DOCSLIB.ORG

Ratio and Proportional Relationships

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text

Load more

Mathematics Instructional Cycle Guide Concept (7.RP.2) Rosemary Burdick, 2014 Connecticut Dream Team teacher Connecticut State Department of Education 0 CT CORE STANDARDS This Instructional Cycle Guide relates to the following Standards for Mathematical Content in the CT Core Standards for Mathematics: Ratio and Proportion 7.RP.1 Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. 7.RP.2 Recognize and represent proportional relationships between quantities, fractional quantities, by testing for equivalent ratios in a table or graphing on a coordinate plane. This Instructional Cycle Guide also relates to the following Standards for Mathematical Practice in the CT Core Standards for Mathematics: Insert the relevant Standard(s) for Mathematical Practice here. MP.4: Model with mathematics MP.7: Look for and make use of structure. MP.8: Look for and express regularity in repeated reasoning. WHAT IS INCLUDED IN THIS DOCUMENT? A Mathematical Checkpoint to elicit evidence of student understanding and identify student understandings and misunderstandings (p. 21) A student response guide with examples of student work to support the analysis and interpretation of student work on the Mathematical Checkpoint (p.3) A follow-up lesson plan designed to use the evidence from the student work and address the student understandings and misunderstandings revealed (p.7)) Supporting lesson materials (p.20-25) Precursory research and review of standard 7.RP.1 / 7.RP.2 and assessment items that illustrate the standard (p. 26) HOW TO USE THIS DOCUMENT 1) Before the lesson, administer the (Which Cylinder?) Mathematical Checkpoint individually to students to elicit evidence of student understanding. 2) Analyze and interpret the student work using the Student Response Guide 3) Use the next steps or follow-up lesson plan to support planning and implementation of instruction to address student understandings and misunderstandings revealed by the Mathematical Checkpoint 4) Make instructional decisions based on the checks for understanding embedded in the follow-up lesson plan MATERIALS REQUIRED o Large poster paper for students to work on and then hang around the room. o Needed for students to complete their Gallery Walk o If possible, a smart board TIME NEEDED Insert Checkpoint Name: Which Container? Insert time needed: 20 minutes Follow-Up Lesson Plan: Insert time needed: 2-3 Class periods Timings are only approximate. Exact timings will depend on the length of the instructional block and needs of the students in the class. Connecticut State Department of Education 1 Step 1: Elicit evidence of student understanding Mathematical Checkpoint Question(s) Purpose (See attached document on page 18) 7.RP.1 Compute unit rates associated with ratios Two liquid storage containers of the same size are being filled. of fractions, including ratios of lengths, areas and CT Core other quantities measured in like or different units. Liquid enters container A at a rate of 2/3 gallon per 1/4 minute. Standard: 7.RP.2 Recognize and represent proportional Liquid pours into container B at a rate of 3/5 gallons per 1/6 minute. relationships between quantities. (Fractional quantities) by testing for equivalent ratios in a table or Container A: Container B: graphing on a coordinate plane. How do students approach a Proportional context involving Fractions, when the unit rate is given as a complex fraction? To what extent do they? • Draw a model that correctly represents the division of time and the amount of container filled. • Connect their model to the situation and how it helped to determine the solution. Use the model to make connections to creating a table of equivalent ratios and to writing an equation. Solve the equation correctly. Target question addressed by this checkpoint: Determine which container is being filled faster. Justify your answer. Support your reasoning by using evidence from the models above. Connecticut State Department of Education 2 Step 2: Analyze and Interpret Student Work Student Response Guide Got It Developing Getting Started What will a response include from a student who has What will a response include from a student who What will a response include from a student who demonstrated conceptual understanding and mastery? demonstrated some understanding and possibly demonstrated minimal understanding and possibly some misunderstandings or undeveloped misconceptions? understanding? . Connecticut State Department of Education 3 Getting Started Student Response Example Indicators What possible indicators may be included in a student response who What will a response include from a student who demonstrated minimal has demonstrated minimal understanding of the standard? understanding and possibly misconceptions? o Lack of understanding between the relationship of the time and gallons flowing into the two tanks. o Lack of a ratio table modeling the relationship between time and gallons. o Lack of understanding a unit rate and how that is connected to this situation. 1 1 o The student calculated and of a minute into seconds 4 6 incorrectly. What strategies, and representations will or will not be used? What understandings or procedural fluency does the student response reveal? o No ratio table to show the progression of time and gallons in each container. o The student tried to calculate the unit rate by using percentages. He showed 3% of the tank filled per second. That cannot be determined, as the amount of water each tank holds was not given. What undeveloped understandings, misconceptions, and common mistakes may be revealed in the student response to this item? o Student made no connect between the amount of time and number of gallons flowing into the tanks. o Student could not recognize a unit rate. o Student did not make the connection between two equal representations of a ratio table. o There was not clear understanding that a comparison had to be made comparing the rates to select which container would be filler faster. Connecticut State Department of Education 4 In the Moment Questions/Prompts Closing the Loop (Interventions/Extensions) What questions could you ask, or feedback could you provide in the moment to LZ video lesson links that may help develop conceptual understanding and develop student understanding, create disequilibrium, or advance student procedural skill needed thinking? What relationship is represented in this problem http://learnzillion.com/courses/43?collection_id=552 Looking at Container A – how much water is flowing into the container and in what time period. Let’s break down the time periods and see how much water will be in the I also use with the student a visual model showing the relationship. This would tank at each time: be found at: http://www.thinkingblocks.com 1 hour – how much water _____________________________ 4 Here students will visually see the connection and relationship between A second 1 hour – how much water ___________________________ 4 numbers. After the student worked through the guided lessons here, I would use Thinking blocks to model this problem 1 After a third hour – how much water _______________________ 4 With this students I would draw the bar model to have them fill in with time – and then the gallons that entered the tank after each 1 hour. 4 I would ask the student how many 1 hours are in 1 whole hour. 4 Then I would ask for them to mark off that time on a Bar model – and see if they can determine the amount of water in the tank. 1 1 1 1 ℎ표푢푟 ℎ표푢푟 ℎ표푢푟 ℎ표푢푟 4 4 4 4 If a student continues to have a hard time with the concept – I would then move to model using half hours – or ONLY whole numbers to see if the student can then see the relationship between the numbers. Connecticut State Department of Education 5 A double number line could also be used to help the students the relationship between time and gallons. ¼ hour ____gallons Connecticut State Department of Education 6 Developing Student Response Example Indicators What possible indicators may be included in a student response who has What will a response include from a student who demonstrated some demonstrated some understanding of the standard? understanding and possibly some misunderstandings or undeveloped o Student showed no ratio table for the relationship between time understanding? and gallons. o Student did not write the unit rate for each tank. o No equation was given to show the relationship of this situation. What strategies, and representations will or will not be used? What understandings or procedural fluency does the student response reveal? o Student did understand that the filling of the containers was in a linear relation – they show the water-level moving in a straight line. What undeveloped understandings, misconceptions, and common mistakes may be revealed in the student response to this item? o For Contain A the student showed a doubling of time increments. He was not consistent with his measurements. o The container that would fill the fastest was not indicated. o Student did not show recognition of unit rate. Connecticut State Department of Education 7 In the Moment Questions/Prompts Closing the Loop (Interventions/Extensions) What questions could you ask, or feedback could you provide in the moment to LZ video lesson links that may help develop conceptual understanding and develop student understanding, create disequilibrium, or advance student procedural skill needed thinking? http://learnzillion.com/courses/43?collection_id=552
Recommended publications
  • Understanding Fractions – Interpretations And

