SEPTOCODE 21
This September, get ready to beat your brains out for the GDSC Club.
Starting from 20th September, all the contributors will be provided with simple programming questions,one per day, which can be written using any programming language of preference. The submissions will be accepted through Google after thorough checking.
This document provides an overview and materials for a lesson on writing algebraic expressions. The lesson was created by Kristie Conners and Sean Moran through the 21st Century Lessons project, which aims to develop high-quality model lessons to support student achievement. The lesson introduces students to writing algebraic expressions by having them match written expressions to algebraic expressions. It includes class activities, assessments, and accommodations for English language learners and students with disabilities. The overview provides objectives, vocabulary, and links to standards and additional resources.
This document contains notes from an algebra class. It summarizes that:
1) All new algebra students are responsible for their own grades, including online and notebook assignments. Students should ask friends or the teacher for details.
2) For the previous quarter, every student who completed less than half of their classwork and online assignments averaged below 50% on tests. Completing assignments prepares students for tests, which make up a large part of the grade.
3) Upcoming topics include graphing systems of equations, systems of equations with elimination, and systems of equations with substitution.
This document provides a lesson on positive and negative numbers on the number line. It begins with an opening exercise reviewing number lines numbered 0-10. Students then construct number lines using a compass to locate positive and negative whole numbers. The lesson defines the opposite of a number as being on the other side of 0 and being the same distance from 0. Examples are used to demonstrate locating positive and negative numbers on horizontal and vertical number lines. Students work in groups to locate given numbers and their opposites on number lines.
This document defines key terms used in algebraic expressions, including variables, constants, factors, coefficients, and terms. It explains that a variable represents an unknown number, a constant is a specific number, factors are numbers multiplied together, and a coefficient is a number next to a variable. The document also describes that the terms of an expression are the parts separated by addition or subtraction signs, and provides examples of expressions with one, two, three, and four terms.
This document is a lesson plan on rational numbers on the number line. It begins with learning objectives about using number lines to locate rational numbers between integers and understanding that rational numbers can be positive or negative. It then provides examples and exercises for students to practice graphing rational numbers on number lines and relating rational numbers to real world contexts involving water levels rising. It concludes with directing students to complete an exit ticket to assess their understanding. The lesson teaches students to represent rational numbers as fractions or decimals, locate them on number lines in relation to integers, and apply rational numbers in word problems involving measurement.
This document provides a lesson on the concept of opposites of numbers. It includes:
1) An opening exercise asking students to identify relationships between sets of opposites words.
2) Examples of locating numbers and their opposites on a number line. The key points are that opposites are the same distance from zero but on opposite sides, and zero is its own opposite.
3) A word problem example modeling a real-world situation involving opposites on a number line, with questions to discuss the representation.
The lesson emphasizes that opposites are equidistant from zero but on opposite sides, and that zero represents the point of reference or no change in various contexts.
1) The document provides a mathematics curriculum guide for first grade addition, subtraction, and number systems. It outlines big ideas, essential questions, unit vocabulary, and Arizona state standards to be covered.
2) Key concepts include counting quantities, comparing numbers, and composing and decomposing numbers. Students will learn strategies for addition and subtraction word problems involving combining, separating, and comparing quantities.
3) The guide provides examples and explanations for how students can use objects, drawings, and equations to represent addition and subtraction word problems involving unknown values in different positions. It emphasizes developing fluency with addition and subtraction facts to 10.
This document provides an overview and materials for a lesson on writing algebraic expressions. The lesson was created by Kristie Conners and Sean Moran through the 21st Century Lessons project, which aims to develop high-quality model lessons to support student achievement. The lesson introduces students to writing algebraic expressions by having them match written expressions to algebraic expressions. It includes class activities, assessments, and accommodations for English language learners and students with disabilities. The overview provides objectives, vocabulary, and links to standards and additional resources.
This document contains notes from an algebra class. It summarizes that:
1) All new algebra students are responsible for their own grades, including online and notebook assignments. Students should ask friends or the teacher for details.
2) For the previous quarter, every student who completed less than half of their classwork and online assignments averaged below 50% on tests. Completing assignments prepares students for tests, which make up a large part of the grade.
3) Upcoming topics include graphing systems of equations, systems of equations with elimination, and systems of equations with substitution.
This document provides a lesson on positive and negative numbers on the number line. It begins with an opening exercise reviewing number lines numbered 0-10. Students then construct number lines using a compass to locate positive and negative whole numbers. The lesson defines the opposite of a number as being on the other side of 0 and being the same distance from 0. Examples are used to demonstrate locating positive and negative numbers on horizontal and vertical number lines. Students work in groups to locate given numbers and their opposites on number lines.
This document defines key terms used in algebraic expressions, including variables, constants, factors, coefficients, and terms. It explains that a variable represents an unknown number, a constant is a specific number, factors are numbers multiplied together, and a coefficient is a number next to a variable. The document also describes that the terms of an expression are the parts separated by addition or subtraction signs, and provides examples of expressions with one, two, three, and four terms.
This document is a lesson plan on rational numbers on the number line. It begins with learning objectives about using number lines to locate rational numbers between integers and understanding that rational numbers can be positive or negative. It then provides examples and exercises for students to practice graphing rational numbers on number lines and relating rational numbers to real world contexts involving water levels rising. It concludes with directing students to complete an exit ticket to assess their understanding. The lesson teaches students to represent rational numbers as fractions or decimals, locate them on number lines in relation to integers, and apply rational numbers in word problems involving measurement.
