This document discusses using positive and negative numbers to represent real-world situations involving elevation, temperature, and bank accounts. It provides examples of how zero represents a fixed reference point, such as sea level, and how positive numbers above zero indicate elevation gains and negative numbers below zero indicate elevation losses. Students work in groups to create posters showing real-world scenarios that use positive and negative numbers, then discuss precisely describing situations involving integers.
Tim opened a savings account with a $150 deposit from his birthday. Later, he deposited $25 from his allowance. He then withdrew $35 to buy a video game, which incurred a $5 fee. His various transactions were represented as positive and negative numbers on a number line, modeling gains as positive and losses as negative amounts.
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.
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 lesson plans and materials for teaching students about calculating the area of acute triangles using height and base. It includes:
- An explanation of how to find the height of an acute triangle by drawing the altitude, which splits the triangle into two right triangles.
- An example of calculating the area of an acute triangle by finding the areas of the two right triangles and adding them together.
- A discussion of how the area of the acute triangle can also be calculated using the area formula for right triangles, A = 1/2 x base x height, by considering the entire acute triangle as one shape.
- Exercises for students to practice calculating areas of acute triangles using both methods to determine that
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 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 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 instruction on graphing functions and qualitative graphs. It includes examples of sketching and describing qualitative graphs based on verbal descriptions of relationships between quantities over time.
2. It provides examples of sketching qualitative graphs to represent a bathtub filling with water, the number of people at a restaurant, a bouncing tennis ball, and a swinging child.
3. Qualitative graphs can be used to model relationships between quantities without specific numerical values by representing the essential features of the situation through the shape of the graph over time.
Tim opened a savings account with a $150 deposit from his birthday. Later, he deposited $25 from his allowance. He then withdrew $35 to buy a video game, which incurred a $5 fee. His various transactions were represented as positive and negative numbers on a number line, modeling gains as positive and losses as negative amounts.
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.
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 lesson plans and materials for teaching students about calculating the area of acute triangles using height and base. It includes:
- An explanation of how to find the height of an acute triangle by drawing the altitude, which splits the triangle into two right triangles.
- An example of calculating the area of an acute triangle by finding the areas of the two right triangles and adding them together.
- A discussion of how the area of the acute triangle can also be calculated using the area formula for right triangles, A = 1/2 x base x height, by considering the entire acute triangle as one shape.
- Exercises for students to practice calculating areas of acute triangles using both methods to determine that
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 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 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 instruction on graphing functions and qualitative graphs. It includes examples of sketching and describing qualitative graphs based on verbal descriptions of relationships between quantities over time.
2. It provides examples of sketching qualitative graphs to represent a bathtub filling with water, the number of people at a restaurant, a bouncing tennis ball, and a swinging child.
3. Qualitative graphs can be used to model relationships between quantities without specific numerical values by representing the essential features of the situation through the shape of the graph over time.
This document provides a strategic intervention material to help students learn about solving real-life problems involving right triangles using trigonometric ratios. It begins with definitions of key terms like line of sight, angle of elevation, and angle of depression. Students are given examples of problems involving these angles and their solutions. Later activities require students to illustrate problem situations, identify given information, formulas used, and solve problems determining unknown angles or distances. The material aims to supplement classroom learning and help students independently practice and understand solving right triangle problems.
This document discusses exponents and exponential expressions. It contains three examples: [1] folding a piece of paper repeatedly in half, where the number of layers doubles each time, modeled by 2n; [2] bacterial growth through binary fission, where the number of bacteria doubles each generation, also modeled by 2n; [3] the volume of a rectangular solid where the dimensions are proportional, leading to an expression of the form 6w3. Students are asked to predict patterns, model situations exponentially, write expressions and evaluate them. Exponents are shown to arise in many real-world applications involving doubling or repeated multiplication.
