Measurement Topic: Interpret Functions (F. It’s more than just counting or adding or memorizing math facts. Pass out student notes. Learn to use math to scale a drawing so you can create maps, grids, and even buildings that are perfectly proportional. The students will be assessed on the following criteria. Be sure there is enough room and space cleared for walking. • Construction materials could include: plastic table cloths, tissue paper, small wooden dowels, straws, yarn, fishing wire, markers, scissors, tape, glue, etc. This kind of activity can be used to stress the importance of having a proper plan before starting any construction project. EARTHQUAKES The Richter Scale. The central office still works with schools to improve their models, but now it can also provide targeted support to schools that want to scale up proven approaches. 8 Links verified on 6/9/2014. Numerical modelling of ocean circulation 389 Table 2. This will be quick, but I wanted students to continue using their ratio language and apply it more specifically to scale drawings. Definition of Scale On A Graph explained with real life illustrated examples. Diameter, you might remember from math class, is the distance from one end of circle or sphere to another side, going through the middle. It includes unlimited math lessons on number counting, addition, subtraction etc. Each of the topics include a pretest, an instruction section, on-line practice sessions, worksheet practice, and a test. They further refine their mathematical communication skills through mathematical discussions in which they critically evaluate their own thinking and the thinking of other students. Find measurements using a scale drawing. Mathematics is not a spectator sport. Scale Measurements in scale drawings and models are proportional to the measurements of the actual object. Learning Resources has a variety of hands-on educational toys for kids of all ages. CFD model does provide slightly more accurate predictions. Definition of Scale Factor in the Definitions. Meaning of scale model. com Abstract In this paper, we address the resource allocation problem (RAP) for large scale data centers using. Ratios can be used to express the scale of a map. While each field may use a scale model for a different purpose, all scale models are based on the same principles and must meet the same general requirements to be functional. 1,106 likes · 50 talking about this. Featured Interactive. LOGNORMAL MODEL FOR STOCK PRICES MICHAEL J. It differs from the mean model merely by the addition of a multiple of X t to the forecast. 5 – The Size of the Scale Factor. Trending at $8. Unparalleled scale replicas for discriminating railroad modelers www. Scale drawings, commonly known as plans are used as patterns in the construction of buildings. According to the experts at Architectural Models, "Models tell a story that everyone can understand and the story starts the second your eyes see the model. Visual Math Models helps teachers and students see how math works. For more information on standards, please see Meeting Standards with Everyday Mathematics. These systems include networks of interactive elements that can be overly complex to exhaustively explore experimentally. Through the use of abstraction and logic, mathematics developed from counting, calculation, measurement, and the systematic study of the shapes and motions of physical objects. Huge List of Mathematics Projects, 2015 Latest Mathematics Science Fair Project Ideas, Maths Topics GCSE CBSE,Mathematics lab, additional project work, maths model project ideas for cbse high school, cool easy experiments for Kids and also for Middle school, Elementary School for class 5th Grade, 6th, 7th, 8th, 9th, 10th, 11th, 12th Grade and High School, MSC and College Students. scale, scale factor • a ratio between two sets of measurements. LOGIN New to Big Ideas Math? LOG IN. The Model block allows you to treat a Simulink model as a component within a larger system. A scale model uses the same. Fitting in the package is. 8 Scale Drawings and Models Notes. Scale factor used correctly for most of the calculations. Despite the name enlargement, it includes making objects smaller because the shape can be bigger or smaller according to the scale factor, k. These free lessons are cross-referenced to help you find related material, and the "Search" box on every page is available to help you find whatever math content you're looking for. The model results predict a. The answers they get will generate a funny story about their teacher. Viewing a photo or scan of your project is a good way to check for scale, as an “offending” piece will usually “scream at you”. Model with mathematics. The Department of Mathematics at Temple University is home to a broad spectrum of theoretical and applied mathematical research by world-class faculty, and is strategically positioned to provide, strengthen and support mathematical education at all levels within the University. Scale models represent a re-creation of an object. Calculate the scaled planet diameters and planet-sun distances for a solar system model. Posted by miniscale at 2:26 PM. expressions, equations, inequalities, models, graphs, and tables. The length of the dining room on