This document provides a lesson on the concept of opposites of numbers. It includes:
1) An opening exercise asking students to identify relationships between sets of opposites words.
2) Examples of locating numbers and their opposites on a number line. The key points are that opposites are the same distance from zero but on opposite sides, and zero is its own opposite.
3) A word problem example modeling a real-world situation involving opposites on a number line, with questions to discuss the representation.
The lesson emphasizes that opposites are equidistant from zero but on opposite sides, and that zero represents the point of reference or no change in various contexts.
1) The document provides a mathematics curriculum guide for first grade addition, subtraction, and number systems. It outlines big ideas, essential questions, unit vocabulary, and Arizona state standards to be covered.
2) Key concepts include counting quantities, comparing numbers, and composing and decomposing numbers. Students will learn strategies for addition and subtraction word problems involving combining, separating, and comparing quantities.
3) The guide provides examples and explanations for how students can use objects, drawings, and equations to represent addition and subtraction word problems involving unknown values in different positions. It emphasizes developing fluency with addition and subtraction facts to 10.
6.RP.A.3 Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.
6.RP.A.3.D Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities.
This document contains a summary of key concepts in number theory, including:
- Rational numbers are numbers that can be expressed as fractions with a non-zero denominator. Irrational numbers cannot be expressed as fractions.
- Prime numbers are numbers greater than 1 that are only divisible by 1 and themselves. Composite numbers are numbers with more than two factors.
- Examples of operations with numbers like showing that numbers are even, odd, rational, or finding factors, multiples, and prime numbers between ranges.
- A word problem about students opening and closing lockers in a pattern to determine how many are left open.
The document provides an overview of the fourth grade mathematics curriculum for Unit 8 on multiplication and division. It includes 3 key ideas: that there are multiple strategies for multiplying and dividing whole numbers, that multiplication and division are related, and that learning these skills has value. The unit covers multiplying up to 4-digit numbers by 1-digit numbers and dividing up to 4-digit dividends by 1-digit divisors. Students will represent and solve multi-step word problems involving all four operations. They will also generate and analyze number patterns that follow given rules.
This lesson plan provides instruction on adding integers using a number line. Students will use a floor number line to act out addition problems such as -3 + 2 by moving left or right the appropriate number of steps. They will also relate adding integers to real-world contexts like changing temperatures. Finally, students will apply their skills to a puzzle game that challenges them to use integer addition to move a creature between gates by placing virtual resonators on the gates.
Lesson plan in mathematics 8 (Factoring Perfect Square Trinomial) Rachel Ann
This lesson plan teaches students how to factor perfect square trinomials. It begins with introducing the learning competency and objectives of factoring perfect square trinomials. Examples are provided to demonstrate the steps: getting the square root of the first and last terms and listing them as a sum or difference. Students practice this by factoring examples as a group activity and individually. They summarize the key points and apply the process to new problems, concluding with an assignment to factor additional perfect square trinomials independently.
Number concept refers to having an understanding of what numbers represent. It involves knowing properties of different types of numbers like odd, even, prime, and composite numbers. Developing number concept also helps build number sense, which is understanding numbers and how to use them to solve problems. The modern number system originated in India and was adapted over time by other cultures before becoming the standard Hindu-Arabic system used today in places like Europe. There are various types of numbers including real and imaginary, rational and irrational, integers, and natural numbers.
This document defines and provides examples of algebraic expressions, polynomials, and equations. It discusses the components of algebraic expressions including terms, variables, constants, and coefficients. It defines polynomials as expressions involving addition, subtraction, multiplication, division, and exponents. The document describes different types of polynomials including monomials, binomials, trinomials, and multinomials. It also discusses determining the degree and type of polynomials. Finally, it provides a definition and examples of algebraic equations.
This video models solving linear equations of the form x + a = b using algebra tiles. It shows three examples of equations solved concretely with tiles: x + 3 = 7, r + 5 = -2, and 3x - 4 = 5. The tiles represent integers and unknowns, with an equals sign separating the left and right sides. Solving involves using the zero property to isolate the unknown, requiring adding the same amount to both sides to maintain balance.
This document provides an algebra lesson plan for grade 10 students. The lesson covers simplifying, adding, subtracting, multiplying, and dividing algebraic fractions. It begins with defining algebra and explaining the learning objectives. The lesson consists of three group activities - simplifying algebraic fractions, adding/subtracting algebraic fractions, and multiplying/dividing algebraic fractions. For each activity, examples are provided and the students work through practice problems in their groups. At the end, students reflect on what they have learned about solving algebraic equations with fractions.
The document provides an overview of Unit 5 of the 4th grade mathematics curriculum for the Isaac School District. The unit focuses on addition, subtraction, and place value with large numbers up to 1,000,000. It includes 27 instructional sessions covering key concepts like using place value to represent numbers in expanded form and standard algorithms for addition and subtraction. Students are expected to fluently perform multi-digit calculations and explain their work by referring to place value. The unit vocabulary and Arizona state math standards addressed are also outlined.
