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 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.
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.
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 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.
Number sense involves understanding numbers and their relationships rather than just following algorithms. It has five key components and is important for skills like mental math, estimation, and problem solving. Developing number sense requires experiences with counting, magnitude, operations, and referents for quantities using a variety of manipulatives and representations.
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 lesson on rational numbers and the number line. It includes:
- Student outcomes of using number lines to locate integers and rational numbers, understanding signs of rational numbers, and opposites of rational numbers.
- An example of graphing the rational number 3/10 and its opposite on a number line.
- An exercise having students graph -7/4 and its opposite on a number line.
- An example using a number line to represent a real-world situation of water levels rising and falling.
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.
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.
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 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.
Number sense involves understanding numbers and their relationships rather than just following algorithms. It has five key components and is important for skills like mental math, estimation, and problem solving. Developing number sense requires experiences with counting, magnitude, operations, and referents for quantities using a variety of manipulatives and representations.
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 lesson on rational numbers and the number line. It includes:
- Student outcomes of using number lines to locate integers and rational numbers, understanding signs of rational numbers, and opposites of rational numbers.
- An example of graphing the rational number 3/10 and its opposite on a number line.
- An exercise having students graph -7/4 and its opposite on a number line.
- An example using a number line to represent a real-world situation of water levels rising and falling.
Teaching graphing systems of equations to special needscanillia
This document provides tips for teaching special needs students how to graph systems of equations. It recommends that students take notes on the starting point and slope of each equation. Direction arrows can help students remember which direction to move up or down based on positive or negative slopes. Identifying the point of intersection requires finding the x- and y-coordinates by following the grid lines from the point down to the x-axis and across to the y-axis. Common misconceptions like forgetting to start on the y-axis or misunderstanding slopes that are not fractions must be addressed. Providing notes and clear instruction on concepts can help special education students learn to graph systems of equations.
This document contains a lesson plan on positive and negative numbers on a number line. It includes exercises and problems for students to complete as a classwork assignment or independently. The lesson introduces plotting points on a number line and finding the opposite of a number. It has students graph points and their opposites, determine if a classmate's number line diagram is correct, choose numbers within ranges and graph their opposites and related integers. The lesson aims to build understanding of opposites and how positive and negative numbers are positioned in relation to each other on a number line.
This document provides an overview of different number systems including decimal, binary, and Mayan systems. It discusses various types of numbers such as natural numbers, integers, rational numbers, and irrational numbers. It also describes properties of numbers including terminating and non-terminating decimals, the number line, and rationalization of expressions involving square roots.
This document outlines a 5-day lesson plan for teaching linear equations to a 9th grade class of 10 boys and 8 girls. The lesson plan covers writing linear equations in various forms, including slope-intercept, point-slope, standard, and using two points. Students will learn through board work, games, and using a SMART board and computers for interactive activities. The goal is for 90% of students to understand linear equations. Technology like the SMART board and computers will be used for problems, crosswords, and games.
Developing Number Concepts in K-2 Learnersmflaming
This document discusses developing number sense in students and outlines several key building blocks or components of number sense, including rote counting, one-to-one correspondence, subitizing, tens frames, keeping track, conservation of number, hierarchical inclusion, compensation, part-whole relationships, unitizing/place value, and relationships between operations. It provides definitions and examples for each concept and suggests they take time and experience to build. A numerically powerful child can decompose numbers flexibly, understand relationships between numbers and operations, and connect numerals to real-life situations.
This document contains a lesson on rational numbers and locating them on a number line. It includes examples of writing fractions as decimals and decimals as fractions, graphing positive and negative rational numbers on the number line, and using rational numbers to represent real-world situations involving distances and locations. Students are asked to locate, graph, and compare rational numbers, write their opposites, and solve word problems placing rational number values on a number line diagram.
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.
1. The lesson plan introduces the concept of similar triangles to students through activities and songs.
2. Students are divided into groups and given activity cards with riddles to solve about triangles. This allows them to review the properties of triangles.