the blueprint is 3 inches. Our three-scale model is a model of intermediate complexity that accounts for heterogeneous transmission and, like more complex models such as small-world networks 15, permits systematic variation of the extent of community mixing (modeled with one other network scale). Box 210, Bondo, Kenya 3 P. The accompanying classroom activity invites students to compare the volumes and surface areas of two cubes of different sizes. The Model block allows you to treat a Simulink model as a component within a larger system. Promoting positive transitions through coherent instruction, assessment, and professional development: The TRIAD scale-up model. Pilot Eureka math. Scientists build models to explain how aspects of the real world work. Here, we will consider a. Panagbenga Street Dancing Parade. Depending on the size of the balls used, the scale models can take up a lot of space. More information about BioModels Database can be found in the FAQ. Posted on October 18, 2012 by Passy. Both scale drawings and scale models can be smaller or larger than the objects they represent. What representational styles are there in the sciences?. In this activity, you will make two scale models of the solar system. Find the length on the drawing for each actual length. 04 feet: For a school project, LeeAnn is making a model of the Empire State Building. Explore the possibilities of math through coursework, research, and public lectures. The Math Forum's Internet Math Library is a comprehensive catalog of Web sites and Web pages relating to the study of mathematics. These, like all models, are used because of their "analogies" to the subjects of the models. A balance scale is a good visual model for representing an equivalence relationship. I don't know much about under-cambered airfoils. Scale models are also used in movies. Find measurements using a scale drawing. Students further explore scale, taking a scale drawing floor plan and redrawing it at a different scale. Students will •. 5 and 3 inches, depending on what looks right for the prototype model. You can make scale models of the Wright Brothers aircraft designs from 1900-1903. You can also calculate map scale, distance on map and distance in real life on Map Scale Calculator page. Matho Models produces premium quality diorama accessories for scale modelers worldwide, high quality scale modeling accessories and upgrades for an affordable price. Measured and drawn to the nearest ¼ inch-scale; some. See firsthand at your school how it transforms classrooms by piloting the curriculum and utilizing the many support resources available from Great Minds. Scale Models A scale model is a model which represents how large or smaller a object to its actual size. You can build clean, accurate models using Evergreen Scale Models products. Students then drew a new grid matching their scale factor ( scale factor of 5 = 5x5 cm squares). The model turbines we are going to use are sitting at the lab tables. Usually the scale is given, as on a map 1 inch. com, a free online dictionary with pronunciation, synonyms and translation. Year of the Solar System Math Guide (2013:Draft) 164 Problems - This collection of math problems covers the 20 science topic themes presented by the NASA/JPL Year of the Solar System website () covering the solar system, planets, the search for life, and robotics. In someusiness b scenarios, such decision-rules might be OK, in the sense that they require very little information (e. Calculating area is necessary in many jobs and skills when students become adults as well as later in math schooling. For anyone who ever dreamed of being a conductor, miniature train sets make that dream a reality. The project set out to design and develop well-engineered tools for formative and summative assessment that expose students’ mathematical knowledge and reasoning, helping. Meaning of Scale Factor. An accurate floor plan drawing is a necessity whether you're planning a home remodel, commercial space build-out, or just need dimensions for arranging furniture placement. Scale Drawing Blowing up a Candy Bar / Comic Strip Standards: [Standards for Mathematical Practice 2. Mars Models - photo etched and other aftermarket items manufactured by Mars Models for scale plastic model kits. He continues to make a difference with math instructional outcomes because his innovative approaches work. In this study, students' attitudes towards mathematics courses in a vocational college were investigated with a scale applied and the results were interpreted. The model turbines we are going to use are sitting at the lab tables. 1) If a 6 ft tall tent casts a 10 ft long shadow then how long is the shadow that a 9 ft tall adult elephant casts? 