Populations LabLAB #3, PART I ESTIMATING POPULATION SIZEO.docxharrisonhoward80223
Populations Lab
LAB #3, PART I: ESTIMATING POPULATION SIZE
OBJECTIVE: To estimate population sizes and dynamics, you will be able to:
1. Compare and contrast methods of estimating population size (CLO #1)
2. Explain and use simple mathematical models of population dynamics (CLO #2)
3. Synthesize your research with the primary literature in ecology (CLO #3)
BACKGROUND INFORMATION:
Estimating the size of populations of organisms is a central problem in field ecology. It is one of the most basic pieces of information we can collect and is an important start for other ecological studies and conservation and management efforts. There are several ways to evaluate organism count (pop. size) or density (count/area), which are two means of characterizing populations
Sometimes, it is sufficient to evaluate organism relative abundance (relative representation of a species in a particular location). In that case, an ecologist can use indices. Indices are anything that can be correlated to the number of organisms in a given habitat (e. g., feces pellets, browsed branches, tracks, plant cover, etc.).
When population size is necessary, population estimates can be developed with a number of sampling and mathematical methods. Since it is rarely feasible to count an entire population, ecologists count a portion of the population and then estimate the total population size using mathematical functions. This can be done a number of ways, but in this exercise we will use two of the most common: density methods and mark-recapture methods.
Density method: In this method, ecologists will count the number of individuals in a prescribed area and then scale this measurement up to estimate the whole population size. Transect methods, in which an ecologist traverses a transect and counts individuals at specific locations along the line, are commonly used for plants and occasionally for animals.
Density methods require a few key assumptions:
1. The population is confined to a specific area
2. Individuals are readily detectable
3. Count areas are extensive relative to area occupied by population
Using these assumptions, ecologists use various models to calculate population size. In this lab, you will use a simple Seber (1973) model:
where N = the population estimate, N0 = the average number of organisms found in a plot. And p = the ratio of the individual plot area to total area (e.g. 25 cm2/820 cm2). Once you have calculated No, use the equation above to calculate N.
Confidence intervals provide a measure of the precision of our estimate (population size, N, in this case). A 95% confidence interval is a range of values that is thought to contain the true population size 95% of the time…that is, if you repeat your sampling and confidence interval calculation 100 times, the confidence intervals will capture the true value 95 of those times. To calculate the 95% confidence interval we can simply calculate the upper and lower confidence limits for N0 and then .
1. The document contains a lesson on angles of elevation and depression. It includes class rules, learning objectives, activities to identify these angles, and a multiple choice test.
2. Students are split into groups to complete activities identifying line of sight and these angles in diagrams. They also search for real-world examples.
3. The lesson evaluates students on correctly identifying these angles, the organization and clarity of their work, and their presentation skills. It emphasizes applying the concepts to daily life.
This lesson teaches students that the area formula for triangles (A = 1/2 x base x height) applies to all types of triangles, including those with:
1) An altitude inside the triangle forming a right angle with the base
2) A side that is the altitude forming a right angle with the base
3) An altitude outside the triangle forming a right angle with the base
Students cut triangles out and fit them into halves of rectangles to show that any triangle has the same area as half of a rectangle with the same base and height. Therefore, the area formula applies regardless of where the altitude is located.
This lesson teaches students how to calculate the area of obtuse triangles using the height and base. It provides examples of decomposing obtuse, right, and acute triangles into rectangles to illustrate that the area formula is one-half the base times the height. Students practice calculating areas of various triangles and explaining their work. The lesson ensures students understand how to identify the base and height of any triangle in order to use the area formula correctly.
This document discusses different methods for graphically presenting quantitative data, including histograms, stem-and-leaf plots, dot plots, and time plots. It provides examples of each using data on great white shark lengths, healing of skin wounds in newts, and guinea pig survival times. Histograms can be used to show the distribution and identify outliers. The number of classes used in a histogram can affect its appearance. Descriptors like shape, center, and spread can characterize histograms. Stem-and-leaf plots and dot plots sort data in an alternative visualization. Time plots are suited for data measured over successive time points.
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.
This lesson teaches students how to calculate the area of acute triangles using the height and base. Students first decompose acute triangles into right triangles by drawing the altitude, and calculate the area of each right triangle. They then realize the total area is the sum of the right triangle areas. Finally, students learn that for any acute triangle, the area can be calculated as A = 1/2 x base x height, where the height is the altitude perpendicular to the base. Through examples, students verify this formula works for both decomposing triangles into right triangles and calculating the area directly.