3. Additional activities have students name and measure angles of triangles, leading them to discover that triangles with equal angles are similar, with sides proportional to their corresponding angles.
4. The lesson reinforces the key points that similar triangles have equal angles and proportional sides through visual aids and poems to aid student understanding of this geometric concept.
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.
This lesson plan is for an 8th grade mathematics class on inverse proportion. The teacher will introduce the concept of inverse proportion by having students analyze how the length and breadth of rectangles must change to maintain a constant area. Students will work in groups on worksheet problems, such as calculating the length and breadth of rectangles with given areas, to understand that as one dimension increases the other must decrease. The lesson aims to help students recognize and provide examples of inverse proportion, as well as solve related problems.
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.
Number sense refers to an intuitive understanding of numbers and their relationships. It develops through exploring numbers in various contexts and relating them in flexible ways. The document discusses key components of number sense development in early grades, including prenumber concepts like patterning and sorting, counting principles like one-to-one correspondence and cardinality, rational counting strategies, and understanding relationships among numbers through benchmarks and part-whole relationships. Effective instruction focuses on developing these foundations of number sense through clear models, guided practice, and review.
Number words, numerals, and counting develop together as children learn mathematics. There are several components to recognizing numbers, including number word sequences, identifying and recognizing numerals, sequencing, ordering, and locating numbers between 1-100. Teachers aim to develop these skills through activities like counting objects, identifying numerals on cards, and counting forwards and backwards within a range of numbers. Counting progresses through distinct stages from rote counting, where children recite numbers but cannot determine quantity, to rational counting, where children demonstrate one-to-one correspondence between objects and numbers.
This mathematics lesson defines even and odd numbers and explores properties of adding and multiplying even and odd numbers. It states that the sum of two even numbers or two odd numbers is even or odd respectively. The sum of an even and odd number is odd. When multiplying, the product of two even numbers is even, two odd numbers is odd, and an even and odd number is even. Students are given examples and exercises to practice identifying whether sums and products are even or odd.
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 is a lesson plan on understanding the opposite of a number's opposite. It includes examples of locating numbers and their opposites on a number line, such as locating -2 and its opposite. The lesson defines the opposite of the opposite of a number as the original number, and provides examples such as the opposite of the opposite of 8 being 8. Students complete exercises to identify numbers and their opposites. The lesson emphasizes that the opposite of the opposite of any number is always the original number.
This lesson plan teaches students how to calculate the area of a parallelogram. It begins with defining key terms like parallelogram and explaining the properties that opposite sides are parallel and equal. Students are divided into groups to build parallelograms out of matchsticks and observe that drawing a perpendicular bisector divides it into two equal rectangles. They learn that the area of the parallelogram is equal to the area of the two rectangles combined, which can be calculated as base x height. Examples are worked through and follow up activities provided to reinforce the area formula for parallelograms.
The document provides a mathematics curriculum guide for third grade students in the Isaac School District. It focuses on unit 8 which covers addition, subtraction, and number systems over 3 sessions. The unit teaches students that numbers can be represented in many ways and used to solve problems. Students will learn about relationships between numbers, place value, and comparing and ordering whole numbers. They will solve 2-step word problems using the four operations and identify arithmetic patterns. Students will also learn to fluently add and subtract within 1000 using strategies based on place value.
The document discusses the concept of finding the opposite of a number's opposite. It provides examples of writing equations to represent this, such as -(-5) = 5, meaning the opposite of the opposite of 5 is 5. Students practice locating numbers and their opposites on a number line. The lesson emphasizes that in general, the opposite of the opposite of any number is the original number.
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.
Teaching graphing systems of equations to special needscanillia
This document provides tips for teaching special needs students how to graph systems of equations. It recommends that students take notes on the starting point and slope of each equation. Direction arrows can help students remember which direction to move up or down based on positive or negative slopes. Identifying the point of intersection requires finding the x- and y-coordinates by following the grid lines from the point down to the x-axis and across to the y-axis. Common misconceptions like forgetting to start on the y-axis or misunderstanding slopes that are not fractions must be addressed. Providing notes and clear instruction on concepts can help special education students learn to graph systems of equations.