    Understanding Fractions – Interpretations And

    Understanding fractions: interpretations and representations An iTalk2Learn Guide for teachers Version 1.0 28-04-2014 1 1 Developing a coherent system for fractions learning Did you know that children’s performance in fractions predicts their mathematics achievement in secondary school, above and beyond the contributions of whole number arithmetic knowledge, verbal and non-verbal IQ, working memory, and family education and income? Seigler et al (2012) The iTalk2Learn project aims at helping primary school children develop robust knowledge in the field of fractions. Fractions are one of the most difficult aspect of mathematics to teach and learn (Charalambous & Pitta-Pantazi, 2007). The difficulty arises because of the complexity of fractions, such as the number of ways they can be interpreted and the number of representations teachers can draw upon to teach. In this paper we discuss these two aspect of fractions and present the iTalk2Learn Fractions Interpretations / Representations Matrix that you may find helpful in your fractions planning and teaching. 1.1 Interpretations of fractions When teaching fractions, we need to take into account that fractions can be interpreted in several different ways (Kieran, 1976, 1993). The interpretations are part-whole, ratio, operator, quotient, and measure. There is inevitable overlapping between the interpretations, but in Table 1 each interpretation is exemplified using the fraction ¾. Table 1. Interpretations of fractions, exemplified using 3/4. Interpretation Commentary Part-whole In part-whole cases, a continuous quantity or a set of discrete objects is partitioned into a number of equal-sized parts. In this interpretation, the numerator must be smaller than the denominator.
  • Chapter 30: Quantum Physics ( ) ( )( ( )( ) ( )( ( )( )