This document provides an overview of fractions including:
- The key components of a fraction are the numerator and denominator
- Examples are given of fractions with different numerators over the same denominator
- Methods for simplifying, multiplying, dividing, adding, and subtracting fractions are described
- Mixed numbers, which are numbers represented by a whole number and fraction, are also introduced
- Contact information is provided for math specialists available to answer additional questions
This is an initial attempt by my students of B.Ed. in creating Programmed Instructional material using the template I had provided them. Your observations and suggestions are welcome!
Unit 6 presentation base ten equality form of a number with trainer notes 7.9.08jcsmathfoundations
The document discusses concepts related to base ten, equality, and forms of numbers. It defines these concepts, examines how students develop an understanding through research on cognitive development, and provides classroom applications and strategies for teaching these concepts effectively. Diagnostic questions are presented to assess student understanding, and examples show how to respond to common student errors or misconceptions in working with numbers.
Differentiates expression from equation, Translate word phrase to numerical e...April Rose Anin
This document outlines a lesson plan on teaching mathematical expressions and equations to 6th grade students. The objectives are for students to differentiate between expressions and equations, translate word phrases to numerical expressions, and write simple equations. The lesson procedures include a review game, discussion of new concepts like expressions and equations, practice exercises, and a group activity to identify examples. Student understanding is evaluated through practice problems writing expressions and solving equations. The teacher reflects on teaching strategies and seeks help from the principal on any difficulties encountered.
The document provides an overview of operations and algebraic thinking standards from kindergarten through 8th grade. It shows that in the early grades, standards focus on representing numbers, addition, subtraction and basic multiplication/division. In later grades, standards expand the scope of numbers and introduce concepts like ratios, proportions, expressions and patterns. Students are expected to apply mathematical operations to increasingly complex word problems and equations over time.
This document provides a math lesson on addition and subtraction for a 1st grade class. It includes definitions and examples of addition and subtraction, using numbers and a number line. Students are instructed to practice addition and subtraction problems using an interactive number line, with the goal of understanding these basic numerical operations. The document relates the lesson to Arizona state math and technology standards for 1st grade level conceptual understanding of operations and their use of technology.
Solving Equations by Factoring KTIP lesson planJosephine Neff
1) The document is a lesson plan for teaching 9th grade algebra students how to factor quadratic equations and use factoring to solve equations and real-world problems.
2) The lesson involves reviewing factoring patterns, teaching students to factor quadratic equations in standard form using various methods, and using factoring to solve physics problems involving height, speed, and time.
3) Formative and summative assessments are used to check students' understanding of factoring quadratic trinomials and using factoring to solve equations.
This document provides an overview of a unit on complex numbers for an 11th grade Algebra 2 class. The unit objectives are to understand imaginary and complex numbers, and to simplify complex number expressions. Students will learn about the imaginary number i, complex numbers in the form a + bi, and operations like addition, subtraction, and multiplication on complex numbers. They will also learn to use conjugates to find quotients of complex numbers. The unit will be assessed through practice problems, homework assignments, classwork, and an online quiz to evaluate students' understanding of imaginary and complex numbers.
This document provides an overview of key concepts in mathematics including:
1) It describes the aims of the Mathematics 1 module which are to reinforce basic numeracy and algebraic manipulation through lectures, seminars and tutorials.
2) It covers various topics in numbers such as place value, real numbers, rational numbers, integers, and properties of number systems.
3) Examples are provided to classify numbers as real, rational, irrational, integer, whole or natural numbers.
This lesson teaches students about even and odd numbers. It begins with defining even and odd numbers and listing examples of each. Students then explore patterns with adding, multiplying, and combining even and odd numbers through examples and group work. They determine that the sum of two even numbers or two odd numbers is even, while the sum of an even and odd number is odd. For multiplication, they find that the product of two even numbers or an even and odd number is even, and the product of two odd numbers is odd. Finally, students discuss how knowing if a number is even or odd can help with division.
The absolute value of a number represents the distance of that number from zero on the number line. It is always positive or zero. Addition of integers can be done using number lines, signed tiles, or rules. When integers have like signs, add the numbers and keep the common sign. When they have unlike signs, subtract the numbers and use the sign of the number with the greater absolute value.
6.RP.A.3 Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.
6.RP.A.3.D Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities.
This document contains a summary of key concepts in number theory, including:
- Rational numbers are numbers that can be expressed as fractions with a non-zero denominator. Irrational numbers cannot be expressed as fractions.
- Prime numbers are numbers greater than 1 that are only divisible by 1 and themselves. Composite numbers are numbers with more than two factors.
- Examples of operations with numbers like showing that numbers are even, odd, rational, or finding factors, multiples, and prime numbers between ranges.
- A word problem about students opening and closing lockers in a pattern to determine how many are left open.
The document provides an overview of the fourth grade mathematics curriculum for Unit 8 on multiplication and division. It includes 3 key ideas: that there are multiple strategies for multiplying and dividing whole numbers, that multiplication and division are related, and that learning these skills has value. The unit covers multiplying up to 4-digit numbers by 1-digit numbers and dividing up to 4-digit dividends by 1-digit divisors. Students will represent and solve multi-step word problems involving all four operations. They will also generate and analyze number patterns that follow given rules.
This lesson plan provides instruction on adding integers using a number line. Students will use a floor number line to act out addition problems such as -3 + 2 by moving left or right the appropriate number of steps. They will also relate adding integers to real-world contexts like changing temperatures. Finally, students will apply their skills to a puzzle game that challenges them to use integer addition to move a creature between gates by placing virtual resonators on the gates.
