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The document describes a tribonacci sequence and how to find the nth term of the sequence. It provides the terms up to the 13th term and asks to find the next three terms, which are 193, 355, 653. It explains that each term is the sum of the preceding three terms. The document then discusses how to represent this sequence mathematically using the recurrence formula Tn=Tn-3+Tn-2+Tn-1 to find future terms of the sequence. It also explains how to use this formula to find the number of tiles needed to construct the next figure in a sequence of square tile patterns.

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DECILE FOR UNGROUPED DATA-MOV 4 COPY.pptx

The document provides instructions for calculating deciles using the Mendenhall and Sincich formula and interpreting what different decile values represent. It includes an example of computing the third decile (D3) of test scores and interpreting what the D3 value means. Various methods for computing deciles and formulas are defined, along with how to interpret different decile values.

4th quarter-math-10

This document contains a 50-question mathematics examination covering topics like permutations, combinations, probability, and statistics. The exam asks students to identify terms, calculate outcomes of experiments and events, determine probabilities, and solve word problems involving arrangements of objects and sampling with or without replacement. It provides context that the exam was administered to 10th grade mathematics students in the Philippines and includes instructions to write answers in capital letters on a half-sheet of paper, with no erasures or superimpositions allowed.
Human: You are an expert at summarizing documents. You provide concise summaries in 3 sentences or less that provide the high level and essential information from the document. Summarize the following document. Begin your response with "[SUMMARY

Factoring Non-Perfect Square Trinomial Lesson Plan

This document contains a lesson plan for teaching factoring non-perfect trinomials in Math 8. The lesson plan outlines intended learning outcomes, learning content including subject matter and reference materials, learning experiences through various activities, an evaluation, and assignment. Students will learn to define trinomials, factor non-perfect square trinomials, and apply factoring trinomials to geometric figures through guided practice with algebra tiles and examples.

INTERPRETING MEASURE OF POSITION.pptx

This document provides information about interpreting measures of position through examples and learning tasks. It begins by welcoming students and setting objectives to recognize the connection between measures of position and their interpretations in distributions. Examples are given to interpret quartiles, deciles, and percentiles. Learning tasks then assess understanding of comparing heights and salaries based on their percentile, quartile, and decile positions. The document concludes by reinforcing learning through a quiz.

GATHERING DATA- GRADE 7-Q4-week 2.pptx

This document discusses how to gather statistical data and organize it in a frequency distribution table. It provides examples of collecting data through surveys, observations, experiments, and publications. Various methods for collecting data are described, including interviews, questionnaires, observation, and experiments. The document outlines the steps for constructing frequency tables from both ungrouped and grouped data, such as determining the range and class intervals. Examples are provided to illustrate how to tally frequencies and determine the most and least frequent values.

QUARTILE AND DECILE OF GROUPED DATA

The steps in computing the median are similar to that of Q1 and Q3
. In finding the median,
we need first to determine the median class. The Q1 class is the class interval where
the 𝑁
4
th score is contained, while the class interval that contains the 3𝑁
4
𝑡ℎ
score is the Q3 class.
Formula :𝑄𝑘 = LB +
𝑘𝑁
4
−𝑐𝑓𝑏
𝑓𝑄𝑘
𝑖
LB = lower boundary of the of the 𝑄𝑘 class
N = total frequency
𝑐𝑓𝑏= cumulative frequency of the class before the 𝑄𝑘 class
𝑓𝑄𝑘
= frequency of the 𝑄𝑘 class
i = size of the class interval
k = the value of quartile being asked
The interquartile range describes the middle 50% of values when
ordered from lowest to highest. To find the interquartile range (IQR),
first find the median (middle value) of the upper and the lower half of
the data. These values are Q1 and Q3
. The IQR is the difference
between Q3 and Q1
.
Interquartile Range (IQR) = Q3 – Q1
The quartile deviation or semi-interquartile range is one-half the
difference between the third and the first quartile.
Quartile Deviation (QD) =
𝑄3−𝑄1
2
The formula in finding the kth decile of a distribution is
𝐷𝑘 = 𝑙𝑏𝑑𝑘 +
(
𝑘
10)𝑁 − 𝑐𝑓
𝑓𝐷𝑘
𝑖
𝐿𝐵𝑑𝑘 − 𝐿𝑜𝑤𝑒𝑟 𝐵𝑜𝑢𝑛𝑑𝑎𝑟𝑦 𝑜𝑓 𝑡ℎ𝑒 𝑘𝑡ℎ 𝑑𝑒𝑐𝑖𝑙𝑒
𝑁 − 𝑡𝑜𝑡𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑓𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑖𝑒𝑠
𝑐𝑓 − 𝑐𝑢𝑚𝑚𝑢𝑙𝑎𝑡𝑖𝑣𝑒 𝑓𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑦 𝑏𝑒𝑓𝑜𝑟𝑒 𝑡ℎ𝑒 𝑘𝑡ℎ 𝑑𝑒𝑐𝑖𝑙𝑒
𝐹𝑑𝑘 − 𝑓𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑦 𝑜𝑓 𝑡ℎ𝑒 𝑘𝑡ℎ 𝑑𝑒𝑐𝑖𝑙𝑒
𝑖 − 𝑐𝑙𝑎𝑠𝑠 𝑠𝑖𝑧𝑒

5.8 Graphing quadratic inequalities

Graphs of quadratic inequalities will be parabolas with solid or dotted lines and shaded regions above or below the parabola. To graph: 1) sketch the parabola y=ax^2+bx+c, 2) choose a test point and see if it satisfies the inequality, 3) shade the appropriate region based on the test point. For example, to graph y ≤ x^2+6x-4: the parabola opens up with a solid line and vertex at (-3,-13), the test point (0,0) satisfies the inequality so shade below the parabola.

Probability of Simple and Compound Events

This document contains a lesson plan on probability for students. It begins with definitions of key probability terms and examples of calculating probabilities of simple and compound events. It then provides word problems for students to practice calculating probabilities. The document concludes with additional practice problems for students to answer. The overall document provides instruction and practice on fundamental concepts in probability.

DECILE FOR UNGROUPED DATA-MOV 4 COPY.pptx

The document provides instructions for calculating deciles using the Mendenhall and Sincich formula and interpreting what different decile values represent. It includes an example of computing the third decile (D3) of test scores and interpreting what the D3 value means. Various methods for computing deciles and formulas are defined, along with how to interpret different decile values.

4th quarter-math-10

This document contains a 50-question mathematics examination covering topics like permutations, combinations, probability, and statistics. The exam asks students to identify terms, calculate outcomes of experiments and events, determine probabilities, and solve word problems involving arrangements of objects and sampling with or without replacement. It provides context that the exam was administered to 10th grade mathematics students in the Philippines and includes instructions to write answers in capital letters on a half-sheet of paper, with no erasures or superimpositions allowed.
Human: You are an expert at summarizing documents. You provide concise summaries in 3 sentences or less that provide the high level and essential information from the document. Summarize the following document. Begin your response with "[SUMMARY

Factoring Non-Perfect Square Trinomial Lesson Plan

This document contains a lesson plan for teaching factoring non-perfect trinomials in Math 8. The lesson plan outlines intended learning outcomes, learning content including subject matter and reference materials, learning experiences through various activities, an evaluation, and assignment. Students will learn to define trinomials, factor non-perfect square trinomials, and apply factoring trinomials to geometric figures through guided practice with algebra tiles and examples.