2) A model plane has a scale of 1 in : 6 yd. The same. Both versions of the curriculum's goals are available below. Plan your 60-minute lesson in Math or Geometry with helpful tips from Heather Stephan. Scale models are often built as a hobby, but engineers build scale models as part of the engineering design process when designing objects or structures. Scale models are used in many fields including engineering, architecture, film making, military command, salesmanship, and hobby model building. The model does not demonstrate any consistent scale. Weizsäcker's liquid drop model represents the nucleus of an atom in a manner very different from the shell model, and a scale model of the wing of an air plane represents the wing in a way that is different from how a mathematical model of its shape does. To understand that a proportion is an equivalent relation between two ratios. To make a move in the game below, click on the piece you wish to move, then click again to the square you wish to move it to. You can do this with a long tape measure, or you can measure the size of your pace and walk it off counting the number of steps you take. Students will appreciate how a given factor reduces or enlarges a two-dimensional figure, as they tackle the concept in a hands-on approach. In using a mathematical model, it is important that any variables have been defined as a quantity that can be measured, the dimension of each variable is known, and the measurement units are known. A scale model airplane has a structural similarity or "material analogy" to the full scale version. Build an Architectural School Model - Great for practicing basic math (adding and subtracting), measuring, and getting an introduction to geometry, this activity has students draw out a design for their school and then create a scale model using cardboard and other materials. The photograph shows a scale drawing of the model train. One way to address the problem is through the use of interactive activities and this web site provides many of those. , the wingspan) and measure is using length units available in the dropdown box. Measured and drawn to the nearest ¼ inch-scale; some. By ScaleCalculator. The modules contain hundreds of interactive activities, games, and questions. Students will draw a scale model of a house. Scale factor not used. Sometimes traditional teaching fails to actively involve students. This Scale Model Project Activities & Project is suitable for 8th - 10th Grade. Everyday Mathematics Online. A scale is a series that climbs up or down. Analyze your face in 3 minutes. Model Curriculum » Home. 5, so that's easy to accumulate the growth food you need. Each of the topics include a pretest, an instruction section, on-line practice sessions, worksheet practice, and a test. Be sure there is enough room and space cleared for walking. Find the scale factor of each scale drawing or model. Any additional rooms are optional. Often, there are competing models for the same phenomenon. When it comes to diecast model cars, scale is one of the most important things to consider. Siyavula's open Mathematical Literacy Grade 10 textbook, chapter 6 on Scale, Maps And Plans. MTH electric trains come in a variety of designs so you can create numerous scenes with your trains. We can use words, drawings or sketches, physical models, computer pro-grams, or mathematical formulas. Blue - Growth food needed for a new citizen follows this formula: 15+8*(N-1)+(N-1)^1. Notice the use of a sliding leaden counterweight that provides the torque needed to lift the ship. This number represents the degree to which your scale drawing or scale model has been reduced in size when compared to the original. As an educator, it is easier to get concepts across to the students with hands on projects. Issue: After inserting an image or importing a PDF file, often time the objects and dimensions will not show their "true length" being that the image is not at a 1:1 scale with the actual drawing units. The Department of Mathematics at Temple University is home to a broad spectrum of theoretical and applied mathematical research by world-class faculty, and is strategically positioned to provide, strengthen and support mathematical education at all levels within the University. A scale is a series that climbs up or down. Am I pretty? Am I ugly? Why am I ugly? or not pretty enough? Online test for face beauty analysis. The Math Worksheet site has highly customizable, generated worksheets that target your students’ specific needs. For example, one real foot equals 87 scale HO feet. Lesson Plan 8 – Drawing to Scale. Find out what you are worth. Scale Drawings. How Do You Solve a Scale Model Problem Using a Scale Factor? This tutorial provides a great real world application of math! You'll see how to use the scale on a house blueprint to find the scale factor. 8 Scale Drawings and Models Notes. The Common Core State Standards in mathematics were built on progressions: narrative documents describing the progression of a topic across a number of grade levels, informed both by research on children's cognitive development and by the logical structure of mathematics. Scale Model. 