Understanding Place Value with Decimals

Can you make multiple choice 2nd grade questions that cover the following: Demonstrate understanding of the ten-to-one relationships among ones, tens, and hundreds, using manipulatives. (a)  Write numerals, using a model or pictorial representation (i.e., a picture of base-10 blocks). (a)  Read three-digit numbers when shown a numeral, a model of the number, or a pictorial representation of the number. (a)  Identify and write the place (ones, tens, hundreds) of each digit in a three-digit numeral. (a)  Determine the value of each digit in a three-digit numeral (e.g., in 352, the 5 represents 5 tens and its value is 50). (a)  Use models to represent numbers in multiple ways, according to place value (e.g., 256 can be 1 hundred, 14 tens, and 16 ones, 25 tens and 6 ones, etc.). (a)  Use place value understanding to identify the number that is 10 more, 10 less, 100 more, or 100 less than a given number, up to 999. (b)  Compare two numbers between 0 and 999 represented with concrete objects, pictorially or symbolically, using the symbols (>, <, or =) and the words greater than, less than or equal to. (c)  Order three whole numbers between 0 and 999 represented with concrete objects, pictorially, or symbolically from least to greatest and greatest to least. (c)  Round two-digit numbers to the nearest ten. (d)?

Certainly, let's expand on each section in detail so you can learn more from the provided text: # Summary This text aims to explain various aspects related to technology, particularly focusing on a concept known as "Tech Disruption." It explores how technology affects different sectors, outlines the conditions for tech disruption, discusses the industrial revolutions, introduces the laws of disruption, and mentions factors influencing technology choices. ## Concept of Technology **Technology** encompasses a range of elements within organizations. It includes **expertise, equipment, and procedures** used to convert inputs, such as resources or raw materials, into outputs, which can be products or services. This involves various aspects, such as **product design, production techniques, quality assurance measures, human resource development, and management systems**. In essence, technology represents the tools and knowledge used to create and deliver goods or services effectively. ## What is Tech Disruption **Tech Disruption** refers to a phenomenon where smaller companies with limited resources successfully challenge well-established incumbent businesses. This disruption is primarily driven by **technology**, which acts as the catalyst, enabler, or even the sole reason behind the change. The significance of this concept lies in the fact that entrepreneurs must make careful and thoughtful decisions when it comes to adopting and investing in technology. **Why it's Important?** These decisions are crucial because they involve significant investments and will have a substantial impact on a company's ability to create, innovate, and operate its services in a sustainable and cost-effective manner. ## Four Main Impact **Tech Disruption** has four main impacts on businesses and industries: 1. **Shifting Customer Expectations**: As technology evolves, customer expectations change. Companies must adapt to meet these evolving demands to remain competitive. 2. **Enhanced Products Through Data**: Data-driven insights improve the productivity and efficiency of assets, leading to better products and services. 3. **New Partnerships and Collaboration**: Tech disruption encourages companies to form new partnerships and collaborations, recognizing the importance of working together to stay relevant. 4. **Transformation of Operating Models**: Traditional operating models are being transformed into digital models, where technology plays a central role in how businesses operate and deliver value. ## The 11 Macro Sources of Distribution The **11 Macro Sources of Distribution** represent various factors that influence the distribution of resources and opportunities in society. These factors include: 1. **Wealth Distribution**: How wealth is distributed among individuals and entities. 2. **Education**: The availability and quality of education opportunities. 3. **Infrastructure**: The state of infrastructure, such as transportation and communication networks. 4. **Government**: Government policies and regulations that impact resource distribution. 5. **Geopolitics**: Geopolitical factors, such as international relations and conflicts. 6. **Economy**: Economic conditions and trends, including markets and financial systems. 7. **Public Health**: The state of healthcare and public health systems. 