Lesson plan in mathematics 8 (Factoring Perfect Square Trinomial) Rachel Ann
This lesson plan teaches students how to factor perfect square trinomials. It begins with introducing the learning competency and objectives of factoring perfect square trinomials. Examples are provided to demonstrate the steps: getting the square root of the first and last terms and listing them as a sum or difference. Students practice this by factoring examples as a group activity and individually. They summarize the key points and apply the process to new problems, concluding with an assignment to factor additional perfect square trinomials independently.
Number concept refers to having an understanding of what numbers represent. It involves knowing properties of different types of numbers like odd, even, prime, and composite numbers. Developing number concept also helps build number sense, which is understanding numbers and how to use them to solve problems. The modern number system originated in India and was adapted over time by other cultures before becoming the standard Hindu-Arabic system used today in places like Europe. There are various types of numbers including real and imaginary, rational and irrational, integers, and natural numbers.
This document defines and provides examples of algebraic expressions, polynomials, and equations. It discusses the components of algebraic expressions including terms, variables, constants, and coefficients. It defines polynomials as expressions involving addition, subtraction, multiplication, division, and exponents. The document describes different types of polynomials including monomials, binomials, trinomials, and multinomials. It also discusses determining the degree and type of polynomials. Finally, it provides a definition and examples of algebraic equations.
This video models solving linear equations of the form x + a = b using algebra tiles. It shows three examples of equations solved concretely with tiles: x + 3 = 7, r + 5 = -2, and 3x - 4 = 5. The tiles represent integers and unknowns, with an equals sign separating the left and right sides. Solving involves using the zero property to isolate the unknown, requiring adding the same amount to both sides to maintain balance.
This document provides an algebra lesson plan for grade 10 students. The lesson covers simplifying, adding, subtracting, multiplying, and dividing algebraic fractions. It begins with defining algebra and explaining the learning objectives. The lesson consists of three group activities - simplifying algebraic fractions, adding/subtracting algebraic fractions, and multiplying/dividing algebraic fractions. For each activity, examples are provided and the students work through practice problems in their groups. At the end, students reflect on what they have learned about solving algebraic equations with fractions.
The document provides an overview of Unit 5 of the 4th grade mathematics curriculum for the Isaac School District. The unit focuses on addition, subtraction, and place value with large numbers up to 1,000,000. It includes 27 instructional sessions covering key concepts like using place value to represent numbers in expanded form and standard algorithms for addition and subtraction. Students are expected to fluently perform multi-digit calculations and explain their work by referring to place value. The unit vocabulary and Arizona state math standards addressed are also outlined.
This document provides an overview of fractions including:
- The key components of a fraction are the numerator and denominator
- Examples are given of fractions with different numerators over the same denominator
- Methods for simplifying, multiplying, dividing, adding, and subtracting fractions are described
- Mixed numbers, which are numbers represented by a whole number and fraction, are also introduced
- Contact information is provided for math specialists available to answer additional questions
This is an initial attempt by my students of B.Ed. in creating Programmed Instructional material using the template I had provided them. Your observations and suggestions are welcome!
Unit 6 presentation base ten equality form of a number with trainer notes 7.9.08jcsmathfoundations
The document discusses concepts related to base ten, equality, and forms of numbers. It defines these concepts, examines how students develop an understanding through research on cognitive development, and provides classroom applications and strategies for teaching these concepts effectively. Diagnostic questions are presented to assess student understanding, and examples show how to respond to common student errors or misconceptions in working with numbers.
Differentiates expression from equation, Translate word phrase to numerical e...April Rose Anin
This document outlines a lesson plan on teaching mathematical expressions and equations to 6th grade students. The objectives are for students to differentiate between expressions and equations, translate word phrases to numerical expressions, and write simple equations. The lesson procedures include a review game, discussion of new concepts like expressions and equations, practice exercises, and a group activity to identify examples. Student understanding is evaluated through practice problems writing expressions and solving equations. The teacher reflects on teaching strategies and seeks help from the principal on any difficulties encountered.
The document provides an overview of operations and algebraic thinking standards from kindergarten through 8th grade. It shows that in the early grades, standards focus on representing numbers, addition, subtraction and basic multiplication/division. In later grades, standards expand the scope of numbers and introduce concepts like ratios, proportions, expressions and patterns. Students are expected to apply mathematical operations to increasingly complex word problems and equations over time.
This document provides a math lesson on addition and subtraction for a 1st grade class. It includes definitions and examples of addition and subtraction, using numbers and a number line. Students are instructed to practice addition and subtraction problems using an interactive number line, with the goal of understanding these basic numerical operations. The document relates the lesson to Arizona state math and technology standards for 1st grade level conceptual understanding of operations and their use of technology.
Solving Equations by Factoring KTIP lesson planJosephine Neff
1) The document is a lesson plan for teaching 9th grade algebra students how to factor quadratic equations and use factoring to solve equations and real-world problems.
2) The lesson involves reviewing factoring patterns, teaching students to factor quadratic equations in standard form using various methods, and using factoring to solve physics problems involving height, speed, and time.
3) Formative and summative assessments are used to check students' understanding of factoring quadratic trinomials and using factoring to solve equations.