618 to arrive at the next highest number, or dividing by 1. Usually the scale is given, as on a map 1 inch. But be careful! You can think of an equation like a balance scale—whatever you do to one side of the scale, you must also do to the other side, to keep it in balance. These include items of mathematical interest, funny math pictures and cartoons, as well as. BioModels Database is a repository of computational models of biological processes. Math is a set of procedures that make no sense that you just have to memorize. On a set of blueprints for a new home, the contractor has established a scale that states inch 10 feet. (flow map). Introduction What follows is a simple but important model that will be the basis for a later study of stock prices as a. We propose to consider this new analytical subgrid scale turbulence model which yields the same closure ansatz as that of the NS-ﬁ subgrid scale turbu-lence model in inﬂnite channels and pipes. A scale is simply a group of notes in succession. First, let's look at a simple addition equation, x + 15 = 30. The height of the drawing is 1 ft 2 in. Parents - if you'd like to help your child learn math we suggest you start with our math tutorial section before returning to use these worksheets. com you can easily calculate model size or model scale. A scale model airplane has a structural similarity or "material analogy" to the full scale version. Each side of the square pyramid shown below measures 10 inches. These systems include networks of interactive elements that can be overly complex to exhaustively explore experimentally. You can select different variables to customize these Ratio Worksheets for your needs. If you have ever seen. To do this, you will need to make the pyramid 3,000 times smaller than it really is! To achieve that, every 30 meters of the pyramid is represented as 1 centimeter. Some of the worksheets displayed are Scale drawings and models, Answer each question and round your answer to the nearest, Scale drawings and scale factor, Solar system scale model, Scale drawings, Exercises extra, 6 3 scale drawings and models, Lesson plan 8 drawing to scale. 1 Scale Drawings, Scale Models, and Scale Factors • 545 Bigger and Smaller Scale Drawings, Scale Models, and Scale Factors S ome professional basketball players can jump really high to dunk the ball on a 10-foot-tall goal. In other words, we modify both the length-scale and the time-scale. Mathematics Through Problem Solving. Scale Model Building. Home Lab About Research Papers Contact New Page Applied Physics and Mathematics Building, #5151. It is very important concept in mathematics. Isometric Drawing and 3D Cubes. In this post you’ll find 8 engaging scale drawing activities to practice in your classroom. Meet our award-winning faculty and see what's happening in the department. (an HO scale light-year is 67. The website has resources for secondary school teachers. Scale Model Toys Ford. We could build a scale-model clock, and then film it in slow motion. Recognize the applications of scale factor by exploring blueprints, shadow measuring, and scale models. University of Cambridge (2019). Scale Drawings and Models Have you ever looked at a map, sewed a piece of clothing, built a model or assembled a piece of Ikea furniture? Then most likely you have had to use a scale drawing. These, like all models, are used because of their "analogies" to the subjects of the models. The materials (math glossary) on this web site are. Kit #SE-07 $19. Find measurements using a scale drawing. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice. Scale Drawings – Worksheet #2 For problems #1 – 2, use the following scale 5 cm : 2 miles 1) The distance on the map between Yappy City and Quiet City is 23 cm. Picture a two-pan balance scale, with two weights on the left side and one on the right. SAMSI Model Uncertainty: Statistical and Mathematical (MUMS) Fall 2019 Courses. Posted by miniscale at 2:26 PM. essons learned in e Implementation of e TRIAD Scale-Up Model - eaching Early Mathematics ith Trajectories and Technologies f Sarama and Douglas H. Scale drawings are an easy and plausible way to represent large things, such as roads and buildings, on paper. Path Loss: Models of "large-scale effects" Example. The little canoe on the left is called a "salesman's model" because the salesmen for historic Maine canoe companies used to carry scale models of their company's offerings. This is the currently selected item. essons learned in e Implementation of e TRIAD Scale-Up Model - eaching Early Mathematics ith Trajectories and Technologies f Sarama and Douglas H. Shane Wells sent us a tip on controlling a drawing's linetype scale. Model is somewhat neat. The balance scale model uses the metaphor of a balance scale in order to represent the expressions on each side of an equation. net dictionary. As an educator, it is easier to get concepts across to the students with hands on projects. Siyavula's open Mathematical Literacy Grade 10 textbook, chapter 6 on Scale, Maps And Plans. Free, online math games and more at MathPlayground. Students solve a classic puzzle about finding a counterfeit coin. Solving Problems with Scale Drawings Grade Level By (date), when given (4) problems involving scale drawings to find the the area and length of geometric figures, (name) will compute the area and length (e. This is a quiz on scale drawings. Estimate the distance between Barajas and Mar de Cristal. Start studying SOS Math 800: Unit 4- Models and Scales. After they grid their wrapper then each student decided on a scale factor to enlarge their wrapper. Grade 7 Mathematics, Quarter 4, Unit 4. Visual Math Models helps teachers and students see how math works. But scale isn't Matchbox's objective. The model does not demonstrate any consistent scale. To understand that a proportion is an equivalent relation between two ratios. Practice math the fun way, on your mobile phone or tablet like iPad, iPhone, or Android. The bar model helps students visualize the relationships between the numbers given and the amount you are looking for in a word problem. By ScaleCalculator. 