    Chapter 30: Quantum Physics ( ) ( )( ( )( ) ( )( ( )( )

    Chapter 30: Quantum Physics 9. The tungsten filament in a standard light bulb can be considered a blackbody radiator. Use Wien’s Displacement Law (equation 30-1) to find the peak frequency of the radiation from the tungsten filament. −− 10 1 1 1. (a) Solve Eq. 30-1 fTpeak =×⋅(5.88 10 s K ) for the peak frequency: =×⋅(5.88 1010 s−− 1 K 1 )( 2850 K) =× 1.68 1014 Hz 2. (b) Because the peak frequency is that of infrared electromagnetic radiation, the light bulb radiates more energy in the infrared than the visible part of the spectrum. 10. The image shows two oxygen atoms oscillating back and forth, similar to a mass on a spring. The image also shows the evenly spaced energy levels of the oscillation. Use equation 13-11 to calculate the period of oscillation for the two atoms. Calculate the frequency, using equation 13-1, from the inverse of the period. Multiply the period by Planck’s constant to calculate the spacing of the energy levels. m 1. (a) Set the frequency T = 2π k equal to the inverse of the period: 1 1k 1 1215 N/m f = = = =4.792 × 1013 Hz Tm22ππ1.340× 10−26 kg 2. (b) Multiply the frequency by Planck’s constant: E==×⋅ hf (6.63 10−−34 J s)(4.792 × 1013 Hz) =× 3.18 1020 J 19. The light from a flashlight can be considered as the emission of many photons of the same frequency. The power output is equal to the number of photons emitted per second multiplied by the energy of each photon.
  • Multidisciplinary Design Project Engineering Dictionary Version 0.0.2

    Multidisciplinary Design Project Engineering Dictionary Version 0.0.2

    Multidisciplinary Design Project Engineering Dictionary Version 0.0.2 February 15, 2006 . DRAFT Cambridge-MIT Institute Multidisciplinary Design Project This Dictionary/Glossary of Engineering terms has been compiled to compliment the work developed as part of the Multi-disciplinary Design Project (MDP), which is a programme to develop teaching material and kits to aid the running of mechtronics projects in Universities and Schools. The project is being carried out with support from the Cambridge-MIT Institute undergraduate teaching programe. For more information about the project please visit the MDP website at http://www-mdp.eng.cam.ac.uk or contact Dr. Peter Long Prof. Alex Slocum Cambridge University Engineering Department Massachusetts Institute of Technology Trumpington Street, 77 Massachusetts Ave. Cambridge. Cambridge MA 02139-4307 CB2 1PZ. USA e-mail: [email protected] e-mail: [email protected] tel: +44 (0) 1223 332779 tel: +1 617 253 0012 For information about the CMI initiative please see Cambridge-MIT Institute website :- http://www.cambridge-mit.org CMI CMI, University of Cambridge Massachusetts Institute of Technology 10 Miller’s Yard, 77 Massachusetts Ave. Mill Lane, Cambridge MA 02139-4307 Cambridge. CB2 1RQ. USA tel: +44 (0) 1223 327207 tel. +1 617 253 7732 fax: +44 (0) 1223 765891 fax. +1 617 258 8539 . DRAFT 2 CMI-MDP Programme 1 Introduction This dictionary/glossary has not been developed as a definative work but as a useful reference book for engi- neering students to search when looking for the meaning of a word/phrase. It has been compiled from a number of existing glossaries together with a number of local additions.
  • Calculus Terminology