This document provides a lesson on absolute value and its uses in determining magnitude and distance on a number line. It includes examples of using absolute value to find the magnitude of quantities like amounts of money, weights, temperatures, and distances from zero on a number line. It also discusses properties of absolute value like how a number and its opposite have the same absolute value. Students are given practice problems to apply these concepts.
The document discusses classroom rules for "Ma'am Tasha" which includes maintaining cleanliness, wearing a facemask, bringing sanitizer, participating in class, and being silent when the teacher is discussing. It also discusses angles of elevation and depression, defining related terms like line of sight and providing examples to identify if an angle is one of elevation or depression. There are activities for students to practice drawing pictures based on scenarios involving elevation and depression angles.
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.
12. Angle of Elevation & Depression.pptxBebeannBuar1
This document discusses angles of elevation and depression. It defines an angle of elevation as the angle formed between a horizontal line and the line of sight to an object located above the horizontal line. An angle of depression is defined as the angle formed between a horizontal line and the line of sight to an object located below the horizontal line. The document provides examples of solving problems involving angles of elevation and depression using trigonometric functions like tangent, sine, and the Pythagorean theorem. It emphasizes drawing a diagram, identifying if it is an angle of elevation or depression, and using the appropriate trigonometric ratio to solve for missing lengths.
This document is a lesson plan on solving real-life problems involving right triangles using trigonometric ratios. It includes examples of using sine, cosine, and tangent to solve problems related to the height of a kite, length of a broken tree, and width of a river. The lesson teaches students how to set up and solve equations using trigonometric ratios for problems involving right triangles and angles of elevation and depression. Students complete an activity in groups and assessment with multiple choice questions to practice applying the concepts.
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.
The document provides an overview of an honors physics class. It discusses topics like vectors, scalars, displacement, velocity, acceleration, and problem-solving techniques. Key concepts are explained through examples, such as calculating displacement and velocity from graphs of position over time. Homework solutions are provided at the end.
This document discusses several key concepts related to the scientific method and quantitative analysis:
1. It outlines the general steps of the scientific method including making observations, forming hypotheses, testing hypotheses through experiments, and developing theories supported by data.
2. It defines key terms like quantitative data, measurements, units, and derived units. The International System of Units (SI) and common prefixes are explained.
3. Rules for determining significant figures in measurements and calculations are presented.
This document discusses using multi-step word problems and equations to model real-world situations involving two variables. It provides examples of identifying independent and dependent variables, writing equations to represent relationships, making tables of ordered pairs, and plotting graphs. Students are given practice writing equations, identifying variables, making tables and graphs for problems involving money saved, books collected, cost of rides, and more. The document emphasizes using graphs to show how the dependent variable changes as the independent variable changes.
The document discusses angle of depression and how to solve problems involving it. It defines angle of depression as the angle formed below the horizontal line when an observer looks at an object lower than their position. Several examples are provided of calculating distances and widths using the angle of depression and known heights. The objectives are to identify and solve word problems involving angle of depression and understand its real-life applications.
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 provides a strategic intervention material to help students learn about solving real-life problems involving right triangles using trigonometric ratios. It begins with definitions of key terms like line of sight, angle of elevation, and angle of depression. Students are given examples of problems involving these angles and their solutions. Later activities require students to illustrate problem situations, identify given information, formulas used, and solve problems determining unknown angles or distances. The material aims to supplement classroom learning and help students independently practice and understand solving right triangle problems.
This document discusses exponents and exponential expressions. It contains three examples: [1] folding a piece of paper repeatedly in half, where the number of layers doubles each time, modeled by 2n; [2] bacterial growth through binary fission, where the number of bacteria doubles each generation, also modeled by 2n; [3] the volume of a rectangular solid where the dimensions are proportional, leading to an expression of the form 6w3. Students are asked to predict patterns, model situations exponentially, write expressions and evaluate them. Exponents are shown to arise in many real-world applications involving doubling or repeated multiplication.