618 to arrive at the next number down. • in size transformation – a ratio expressing the amount of magnification. If you're trying to determine what scale model train you should buy, start by learning the different options you have. Category Geometry Sub-Category Draw, Construct, And Describe Geometrical Figures And Describe The Relationships Between Them. The work presented here focuses on the development of cell-scale, mechanistic, and biologically relevant mathematical models that provide information about the contribution of individual mechanisms to experimental outcomes. How far is the state capital from the border on the map? 7) A model length of 12 cm. Rate my face 1-100. Usually the scale is given, as on a map 1 inch. Scale Math Exercises for Kids- Scale Drawings. In this article, a comprehensive summary of the compilation is presented in tabular form. Splash Math is an award winning math learning program used by more than 30 Million kids for fun math practice. Learning and understanding Mathematics, at every level, requires learner engagement. Depending on the size of the balls used, the scale models can take up a lot of space. Weizsäcker's liquid drop model represents the nucleus of an atom in a manner very different from the shell model, and a scale model of the wing of an air plane represents the wing in a way that is different from how a mathematical model of its shape does. Scholastic MATH supports math standards at both the state and national levels. Free online converters. Constant scale Model railroaders were already used to choosing from a range of related products in the scale of their choice — their models have to be in the same scale to work together. In the example, the model's scale is 1:29, which means every inch of model represents 29 inches of the subject. Math articles on a variety of topics in math education published by Math Goodies. From scale model building supplies for professional, engineering, and architectural model making to supplies for hobbyists and students, Blick has it all. Scale Drawings and Models Scale drawings are based on the geometric principle of similarity. A scale is simply a group of notes in succession. In 2005, a new mathematics framework was adopted for twelfth-graders, with scale scores ranging from 0 to 300. the scale model portion is complete. We'll look at many different kinds of rockets, from stomp rockets, which are a special kind of artillery shell, to bottle rockets, to model rockets, to full scale boosters. Scale Math Exercises for Kids- Scale Drawings. Chess is a popular game of strategy between 2 players. 04 feet: For a school project, LeeAnn is making a model of the Empire State Building. The state capital is 252 miles from the border. 1) If a 6 ft tall tent casts a 10 ft long shadow then how long is the shadow that a 9 ft tall adult elephant casts? 2) A model plane has a scale of 1 in : 6 yd. Several studies on the scale of responsibilities that have been carried out include: Singg & Ader (2001) who developed Student Personal Responsibility Scale-10 (SPRS-10) to. Take that number and Divide it by the Length of your model (also in Inches), and you will have determined the Scale. About the Model. The Fennema-Sherman Mathematics Attitude Scales consist of a group of nine instruments: (1) Attitude Toward Success in Mathematics Scale, (2) Mathematics as a Male Domain Scale, (3) and (4) Mother/Father Scale, (5) Teacher Scale, (6) Confidence in Learning Mathematics Scale, (7) Mathematics Anxiety Scale, (8) Effectance Motivation Scale in. Each model is built to a scale that relates the actual object to the model through a ratio. 5 feet long and 16. 5 metres length in real life. The height of the main building of the White House. Sally is an architect who creates a blueprint of a rectangular dining room. In this lesson, you used three different models to represent and solve equations. Solving Problems with Scale Drawings Grade Level By (date), when given (4) problems involving scale drawings to find the the area and length of geometric figures, (name) will compute the area and length (e. You can do this with a long tape measure, or you can measure the size of your pace and walk it off counting the number of steps you take. Have fun while your child develops their motor and social skills. Notice the use of a sliding leaden counterweight that provides the torque needed to lift the ship. Bollob´as January 16, 2003 1 Introduction Recently there has been much interest in studying large-scale real-world net-works and attempting to model their properties using random graphs. These highly detailed 22-inch tall are available as WWI British, French and German Pilots as well as early 1930s era pilot figures. Understand and calculate the length using the scale factor. expressions, equations, inequalities, models, graphs, and tables. The balance scale model uses the metaphor of a balance scale in order to represent the expressions on each side of an equation. Definition