INTERPRETING MEASURE OF POSITION.pptx

This document provides information about interpreting measures of position through examples and learning tasks. It begins by welcoming students and setting objectives to recognize the connection between measures of position and their interpretations in distributions. Examples are given to interpret quartiles, deciles, and percentiles. Learning tasks then assess understanding of comparing heights and salaries based on their percentile, quartile, and decile positions. The document concludes by reinforcing learning through a quiz.

GATHERING DATA- GRADE 7-Q4-week 2.pptx

This document discusses how to gather statistical data and organize it in a frequency distribution table. It provides examples of collecting data through surveys, observations, experiments, and publications. Various methods for collecting data are described, including interviews, questionnaires, observation, and experiments. The document outlines the steps for constructing frequency tables from both ungrouped and grouped data, such as determining the range and class intervals. Examples are provided to illustrate how to tally frequencies and determine the most and least frequent values.

QUARTILE AND DECILE OF GROUPED DATA

The steps in computing the median are similar to that of Q1 and Q3
. In finding the median,
we need first to determine the median class. The Q1 class is the class interval where
the 𝑁
4
th score is contained, while the class interval that contains the 3𝑁
4
𝑡ℎ
score is the Q3 class.
Formula :𝑄𝑘 = LB +
𝑘𝑁
4
−𝑐𝑓𝑏
𝑓𝑄𝑘
𝑖
LB = lower boundary of the of the 𝑄𝑘 class
N = total frequency
𝑐𝑓𝑏= cumulative frequency of the class before the 𝑄𝑘 class
𝑓𝑄𝑘
= frequency of the 𝑄𝑘 class
i = size of the class interval
k = the value of quartile being asked
The interquartile range describes the middle 50% of values when
ordered from lowest to highest. To find the interquartile range (IQR),
first find the median (middle value) of the upper and the lower half of
the data. These values are Q1 and Q3
. The IQR is the difference
between Q3 and Q1
.
Interquartile Range (IQR) = Q3 – Q1
The quartile deviation or semi-interquartile range is one-half the
difference between the third and the first quartile.
Quartile Deviation (QD) =
𝑄3−𝑄1
2
The formula in finding the kth decile of a distribution is
𝐷𝑘 = 𝑙𝑏𝑑𝑘 +
(
𝑘
10)𝑁 − 𝑐𝑓
𝑓𝐷𝑘
𝑖
𝐿𝐵𝑑𝑘 − 𝐿𝑜𝑤𝑒𝑟 𝐵𝑜𝑢𝑛𝑑𝑎𝑟𝑦 𝑜𝑓 𝑡ℎ𝑒 𝑘𝑡ℎ 𝑑𝑒𝑐𝑖𝑙𝑒
𝑁 − 𝑡𝑜𝑡𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑓𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑖𝑒𝑠
𝑐𝑓 − 𝑐𝑢𝑚𝑚𝑢𝑙𝑎𝑡𝑖𝑣𝑒 𝑓𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑦 𝑏𝑒𝑓𝑜𝑟𝑒 𝑡ℎ𝑒 𝑘𝑡ℎ 𝑑𝑒𝑐𝑖𝑙𝑒
𝐹𝑑𝑘 − 𝑓𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑦 𝑜𝑓 𝑡ℎ𝑒 𝑘𝑡ℎ 𝑑𝑒𝑐𝑖𝑙𝑒
𝑖 − 𝑐𝑙𝑎𝑠𝑠 𝑠𝑖𝑧𝑒

5.8 Graphing quadratic inequalities

Graphs of quadratic inequalities will be parabolas with solid or dotted lines and shaded regions above or below the parabola. To graph: 1) sketch the parabola y=ax^2+bx+c, 2) choose a test point and see if it satisfies the inequality, 3) shade the appropriate region based on the test point. For example, to graph y ≤ x^2+6x-4: the parabola opens up with a solid line and vertex at (-3,-13), the test point (0,0) satisfies the inequality so shade below the parabola.

Probability of Simple and Compound Events

This document contains a lesson plan on probability for students. It begins with definitions of key probability terms and examples of calculating probabilities of simple and compound events. It then provides word problems for students to practice calculating probabilities. The document concludes with additional practice problems for students to answer. The overall document provides instruction and practice on fundamental concepts in probability.

Union and intersection of events (math 10)

The document discusses probability concepts like sample space, number of outcomes of an event, and calculating probability. It provides examples like rolling a die, picking balls from an urn, and drawing cards from a deck. It also covers compound events and calculating probability for multiple outcomes. The examples are meant to illustrate key probability terms and how to set up and solve probability problems.

Rational Expressions Module

This document provides instruction on rational expressions. It begins with a definition of rational expressions as algebraic expressions where both the numerator and denominator are polynomials. The document then outlines the key lessons to be covered: illustrating, simplifying, and performing operations on rational expressions. Examples are provided of simplifying rational expressions by factoring and canceling common factors between the numerator and denominator. The document also demonstrates multiplying rational expressions using the same rules as multiplying fractions, as well as canceling common factors.

Mathematics 10 - Lesson 1: Number Pattern

This powerpoint presentation discusses about the first lesson in Grade 10 Math. It is all about Number Pattern. It also shows the definition, examples and how to find the nth term and general formula.

Statistics and probability lesson6&7

This document provides examples and explanations of key measures of central tendency (mean, median, mode) and location (percentiles, deciles, quartiles) using data from test scores. It discusses how to calculate each measure and their properties. For a grouped data set of 130 test scores ranging from 10-108, it demonstrates calculating the mean as 61.45 and identifies the median class as 54-64 since it contains the value of 65, which is the midpoint of the data set. The document provides guidance on finding percentiles, deciles, and quartiles using the percentile formula and examples.

Finite Geometric Series dlp

This document outlines a lesson plan for teaching students about finding the sum of terms in finite geometric sequences. It includes objectives, content discussion, example problems and solutions, supplementary activities, and assessment questions. The lesson begins with a review game to identify finite vs infinite sequences. Students then learn the formula to calculate the sum and practice with example sequences. Additional individual and group activities reinforce the concept, and real-world applications are provided. The plan concludes with a reflection on student learning outcomes and areas for improvement.

Evaluating Rational Algebraic Expressions

This document provides instruction on evaluating rational algebraic expressions. It begins with learning objectives and a review of translating verbal phrases to rational expressions. It then presents an example of evaluating expressions when variables are given values. The document gives an example problem about a teacher printing modules for students and evaluating the rational expression to determine the number of pages and students. It defines rational algebraic expressions and the steps for evaluating them. Finally, it provides examples of evaluating expressions and an activity for the learner to complete. It emphasizes not dividing by zero which would result in an undefined expression.

Measures of position

The document contains lyrics from 18 different songs. It discusses a variety of themes related to love and relationships, including being together, being apart, waiting for someone, and remembering past loves and relationships. Locations like "here," "there," and "somewhere" are referenced in several of the songs. The lyrics are in English and Tagalog.

1st Mathematics 7 Quiz Bee 2023.pptx

1. The document outlines the rules and questions for a 1st grade 7 mathematics quiz bee with 4 teams of 14 students each.
2. The contest will include 10 easy questions worth 1 point each, 5 average questions worth 3 points each, and 5 difficult questions worth 5 points each. Questions will be read twice and teams must write their final answer during the allotted time.
3. The questions range from basic arithmetic to simplifying polynomials and cover topics like exponents, coefficients, degrees of polynomials, evaluation, addition/multiplication of polynomials, and word problems. The highest scoring team will be awarded a certificate and extra credit in their final grade.