This document contains a lesson plan on positive and negative numbers on a number line. It includes exercises and problems for students to complete as a classwork assignment or independently. The lesson introduces plotting points on a number line and finding the opposite of a number. It has students graph points and their opposites, determine if a classmate's number line diagram is correct, choose numbers within ranges and graph their opposites and related integers. The lesson aims to build understanding of opposites and how positive and negative numbers are positioned in relation to each other on a number line.
This document provides an overview of different number systems including decimal, binary, and Mayan systems. It discusses various types of numbers such as natural numbers, integers, rational numbers, and irrational numbers. It also describes properties of numbers including terminating and non-terminating decimals, the number line, and rationalization of expressions involving square roots.
This document outlines a 5-day lesson plan for teaching linear equations to a 9th grade class of 10 boys and 8 girls. The lesson plan covers writing linear equations in various forms, including slope-intercept, point-slope, standard, and using two points. Students will learn through board work, games, and using a SMART board and computers for interactive activities. The goal is for 90% of students to understand linear equations. Technology like the SMART board and computers will be used for problems, crosswords, and games.
Developing Number Concepts in K-2 Learnersmflaming
This document discusses developing number sense in students and outlines several key building blocks or components of number sense, including rote counting, one-to-one correspondence, subitizing, tens frames, keeping track, conservation of number, hierarchical inclusion, compensation, part-whole relationships, unitizing/place value, and relationships between operations. It provides definitions and examples for each concept and suggests they take time and experience to build. A numerically powerful child can decompose numbers flexibly, understand relationships between numbers and operations, and connect numerals to real-life situations.
This document contains a lesson on rational numbers and locating them on a number line. It includes examples of writing fractions as decimals and decimals as fractions, graphing positive and negative rational numbers on the number line, and using rational numbers to represent real-world situations involving distances and locations. Students are asked to locate, graph, and compare rational numbers, write their opposites, and solve word problems placing rational number values on a number line diagram.
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.
1. The lesson plan introduces the concept of similar triangles to students through activities and songs.
2. Students are divided into groups and given activity cards with riddles to solve about triangles. This allows them to review the properties of triangles.
3. Additional activities have students name and measure angles of triangles, leading them to discover that triangles with equal angles are similar, with sides proportional to their corresponding angles.
4. The lesson reinforces the key points that similar triangles have equal angles and proportional sides through visual aids and poems to aid student understanding of this geometric concept.
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.
This lesson plan is for an 8th grade mathematics class on inverse proportion. The teacher will introduce the concept of inverse proportion by having students analyze how the length and breadth of rectangles must change to maintain a constant area. Students will work in groups on worksheet problems, such as calculating the length and breadth of rectangles with given areas, to understand that as one dimension increases the other must decrease. The lesson aims to help students recognize and provide examples of inverse proportion, as well as solve related problems.
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.
Number sense refers to an intuitive understanding of numbers and their relationships. It develops through exploring numbers in various contexts and relating them in flexible ways. The document discusses key components of number sense development in early grades, including prenumber concepts like patterning and sorting, counting principles like one-to-one correspondence and cardinality, rational counting strategies, and understanding relationships among numbers through benchmarks and part-whole relationships. Effective instruction focuses on developing these foundations of number sense through clear models, guided practice, and review.
Number words, numerals, and counting develop together as children learn mathematics. There are several components to recognizing numbers, including number word sequences, identifying and recognizing numerals, sequencing, ordering, and locating numbers between 1-100. Teachers aim to develop these skills through activities like counting objects, identifying numerals on cards, and counting forwards and backwards within a range of numbers. Counting progresses through distinct stages from rote counting, where children recite numbers but cannot determine quantity, to rational counting, where children demonstrate one-to-one correspondence between objects and numbers.