    Calculus Terminology

    AP Calculus BC Calculus Terminology Absolute Convergence Asymptote Continued Sum Absolute Maximum Average Rate of Change Continuous Function Absolute Minimum Average Value of a Function Continuously Differentiable Function Absolutely Convergent Axis of Rotation Converge Acceleration Boundary Value Problem Converge Absolutely Alternating Series Bounded Function Converge Conditionally Alternating Series Remainder Bounded Sequence Convergence Tests Alternating Series Test Bounds of Integration Convergent Sequence Analytic Methods Calculus Convergent Series Annulus Cartesian Form Critical Number Antiderivative of a Function Cavalieri’s Principle Critical Point Approximation by Differentials Center of Mass Formula Critical Value Arc Length of a Curve Centroid Curly d Area below a Curve Chain Rule Curve Area between Curves Comparison Test Curve Sketching Area of an Ellipse Concave Cusp Area of a Parabolic Segment Concave Down Cylindrical Shell Method Area under a Curve Concave Up Decreasing Function Area Using Parametric Equations Conditional Convergence Definite Integral Area Using Polar Coordinates Constant Term Definite Integral Rules Degenerate Divergent Series Function Operations Del Operator e Fundamental Theorem of Calculus Deleted Neighborhood Ellipsoid GLB Derivative End Behavior Global Maximum Derivative of a Power Series Essential Discontinuity Global Minimum Derivative Rules Explicit Differentiation Golden Spiral Difference Quotient Explicit Function Graphic Methods Differentiable Exponential Decay Greatest Lower Bound Differential
  • Calculus Formulas and Theorems

    Calculus Formulas and Theorems

    Formulas and Theorems for Reference I. Tbigonometric Formulas l. sin2d+c,cis2d:1 sec2d l*cot20:<:sc:20 +.I sin(-d) : -sitt0 t,rs(-//) = t r1sl/ : -tallH 7. sin(A* B) :sitrAcosB*silBcosA 8. : siri A cos B - siu B <:os,;l 9. cos(A+ B) - cos,4cos B - siuA siriB 10. cos(A- B) : cosA cosB + silrA sirrB 11. 2 sirrd t:osd 12. <'os20- coS2(i - siu20 : 2<'os2o - I - 1 - 2sin20 I 13. tan d : <.rft0 (:ost/ I 14. <:ol0 : sirrd tattH 1 15. (:OS I/ 1 16. cscd - ri" 6i /F tl r(. cos[I ^ -el : sitt d \l 18. -01 : COSA 215 216 Formulas and Theorems II. Differentiation Formulas !(r") - trr:"-1 Q,:I' ]tra-fg'+gf' gJ'-,f g' - * (i) ,l' ,I - (tt(.r))9'(.,') ,i;.[tyt.rt) l'' d, \ (sttt rrJ .* ('oqI' .7, tJ, \ . ./ stll lr dr. l('os J { 1a,,,t,:r) - .,' o.t "11'2 1(<,ot.r') - (,.(,2.r' Q:T rl , (sc'c:.r'J: sPl'.r tall 11 ,7, d, - (<:s<t.r,; - (ls(].]'(rot;.r fr("'),t -.'' ,1 - fr(u") o,'ltrc ,l ,, 1 ' tlll ri - (l.t' .f d,^ --: I -iAl'CSllLl'l t!.r' J1 - rz 1(Arcsi' r) : oT Il12 Formulas and Theorems 2I7 III. Integration Formulas 1. ,f "or:artC 2. [\0,-trrlrl *(' .t "r 3. [,' ,t.,: r^x| (' ,I 4. In' a,,: lL , ,' .l 111Q 5. In., a.r: .rhr.r' .r r (' ,l f 6. sirr.r d.r' - ( os.r'-t C ./ 7. /.,,.r' dr : sitr.i'| (' .t 8. tl:r:hr sec,rl+ C or ln Jccrsrl+ C ,f'r^rr f 9.
  • Ratios Rates and Unit Rates Worksheet