DLL_WEEK3_LC39-40.docx

This document contains a daily lesson plan for a mathematics class. It outlines the objectives, content, learning resources, procedures, and assessment for a lesson on the union and intersection of events and probability of simple events. The procedures include activities like games and word problems to illustrate and practice these concepts. Formative assessment is conducted through worksheets requiring students to calculate probabilities and analyze Venn diagrams showing relationships between events. The lesson aims to help students understand and apply probability concepts in real-world decision making.

Arithmetic Sequence and Arithmetic Series

The document provides information about arithmetic sequences and arithmetic series. It defines an arithmetic sequence as a sequence of numbers where each term after the first is obtained by adding the same constant to the previous term. It gives examples of arithmetic sequences and explains how to find the common difference, the nth term of a sequence using the general formula, and how to solve problems involving arithmetic sequences and series. The last paragraph tells a story about how Carl Friedrich Gauss was able to quickly calculate the sum of all numbers from 1 to 100 by recognizing it as an arithmetic series.

Arithmetic Sequence

The document defines sequences and series, and discusses arithmetic sequences in particular. An arithmetic sequence is a sequence where each term after the first is obtained by adding a fixed number, called the common difference, to the preceding term. The document provides examples of finding the common difference using the formulas d=an+1-an and d=an-a1. It also gives examples of finding specific terms of an arithmetic sequence given information like the first term, common difference, and nth term.

Math-Quiz-Bee.ppt

This document contains 3 rounds of a math quiz bee with 20 questions each. The easy round covers basic math concepts like properties of numbers, exponents, sequences, percentages and ratios. The average round increases difficulty slightly with questions on coordinate planes, proportions, percentages and prime numbers. The difficult round contains multi-step word problems involving interest, probabilities, combinatorics and geometry.

Strategic intervention material discriminant and nature of the roots

This document provides guidance on identifying the nature of roots for quadratic equations. It begins by explaining that the discriminant, which is calculated as b^2 - 4ac, can be used to determine if the roots are real, rational, equal, etc. Several examples are worked through to demonstrate rewriting equations in standard form, finding a, b, and c values, and calculating the discriminant. Activities are included for students to practice these skills. The document concludes by summarizing that a positive discriminant indicates real, unequal roots, a negative discriminant indicates non-real roots, and a zero discriminant indicates real, equal roots.

DECILE : MEASURES OF POSITION FOR GROUPED DATA

DECILE : MEASURES OF POSITION FOR GROUPED DATA
Grade 10 Mathematics - 4th Quarter
Video Link: https://www.youtube.com/watch?v=GBWS5iPTNDc

probabilityofsimpleandcompoundevents-190217133041.pptx

Here are the solutions to the probability questions:
1. The probability of picking a Geometry book first is 3/8. The probability of picking an Algebra book second is 5/7. By the multiplication principle, the probability of picking a Geometry book first and an Algebra book second is (3/8) × (5/7) = 15/56.
2. The probability of picking a vowel (E, O, A) from Bag 1 is 3/5. The probability of picking a consonant (V, L, D, R, Z) from Bag 2 is 5/7. By the multiplication principle, the probability of picking a vowel from Bag 1 and a consonant from Bag 2 is (

MEASURES OF POSITION GROUPED DATA.pptx

This document discusses measures of position for grouped data including quartiles, deciles, and percentiles. It provides formulas to calculate these measures using the lower boundary, class frequency, total frequency, and cumulative frequency from a frequency distribution table. An example calculates the first quartile (Q1), third quartile (Q3), fifth decile (D5), and 90th percentile (P90) for a data set of student heights. It shows how to identify the relevant class interval and apply the appropriate formula to find each measure of position. The document also provides applications and examples of interpreting these results.

MEASURES OF POSITION

1. The document provides information about measures of position (quartiles, deciles, percentiles) and how to calculate them. It gives an example of finding the first quartile (Q1), second quartile (Q2), and third quartile (Q3) from a data set of students' test scores.
2. Steps for calculating quartiles include arranging the data in order, dividing it into four equal parts, and finding the values that split the data into the 25th, 50th, and 75th percentiles.
3. Interpolation may be needed if the quartile value falls between two data points; this involves calculating the difference between points and multiplying by the decimal portion.

Multiplying Rational Expressions

This document contains a lesson plan for teaching multiplying rational expressions in Math 8. The lesson plan outlines the intended learning outcomes, learning content including subject matter and references, learning experiences such as classifying rational expressions, and an assignment for students to practice multiplying rational expressions. The lesson plan provides step-by-step instructions for multiplying rational expressions by factoring, canceling common factors, and simplifying the resulting expression.

Rewriting Linear Equation from standard form to slope intercept form

This SIM was crafted to address the needs of learners with difficulty in rewriting linear equation from standard form into slope intercept form

Deciles & Quartiles - Point Measures

This document defines and provides formulas and examples for calculating quartiles and deciles from both ungrouped and grouped data. Quartiles and deciles are statistical measures used to divide a data set into four and ten equal parts, respectively. The document explains that quartiles are calculated as Q1, Q2, Q3 to divide the data into the lower 25%, middle 50%, and upper 25%. Deciles are calculated as D1-D9 to divide the data into ten equal parts. Modified formulas are provided to calculate quartiles and deciles from grouped frequency distribution data. Examples are included to demonstrate calculating these measures.

Math blocks

This document provides an activity exploring mathematical patterns using blocks. It contains 17 questions for students to explore patterns in addition tables, multiplication tables, squares, cubes, and triangles built with blocks. Some key objectives are to discover algebraic formulas and understand why the product of two negative numbers is positive. The activity is suitable for grades 4-12 and can be done in one or multiple 60-minute sessions using wooden blocks.

Chapter 3: Figurate Numbers

This document discusses different types of figurate numbers including triangular, square, pentagonal, and hexagonal numbers. It provides examples of the patterns formed by each type of number and formulas to calculate the nth term. Relations between different figurate numbers are also explored, such as how the 4th square number can be expressed as the sum of the 3rd and 4th triangular numbers. A brief history of polygonal numbers is given, noting they were first studied by Pythagoras.

Union and intersection of events (math 10)

The document discusses probability concepts like sample space, number of outcomes of an event, and calculating probability. It provides examples like rolling a die, picking balls from an urn, and drawing cards from a deck. It also covers compound events and calculating probability for multiple outcomes. The examples are meant to illustrate key probability terms and how to set up and solve probability problems.

Rational Expressions Module

This document provides instruction on rational expressions. It begins with a definition of rational expressions as algebraic expressions where both the numerator and denominator are polynomials. The document then outlines the key lessons to be covered: illustrating, simplifying, and performing operations on rational expressions. Examples are provided of simplifying rational expressions by factoring and canceling common factors between the numerator and denominator. The document also demonstrates multiplying rational expressions using the same rules as multiplying fractions, as well as canceling common factors.

Mathematics 10 - Lesson 1: Number Pattern

This powerpoint presentation discusses about the first lesson in Grade 10 Math. It is all about Number Pattern. It also shows the definition, examples and how to find the nth term and general formula.

Statistics and probability lesson6&7

This document provides examples and explanations of key measures of central tendency (mean, median, mode) and location (percentiles, deciles, quartiles) using data from test scores. It discusses how to calculate each measure and their properties. For a grouped data set of 130 test scores ranging from 10-108, it demonstrates calculating the mean as 61.45 and identifies the median class as 54-64 since it contains the value of 65, which is the midpoint of the data set. The document provides guidance on finding percentiles, deciles, and quartiles using the percentile formula and examples.