8. **Demographics**: Characteristics of the population, such as age and gender. 9. **Environment**: Environmental factors and sustainability concerns. 10. **Media and Telecommunications**: The role of media and communication technologies. 11. **Technology**: Technological advancements and their impact on society. ## When Does Tech Disruption Happen? **Tech Disruption** occurs when specific conditions are met: ### Technology Is Mature Enough - **Technology Accessibility**: Technology must be accessible to a wide range of people and organizations. - **Critical Mass**: It should have reached a critical mass where it can create significant impact. - **Affordability**: Technology must be affordable for businesses to adopt. ### Sector Is Ready For Change - **Tech Infrastructure**: The sector should have the necessary technological infrastructure in place. - **Policy Framework**: A conducive policy framework is essential to support and regulate the use of technology. - **Lack of Disruption**: If the sector is stagnant or facing issues, it becomes ripe for tech disruption. ### Sector + Technology + Timing + Product - **Mature Technology with an Unready Sector**: If technology is mature but the sector is not ready, it can lead to building the wrong product based on incorrect assumptions. - **Unmatured Technology with a Ready Sector**: Conversely, if technology is not matured but the sector is ready, it may take longer to develop the product. ## Ready for Industri 5.0? This section briefly outlines the five industrial revolutions: 1. **Industri 1.0 (1784)**: Marked by mass production assembly lines using electrical power. 2. **Industri 2.0 (1870)**: Introduced mechanization, steam, and water power. 3. **Industri 3.0 (1969)**: Characterized by automated production, computers, IT systems, and robotics. 4. **Industri 4.0 (Present)**: Involves smart factories, autonomous systems, IoT (Internet of Things), and machine learning. 5. **Industri 5.0 (Future)**: Envisions mass customization and cyber-physical cognitive systems. ## Three Laws of Disruption These laws explain the nature of disruption: 1. **Disruption Comes to All**: Disruption is a universal phenomenon; it affects all industries and businesses sooner or later. 2. **Product-Market Fit**: Disruption occurs due to changes in Product-Market Fit, which means aligning a product with its target market effectively. 3. **Methods to Change Product-Market Fit**: To address disruption, a company can change the product, the target market, or influence people's preferences regarding the product. ## The 40% Rule This rule provides a framework for evaluating the fit between a product and its market: - **Value Proposition**: The product should solve customers' problems effectively. - **Channels**: The product should be able to reach customers cost-effectively. - **Monetization**: Customers should be willing to pay for the product. ## PMF Framework: 5 Steps to Product/Market Fit The **PMF (Product/Market Fit) Framework** consists of five steps: 1. **Business Modeling**: Developing a business model that aligns with the market. 2. **Market Validation**: Confirming that there is demand for the product in the market. 3. **Customer Interviews**: Gaining insights from potential customers. 4. **Product Development and Customer Acquisition**: Creating the product and acquiring customers. 5. **Product Analytics**: Using data to determine if the product has achieved Product/Market Fit. ## Factors Determining the Choice of Technology Several factors influence the choice of technology: 1. **Government Policy**: Government regulations and policies can encourage or restrict the adoption of specific technologies. 2. **Available Resources**: The resources, both financial and human, impact the adoption of technology. 3. **Technological Capability**: The organization's technological capabilities influence the choice of technology. 4. **Existing Technological Level**: The current technological state of the industry or organization plays a role. 5. **Institutional Arrangement**: Organizational structures and arrangements affect technology choices. ## Conclusion In conclusion, the text emphasizes the critical role of technology in driving change and disruption in various industries. It highlights the need for informed decision-making when it comes to technology investments, as well as the conditions necessary for tech disruption to occur. Understanding the historical context of industrial revolutions, the laws of disruption, and the factors influencing technology choices is essential in today's fast-paced and tech-driven business environment. Embracing technology disruption is crucial for transforming business models and adapting to evolving market dynamics.