Populations LabLAB #3, PART I ESTIMATING POPULATION SIZEO.docxharrisonhoward80223
Populations Lab
LAB #3, PART I: ESTIMATING POPULATION SIZE
OBJECTIVE: To estimate population sizes and dynamics, you will be able to:
1. Compare and contrast methods of estimating population size (CLO #1)
2. Explain and use simple mathematical models of population dynamics (CLO #2)
3. Synthesize your research with the primary literature in ecology (CLO #3)
BACKGROUND INFORMATION:
Estimating the size of populations of organisms is a central problem in field ecology. It is one of the most basic pieces of information we can collect and is an important start for other ecological studies and conservation and management efforts. There are several ways to evaluate organism count (pop. size) or density (count/area), which are two means of characterizing populations
Sometimes, it is sufficient to evaluate organism relative abundance (relative representation of a species in a particular location). In that case, an ecologist can use indices. Indices are anything that can be correlated to the number of organisms in a given habitat (e. g., feces pellets, browsed branches, tracks, plant cover, etc.).
When population size is necessary, population estimates can be developed with a number of sampling and mathematical methods. Since it is rarely feasible to count an entire population, ecologists count a portion of the population and then estimate the total population size using mathematical functions. This can be done a number of ways, but in this exercise we will use two of the most common: density methods and mark-recapture methods.
Density method: In this method, ecologists will count the number of individuals in a prescribed area and then scale this measurement up to estimate the whole population size. Transect methods, in which an ecologist traverses a transect and counts individuals at specific locations along the line, are commonly used for plants and occasionally for animals.
Density methods require a few key assumptions:
1. The population is confined to a specific area
2. Individuals are readily detectable
3. Count areas are extensive relative to area occupied by population
Using these assumptions, ecologists use various models to calculate population size. In this lab, you will use a simple Seber (1973) model:
where N = the population estimate, N0 = the average number of organisms found in a plot. And p = the ratio of the individual plot area to total area (e.g. 25 cm2/820 cm2). Once you have calculated No, use the equation above to calculate N.
Confidence intervals provide a measure of the precision of our estimate (population size, N, in this case). A 95% confidence interval is a range of values that is thought to contain the true population size 95% of the time…that is, if you repeat your sampling and confidence interval calculation 100 times, the confidence intervals will capture the true value 95 of those times. To calculate the 95% confidence interval we can simply calculate the upper and lower confidence limits for N0 and then .
1. The document contains a lesson on angles of elevation and depression. It includes class rules, learning objectives, activities to identify these angles, and a multiple choice test.
2. Students are split into groups to complete activities identifying line of sight and these angles in diagrams. They also search for real-world examples.
3. The lesson evaluates students on correctly identifying these angles, the organization and clarity of their work, and their presentation skills. It emphasizes applying the concepts to daily life.
This lesson teaches students that the area formula for triangles (A = 1/2 x base x height) applies to all types of triangles, including those with:
1) An altitude inside the triangle forming a right angle with the base
2) A side that is the altitude forming a right angle with the base
3) An altitude outside the triangle forming a right angle with the base
Students cut triangles out and fit them into halves of rectangles to show that any triangle has the same area as half of a rectangle with the same base and height. Therefore, the area formula applies regardless of where the altitude is located.
This lesson teaches students how to calculate the area of obtuse triangles using the height and base. It provides examples of decomposing obtuse, right, and acute triangles into rectangles to illustrate that the area formula is one-half the base times the height. Students practice calculating areas of various triangles and explaining their work. The lesson ensures students understand how to identify the base and height of any triangle in order to use the area formula correctly.
This document discusses different methods for graphically presenting quantitative data, including histograms, stem-and-leaf plots, dot plots, and time plots. It provides examples of each using data on great white shark lengths, healing of skin wounds in newts, and guinea pig survival times. Histograms can be used to show the distribution and identify outliers. The number of classes used in a histogram can affect its appearance. Descriptors like shape, center, and spread can characterize histograms. Stem-and-leaf plots and dot plots sort data in an alternative visualization. Time plots are suited for data measured over successive time points.
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.