Finite Geometric Series dlp

This document outlines a lesson plan for teaching students about finding the sum of terms in finite geometric sequences. It includes objectives, content discussion, example problems and solutions, supplementary activities, and assessment questions. The lesson begins with a review game to identify finite vs infinite sequences. Students then learn the formula to calculate the sum and practice with example sequences. Additional individual and group activities reinforce the concept, and real-world applications are provided. The plan concludes with a reflection on student learning outcomes and areas for improvement.

Evaluating Rational Algebraic Expressions

This document provides instruction on evaluating rational algebraic expressions. It begins with learning objectives and a review of translating verbal phrases to rational expressions. It then presents an example of evaluating expressions when variables are given values. The document gives an example problem about a teacher printing modules for students and evaluating the rational expression to determine the number of pages and students. It defines rational algebraic expressions and the steps for evaluating them. Finally, it provides examples of evaluating expressions and an activity for the learner to complete. It emphasizes not dividing by zero which would result in an undefined expression.

Measures of position

The document contains lyrics from 18 different songs. It discusses a variety of themes related to love and relationships, including being together, being apart, waiting for someone, and remembering past loves and relationships. Locations like "here," "there," and "somewhere" are referenced in several of the songs. The lyrics are in English and Tagalog.

1st Mathematics 7 Quiz Bee 2023.pptx

1. The document outlines the rules and questions for a 1st grade 7 mathematics quiz bee with 4 teams of 14 students each.
2. The contest will include 10 easy questions worth 1 point each, 5 average questions worth 3 points each, and 5 difficult questions worth 5 points each. Questions will be read twice and teams must write their final answer during the allotted time.
3. The questions range from basic arithmetic to simplifying polynomials and cover topics like exponents, coefficients, degrees of polynomials, evaluation, addition/multiplication of polynomials, and word problems. The highest scoring team will be awarded a certificate and extra credit in their final grade.

DLL_WEEK3_LC39-40.docx

This document contains a daily lesson plan for a mathematics class. It outlines the objectives, content, learning resources, procedures, and assessment for a lesson on the union and intersection of events and probability of simple events. The procedures include activities like games and word problems to illustrate and practice these concepts. Formative assessment is conducted through worksheets requiring students to calculate probabilities and analyze Venn diagrams showing relationships between events. The lesson aims to help students understand and apply probability concepts in real-world decision making.

Arithmetic Sequence and Arithmetic Series

The document provides information about arithmetic sequences and arithmetic series. It defines an arithmetic sequence as a sequence of numbers where each term after the first is obtained by adding the same constant to the previous term. It gives examples of arithmetic sequences and explains how to find the common difference, the nth term of a sequence using the general formula, and how to solve problems involving arithmetic sequences and series. The last paragraph tells a story about how Carl Friedrich Gauss was able to quickly calculate the sum of all numbers from 1 to 100 by recognizing it as an arithmetic series.

Arithmetic Sequence

The document defines sequences and series, and discusses arithmetic sequences in particular. An arithmetic sequence is a sequence where each term after the first is obtained by adding a fixed number, called the common difference, to the preceding term. The document provides examples of finding the common difference using the formulas d=an+1-an and d=an-a1. It also gives examples of finding specific terms of an arithmetic sequence given information like the first term, common difference, and nth term.

Math-Quiz-Bee.ppt

This document contains 3 rounds of a math quiz bee with 20 questions each. The easy round covers basic math concepts like properties of numbers, exponents, sequences, percentages and ratios. The average round increases difficulty slightly with questions on coordinate planes, proportions, percentages and prime numbers. The difficult round contains multi-step word problems involving interest, probabilities, combinatorics and geometry.

Strategic intervention material discriminant and nature of the roots

This document provides guidance on identifying the nature of roots for quadratic equations. It begins by explaining that the discriminant, which is calculated as b^2 - 4ac, can be used to determine if the roots are real, rational, equal, etc. Several examples are worked through to demonstrate rewriting equations in standard form, finding a, b, and c values, and calculating the discriminant. Activities are included for students to practice these skills. The document concludes by summarizing that a positive discriminant indicates real, unequal roots, a negative discriminant indicates non-real roots, and a zero discriminant indicates real, equal roots.

DECILE : MEASURES OF POSITION FOR GROUPED DATA

DECILE : MEASURES OF POSITION FOR GROUPED DATA
Grade 10 Mathematics - 4th Quarter
Video Link: https://www.youtube.com/watch?v=GBWS5iPTNDc

probabilityofsimpleandcompoundevents-190217133041.pptx

Here are the solutions to the probability questions:
1. The probability of picking a Geometry book first is 3/8. The probability of picking an Algebra book second is 5/7. By the multiplication principle, the probability of picking a Geometry book first and an Algebra book second is (3/8) × (5/7) = 15/56.
2. The probability of picking a vowel (E, O, A) from Bag 1 is 3/5. The probability of picking a consonant (V, L, D, R, Z) from Bag 2 is 5/7. By the multiplication principle, the probability of picking a vowel from Bag 1 and a consonant from Bag 2 is (

MEASURES OF POSITION GROUPED DATA.pptx

This document discusses measures of position for grouped data including quartiles, deciles, and percentiles. It provides formulas to calculate these measures using the lower boundary, class frequency, total frequency, and cumulative frequency from a frequency distribution table. An example calculates the first quartile (Q1), third quartile (Q3), fifth decile (D5), and 90th percentile (P90) for a data set of student heights. It shows how to identify the relevant class interval and apply the appropriate formula to find each measure of position. The document also provides applications and examples of interpreting these results.

MEASURES OF POSITION

1. The document provides information about measures of position (quartiles, deciles, percentiles) and how to calculate them. It gives an example of finding the first quartile (Q1), second quartile (Q2), and third quartile (Q3) from a data set of students' test scores.
2. Steps for calculating quartiles include arranging the data in order, dividing it into four equal parts, and finding the values that split the data into the 25th, 50th, and 75th percentiles.
3. Interpolation may be needed if the quartile value falls between two data points; this involves calculating the difference between points and multiplying by the decimal portion.

Multiplying Rational Expressions

This document contains a lesson plan for teaching multiplying rational expressions in Math 8. The lesson plan outlines the intended learning outcomes, learning content including subject matter and references, learning experiences such as classifying rational expressions, and an assignment for students to practice multiplying rational expressions. The lesson plan provides step-by-step instructions for multiplying rational expressions by factoring, canceling common factors, and simplifying the resulting expression.

Rewriting Linear Equation from standard form to slope intercept form

This SIM was crafted to address the needs of learners with difficulty in rewriting linear equation from standard form into slope intercept form

Deciles & Quartiles - Point Measures

This document defines and provides formulas and examples for calculating quartiles and deciles from both ungrouped and grouped data. Quartiles and deciles are statistical measures used to divide a data set into four and ten equal parts, respectively. The document explains that quartiles are calculated as Q1, Q2, Q3 to divide the data into the lower 25%, middle 50%, and upper 25%. Deciles are calculated as D1-D9 to divide the data into ten equal parts. Modified formulas are provided to calculate quartiles and deciles from grouped frequency distribution data. Examples are included to demonstrate calculating these measures.