This mathematics lesson defines even and odd numbers and explores properties of adding and multiplying even and odd numbers. It states that the sum of two even numbers or two odd numbers is even or odd respectively. The sum of an even and odd number is odd. When multiplying, the product of two even numbers is even, two odd numbers is odd, and an even and odd number is even. Students are given examples and exercises to practice identifying whether sums and products are even or odd.
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 is a lesson plan on understanding the opposite of a number's opposite. It includes examples of locating numbers and their opposites on a number line, such as locating -2 and its opposite. The lesson defines the opposite of the opposite of a number as the original number, and provides examples such as the opposite of the opposite of 8 being 8. Students complete exercises to identify numbers and their opposites. The lesson emphasizes that the opposite of the opposite of any number is always the original number.
This lesson plan teaches students how to calculate the area of a parallelogram. It begins with defining key terms like parallelogram and explaining the properties that opposite sides are parallel and equal. Students are divided into groups to build parallelograms out of matchsticks and observe that drawing a perpendicular bisector divides it into two equal rectangles. They learn that the area of the parallelogram is equal to the area of the two rectangles combined, which can be calculated as base x height. Examples are worked through and follow up activities provided to reinforce the area formula for parallelograms.
The document provides a mathematics curriculum guide for third grade students in the Isaac School District. It focuses on unit 8 which covers addition, subtraction, and number systems over 3 sessions. The unit teaches students that numbers can be represented in many ways and used to solve problems. Students will learn about relationships between numbers, place value, and comparing and ordering whole numbers. They will solve 2-step word problems using the four operations and identify arithmetic patterns. Students will also learn to fluently add and subtract within 1000 using strategies based on place value.
The document discusses the concept of finding the opposite of a number's opposite. It provides examples of writing equations to represent this, such as -(-5) = 5, meaning the opposite of the opposite of 5 is 5. Students practice locating numbers and their opposites on a number line. The lesson emphasizes that in general, the opposite of the opposite of any number is the original number.
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.
This document provides a lesson on absolute value, magnitude, and distance. It begins with an opening exercise where students find pairs of numbers that are the same distance from zero. They conclude that numbers and their opposites will have the same absolute value. Examples and exercises are then provided to illustrate using absolute value to represent the distance between a number and zero, and to find the magnitude of positive and negative quantities. The lesson emphasizes that absolute value is always positive and represents the distance from zero.
This document summarizes lessons 1 and 2 from module 3 on rational numbers. It discusses positive and negative numbers on the number line, with integers being whole numbers and their opposites including zero. Students learn that negative numbers are located to the left of zero and decrease in value as they move further left, while positive numbers are to the right of zero and increase in value as they move further right. Real-world examples using temperature scales, bank accounts, and elevation are provided to demonstrate uses of positive and negative numbers. Exercises have students classify terms as positive or negative numbers and represent debit and credit on a number line.
6.NS.C.5 Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation.
Objective: Students will find the opposite of an integer by using a number line.
This document defines integers and discusses their properties and real-world applications. It begins by defining integers as whole numbers and their opposites, such as 6 and -6. It then discusses how integers are used to represent temperatures below zero, locations below sea level, and debt. The document explains how to add and subtract integers by finding opposites and absolute value. It provides examples of using integers to measure distance on a number line.
This document defines integers and discusses their properties and real-world applications. Integers include whole numbers and their opposites, such as 6 and -6. Negative numbers are used to represent temperatures below zero, locations below sea level, and amounts of debt. The absolute value of a number represents its distance from zero on the number line. Opposite numbers are integers that are the same distance from zero but in opposite directions. Distance between integers can be found by subtracting their absolute values if they are on the same side of zero, and adding if they are on opposite sides.
integers_distance and absolute value (1).pptShefaCapuras1
This document defines integers and discusses their properties and real-world applications. It begins by defining integers as whole numbers and their opposites, such as 6 and -6. Negative numbers are then introduced as numbers less than zero, and examples are given of how they are used to represent temperatures below zero, locations below sea level, and debt. The key concepts of opposites, absolute value, and comparing integers are explained. Real-world examples of distance are provided to introduce the concept of finding the distance between integers on a number line.