This lesson teaches students how to calculate the area of acute triangles using the height and base. Students first decompose acute triangles into right triangles by drawing the altitude, and calculate the area of each right triangle. They then realize the total area is the sum of the right triangle areas. Finally, students learn that for any acute triangle, the area can be calculated as A = 1/2 x base x height, where the height is the altitude perpendicular to the base. Through examples, students verify this formula works for both decomposing triangles into right triangles and calculating the area directly.
This document provides a lesson on absolute value and its uses in determining magnitude and distance on a number line. It includes examples of using absolute value to find the magnitude of quantities like amounts of money, weights, temperatures, and distances from zero on a number line. It also discusses properties of absolute value like how a number and its opposite have the same absolute value. Students are given practice problems to apply these concepts.
The document discusses classroom rules for "Ma'am Tasha" which includes maintaining cleanliness, wearing a facemask, bringing sanitizer, participating in class, and being silent when the teacher is discussing. It also discusses angles of elevation and depression, defining related terms like line of sight and providing examples to identify if an angle is one of elevation or depression. There are activities for students to practice drawing pictures based on scenarios involving elevation and depression angles.
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.
12. Angle of Elevation & Depression.pptxBebeannBuar1
This document discusses angles of elevation and depression. It defines an angle of elevation as the angle formed between a horizontal line and the line of sight to an object located above the horizontal line. An angle of depression is defined as the angle formed between a horizontal line and the line of sight to an object located below the horizontal line. The document provides examples of solving problems involving angles of elevation and depression using trigonometric functions like tangent, sine, and the Pythagorean theorem. It emphasizes drawing a diagram, identifying if it is an angle of elevation or depression, and using the appropriate trigonometric ratio to solve for missing lengths.
This document is a lesson plan on solving real-life problems involving right triangles using trigonometric ratios. It includes examples of using sine, cosine, and tangent to solve problems related to the height of a kite, length of a broken tree, and width of a river. The lesson teaches students how to set up and solve equations using trigonometric ratios for problems involving right triangles and angles of elevation and depression. Students complete an activity in groups and assessment with multiple choice questions to practice applying the concepts.
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.
The document provides an overview of an honors physics class. It discusses topics like vectors, scalars, displacement, velocity, acceleration, and problem-solving techniques. Key concepts are explained through examples, such as calculating displacement and velocity from graphs of position over time. Homework solutions are provided at the end.
This document discusses several key concepts related to the scientific method and quantitative analysis:
1. It outlines the general steps of the scientific method including making observations, forming hypotheses, testing hypotheses through experiments, and developing theories supported by data.
2. It defines key terms like quantitative data, measurements, units, and derived units. The International System of Units (SI) and common prefixes are explained.
3. Rules for determining significant figures in measurements and calculations are presented.
This document discusses using multi-step word problems and equations to model real-world situations involving two variables. It provides examples of identifying independent and dependent variables, writing equations to represent relationships, making tables of ordered pairs, and plotting graphs. Students are given practice writing equations, identifying variables, making tables and graphs for problems involving money saved, books collected, cost of rides, and more. The document emphasizes using graphs to show how the dependent variable changes as the independent variable changes.
The document discusses angle of depression and how to solve problems involving it. It defines angle of depression as the angle formed below the horizontal line when an observer looks at an object lower than their position. Several examples are provided of calculating distances and widths using the angle of depression and known heights. The objectives are to identify and solve word problems involving angle of depression and understand its real-life applications.
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.
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 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.
This document provides a lesson on drawing polygons on the coordinate plane. It includes 4 examples of plotting points and drawing polygons to connect those points. It then provides the name of each polygon drawn and how to calculate its area, whether by using formulas for basic shapes like triangles or decomposing complex shapes into simpler ones. The document emphasizes using coordinates to determine side lengths and plotting points accurately on the coordinate plane in order to find polygon areas.
This document provides examples and exercises for plotting polygons on a coordinate plane and calculating their areas. It includes examples of plotting triangles, rectangles, and other polygons given their vertices and calculating their areas. It then gives practice problems for students to plot polygons on their own, name the shapes, determine the areas using formulas, and write expressions to represent the area calculations. The final problems involve finding missing vertices of polygons when given some vertices and the total area.