This document provides an overview of a unit on complex numbers for an 11th grade Algebra 2 class. The unit objectives are to understand imaginary and complex numbers, and to simplify complex number expressions. Students will learn about the imaginary number i, complex numbers in the form a + bi, and operations like addition, subtraction, and multiplication on complex numbers. They will also learn to use conjugates to find quotients of complex numbers. The unit will be assessed through practice problems, homework assignments, classwork, and an online quiz to evaluate students' understanding of imaginary and complex numbers.
This document provides an overview of key concepts in mathematics including:
1) It describes the aims of the Mathematics 1 module which are to reinforce basic numeracy and algebraic manipulation through lectures, seminars and tutorials.
2) It covers various topics in numbers such as place value, real numbers, rational numbers, integers, and properties of number systems.
3) Examples are provided to classify numbers as real, rational, irrational, integer, whole or natural numbers.
This lesson teaches students about even and odd numbers. It begins with defining even and odd numbers and listing examples of each. Students then explore patterns with adding, multiplying, and combining even and odd numbers through examples and group work. They determine that the sum of two even numbers or two odd numbers is even, while the sum of an even and odd number is odd. For multiplication, they find that the product of two even numbers or an even and odd number is even, and the product of two odd numbers is odd. Finally, students discuss how knowing if a number is even or odd can help with division.
The absolute value of a number represents the distance of that number from zero on the number line. It is always positive or zero. Addition of integers can be done using number lines, signed tiles, or rules. When integers have like signs, add the numbers and keep the common sign. When they have unlike signs, subtract the numbers and use the sign of the number with the greater absolute value.
1) The document introduces the absolute value function and piecewise-defined functions. It contains examples investigating college tuition rates as a piecewise function and a stock trading rule involving absolute value.
2) Tables are used to represent piecewise functions and the absolute value of various inputs is calculated. Equations are written to represent piecewise functions and the meaning of absolute value is discussed.
3) The document emphasizes understanding rates of change and absolute value, especially in business applications. It stresses the importance of studying these concepts and notes that absolute value is always positive.
STI Course A Closer Look at Singapore Math by Yeap Ban HarJimmy Keng
This weekend course conducted at Scarsdale Teachers Institute, New York focused on the use of anchor problem to enhance the teaching and learning of mathematics.
This document provides a daily lesson log for a 7th grade mathematics class covering operations on integers. The lesson covers addition, subtraction, multiplication, and division of integers over four sessions. Each session includes objectives, content, learning resources, procedures, and an evaluation. The procedures describe activities to motivate students, present examples, discuss concepts, and apply the skills to word problems. The goal is for students to understand and be able to perform the four fundamental operations on integers.
This document provides examples and step-by-step explanations of how to add, subtract, multiply and divide integers according to their signs. It begins with writing integers for word problems, then evaluates expressions. The main content explains that to add integers with the same sign, add their absolute values and the sum is positive if both are positive or negative if both are negative. To add integers with different signs, subtract the absolute values and the sum is positive if the positive value is greater or negative if the negative value is greater. Several worked examples are provided to illustrate the rules.
This document discusses counting techniques used in probability and statistics. It introduces the fundamental principle of counting and the multiplication rule for determining the total number of possible outcomes of multi-step processes. Specific counting techniques covered include the tree diagram, permutations, and combinations. Examples are provided to demonstrate how to apply these techniques to problems involving determining the number of arrangements of different objects.
The document discusses permutations and combinations. It provides examples of calculating permutations and combinations for different scenarios like selecting committees from a group of people and arranging books on a shelf. Formulas for permutations (nPr) and combinations (nCr) are given. Order matters for permutations but not for combinations. The key difference between the two is explained.
The document discusses key aspects of implementing the MIND Algebra Readiness curriculum. It describes the two-day training agenda which includes an overview of lesson one on the number line, breaks, lunch, review, evaluation, and lab work. The document emphasizes that the curriculum supports learning through rebuilding mathematical foundations, providing structures for learning and retention, using visual models, and teaching big ideas. It provides guidance for teachers on facilitating student learning with ST Math games by making connections between the visualizations in the games and classroom mathematics concepts.
The document provides an overview of topics covered in a Tech Math 2 class, including:
- Letter patterns and levels
- Classroom expectations
- Review of real number types and operations
- Coordinate plane and plotting points
- Exponent rules
The teacher provides warm-up problems, course expectations, and a review of key concepts like real numbers, the coordinate plane, exponents, and comparing/operating on real numbers.
A Problem Solving Approach To Mathematics For Elementary School TeachersKimberly Pulley
The document summarizes key concepts about addition and subtraction of whole numbers:
1) It defines addition of whole numbers using set models and as the union of two disjoint finite sets. The sum is the cardinal number of the combined set.
2) It describes the number line model for addition, showing how to represent addends as vectors on the number line and find their sum.
3) It defines less than and greater than relations using the number line, and discusses ordering whole numbers.
4) It introduces important properties of whole number addition, including closure, commutativity, associativity, and the identity property.
The document discusses different types of numbers and operations involving positive and negative numbers. It explains rules for addition, subtraction, multiplication, and division of positive and negative numbers. It also covers order of operations using PEMDAS and provides examples of solving expressions using proper order. Finally, it discusses properties and rules for exponents, including adding, subtracting, multiplying, and dividing terms with the same base and combining exponents.
Exercises for pupils in primary education(0 4)-enGeorgeta Manafu
The document discusses teaching methods and tools for presenting pseudocode language to students. It provides:
- Keywords used in pseudocode like read, write, if, then, else, while, and for to define instructions. Algorithms start with "Algorithm name" and end with "Stop".