integers_distance and absolute value.pptSanjayDhyani8
This document defines integers and discusses their properties and real-world applications. Integers include whole numbers and their opposites, such as 6 and -6. Negative numbers are used to represent temperatures below zero, locations below sea level, and amounts of debt. The absolute value of a number represents its distance from zero on the number line. Opposite numbers are integers that are the same distance from zero but in opposite directions. Distance between integers can be calculated by subtracting or adding their absolute values depending on whether they are on the same or opposite sides of zero.
integers_distance and absolute value (2).pptAgrimDhyani
This document defines integers and discusses their properties and real-world applications. Integers include whole numbers and their opposites, such as 6 and -6. Negative numbers are used to represent temperatures below zero, locations below sea level, and amounts of debt. The absolute value of a number represents its distance from zero on the number line. Opposite numbers are integers that are the same distance from zero but in opposite directions. Distance between integers can be calculated by subtracting or adding their absolute values depending on whether they are on the same or opposite sides of zero.
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 discusses using an empty number line as a mental math strategy for primary grade students. It explains that the empty number line allows students to create a mental image of math strategies and more easily make the leap to mental calculations without paper. Using the empty number line also increases students' number sense and flexibility with numbers. The document provides an example of how to introduce the empty number line technique to students and have them use it to solve math problems.
This document provides a lesson on identifying true and false number sentences involving equations and inequalities. The lesson begins with examples of evaluating simple number sentences as true or false. Students then work through examples of identifying values for a variable that make equations and inequalities true or false. The examples are designed to help students recognize that the simpler form of an equation or inequality clearly shows the solution. The lesson concludes with exercises where students state when equations and inequalities will be true or false based on the value of the variable.
The document provides an overview of different number systems including decimal, binary, Mayan, natural numbers, integers, rational numbers, and irrational numbers. It discusses key concepts like place value, bases, rationalization, and successive magnification on the number line. The document was written by a student as part of a school project on mathematical numbers and systems.
The document describes a mathematics lesson on the coordinate plane. It introduces students to locating points on the coordinate plane using ordered pairs of numbers. It discusses extending the x- and y-axes to include negative numbers, revealing all four quadrants. Students learn to identify the origin and locate points in each quadrant based on the signs of the coordinates in the ordered pair. Exercises have students graph points and analyze similarities within each quadrant based on sign patterns in the coordinates.
FS Maths Level 2 – February 28, 2023 (All about numbers).LeadAcademy3
The document provides information about different types of numbers:
- Integers are whole numbers that can be positive, negative, or zero. Prime numbers only divide by 1 and themselves.
- Rational numbers can be written as fractions or recurring decimals. Irrational numbers are never-ending, non-repeating decimals like π.
- Positive numbers are greater than 0, negative numbers are less than 0. A number line can help visualize differences between positive and negative numbers.
- Place value refers to the value of each digit in a number depending on its position - the further left, the greater the value. Large numbers can be written with commas separating groups of three digits.
FS Maths Level 2 - February 28, 2023 (All about numbers)LeadAcademy3
The document provides information about different types of numbers:
- Integers are whole numbers that can be positive, negative, or zero. Prime numbers only divide by 1 and themselves.
- Rational numbers can be written as fractions or recurring decimals. Irrational numbers are never-ending, non-repeating decimals like π.
- Positive numbers are greater than 0, negative numbers are less than 0. A number line can help visualize positive and negative numbers and find differences between them.
- Place value refers to the value of each digit in a number depending on its position - the further left, the greater the value. Large numbers can be written with commas separating groups of three digits.
FS English Level 2 – March 02, 2023 (Spelling, Punctuation and Grammar : Usin...MdImran691
The document provides information about different types of numbers:
- Integers are whole numbers that can be positive, negative, or zero. Prime numbers only divide by 1 and themselves.
- Rational numbers can be written as fractions or recurring decimals. Irrational numbers are never-ending, non-repeating decimals like π.