The advantage of direct method is that the teacher can control the class and fit in a lot of activity into a short class period. This leaves plenty of opportunities for the students to hone their skills, especially new ones. On the other hand, because the class is centered around the teacher, some students may not receive proper feedback, and creativity is limited. Also, the lesser talented athletes often tend to get lost in the shuffle while the great athletes shine. However, there are now a multitude of various teaching strategies that can be employed in addition to that method. Ex: Announcements, Module/Unit introductions, Descriptions/modeling of assignments and learning activities, Written or video lectures, Demonstration videos, Presentations, Discussions moderated by instructors, Interactive tutorials. Indirect Method The Indirect Teaching Style allows students to be involved in their own learning through experience and other peer’s knowledge. Students can use critical thinking to expand their learning capabilities by seeing what others may be doing correct and adjusting this to their own knowledge. The Indirect approach is the opposite of what the direct style suggests, but they are both strictly related, meaning you can’t have one without the other. Direct teaching: The instructor stands in front of the class or group and lectures or advises. Indirect teaching: The instructor assumes a more passive role and guides the student interactions. Movement exploration: Incorporates the use of equipment that involves movement. Movement Exploration The movement exploration class is founded on developing a strong, positive association to physical activity. Classes are aimed at developing movement skills and foundational strength through fun and engaging activities. The activities are age appropriate and include games, challenges, and exploration that positively challenge children’s competency while improving their physical capabilities. Skills such as the ability to climb, hold animal shapes, gymnastic style activities, and the introduction to athletic motor skill competencies are the foundations to youth training. This class provides the introduction to strength training to give children the opportunity to learn the skills required to safely and confidently engage in resistance training. Cooperative Skills Cooperative activities teach students to work together for their group's common good. By participating in these activities, students can learn the skills of listening, discussing, thinking as a group, group decision making, and sacrificing individual wants for the common good. There are two primary objectives guiding the teaching of cooperative activities. First, cooperative activities allow students to apply a variety of fundamental motor skills in a unique setting. Students are typically asked to perform motor skills in a specific way, such as “skip in general space” or “balance on one foot and one elbow.” Cooperative activities ask students to perform different activities such as skip with their hands on the shoulders of someone in front of them, walk with big steps while placing their feet on small spots, or walk across an area blindfolded while someone directs their moves. Due to the uniqueness of such experiences, students often find cooperative activities exciting and motivating. Second, cooperative activities are a wonderful medium for teaching social and emotional learning (SEL). SEL offers students an opportunity to understand and manage their emotions. In addition, such activities offer an opportunity to show empathy for others and develop positive relationships. Cooperative activities demand that all students play a role in completing the task or solving the movement problem. Every student, regardless of ability level, is important and contributes to group goals. 9 traits a PE teacher often needs Here are nine essential traits of an effective PE teacher: 1. Athletic ability Athletic ability is an essential trait for a PE teacher because they're often showing kids how to perform exercises. To demonstrate proper form and encourage the kids to continue their fitness education, it's important they can perform the exercises themselves. Having experience with fitness training can enhance a PE teacher's lesson planning because they're familiar with how each exercise affects a person's body. Athletic ability can also refer to an aptitude for sports and games. PE teachers can instruct students on how to play these games or lead after-school activities involving them, like soccer or basketball. An aptitude for sports and games can help a PE teacher encourage students to participate in the activities during class. If the PE teacher enjoys physical activity, they may make the lessons more enjoyable for the student. 