurement should be written down. It then provides examples of determining the number of significant figures in different measurements using the "Pacific-Atlantic rule". Rules for addition, subtraction, multiplication and division based on significant figures are also outlined. Finally, examples of using dimensional analysis to convert between different units are given.
This document provides instructions for the free response section of an exam consisting of 6 questions over 90 minutes. It is divided into two parts:
Part A consists of 2 questions over 30 minutes and requires the use of a graphing calculator. Part B consists of 4 questions over 60 minutes and does not allow the use of a calculator. Students may continue working on Part A during Part B but cannot use their calculator.
The document provides strategies for completing the free response questions, such as showing all work, writing clearly, and circling problems that need to be returned to later. It also specifies rules for calculator use and acceptable notation.
The document discusses the importance and applications of counting in mathematics and daily life. It provides examples of how counting is used in basic arithmetic operations like addition and multiplication. It also explains how counting is applied in business for inventory management and logistics. The key points are that counting is fundamental to verifying mathematical operations, it can be done in various units of measurement, and accuracy in counting is important for accounting of physical goods.
This document provides an introduction to negative numbers for students in Year 8 maths. It includes examples of where negative numbers are used, such as temperatures below zero and bank account balances in debt. Students are introduced to concepts like adding and subtracting negative numbers using a number line. Rules for multiplying positive and negative numbers are explained, such as a positive times a negative equals a negative, and a negative times a negative equals a positive. Students are provided practice problems to solve involving addition, subtraction, and multiplication of negative numbers.
This document outlines an activity to practice modeling and predicting values using simple linear regression. Students are asked to:
1. Record guesses and actual values for various jars of jelly beans to see how off their guesses are.
2. Use the differences between guesses and actuals to develop a formula to "correct" future guesses.
3. Apply the same process to guessing college football wins to refine their predictive model.
4. Complete tables and calculations in StatCrunch to fit linear and quadratic models to their data and evaluate which model fits best. They are asked to use the model to predict further values and evaluate residuals.
The document provides an overview and tutorial of the MathCAD software program. It discusses (1) what MathCAD is and its main functions, (2) how to open and navigate the MathCAD interface and toolbars, and (3) examples of how to enter equations, plot graphs, and perform calculations in MathCAD. The tutorial aims to explain the basic concepts and features of MathCAD to help readers learn how to use it to solve engineering and mathematics problems.
This document provides information about an upcoming school trip from a secondary school in Birley, England to Paris, France from July 19-21, 2010. It includes details about the itinerary, packing list, code of conduct, medical forms, and points of contact. 38 year 7-9 students and 5 teachers will visit sites like the Science Museum, Notre Dame, and the Eiffel Tower, staying in a hotel and taking day trips. Parents are informed about travel arrangements, activities, expectations for students, and how to stay updated during the visit.
The document discusses a STEM club activity where students will learn about tessellations by creating tiles out of clay that fit together without overlaps or gaps. It provides background on tessellations and famous artist M.C. Escher's tessellation art. The activity will have students choose a design, make clay tiles, paint them, and display their tessellation creation.
Step by step guide to adding cells/rows/columns to a spreadsheet and deleting them.
All screenshots and instructions are based on Microsoft Excel, because that's what we use with at my school.
In this unit, you will complete several tasks involving common digital skills like file management, email, spreadsheets, databases, and presentations. You will gain an OCR Level 2 National First Award in ICT, equivalent to a GCSE qualification. Specifically, you will create and manage folders; find and organize online information; send and receive emails with attachments; make a spreadsheet for music downloads; use a database to record customer details; create business documents like letters and memos; make a two-page newsletter; and develop a PowerPoint presentation with at least three slides.
Simultaneous equations are two or more equations with the same unknown variables. There are two main methods to solve simultaneous equations:
1) Using graphs - make a table of values, plot the equations on a graph, and find where the graphs intersect.
2) Using algebra - organize the equations, make coefficients equal, eliminate a variable, solve the resulting equation, substitute values back into the original equations, and check the answer. The algebraic method follows the steps of NO MESS: Organize, Make equal, Eliminate, Solve, Substitute.
Information and Communication Technology in EducationMJDuyan
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(๐๐๐ ๐๐๐) (๐๐๐ฌ๐ฌ๐จ๐ง 2)-๐๐ซ๐๐ฅ๐ข๐ฆ๐ฌ
๐๐ฑ๐ฉ๐ฅ๐๐ข๐ง ๐ญ๐ก๐ ๐๐๐ ๐ข๐ง ๐๐๐ฎ๐๐๐ญ๐ข๐จ๐ง:
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.
๐๐ข๐ฌ๐๐ฎ๐ฌ๐ฌ ๐ญ๐ก๐ ๐ซ๐๐ฅ๐ข๐๐๐ฅ๐ ๐ฌ๐จ๐ฎ๐ซ๐๐๐ฌ ๐จ๐ง ๐ญ๐ก๐ ๐ข๐ง๐ญ๐๐ซ๐ง๐๐ญ:
-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.
Gender and Mental Health - Counselling and Family Therapy Applications and In...PsychoTech Services
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A proprietary approach developed by bringing together the best of learning theories from Psychology, design principles from the world of visualization, and pedagogical methods from over a decade of training experience, that enables you to: Learn better, faster!
Elevate Your Nonprofit's Online Presence_ A Guide to Effective SEO Strategies...TechSoup
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Whether you're new to SEO or looking to refine your existing strategies, this webinar will provide you with actionable insights and practical tips to elevate your nonprofit's online presence.
CapTechTalks Webinar Slides June 2024 Donovan Wright.pptxCapitolTechU
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Slides from a Capitol Technology University webinar held June 20, 2024. The webinar featured Dr. Donovan Wright, presenting on the Department of Defense Digital Transformation.
How to Setup Default Value for a Field in Odoo 17Celine George
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In Odoo, we can set a default value for a field during the creation of a record for a model. We have many methods in odoo for setting a default value to the field.
This presentation was adapted from one that I used with my class. There is also a set of work cards, designed for students to use in groups as they work on a chapter. All the resources are available to download via www.morethanmaths.com/m6