- Positive numbers are greater than 0, negative numbers are less than 0. A number line can help visualize positive and negative numbers and find differences between them.
- Place value refers to the value of each digit in a number depending on its position - the further left, the greater the value. Large numbers can be written with commas separating groups of three digits.
This document provides a lesson on determining if number sentences are true or false based on the symbols used. It begins by explaining the meaning of the equality and inequality symbols =, <, >, ≤, and ≥. Students then practice identifying true and false number sentences by substituting values for variables and evaluating. The lesson emphasizes that number sentences always evaluate to either true or false, which is important for understanding solutions to equations.
This lesson teaches students about locating ordered pairs on the coordinate plane:
- It reviews extending the x-axis and y-axis to include negative numbers, dividing the plane into four quadrants.
- Students learn to identify the origin and locate points on the axes or in the quadrants by their ordered pair coordinates.
- Exercises have students graph points, identify quadrants, and note properties of points based on their coordinates.
This document is a study guide for nouns created by Mrs. Labuski. It contains vocabulary terms related to nouns and lists 21 lessons on different types of nouns including concrete nouns, abstract nouns, common nouns, proper nouns, singular nouns, plural nouns, and possessive nouns. For each lesson, it provides links to online interactive activities and practice exercises related to the noun topic. It also lists additional grammar resources for further practice.
This document contains a quiz on nouns with questions about identifying different types of nouns such as proper, concrete, abstract, and plural nouns. It also contains exercises on forming plural nouns and possessive nouns as well as a short story and questions to identify nouns in the story. The key provides the answers to the quiz and exercises.
This document outlines the curriculum, expectations, and supplies for a 6th grade social studies class. It includes:
- An overview of the course content which will cover the geography and history of the Eastern Hemisphere, including major ancient and modern civilizations.
- A list of required supplies and materials for classwork and homework assignments.
- Classroom expectations which emphasize being prepared, respectful, and asking questions.
- Details on grading, homework policies, absences, units to be covered, and contact information for the teachers and website.
The document is a supply list for Team Orion's sixth grade class for the 2015-2016 school year. It lists the required supplies for the team binder and various subjects including science, social studies, English Language Arts (ELA), and math. Some common required items across subjects are binders, loose-leaf paper, dividers, and tissues. Supplies are tailored to individual teachers for ELA and math. Students are only allowed to carry two binders between classes and will have time to go to lockers between periods.
This document provides an outline for writing a book report with 4 paragraphs: an introduction summarizing the book's events and setting, a character description paragraph with evidence, an excerpt explanation paragraph, and a conclusion discussing the author's purpose and theme. The book report format emphasizes including textual evidence and explaining the relevance and significance of key moments in the story.
The document outlines the supply list for Team Orion's sixth grade students for the 2015-2016 school year. It details the supplies needed for a team binder to be carried between all classes, as well as subject-specific supplies for science, social studies, English language arts, and math. Students are asked to have a team binder, subject binders, loose-leaf paper, dividers, notebooks, folders, and other classroom supplies such as tissues and post-it notes. They are not allowed to carry backpacks between classes.
This document provides an outline for writing a business letter summarizing a recently read book. The letter should include an introduction paragraph with the title, author, genre, and brief summary. A second paragraph should make a claim about a main character and provide textual evidence. A third paragraph should include a scene excerpt, its relevance, and why it was chosen. The conclusion paragraph should discuss the author's purpose and theme. A bibliography is required at the end. The letter must follow proper formatting guidelines.
This document contains a review sheet for a math final exam. It includes two parts - a multiple choice section with 37 questions covering various math concepts, and a short answer section with 7 word problems requiring calculations and explanations. The review sheet provides the questions, space to write answers, and an answer key in the back to check work.
This document contains a multi-part math exam review with multiple choice and short answer questions. It provides practice problems covering topics like geometry, ratios, equations, expressions, and word problems. The review is designed to help students prepare for their math final exam.