2. Teaching ability A PE teacher is a member of a school faculty, so it's essential they have the teaching ability that allows them to communicate lessons to students. There are various skills involved in teaching, including the technical capabilities associated with each professional's particular field. Learning these skills can help PE teacher plan their lessons effectively and connect with their students, meaning they can encourage students to practice fitness skills in optimal ways for their health. Here are some important teaching skills for PE teachers: Having an engaging classroom presence  Real-world learning  Project building  Lesson planning  Technology 3. Interpersonal skills PE coaches are part of faculty teams, so working alongside other teachers is an essential part of their job. They often collaborate with a student's general education teacher to address any behavioral issues that arise. They can also team up with other classes to plan activities for students, like field days and special field trips. Communicating with peers can ensure these interactions remain productive and create opportunities for more fulfilling lessons. Teachers can also model emotional skills for their students by displaying positive social interactions. Interpersonal skills can also help PE teachers interact with students and their families. If a student can make a student feel comfortable expressing their needs and preferences, they can often perform physical exercises or play games to the best of their individual capacities. Understanding how to soothe nerves and support students' emotional needs are important examples of interpersonal skills. When interacting with family members, you may use some of these same techniques to communicate effectively and best uplift students. 4. Written and verbal communication Both verbal and written communication is important for PE teachers because they often communicate with students, families and various personnel on a day-to-day basis. For example, a PE teacher uses their communication skills in a lesson plan to describe any student assignments or expectations accurately. They may also write instructions in a document, then explain them in a classroom lecture. They also use communication skills to share their lesson plans with other PE teachers during conferences or classroom development exercises. Many teachers continue to learn their trade even after working as a teacher for many years. They may share tips with each other or special lessons they've developed if they feel another teacher may benefit from it. Creating a community can help PE teachers continue to expand their teaching methodology and receive feedback on their lessons. 5. Patience and adaptability Working with children can require patience and adaptability because they're encountering many new concepts at the same time and learning how to regulate their emotions. As a result, it's important to treat them with patience and care while they're in your class so they can feel comfortable and feel motivated to complete assignments. As children become teenagers, they may require patience and adaptability to account for their changing bodies and attention spans. Like any job where you perform tasks in real-time, certain circumstances may occur that require you to adapt lesson plans. For example, if the weather turns from sunshine to rain on a day you planned for students to run a mile outside, you may need to adapt the lesson plan so they can practice endurance sports inside a gymnasium instead. 6. Organization PE teachers can use organization skills to improve their lesson planning sessions. For example, they can keep their plans in one place, and determine which parts of a semester or quarter to introduce new concepts. Throughout the year, these objectives may change because of unforeseen setbacks, but organizational skills can help PE teachers control the trajectory of their class curriculum. PE teachers can also use organizational skills to maintain their classroom space. Physical education frequently requires balls, equipment and tools to play games that may be on a lesson plan. They also organize equipment and decide where to store it within their classroom or storage space. 7. Creativity Creativity can help a PE teacher develop fun ways to introduce new material to their students or reinforce previous lessons. They can teach new games or devise interesting ideas to change the rules of a game to help keep students engaged. To find inspiration for their lesson plans, they can turn to personal hobbies or media aspects they enjoy, like movie scenes, songs or dances. A varied lesson plan can foster more engagement among students who prefer action- based learning activities, rather than lectures. 8. Focus Focus is an essential trait of a PE teacher because students often require their full attention during class, especially if they're learning a complicated physical task. You can focus your lesson plans around specific elements of physical education you believe are essential for students of a certain age group or skill level. If students require mentorship, you can also focus on each student's needs to supply them with a steady support system. Focusing on your students can help guide your career purpose. It can give you a core value system that informs your lesson plans and mentorship activities. This passion for your student's well-being can also help you become an advocate for each student in your class. You can also help organize funding for different field trips or establish after-school activities to support their interests. 9. Enthusiasm for teaching sports and fitness Enthusiasm is essential for a PE teacher. Many physical education activities require high energy and may suit someone who enjoys teaching them to others. Being an effective PE teacher also requires an enthusiasm for working with kids and making a positive impact on their lives.