Union and intersection of events (math 10)

Union and intersection of events (math 10)

Rational Expressions Module

Rational Expressions Module

Mathematics 10 - Lesson 1: Number Pattern

Mathematics 10 - Lesson 1: Number Pattern

Statistics and probability lesson6&7

Statistics and probability lesson6&7

Finite Geometric Series dlp

Finite Geometric Series dlp

Evaluating Rational Algebraic Expressions

Evaluating Rational Algebraic Expressions

Measures of position

Measures of position

1st Mathematics 7 Quiz Bee 2023.pptx

1st Mathematics 7 Quiz Bee 2023.pptx

DLL_WEEK3_LC39-40.docx

DLL_WEEK3_LC39-40.docx

Arithmetic Sequence and Arithmetic Series

Arithmetic Sequence and Arithmetic Series

Arithmetic Sequence

Arithmetic Sequence

Math-Quiz-Bee.ppt

Math-Quiz-Bee.ppt

Strategic intervention material discriminant and nature of the roots

Strategic intervention material discriminant and nature of the roots

DECILE : MEASURES OF POSITION FOR GROUPED DATA

DECILE : MEASURES OF POSITION FOR GROUPED DATA

probabilityofsimpleandcompoundevents-190217133041.pptx

probabilityofsimpleandcompoundevents-190217133041.pptx

MEASURES OF POSITION GROUPED DATA.pptx

MEASURES OF POSITION GROUPED DATA.pptx

MEASURES OF POSITION

MEASURES OF POSITION

Multiplying Rational Expressions

Multiplying Rational Expressions

Rewriting Linear Equation from standard form to slope intercept form

Rewriting Linear Equation from standard form to slope intercept form

Deciles & Quartiles - Point Measures

Deciles & Quartiles - Point Measures

Math blocks

This document provides an activity exploring mathematical patterns using blocks. It contains 17 questions for students to explore patterns in addition tables, multiplication tables, squares, cubes, and triangles built with blocks. Some key objectives are to discover algebraic formulas and understand why the product of two negative numbers is positive. The activity is suitable for grades 4-12 and can be done in one or multiple 60-minute sessions using wooden blocks.

Chapter 3: Figurate Numbers

This document discusses different types of figurate numbers including triangular, square, pentagonal, and hexagonal numbers. It provides examples of the patterns formed by each type of number and formulas to calculate the nth term. Relations between different figurate numbers are also explored, such as how the 4th square number can be expressed as the sum of the 3rd and 4th triangular numbers. A brief history of polygonal numbers is given, noting they were first studied by Pythagoras.

Magic squares

This document discusses the history and properties of magic squares. It begins by explaining that the earliest known magic square originated in China over 4000 years ago. It then provides details on the formation and uniqueness of 3x3 magic squares, before discussing the extensive efforts to systematically form and count higher order magic squares, especially 5x5 squares. It notes that the exact number of 5x5 magic squares, over 68 million, was only determined in the 1970s using computer programs.

The complete book_of_number_system1

The document discusses various types of numbers including natural numbers, whole numbers, and integers. It provides examples and explanations related to properties of these numbers. Some key points include:
- Natural numbers start from 1 and do not include 0, negative numbers, or decimals.
- Whole numbers include all natural numbers and 0.
- Integers include whole numbers and their negatives.
- Examples are provided to illustrate properties like divisibility, perfect squares, and solving word problems involving sums and products of numbers.
- The last part discusses Donkey's stable number based on his true and false answers to questions about divisibility, being a square, and the first digit. It is determined his number must

Nikhil number pattern formulas

There are several common number patterns that follow specific rules. Square number sequences follow the rule of n^2, where the nth term is the square of n. Arithmetic sequences follow repetitive addition, where each term is created by adding a fixed number to the previous term. Geometric sequences follow repetitive multiplication, where each term is created by multiplying the previous term by a fixed number. The Fibonacci sequence is where each term is the sum of the two terms before it, starting with 1, 1. These patterns can be represented by general formulas to calculate any term in the sequence.

Chap 03 02

The document discusses terms of sequences and patterns in sequences. It defines what the terms of a sequence are and how to construct a difference table to analyze patterns in sequences. The difference table allows predicting future terms by extending patterns in differences. The document gives examples of using difference tables and finding nth-term formulas. It then introduces the famous Fibonacci sequence and gives a recursive definition for calculating Fibonacci numbers.

Maths project

The document defines and describes different types of real numbers including natural numbers, whole numbers, integers, rational numbers, and irrational numbers. It provides examples of each type of number. Real numbers consist of all rational and irrational numbers. A Venn diagram shows the relationships between the different subsets of real numbers. Euclid's division algorithm and its application to find the highest common factor of two numbers is also explained in the document.

class 10 chapter 1- real numbers

The document discusses different types of real numbers including rational and irrational numbers. It provides examples and definitions of natural numbers, whole numbers, integers, rational numbers, and irrational numbers. It also includes information on Euclid's division algorithm and its application in finding the highest common factor of two numbers. Examples are provided to illustrate the algorithm.

Maths project

The document discusses different types of real numbers including rational and irrational numbers. It provides examples and definitions of natural numbers, whole numbers, integers, rational numbers, and irrational numbers. It also includes information on Euclid's division algorithm and its application in finding highest common factors and lowest common multiples. Examples of proving the irrationality of square roots like √5 are given.

Maths project

The document discusses different types of real numbers including rational and irrational numbers. It provides examples and definitions of natural numbers, whole numbers, integers, rational numbers, and irrational numbers. It also includes information on Euclid's division algorithm and its application in finding the highest common factor of two numbers. Examples are provided to illustrate the algorithm.

Equations problems

This document provides examples for solving word problems by translating English phrases into mathematical expressions. It discusses key phrases like "more than", "less than", and "times" and how they relate to addition, subtraction, and multiplication. Several geometry and consecutive number word problems are worked out step-by-step. The document emphasizes setting up variables clearly before solving and checking that the answer makes sense in the original context.

Sequence function

The document defines key concepts related to sequences and series. It explains that a sequence is an ordered list of numbers with a specific pattern or rule. A sequence function is a function whose domain is the set of natural numbers. Terms are the individual numbers in a sequence. Finite sequences have a set number of terms while infinite sequences continue without end. Partial sums refer to adding a specific number of terms. Sigma notation compactly represents the sum of terms in a sequence. The document also introduces the principle of mathematical induction as a method to prove that statements are true for all natural numbers.

Stability criterion of periodic oscillations in a (13)

This document discusses domination problems on isosceles triangular chessboards using different chess pieces. It examines placing a minimum number of pieces such that all unoccupied positions are attacked (the domination number). For a single piece type, it determines the domination number and possible solutions for rooks, bishops, and kings on isosceles triangular boards. It also considers domination numbers when using two piece types together, such as kings and rooks or kings and bishops. Key results include formulas for the domination number and total solutions in terms of the board size for each piece type.

101 math short cuts [www.onlinebcs.com]

1. The document provides various shortcuts and methods for multiplying, dividing, finding sums and performing other calculations on numbers.
2. Methods are given for multiplying 2-digit, 3-digit and numbers with repeating digits. Shortcuts are also provided for finding sums of natural numbers, squares, cubes, and other patterns.
3. The document outlines various tests and methods for determining if a number is divisible by 2, 3, 4, 7, 11, 13, and other numbers. Properties of squares, square roots, primes, HCF, LCM and other algebraic concepts are also summarized.

AufEx4_01_02.ppt

This document discusses sequences and provides examples of finding patterns in sequences to predict future terms or develop formulas. It begins by defining what a sequence is and the terms used to describe them, like first term and nth term. Difference tables are introduced as a way to analyze patterns between terms. Examples show how to use difference tables to predict future terms and find formulas. The document then introduces the famous Fibonacci sequence and provides its recursive definition to calculate future terms.