This document contains a review sheet for a math final exam. It includes multiple choice and short answer questions covering topics like geometry, algebra, ratios, and word problems. It also provides the answers to the multiple choice section. The short answer questions require showing work and include problems finding areas, writing equations, comparing ratios, and solving word problems involving money.
This document contains a math lesson on calculating the volume of rectangular prisms. It provides examples of three rectangular prisms with different heights but the same length and width, and has students write expressions for the volume of each. It then has students recognize that these expressions all represent the area of the base multiplied by the height. Students are asked to determine the volumes of additional prisms using this area of base times height formula.
This document contains notes from a math lesson on volume. It discusses determining the volume of composite figures using decomposition into simpler shapes. Students will practice finding the volume of various objects. The document contains examples of area problems and notes for students to solve.
1) This lesson teaches students the formulas for calculating the volume of right rectangular prisms and cubes. It provides examples of using the formulas to find the volume when given the length, width, height or area of the base.
2) Students complete exercises that explore how changes to the lengths or heights affect the volume. They discover that if the height is doubled, the volume is also doubled, and if the height is tripled the volume is tripled.
3) No matter the shape, when the side lengths are changed by the same fractional amount, the volume changes by that fractional amount cubed. For example, if the sides are halved, the volume is one-eighth of the original.
This document provides examples and exercises about calculating the volumes of cubes and rectangular prisms using formulas. It begins with examples of calculating the volume of a cube with sides of 2 1/4 cm and a rectangular prism with a base area of 7/12 ft^2 and height of 1/3 ft. The exercises then involve calculating volumes of cubes and prisms when dimensions are changed, identifying relationships between dimensions and volumes, and writing expressions for volumes.
This lesson teaches students about calculating the volume of rectangular prisms using two different formulas: 1) length × width × height and 2) area of the base × height. Students work through examples calculating the volume of various rectangular prisms using both formulas. They learn that it does not matter which face is used as the base, as the volume will be the same. The lesson reinforces that volume can be expressed in multiple equivalent ways and emphasizes using the area of the base times the height.
This document provides examples and problems about calculating the volume of rectangular prisms. It begins by showing different rectangular prisms and having students write expressions for the volume of each using length, width, and height. It explains that the volume can also be written as the area of the base times the height. Students then practice calculating volumes using both methods. Later problems involve calculating volume when given the area of the base and height or vice versa. The goal is for students to understand that the volume of a rectangular prism is the area of its base multiplied by its height.
1) The document outlines a math lesson plan for a week in May that includes topics on polygons, area, surface area, and volume.
2) On Tuesday, students will work on problem sets for Lesson 9 and 13, which cover finding the perimeter and area of polygons on the coordinate plane.
3) On Thursday, students will work on a Lesson 15 worksheet, and on Friday they are asked to bring in a rectangular prism from home to create a net and label edge lengths.
Lesson 9 focuses on determining the area and perimeter of polygons on the coordinate plane. Students will find the perimeter of irregular figures by using coordinates to find the length of sides joining points with the same x- or y-coordinate. Students will also find the area enclosed by a polygon by composing or decomposing it into polygons with known area formulas. The lesson provides examples of calculating perimeter and area, as well as exercises for students to practice these skills by decomposing polygons in different ways.
This lesson teaches students how to determine the area and perimeter of polygons on a coordinate plane. It includes examples of calculating area and perimeter of polygons. Students are given exercises to calculate the area of various polygons, determine both the area and perimeter of shapes, and write expressions to represent the area calculated in different ways. The lesson aims to help students practice finding area and perimeter of polygons located on a coordinate plane.
This document discusses a lesson on drawing polygons on the coordinate plane. The lesson objectives are for students to use absolute value to determine distances between integers on the coordinate plane in order to find side lengths of polygons. The document includes examples of polygons drawn on the coordinate plane and questions about determining their areas and shapes. It closes by asking students to complete an exit ticket to assess their understanding of determining areas of polygons using different methods, and how the polygon shape influences the area calculation method.