Understanding Quantum Theory of Electrons in Atoms The goal of this section is to understand the electron orbitals (location of electrons in atoms), their different energies, and other properties. The use of quantum theory provides the best understanding to these topics. This knowledge is a precursor to chemical bonding. As was described previously, electrons in atoms can exist only on discrete energy levels but not between them. It is said that the energy of an electron in an atom is quantized, that is, it can be equal only to certain specific values and can jump from one energy level to another but not transition smoothly or stay between these levels. The energy levels are labeled with an n value, where n = 1, 2, 3, …. Generally speaking, the energy of an electron in an atom is greater for greater values of n. This number, n, is referred to as the principal quantum number. The principal quantum number defines the location of the energy level. It is essentially the same concept as the n in the Bohr atom description. Another name for the principal quantum number is the shell number. The shells of an atom can be thought of concentric circles radiating out from the nucleus. The electrons that belong to a specific shell are most likely to be found within the corresponding circular area. The further we proceed from the nucleus, the higher the shell number, and so the higher the energy level (Figure 9.4.1). The positively charged protons in the nucleus stabilize the electronic orbitals by electrostatic attraction between the positive charges of the protons and the negative charges of the electrons. So the further away the electron is from the nucleus, the greater the energy it has. This quantum mechanical model for where electrons reside in an atom can be used to look at electronic transitions, the events when an electron moves from one energy level to another. If the transition is to a higher energy level, energy is absorbed, and the energy change has a positive value. To obtain the amount of energy necessary for the transition to a higher energy level, a photon is absorbed by the atom. A transition to a lower energy level involves a release of energy, and the energy change is negative. This process is accompanied by emission of a photon by the atom. The following equation summarizes these relationships and is based on the hydrogen atom: The values nf and ni are the final and initial energy states of the electron. The principal quantum number is one of three quantum numbers used to characterize an orbital. An atomic orbital, which is distinct from an orbit, is a general region in an atom within which an electron is most probable to reside. The quantum mechanical model specifies the probability of finding an electron in the three-dimensional space around the nucleus and is based on solutions of the Schrödinger equation. In addition, the principal quantum number defines the energy of an electron in a hydrogen or hydrogen-like atom or an ion (an atom or an ion with only one electron) and the general region in which discrete energy levels of electrons in a multi-electron atoms and ions are located. Another quantum number is l, the angular momentum quantum number. It is an integer that defines the shape of the orbital, and takes on the values, l = 0, 1, 2, …, n – 1. This means that an orbital with n = 1 can have only one value of l, l = 0, whereas n = 2 permits l = 0 and l = 1, and so on. The principal quantum number defines the general size and energy of the orbital. The l value specifies the shape of the orbital. Orbitals with the same value of l form a subshell. In addition, the greater the angular momentum quantum number, the greater is the angular momentum of an electron at this orbital. Orbitals with l = 0 are called s orbitals (or the s subshells). The value l = 1 corresponds to the p orbitals. For a given n, p orbitals constitute a p subshell (e.g., 3p if n = 3). The orbitals with l = 2 are called the d orbitals, followed by the f-, g-, and h-orbitals for l = 3, 4, 5, and there are higher values we will not consider. There are certain distances from the nucleus at which the probability density of finding an electron located at a particular orbital is zero. In other words, the value of the wavefunction ψ is zero at this distance for this orbital. Such a value of radius r is called a radial node. The number of radial nodes in an orbital is n – l – 1. Consider the examples in Figure 9.4.2. The orbitals depicted are of the s type, thus l = 0 for all of them. It can be seen from the graphs of the probability densities that there are 1 – 0 – 1 = 0 places where the density is zero (nodes) for 1s (n = 1), 2 – 0 – 1 = 1 node for 2s, and 3 – 0 – 1 = 2 nodes for the 3s orbitals. The s subshell electron density distribution is spherical and the p subshell has a dumbbell shape. The d and f orbitals are more complex. These shapes represent the three-dimensional regions within which the electron is likely to be found. Principal quantum number (n) & Orbital angular momentum (l): The Orbital Subshell: https://youtu.be/ms7WR149fAY If an electron has an angular momentum (l ≠ 0), then this vector can point in different directions. In addition, the z component of the angular momentum can have more than one value. This means that if a magnetic field is applied in the z direction, orbitals with different values of the z component of the angular momentum will have different energies resulting from interacting with the field. The magnetic quantum number, called ml, specifies the z component of the angular momentum for a particular orbital. For example, for an s orbital, l = 0, and the only value of ml is zero. For p orbitals, l = 1, and ml can be equal to –1, 0, or +1. Generally speaking, ml can be equal to –l, –(l – 1), …, –1, 0, +1, …, (l – 