    Ratios Rates and Unit Rates Worksheet

    Ratios Rates And Unit Rates Worksheet Foaming and unhatched Hill circles fore and decalcifies his dogmatizer invectively and inquisitively. Atheistic Smitty never can so stylishly or wire any Goidelic hottest. Traveling Bernie farcings that MacArthur misshape nowadays and economising pickaback. Ratios worksheets are part of a checklist format in good food web worksheet. Grade. A mute is a guideline or little that defines how oil of one chamber have compared to utilize Unit rates are just a factory more money A discrete rate distinguishes the. Clearance for every part of the denominator have little coloring activity is a different units of. Polish your email address will help you will challenge kids less formal way of soda you compare two pairs have iframes disabled or as fractions. Write ratios and rates as fractions in simplest form and unit rates Find unit prices. Unit rates for bell ringers, check if there will always be kept dry completely before. Mathlinks grade 6 student packet 11 ratios and unit rates. Street clothes for the worksheet library, not have been saved in excel overview now please try again with minutes in an example. How to Calculate Unit Rates & Unit Prices Video & Lesson. High resolution image in the numerator and organized house cleaning tips and tub and if you. Find each worksheet to number of our extensive math. It really see what percent is. Unit Rates Ratios Proportional Reasoning Double Number. Unit Rates and Equivalent Rates Grade 6 Practice with. To heighten their logical reasoning with this worksheet shown above example of math worksheets kiddy math problems related to opt out of penguins and experienced seniors sharing templates.
  • Electrical Power and Energy

    Electrical Power and Energy

    Electric Circuits Name: Electrical Power and Energy Read from Lessons 2 and 3 of the Current Electricity chapter at The Physics Classroom: http://www.physicsclassroom.com/Class/circuits/u9l2d.html http://www.physicsclassroom.com/Class/circuits/u9l3d.html MOP Connection: Electric Circuits: sublevel 3 Review: 1. The electric potential at a given location in a circuit is the amount of _____________ per ___________ at that location. The location of highest potential within a circuit is at the _______ ( +, - ) terminal of the battery. As charge moves through the external circuit from the ______ ( +, - ) to the ______ ( +, - ) terminal, the charge loses potential energy. As charge moves through the battery, it gains potential energy. The difference in electric potential between any two locations within the circuit is known as the electric potential difference; it is sometimes called the _____________________ and represented by the symbol ______. The rate at which charge moves past any point along the circuit is known as the ___________________ and is expressed with the unit ________________. The diagram at the right depicts an electric circuit in a car. The rear defroster is connected to the 12-Volt car battery. Several points are labeled along the circuit. Use this diagram for questions #2-#6. 2. Charge flowing through this circuit possesses 0 J of potential energy at point ___. 3. The overall effect of this circuit is to convert ____ energy into ____ energy. a. electrical, chemical b. chemical, mechanical c. thermal, electrical d. chemical, thermal 4. The potential energy of the charge at point A is ___ the potential energy at B.
  • Grade 5 Math Index For

    Grade 5 Math Index For

    Common Core Standards Plus – Mathematics – Grade 5 with Common Core ELD Standard Alignment Domain Lesson Focus Standard(s) ELD Standards 1 Place Value Patterns 5.NBT.1: Recognize that in a multi‐digit 2 Place Value Patterns number, a digit in one place represents 10 times as much as it represents in the place ELD.PI.5.5: Listening actively and 3 Place Value Patterns asking/ answering questions about what to its right and 1/10 of what it represents was heard. 4 Place Value Patterns in the place to its left. E1 Evaluation ‐ Place Value Patterns 5 Powers of Ten 5.NBT.2: Explain patterns in the number of zeros of the product when multiplying a 6 Multiply by Powers of Ten number by powers of 10, and explain patterns in the placement of the decimal ELD.PI.5.5: Listening actively and 7 Divide by Powers of Ten asking/ answering questions about what point when a decimal is multiplied or was heard. 8 Multiply & Divide by Powers of Ten divided by a power of 10. Use whole‐ ELD.PI.5.10: Composing/writing number exponents to denote powers of literary and informational texts. E2 Evaluation ‐ Powers of Ten 10. P1 Performance Lesson #1 Power of Ten (5.NBT.1, 5.NBT.2) 5.NBT.7 Word Form of Decimals ‐ 9 5.NBT.3: Read, write, and compare 10 Expanded Form of Decimals decimals to thousandths. ELD.PI.5.5: Listening actively and Ten 5.NBT.3a: Read and write decimals to asking/ answering questions about what 5.NBT.1 Standard Form of Decimals thousandths using base‐ten numerals, was heard.
  • Study in Egyptian Fractions