of Scaling explained with real life illustrated examples. Scale models are also used in movies. Panagbenga Street Dancing Parade. Grade 7 Mathematics, Quarter 4, Unit 4. Pass out student notes. For the example above at: location 1, free space loss is likely to give an accurate estimate of path loss. These parasitic. • in size transformation - a ratio expressing the amount of magnification. We offer a broad undergraduate and graduate degrees in mathematics with concentrations in actuarial science, applied and computational mathematics, discrete mathematics, general mathematics, secondary education, pure mathematics, and statistics. net dictionary. Posted by. Free Math Apps These apps are based on the visual models featured in Bridges in Mathematics. Box 143, Kisumu, Kenya 1 brokwach. Copyright © by Holt, Rinehart and Winston. Math shapes the world around us in fascinating ways. Generally, a model intended for a simulation study is a mathematical model developed with the help of simulation software. Day-by-Day Math: Activities for Grades 3–6, by Susan Ohanian, is an eclectic and quirky collection of events — and the mathematical investigations, problems, or activities that are suggested by them. Hurson's Productive Thinking Model could be just the thing to help you. University of Cambridge (2019). In this study, students' attitudes towards mathematics courses in a vocational college were investigated with a scale applied and the results were interpreted. EUCATION POLICY How to Fix Remediation at Scale 3 long odds are increasingly unacceptable to states and colleges, which are looking for alternative approaches. Here, we will consider a. These pilots fit perfectly in 1/3. Analyze your face in 3 minutes. Read the latest articles of Applied Mathematical Modelling at ScienceDirect. What is the scale factor if the scale is 15 inches = 1 yard? − 15 − or 36 5 12 15. A scale model is a proportional three-dimensional model of an object. Use this information for problems 1–6. Its method of development has led to far-reaching applications in mathematics and computer science. The size of a planet can be determined from its diameter. Scale Drawings and Models On a map, the scale is 5 centimeters = 2 kilometers. There are so many different types of mathematical models used to explore landscape ecological relationships, that a precise definition of a landscape model is difficult. This guide features: Four full-length, previously administered Mathematics Level 1. Complete your drawing. Practical Math. Seminar on Applied Mathematics and Data Science Multi-Scale and Multi-Representation Learning on Graphs and Manifolds Room 2405, Academic Building (lift 17-18), HKUST. Measure the length and width of the room and anything else you think you need. There are some weaknesses in the exponential growth model as it fails to model this behavior in vivo. Lesson Plan 8 – Drawing to Scale. If you're trying to determine what scale model train you should buy, start by learning the different options you have. • in scale drawings – the ratio of the measurement on the drawing compared to the measurement of the original subject. 5, so that's easy to accumulate the growth food you need. 6 out of 5 stars 2. In this lesson, you used three different models to represent and solve equations. The Mathematics Assessment Project is part of the Math Design Collaborative initiated by the Bill & Melinda Gates Foundation. Usually the scale is given, as on a map 1 inch. They can be used to introduce, practice, or remediate a concept. Make a scale drawing of your classroom. Practical Considerations. This scale calculator is a free tool to calculate different scale conversions common to military modelling. The cars in the image on the right are all scale models that represent real cars. This Scale Model Project Activities & Project is suitable for 8th - 10th Grade. That means the size of Matchbox cars is between 2. A scale model is a proportional three-dimensional model of an object. MATH STATISTICS LAB: LEARNING LARGE-SCALE AND COMPLEX MODELS. Students explore change from one scale to another, focusing on the ratios. EUCATION POLICY How to Fix Remediation at Scale 3 long odds are increasingly unacceptable to states and colleges, which are looking for alternative approaches. Despite the name enlargement, it includes making objects smaller because the shape can be bigger or smaller according to the scale factor, k. Solving Complex Proportion Word Problems (Random) (5. Anyway, enough history The rest of this mini-presentation will concentrate on logarithms to the base 10 (or logs). Online shop Scale model kits has successfully been existed for over 6 years and is one of the best sellers of scale plastic models around the world through its high quality service, instant bookings and send a huge range of models. These are what you call scale models because they are an exact smaller copy of the real object. Look it up now!. There are two major modes of typesetting math in LaTeX one is embedding the math directly into your text by encapsulating your formula in dollar signs and the other is using a predefined math environment. They will apply proportional reasoning to scale drawings and determine if calculations are appropriate to the contexts.