- Examples of read-write instructions using keywords read and write to input and output data.
- Exercises for students to practice using pseudocode keywords and instructions like reading numbers, writing outputs, and comparing values in if statements.
- Discussion of theoretical concepts like assigning values, expressions, variables, and data types to introduce in pseudocode programming.
The document provides examples and explanations about calculating averages and means. It discusses using averages in applied problems related to grades. It explains that averages are used to determine grades and can be impacted by subsequent scores. The document also notes that it is often easier to prevent problems than deal with consequences later, relating to the saying that "an ounce of prevention is worth a pound of cure."
The document contains sample solutions to exit ticket questions from 12 math lessons on integers and the number line. The questions cover skills like ordering integers, writing story problems using integers, graphing integers on a number line, interpreting number lines, and using absolute value. The sample solutions demonstrate how to correctly answer the questions by applying skills taught in each lesson, such as identifying opposites, determining relative positions on the number line, and interpreting zero.
1) When multiplying integers with the same sign, the product is positive, but with different signs, the product is negative.
2) For exponents, if the base is in parentheses, you raise that number to the power. If the base is negative without parentheses, you raise the absolute value to the power and then make the answer negative.
3) The distributive property distributes the number being multiplied over terms in parentheses by multiplying each term individually and then combining like terms.
This document discusses standards for educational and professional testing. It provides an overview of the content and format of quantitative ability questions that may appear on tests, including topics like arithmetic, algebra, geometry, and data analysis. It also reviews important mathematical concepts in each of these areas, such as properties of numbers, fractions, decimals, exponents, and inequalities. The document is intended to help candidates prepare for quantitative questions that adhere to established testing standards.
This document discusses teaching integer numbers in elementary school. It covers introducing integers by combining natural and whole numbers with their negatives, using a number line to represent integers, and the four basic operations on integers. It emphasizes using examples and exercises to help students understand concepts like comparing and ordering integers, opposites, and properties of integer operations like closure, commutativity, and distributivity. Teachers are advised to use exposure and questioning methods to explain concepts and ensure student comprehension.
This presentation was provided by Steph Pollock of The American Psychological Association’s Journals Program, and Damita Snow, of The American Society of Civil Engineers (ASCE), for the initial session of NISO's 2024 Training Series "DEIA in the Scholarly Landscape." Session One: 'Setting Expectations: a DEIA Primer,' was held June 6, 2024.
How to Fix the Import Error in the Odoo 17Celine George
An import error occurs when a program fails to import a module or library, disrupting its execution. In languages like Python, this issue arises when the specified module cannot be found or accessed, hindering the program's functionality. Resolving import errors is crucial for maintaining smooth software operation and uninterrupted development processes.
Executive Directors Chat Leveraging AI for Diversity, Equity, and InclusionTechSoup
Let’s explore the intersection of technology and equity in the final session of our DEI series. Discover how AI tools, like ChatGPT, can be used to support and enhance your nonprofit's DEI initiatives. Participants will gain insights into practical AI applications and get tips for leveraging technology to advance their DEI goals.
A review of the growth of the Israel Genealogy Research Association Database Collection for the last 12 months. Our collection is now passed the 3 million mark and still growing. See which archives have contributed the most. See the different types of records we have, and which years have had records added. You can also see what we have for the future.
Strategies for Effective Upskilling is a presentation by Chinwendu Peace in a Your Skill Boost Masterclass organisation by the Excellence Foundation for South Sudan on 08th and 09th June 2024 from 1 PM to 3 PM on each day.
How to Make a Field Mandatory in Odoo 17Celine George
In Odoo, making a field required can be done through both Python code and XML views. When you set the required attribute to True in Python code, it makes the field required across all views where it's used. Conversely, when you set the required attribute in XML views, it makes the field required only in the context of that particular view.
2. CET-B
DAY-1
Problem Statement: In a certain game, a player's score is
decided by the formula a+b*c/a-b , where a, b and c denote
his score on levels 1 2 and 3. Given input as a, b and c, you have
to find the resulting score of the player.
Approach: Taking the all numbers input first you can just
calculate just by giving the expression in the code.
The system will automatically solve the expression and give the
output.
3. CET-B
DAY-2
Problem Statement: You are going to appear a fast-aptitude
exam, but only people with a calculating mind can clear it.
Given 2 years, write a program to calculate the total number of
days in both years.
Approach: Basically, you need to calculate whether the year is
leap year or not. If leap year the year will have 366 days else
365 days.
A number is a leap year if it is divisible by 4 and not divisible by
100 or its divisible by 400.
4. CET-B
DAY-3
Problem Statement: Given that your semester results are out
and you have received the credits of each subject. Frame a pro-
gram to input your credit of each subject in a line in form of a
string separated by commas.
Approach: After taking the input string, write a condition in
which the iterator goes to the new line if there is a comma (,)
else it will print the characters.
5. CET-B
DAY-4
Problem Statement: Zumba sports club has the following grading
policy: -
- Every player receives a point in the inclusive range from 0 to 100.
- If a player scores a point less than 35, he is disqualified
Joy is a coach at the sports club who likes to round each student's
point according to these rules: -
- If the difference between the point and the next multiple of 5 is less
than 3, round point up to the next multiple of 5.
- If the value of point is less than equal to 33, no rounding occurs as the
result will still be a disqualifying score.