1), l. The total number of possible orbitals with the same value of l (a subshell) is 2l + 1. Thus, there is one s-orbital for ml = 0, there are three p-orbitals for ml = 1, five d-orbitals for ml = 2, seven f-orbitals for ml = 3, and so forth. The principal quantum number defines the general value of the electronic energy. The angular momentum quantum number determines the shape of the orbital. And the magnetic quantum number specifies orientation of the orbital in space, as can be seen in Figure 9.4.3. Figure 9.4.4 illustrates the energy levels for various orbitals. The number before the orbital name (such as 2s, 3p, and so forth) stands for the principal quantum number, n. The letter in the orbital name defines the subshell with a specific angular momentum quantum number l = 0 for s orbitals, 1 for p orbitals, 2 for d orbitals. Finally, there are more than one possible orbitals for l ≥ 1, each corresponding to a specific value of ml. In the case of a hydrogen atom or a one-electron ion (such as He+, Li2+, and so on), energies of all the orbitals with the same n are the same. This is called a degeneracy, and the energy levels for the same principal quantum number, n, are called degenerate energy levels. However, in atoms with more than one electron, this degeneracy is eliminated by the electron–electron interactions, and orbitals that belong to different subshells have different energies. Orbitals within the same subshell (for example ns, np, nd, nf, such as 2p, 3s) are still degenerate and have the same energy. While the three quantum numbers discussed in the previous paragraphs work well for describing electron orbitals, some experiments showed that they were not sufficient to explain all observed results. It was demonstrated in the 1920s that when hydrogen-line spectra are examined at extremely high resolution, some lines are actually not single peaks but, rather, pairs of closely spaced lines. This is the so-called fine structure of the spectrum, and it implies that there are additional small differences in energies of electrons even when they are located in the same orbital. These observations led Samuel Goudsmit and George Uhlenbeck to propose that electrons have a fourth quantum number. They called this the spin quantum number, or ms. The other three quantum numbers, n, l, and ml, are properties of specific atomic orbitals that also define in what part of the space an electron is most likely to be located. Orbitals are a result of solving the Schrödinger equation for electrons in atoms. The electron spin is a different kind of property. It is a completely quantum phenomenon with no analogues in the classical realm. In addition, it cannot be derived from solving the Schrödinger equation and is not related to the normal spatial coordinates (such as the Cartesian x, y, and z). Electron spin describes an intrinsic electron “rotation” or “spinning.” Each electron acts as a tiny magnet or a tiny rotating object with an angular momentum, even though this rotation cannot be observed in terms of the spatial coordinates. The magnitude of the overall electron spin can only have one value, and an electron can only “spin” in one of two quantized states. One is termed the α state, with the z component of the spin being in the positive direction of the z axis. This corresponds to the spin quantum number ms=12. The other is called the β state, with the z component of the spin being negative and ms=−12. Any electron, regardless of the atomic orbital it is located in, can only have one of those two values of the spin quantum number. The energies of electrons having ms=−12 and ms=12 are different if an external magnetic field is applied. Figure 9.4.5 illustrates this phenomenon. An electron acts like a tiny magnet. Its moment is directed up (in the positive direction of the z axis) for the 12 spin quantum number and down (in the negative z direction) for the spin quantum number of −12. A magnet has a lower energy if its magnetic moment is aligned with the external magnetic field (the left electron) and a higher energy for the magnetic moment being opposite to the applied field. This is why an electron with ms=12 has a slightly lower energy in an external field in the positive z direction, and an electron with ms=−12 has a slightly higher energy in the same field. This is true even for an electron occupying the same orbital in an atom. A spectral line corresponding to a transition for electrons from the same orbital but with different spin quantum numbers has two possible values of energy; thus, the line in the spectrum will show a fine structure splitting. The Pauli Exclusion Principle An electron in an atom is completely described by four quantum numbers: n, l, ml, and ms. The first three quantum numbers define the orbital and the fourth quantum number describes the intrinsic electron property called spin. An Austrian physicist Wolfgang Pauli formulated a general principle that gives the last piece of information that we need to understand the general behavior of electrons in atoms. The Pauli exclusion principle can be formulated as follows: No two electrons in the same atom can have exactly the same set of all the four quantum numbers. What this means is that electrons can share the same orbital (the same set of the quantum numbers n, l, and ml), but only if their spin quantum numbers ms have different values. Since the spin quantum number can only have two values (±12), no more than two electrons can occupy the same orbital (and if two electrons are located in the same orbital, they must have opposite spins). Therefore, any atomic orbital can be populated by only zero, one, or two electrons. The properties and meaning of the quantum numbers of electrons in atoms are briefly

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