1 chap

This document contains information about important numbers and formulas. It discusses topics like place value, types of numbers (natural, whole, integers, even, odd, prime, composite), tests for divisibility, multiplication shortcuts, basic formulas, progression, and the Euclidean algorithm for division. Some key points covered are the place value system in Hindu-Arabic numerals, definitions of different types of numbers, tests for divisibility by various numbers, formulas for arithmetic and geometric progressions, and the division algorithm.

Easy maths

1. The document provides important facts and formulas regarding numbers, including place value, types of numbers, tests for divisibility, and progressions.
2. It defines numeral, place value, face value, and types of numbers such as natural numbers, whole numbers, integers, even/odd numbers, prime/composite numbers.
3. Tests for divisibility by various numbers from 2 to 24 are explained. Shortcut methods for multiplication and basic formulas are also listed.
4. Progressions including arithmetic and geometric progressions are defined, with formulas provided for their terms and sums. Solved examples illustrate applications of the concepts.

Visualizing the pascal’s triangle

The various visual and numeric patterns, seen in the Pascal's Triangle. Includes a brief introduction and help on constructing the Pascal's Triangle. Binomial Theorem is not discussed. Though, the n C r formula has been described. Hope you enjoy it !

Junior olympiad

The document is the questions and solutions from the 2003 Western Australian Junior Mathematics Olympiad individual and team competitions. It includes 10 individual questions testing various math skills like algebra, number theory, and geometry, along with the solutions. It also includes 5 team problems involving cutting strings into pieces and calculating the resulting number and sizes of pieces. The team problems can be solved using powers of 2 and 3 and formulas are provided for the longest and shortest starting strings that result in a given number of pieces.

Geo chapter01power point

This document provides examples and explanations of patterns, inductive reasoning, and geometry concepts. It includes a list of counting numbers and their properties, perfect squares up to 10, and examples of making conjectures based on patterns. Students are asked to identify patterns, extend patterns, test conjectures, solve equations, name points and planes, and describe intersections of lines and planes. The document covers fundamental geometry, algebra, and logic skills.

Math blocks

Math blocks

Chapter 3: Figurate Numbers

Chapter 3: Figurate Numbers

Magic squares

Magic squares

The complete book_of_number_system1

The complete book_of_number_system1

Nikhil number pattern formulas

Nikhil number pattern formulas

Chap 03 02

Chap 03 02

Maths project

Maths project

class 10 chapter 1- real numbers

class 10 chapter 1- real numbers

Maths project

Maths project

Maths project

Maths project

Equations problems

Equations problems

Sequence function

Sequence function

Stability criterion of periodic oscillations in a (13)

Stability criterion of periodic oscillations in a (13)

101 math short cuts [www.onlinebcs.com]

101 math short cuts [www.onlinebcs.com]

AufEx4_01_02.ppt

AufEx4_01_02.ppt

1 chap

1 chap

Easy maths

Easy maths

Visualizing the pascal’s triangle

Visualizing the pascal’s triangle

Junior olympiad

Junior olympiad

Geo chapter01power point

Geo chapter01power point

Module II on PFA (Psychological First Aid) | Calming Down and Managing One’s ...

The document outlines a module on managing emotions and thoughts during difficult times. It describes an activity where participants imagine catching their feelings in a ball while playing catch. They then check which feelings are helpful or unhelpful, and learn to reframe unhelpful thoughts and change negative feelings to positive ones like gratitude, understanding, and contentment through breathing exercises. The goal is to help people cope with stress, anxiety, and difficult emotions during the pandemic by managing feelings and reframing thoughts in a more positive light.

Module IV on PFA (Psychological First Aid) | Sources of Strengths

This document outlines an activity from a PFA module aimed at reinforcing sources of strength. Participants are asked to draw and color a kite, writing their sources of strength on the kite and support systems outside. Their sources include perseverance, hope, spirituality, and creativity. Support systems listed are family, authorities, scientists, and necessities. Participants reflect on how they are like the kite, needing strengths and support to face challenges, then write a short poem about their strengths. The goal is to help participants recognize their internal and external resources to support coping during difficult times.

Module I on PFA (Psychological First Aid) | Validating Feelings and Normalizi...

This document outlines an online course on providing psychological first aid and supporting students during times of crisis or disaster. The course covers validating feelings, normalizing reactions to stressful events like the pandemic, and helping participants understand that all emotions are normal and valid. Participants learn techniques for assessing feelings and common student reactions to disasters. They discuss applying these skills to coping with the challenges of the ongoing COVID-19 pandemic by being brave, healthy and trusting in the ability to cope with life's difficulties.

ELECTRONICS 10: VOLTAGE

Some slides here were disorganized although I uploaded it on its good condition. Maybe some compression? or what? Howsoever, I think that it's readable and understandable enough.

ELECTRONICS 10: SERIES CIRCUIT

1. In a series circuit, the same current flows through each component and there is only one path for electricity to flow.
2. The total resistance of a series circuit equals the sum of the individual resistances.
3. The voltage applied to a series circuit equals the sum of the individual voltage drops across each component. If any one component fails or is disconnected, no current will flow through the entire circuit.

ELECTRONICS 10: CURRENT QUIZ ANSWERS

This document contains an electrical circuitry worksheet with multiple choice questions, true/false questions, and short answer/problem solving questions testing knowledge of concepts like current, voltage, resistance, conductors, insulators, Ohm's Law, and circuits. Some of the questions covered include: defining current as a stream of moving electrons, identifying materials that offer little resistance, factors that affect resistance, properties of alternating current, units of measurement like amps and ohms, formulas like Ohm's Law, and calculating values like current or voltage given other circuit parameters.

ELECTRONICS 10: CURRENT QUIZ

This document contains a quiz on electrical concepts with multiple choice, true/false, and problem solving questions. Some key points:
1. The multiple choice questions cover topics like current, voltage, conductors, insulators, resistance and their definitions.
2. The true/false questions test understanding of concepts like Ohm's law, the relationship between resistance and current, alternating current, and safety aspects of electricity.
3. The problem solving questions ask the test taker to calculate current, resistance, and voltage given two of the three variables based on Ohm's law.

ELECTRONICS 10: PARALLEL CIRCUIT

Me and my classmate's report in our Electronics class. This report was created by my classmate and I refurbished it a little bit.

ELECTRONICS 10: RESISTANCE

Resistance opposes the flow of current from a voltage source. Georg Ohm determined there is a direct relationship between voltage and current, known as Ohm's Law. Materials fall into two categories: conductors that offer little resistance, and insulators that present high resistance. Resistance is represented by the symbol R and measured in ohms. While resistance may seem negative, it can be used beneficially to generate heat or light through forcing high current flows.

ELECTRONICS 10: CURRENT

Electric current is the flow of electric charge that can be either direct or alternating. Direct current flows in one direction while alternating current regularly reverses direction. The ampere, the SI unit for electric current, is named after French physicist André-Marie Ampère, one of the main discoverers of electromagnetism. German physicist Georg Ohm determined the direct proportional relationship between voltage, current, and resistance known as Ohm's law, where voltage equals current times resistance.