Approach: First check that the number is less than or equal to 33 or not.
If condition satisfies no rounding occurs.
For finding the nearest multiple of 5 we can take a loop starting from i=1
and it will be added with the input number. Then you can check after
adding that the resulting number is divisible by 5 or not and if divisible
it’s the nearest multiple of 5. Then we can check by calculating the
difference between multiple of 5 and input number and if less than 3
then round off else not.
You can also find the modulus of the number with 5 and use the remain-
der value to find the net multiple of 5
6. CET-B
DAY-5
Problem Statement: Given an array of n integers. Find the
unique elements in the array and print them.
Unique elements are the elements which occur only once in
the array.
Approach: After taking the input string, take a nested loop
along with a counter variable. First array will check each
element and the other element will iterate through the total
array and check its second occurrence. If it occurs once more
then the counter variable increases.
If the counter variable equals to 1 then the element will be
printed.
8. CET-B
DAY-7
Problem Statement: Himansh loves billiards very much. One
day while playing a match , he found out a new trick in the
game. He interpreted each red balls as 0 and each white balls
as 1 .He started taking a note of the positions of white and red
balls in the table. If there are at least 6 balls of same color
placed one after another, then the situation is considered dan-
gerous else its out of danger.
Approach: After taking the input string, with the help of pre-
defined function taking a string containing six 0's and six 1's
compare and search if that string is found inside the main
input string .
If it is found then print "DANGEROUS" else "NOT DANGEROUS".
9. CET-B
DAY-8
Problem Statement: While checking the English papers of the
board exams ,the professor often gets frustated by the writing
format of words of the student in the examination paper. The words
were a net mix of upper case and the lower case letters in every
words. An idea struck into the mind of the professor to develop an
extension that would change the letters' register in every word so
that it either only consisted of lower case letters or, vice cersa, only
of uppercase ones. At that as little as possible letters should be
changed in the word. For example, the word HoUse must be
replaced with house, and the word ViP — with VIP.
Approach: After taking the input check how many upper case and
lower case letters are present by using a count variable.
If more number of lower case are present then convert the whole
string to lowercase else convert it to uppercase.
10. CET-B
DAY-9
Problem Statement: There are n students standing in a row for a
drill. They are given Red(R), Blue(B) and Green(G) colored tshirts.
The instructor wanted to remove some students from the row
such that two neighboring students don't have the same color
tshirts. Students in a row are considered neighboring if there are
no other students between them.
Approach: Create a loop which take iteration for every charac-
ter in an input string and check whether the character is equal to
it's adjescent character.
If it is so then increase the value of variable by one which was
initially declared as zero. Finally print the value of variable after
the loop over. Repeat the process for number of test cases.
11. CET-B
DAY-10
Problem Statement: A primary school teacher has taught the
students english alphabets. He now wants to test the
students. He has given his n students a task to write sentenc-
es with every alphabet occuring atleast once. He has taught
the students only lowercase alphabets. Given a string without
spaces findif every alphabet of english language has occured
atleast once. If the student has passed the test the teacher
gave them a pass mark.The sentences need not be meaning-
ful.
Approach: Create an integer array of size 26 where each place
represent the ascii character of each lower case alphabet.
Then just increment the values
in the appropriate places when that character appear in the
sentence. Loop through the characters of the string and sub-
tract the ascii from 97
to get values ranging from 1-26 then increment the value in
the array. Then check if any position is having value 0 then
print fail else pass.
12. CET-B
DAY-11
Problem Statement: There are n marbles in a row. A child has
to divide the marbles in halves untill he gets one marble. Find
the minimum number of steps required to get the single
marble. The halves can be unequal for odd numbers. After a
division from odd even pair the child has to choose the even
pair for futher division if the odd number is not 1.
Approach: First you need to enter the number of marbles in a
row. Then keep on dividing the number of marbles till there is
only one marble left. Count the minimum number of steps
required to get a single marble. If the number gets divided to
and even and odd number, continue the division with the even
one.
13. CET-B
DAY-12
Problem Statement: Given a square matrix, calculate the absolute
difference between the sums of its opposite rows and opposite
columns.
For example, the square matrix arr is shown below:
1 2 3
7 5 6
9 8 9
The sum of the rows = 1+2+3+9+8+9= 32. The sum of the columns =
1+7+9+3+6+9= 35. Their absolute difference is |32-35|=3.
Approach: ake the matrix as input.Then add all the elements of first row
with that of the last row and store in a variable. Add all the elements of
first
column with that of the last column and store in another variable. Print
the absolute difference between them.
14. CET-B
DAY-14
Problem Statement: There are n students in a class. They are given
numbers according to their height, like if two students have same
heights they are given same number. They are arranged in a pyra-
mid manner.
A pyramid manner is basically a sequence of numbers, with initially
an increasing order, then the peak, then a decreasing order, look-
ing like a pyramid.
Now, the class teacher needs to find the place where the tallest
student is standing.
Approach: Initially create two variable, the first variable store the
starting index and second variable store the ending index of input
array.
Then create a continuous loop which ends when both the variable
have same value. In each iteration find the middle index and com-
pare the
value at that position with upper value, if it is greater then second
variable should store the middle index else first variable should
store the upper middle index. Repeat this until the loop over. After
the loop over print the upper index of first variable.
16. CET-B
DAY-15
Problem Statement: There are n students appearing an online
exam. Each of them are given serial numbers starting from 1 to
n. No two students can have the same serial number. Each of
the students are asked to write their serial numbers on the top.
One of the student copied all the answers from another
student. He forgot to change his serial number and submitted
his answer sheet with the other students serial number. Find
the student who cheated. The teacher has recieved the
answer sheets in a random manner. If no students has cheated
print 0.
Approach: Create a continuous loop which occurs for t times,
t is the number of test cases. In each iteration take inupt array
and store in a variable.
Then create two loop to check which number is missing in the
range from 1 to n. finally print the missing number.
17. CET-B
DAY-16
Problem Statement: Mirsha is a computer science student in her
final year. During a certain event, she was faced with an interesting
problem.
Given a list of numbers, all except one numbers follows a certain
odd-even pattern. Basically this means, from the list, 1 number will
be odd, and rest even, or vice versa. Your task is to find the index of
the number which doesn't follow the pattern.
The indexing here starts from 1.
Approach: Initialize two variable k1 and k2 with integer value zero.
Then for each number in the array check if it is even or odd, for
even number
increase the value of k1 by and for odd number do same with k2.
Finally if k1 is greater then k2, then find the index of odd number
and print it
else find the index of even number and print it. Repeat the process
for all test cases.
18. CET-B
DAY-17
Problem Statement: A company decided to start a lucky draw for its
customers. The company gave its customers a lucky draw coupon with a
serial number printed on it.
The serial number ranges from 1 to n. The company devised a rule to
decide the lucky numbers:-
-Starting with the serial number, replace the serial number by the sum of
the squares of its digits.
-Repeat the process until the number equals 1 (where it will stay), or it
loops endlessly in a cycle which does not include 1.
-Those numbers for which this process ends in 1 are lucky.
The customers are asked to submit their tickets at the counter and their
serial numbers are checked their and lucky or unlucky is printed over their
tickets based on their serial number.
Approach: After taking the input first check if the number is greater than
9 or not. If smaller than 9 then its unlucky. Then calculate the sum of each
digits in the number and if it results to something other than 1 then the
number will be the sum and like this it checks in a loop.
19. CET-B
DAY-18
Problem Statement: A number of balls are kept in a basket each
named in the range [1,n]. some students picked few balls randomly
and changed their numbers to existing numbers in the box and
then added back. Now box has unique numbers + duplicate num-
bers. Find the original numbers on the balls whose numbers were
changed.
Approach: First input the number of test cases.
Input size of array(arr[]) and then input the array elements.
Then another array(reg[]) has been created to check which all
elements are present in the array from 1-n. The value of this array
will contain eiher 1 or 0 depicting which elements are present(val-
ue=1) and which are absent(value=0).
Once it's done, Then we once again traverse this reg[] array and
print the index value where the value is 0(depicting absent).
20. CET-B
DAY-19
Problem Statement: Given a number of balls placed on top of each other in
an order. It is kept in such a way that the number of balls goes on increasing in
a column and then decreasing which resembles a mountain pattern.Jonita has
been asked by her teacher to find whether the mountain has steep slope or
gentle slope. Help Jonita solving out this problem.
Approach: In this problem four loop is required. Using first loop store the
largest value from array in a variable. In the second loop find the index for
lagest value from the array and name it middle_index.
then divide the array into two part from middle_index. In the 3rd loop check if
any number repeat in first part of array and if so then print "gentle" and break
the loop, if not go to 4th loop.
In 4th loop check if any number repeat in second part of array if so print
"gentle" and break the loop, if not then just out from the loop and print
"steep".
21. CET-B
DAY-20
Problem Statement: Tony has been assigned a number n and
was asked to represent it as a sum of maximum possible
number of prime numbers.One can prove that such represen-
tation exists for any integer greater than 1. Help Tony to solve
this problem.
Approach: First check the number n is even or odd. For even
number print "n/2" then print "2" for n/2 times and for odd
number print interger value
of n/2 then print (n-3)/2 times "2" and one times "3". Repeat
this process for all test cases.
22. CET-B
DAY-21
Problem Statement: A baker wants to raise some yeast in a container for making bread.
Initially, the container is empty. Each morning, the baker can put any number of yeast into the
container. And each night, every yeast cell in the container will split into two yeast cells. You
hope to see exactly x yeast cells in the container at some moment.
What is the minimum number of yeast cells the baker needs to put into the container across
those days?
Approach: Initialize an integer variable k with zero. Check if the input integer is odd number
then increase k by one and the new value of n should be
(n-1)/2 , if number is even then just change n to n/2. All these process should be under an
continuous loop whose boolean value always be True,
if n reach to one then break the loop by incresing k by one. Finally print the value of k. Repeat
the process for all test cases.
Or,
FUNCTION TO SOLVE FOR N
Basically we need to form n(given number) as a sum of powers of 2
for example take 15
15 = (2^3) + (2^2) + (2^1) + (2^0)
and as it is clear there is no better way than expressing the number in binary
15 = 1111
to express 15 we need 4 powers of 2 (therefore 4 1's in the binary form of 15)
hence the answer to n is the number of 1's in the binary form of n
verify this on 5
5 = 0101 thus the answer is 2
Set a counter 'ctr' for counting no. of 1's
In the end:
for (int m = n;m>0; m/=2)
{
ctr += m%2;
}
return ctr;