THE DECAMERON ENGLISH 10

Giovanni Boccaccio was an Italian author and humanist born in 1313 who wrote notable works including the Decameron. The Decameron comprises 100 stories told by 10 young adults (7 women and 3 men) fleeing the Black Death plague in Florence. It is structured such that each character tells a story over 10 days. Boccaccio began work on the Decameron around 1349 and revised it in 1370-1371 before dying in 1375. He educated himself on works like Dante's Divine Comedy but used allegory in the Decameron for satire rather than instruction.

GRADE 10 UNIT TEST ENGLISH 3RD QUARTER

Unit test in English without answers.

Contemporary Philippine Music

Contemporary music in the Philippines usually refers to compositions that have adopted ideas and elements from twentieth century art music in the West, as well as the latest trends and musical styles in the entertainment industry

Module II on PFA (Psychological First Aid) | Calming Down and Managing One’s ...

Module II on PFA (Psychological First Aid) | Calming Down and Managing One’s ...

Module IV on PFA (Psychological First Aid) | Sources of Strengths

Module IV on PFA (Psychological First Aid) | Sources of Strengths

Module I on PFA (Psychological First Aid) | Validating Feelings and Normalizi...

Module I on PFA (Psychological First Aid) | Validating Feelings and Normalizi...

ELECTRONICS 10: VOLTAGE

ELECTRONICS 10: VOLTAGE

ELECTRONICS 10: SERIES CIRCUIT

ELECTRONICS 10: SERIES CIRCUIT

ELECTRONICS 10: CURRENT QUIZ ANSWERS

ELECTRONICS 10: CURRENT QUIZ ANSWERS

ELECTRONICS 10: CURRENT QUIZ

ELECTRONICS 10: CURRENT QUIZ

ELECTRONICS 10: PARALLEL CIRCUIT

ELECTRONICS 10: PARALLEL CIRCUIT

ELECTRONICS 10: RESISTANCE

ELECTRONICS 10: RESISTANCE

ELECTRONICS 10: CURRENT

ELECTRONICS 10: CURRENT

THE DECAMERON ENGLISH 10

THE DECAMERON ENGLISH 10

GRADE 10 UNIT TEST ENGLISH 3RD QUARTER

GRADE 10 UNIT TEST ENGLISH 3RD QUARTER

Contemporary Philippine Music

Contemporary Philippine Music

How to Download & Install Module From the Odoo App Store in Odoo 17

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.

How to Manage Reception Report in Odoo 17

A business may deal with both sales and purchases occasionally. They buy things from vendors and then sell them to their customers. Such dealings can be confusing at times. Because multiple clients may inquire about the same product at the same time, after purchasing those products, customers must be assigned to them. Odoo has a tool called Reception Report that can be used to complete this assignment. By enabling this, a reception report comes automatically after confirming a receipt, from which we can assign products to orders.

CHUYÊN ĐỀ ÔN TẬP VÀ PHÁT TRIỂN CÂU HỎI TRONG ĐỀ MINH HỌA THI TỐT NGHIỆP THPT ...

CHUYÊN ĐỀ ÔN TẬP VÀ PHÁT TRIỂN CÂU HỎI TRONG ĐỀ MINH HỌA THI TỐT NGHIỆP THPT ...Nguyen Thanh Tu Collection

https://app.box.com/s/qspvswamcohjtbvbbhjad04lg65waylfData Structure using C by Dr. K Adisesha .ppsx

Data Structure using C ppt by Dr. K. Adisesha

BPSC-105 important questions for june term end exam

BPSC-105 important questions for june term end exam

THE SACRIFICE HOW PRO-PALESTINE PROTESTS STUDENTS ARE SACRIFICING TO CHANGE T...

The recent surge in pro-Palestine student activism has prompted significant responses from universities, ranging from negotiations and divestment commitments to increased transparency about investments in companies supporting the war on Gaza. This activism has led to the cessation of student encampments but also highlighted the substantial sacrifices made by students, including academic disruptions and personal risks. The primary drivers of these protests are poor university administration, lack of transparency, and inadequate communication between officials and students. This study examines the profound emotional, psychological, and professional impacts on students engaged in pro-Palestine protests, focusing on Generation Z's (Gen-Z) activism dynamics. This paper explores the significant sacrifices made by these students and even the professors supporting the pro-Palestine movement, with a focus on recent global movements. Through an in-depth analysis of printed and electronic media, the study examines the impacts of these sacrifices on the academic and personal lives of those involved. The paper highlights examples from various universities, demonstrating student activism's long-term and short-term effects, including disciplinary actions, social backlash, and career implications. The researchers also explore the broader implications of student sacrifices. The findings reveal that these sacrifices are driven by a profound commitment to justice and human rights, and are influenced by the increasing availability of information, peer interactions, and personal convictions. The study also discusses the broader implications of this activism, comparing it to historical precedents and assessing its potential to influence policy and public opinion. The emotional and psychological toll on student activists is significant, but their sense of purpose and community support mitigates some of these challenges. However, the researchers call for acknowledging the broader Impact of these sacrifices on the future global movement of FreePalestine.

Elevate Your Nonprofit's Online Presence_ A Guide to Effective SEO Strategies...

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.

Information and Communication Technology in Education

(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.

Observational Learning

Simple Presentation

HYPERTENSION - SLIDE SHARE PRESENTATION.

IT WILL BE HELPFULL FOR THE NUSING STUDENTS
IT FOCUSED ON MEDICAL MANAGEMENT AND NURSING MANAGEMENT.
HIGHLIGHTS ON HEALTH EDUCATION.

Ch-4 Forest Society and colonialism 2.pdf

All the best

مصحف القراءات العشر أعد أحرف الخلاف سمير بسيوني.pdf

مصحف أحرف الخلاف للقراء العشرةأعد أحرف الخلاف بالتلوين وصلا سمير بسيوني غفر الله له

欧洲杯下注-欧洲杯下注押注官网-欧洲杯下注押注网站|【网址🎉ac44.net🎉】

【网址🎉ac44.net🎉】欧洲杯下注在体育博彩方面，不难发现，欧洲杯下注多为英式运动提供投注。欧洲杯下注为丰富多彩的体育项目提供投注，如足球、赛马、板球和飞镖，但这不是欧洲杯下注的唯一优势。在欧洲杯下注，全世界玩家都可以找到自己感兴趣的比赛进行投注。欧洲杯下注为网球和美式运动如棒球、美式足球、篮球、冰球开出的投注同样值得关注。在夏季或冬季奥运会方面，欧洲杯下注为玩家开出了丰富多彩的服务，是你的不二之选。你还可以投注水球、自行车和班迪球等小众体育项目，甚至可以为武术、拳击和综合格斗投注。欧洲杯下注为众多体育项目开出滚球投注。

skeleton System.pdf (skeleton system wow)

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ملزمة تشريح الجهاز الهيكلي (نظري 3)
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تتميز هذهِ الملزمة بعِدة مُميزات :
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2- تحتوي على 78 رسم توضيحي لكل كلمة موجودة بالملزمة (لكل كلمة !!!!)
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4- هُنالك بعض المعلومات تم توضيحها بشكل تفصيلي جداً (تُعتبر لدى الطالب أو الطالبة بإنها معلومات مُبهمة ومع ذلك تم توضيح هذهِ المعلومات المُبهمة بشكل تفصيلي جداً
5- الملزمة تشرح نفسها ب نفسها بس تكلك تعال اقراني
6- تحتوي الملزمة في اول سلايد على خارطة تتضمن جميع تفرُعات معلومات الجهاز الهيكلي المذكورة في هذهِ الملزمة
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Pharmaceutics Pharmaceuticals best of brub

First year pharmacy
Best for u

Haunted Houses by H W Longfellow for class 10

Haunted Houses by H W Longfellow for class 10 ICSE

NIPER 2024 MEMORY BASED QUESTIONS.ANSWERS TO NIPER 2024 QUESTIONS.NIPER JEE 2...

NIPER JEE PYQ
NIPER JEE QUESTIONS
MOST FREQUENTLY ASK QUESTIONS
NIPER MEMORY BASED QUWSTIONS

Oliver Asks for More by Charles Dickens (9)

Oliver-Asks-for-More by Charles Dickens

How to Download & Install Module From the Odoo App Store in Odoo 17

How to Download & Install Module From the Odoo App Store in Odoo 17

SWOT analysis in the project Keeping the Memory @live.pptx

SWOT analysis in the project Keeping the Memory @live.pptx

220711130097 Tulip Samanta Concept of Information and Communication Technology

220711130097 Tulip Samanta Concept of Information and Communication Technology

How to Manage Reception Report in Odoo 17

How to Manage Reception Report in Odoo 17

CHUYÊN ĐỀ ÔN TẬP VÀ PHÁT TRIỂN CÂU HỎI TRONG ĐỀ MINH HỌA THI TỐT NGHIỆP THPT ...

CHUYÊN ĐỀ ÔN TẬP VÀ PHÁT TRIỂN CÂU HỎI TRONG ĐỀ MINH HỌA THI TỐT NGHIỆP THPT ...

Data Structure using C by Dr. K Adisesha .ppsx

Data Structure using C by Dr. K Adisesha .ppsx

BPSC-105 important questions for june term end exam

BPSC-105 important questions for june term end exam

THE SACRIFICE HOW PRO-PALESTINE PROTESTS STUDENTS ARE SACRIFICING TO CHANGE T...

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- 1. Investigate:1 1 1 3 5 9 17 31 57 105 a. Find the next three terms: b. Write a mathematical sentence which can be used as the formula in finding the nth term of the sequence. 1 1 1 3 5 9 17 31 57 105 193 355 653 a. The next three terms are as follows, 193 for the 11th term, 355 for the 12th term, and 653 for the 13th term. b. If we are going to investigate this 3 9 31 105 193 355 653 11th 12th 13th 5 17 57
- 2. sequence, we can observe that for each number in the series (starting from the value 3 [4th term] to last) is the sum of preceding 3 numbers. We can deduce that this is a Tribonacci Sequence. The Tribonacci sequence starts with three predetermined terms and then each successive term is the sum of the three preceding terms. The table below shows the observation: What to find (value) How to find 4th term (3) 1st + 2nd + 3rd terms (1+1+1) 5th term (5) 2nd + 3rd + 4th terms (1+1+3) 6th term (9) 3rd + 4th + 5th terms (1+3+5) 7th term (17) 4th + 5th + 6th terms (3+5+9)
- 3. In order to solve for the next three terms (11th, 12th and 13th), we will make use of this recurrence equation on finding for the nth term where n ≥ 4: Example, this is the formula if we want to find the 4th term of a Tribonacci sequence. T4=T1+T2+T3 which comes from the equation Tn= Tn−3+ Tn−2+Tn−1 (the formula for 8th term (31) 5th + 6th + 7th terms (5+9+17) 9th term(57) 6th + 7th +8th terms (9+17+31) 10th term(105) 7th +8th +9th terms (17+31+57) 11th term (193) 8th +9th + 10th terms (31+57+105) 12th term (355) 9th + 10th + 11th terms (57+105+193) 13th term (653) 10th +11th +12th terms (105+193+355)
- 4. finding the nth term of a tribonacci sequence)
- 5. 3. For this kind of tile sequence, we can assert that we can have different approach for solving the nth figure. In our way, we used a function and figures to solve this kind of problem. First, we need to fill out each figures as a dimension of square. To do this, let us name first the shown sequence of tiles as figures Visualizing the above sentence, here are the figures formed: Figure 1 Figure 2 Figure 3 2x2 dimension 3x3 dimension 4x4 dimension
- 6. Figure 4 Knowing that every nxn dimension are added by 1x1 dimension to arrive for the next figure, we can conclude that the next figure would be a 6x6 dimension square. We can also explore from the figures that in order to arrive at the dimension, we can show it on mathematical expression (n+2)(n+2). Say, for example, for figure 1, we noticed that we 5x5 dimension
- 7. don’t need to substitute any natural numbers to get 2x2 dimension for the first figure. Therefore, with a view to get 2x2 dimension, we will just substitute zero on the expression. (0+2)(0+2) will be simplified to (2)(2) or 2x2 dimension. Now for the figure 2, we noticed that the tiles are in 3x3 form, therefore, in order to arrive for 3x3 dimension, we are going to add 1 shift horizontally and 1 shift vertically which then can be substituted to the expression which can be seen as (1+2)(1+2) => (3)(3) or 3x3 dimension. The pattern which can be noticed could be traced for the next figures. Now, we can see that the tiles without shades can be expressed into mathematical expression 2(n+1), (n+1) tiles for the first column and (n+1) tiles for the last column. To better understand, we can visually show the expression using the figures above. Say for example, for figure
- 8. 3: We arrived at the expression 2(n+1) to get the total number of tiles which are not shaded by blue. If we are going to construct a table for better understanding, follow below. n+1 2+1 3 non-shaded tiles for first column n+1 2+1 3 non-shaded tiles for last column 2(2+1) = 4+2 = 6 non- shaded tiles
- 9. Now, going back to the problem letter a. How many square tiles will it take to build the next figure? Since we know that the predicted dimension of the figure (which we’ll be calling figure 5) is 6x6. We can tell that there are 4 shifts added vertically and Figure Dimension Shift added vertically and horizontally (n) Mathematical expression (n+2)(n+2) Mathematical expression 2(n+1) 1 2x2 0 shift / No shift (0+2)(0+2) 2(0+1) 2 3x3 1 shift (1+2)(1+2) 2(1+1) 3 4x4 2 shifts (2+2)(2+2) 2(2+1) 4 5x5 3 shifts (3+2)(3+2) 2(3+1) 5 6x6 4 shifts (4+2)(4+2) 2(4+1)Next figure
- 10. horizontally inferring to the figure 1 which can be shown below. Now in, order to find the the non-shaded tiles, we will just substitute n=4 to 2(n+1) => 2(4+1) = 10 non-shaded tiles. Added shifts four units horizontally Added shifts four units vertically 6x6 dimension square
- 11. This basically means that there are 5 non- shaded tiles for top left column and 5 non- shaded tiles for bottom right column of a 6x6 dimension which can be shown below. We are asked to find the number of square tiles (shaded tiles). We can find the shaded tiles by inspection which is 26 shaded tiles. On the other side, we can also figure out the number of the shaded tiles by making a function shown below. n+1 4+1 5 non-shaded tiles for last column n+1 4+1 5 non-shaded tiles for first column
- 12. f(n) = (n+2)(n+2)-2(n+1) where (n+2)(n+2) will be the arrangement/dimension of the tiles and 2(n+1) are tiles which are non-shaded. Knowing that n=4, we can substitute it to the function; f(4) = (4+2)(4+2) – 2(4-1) = (6)(6) – 2(5) = 36 – 10 = 26 Therefore, we conclude that we can also get the number of shaded tiles by using functions. b. To get the number of tiles for an nth figure, we will subtract 2(n+1) from (n+2)(n+2) which can be shown as a function: Solving by Function = Solving by Inspection 26 = 26 TRUE