    Study in Egyptian Fractions

    1 STUDY IN EGYPTIAN FRACTIONS Robert P. Schneider Whether operating with fingers, stones or hieroglyphic symbols, the ancient mathematician would have been in many respects as familiar with the integers and rational numbers as is the modern researcher. If we regard both written symbols and unwritten arrangements of objects to be forms of notation for numbers, then through the ancient notations and their related number systems flowed the same arithmetic properties—associativity, commutativity, distributivity—that we know so intimately today, having probed and extended these empirical laws using modern tools such as set theory and Peano’s axioms. It is fascinating to contemplate that we share our base-ten number system and its arithmetic, almost as natural to us as sunlight and the air we breathe, with the scribes of ancient Egypt [1, p. 85]. We use different symbols to denote the numbers and operations, but our arithmetic was theirs as well. Our notation for fractions even mimics theirs with its two-tiered arrangement foreshadowing our numerator and denominator; however, the Egyptian notation for fractions leaves no space for numbers in the numerator, the position being filled by a hieroglyphic symbol meaning “part” [1, p. 93]. Aside from having special symbols to denote 2/3 and 3/4, the Egyptians always understood the numerator to be equal to unity in their fractions [4]. The representation of an improper fraction as the sum of distinct unit fractions, or fractions having numerators equal to one, is referred to as an “Egyptian fraction” [3]. I found the Egyptians’ use of fractions, as well as their multiplication and division algorithms [1, pp.
  • Eureka Math™ Tips for Parents Module 2

    Eureka Math™ Tips for Parents Module 2

    Grade 6 Eureka Math™ Tips for Parents Module 2 The chart below shows the relationships between various fractions and may be a great Key Words tool for your child throughout this module. Greatest Common Factor In this 19-lesson module, students complete The greatest common factor of two whole numbers (not both zero) is the their understanding of the four operations as they study division of whole numbers, division greatest whole number that is a by a fraction, division of decimals and factor of each number. For operations on multi-digit decimals. This example, the GCF of 24 and 36 is 12 expanded understanding serves to complete because when all of the factors of their study of the four operations with positive 24 and 36 are listed, the largest rational numbers, preparing students for factor they share is 12. understanding, locating, and ordering negative rational numbers and working with algebraic Least Common Multiple expressions. The least common multiple of two whole numbers is the least whole number greater than zero that is a What Came Before this Module: multiple of each number. For Below is an example of how a fraction bar model can be used to represent the Students added, subtracted, and example, the LCM of 4 and 6 is 12 quotient in a division problem. multiplied fractions and decimals (to because when the multiples of 4 and the hundredths place). They divided a 6 are listed, the smallest or first unit fraction by a non-zero whole multiple they share is 12. number as well as divided a whole number by a unit fraction.
  • Best Glide Speed and Distance

    Best Glide Speed and Distance

    General Aviation FAA Joint Steering Committee Aviation Safety Safety Enhancement Topic Best Glide Speed and Distance The General Aviation Joint Steering Committee (GAJSC) has determined that a significant number of general aviation fatalities could be avoided if pilots were better informed and trained in determining and flying their aircraft at the best glide speed while maneuvering to complete a forced landing. What is Best Glide Speed? Keep in mind that this speed will increase with weight so most manufacturers will establish Is it the speed that will get you the greatest the best glide speed at gross weight for the aircraft. distance? Or is it the speed that gets you the That means your best glide speed will be a little longest time in the air? Or are these two the same lower for lower aircraft weights. — the longer you fly, the further you go? Well, as so often is the case, best glide speed depends on what Need More Time? you’re trying to do. If you’re more interested in staying in the air Going the Distance as long as possible to either fix the problem or to communicate your intentions and prepare for a If it’s distance you want, than you’ll need to forced landing, then minimum sink speed is what use the speed and configuration that will get you you’ll need. This speed is rarely found in Pilot the most distance forward for each increment of Operating Handbooks, but it will be a little slower altitude lost. This is often referred to as best glide than maximum glide range speed.
  • Inertia and Rate of Change of Frequency (Rocof)

    Inertia and Rate of Change of Frequency (Rocof)

    Inertia and Rate of Change of Frequency (RoCoF) Version 17 SPD – Inertia TF 16. Dec. 2020 ENTSO-E AISBL • Rue de Spa 8 • 1000 Brussels • Belgium • Tel + 32 2 741 09 50 • Fax + 32 2 741 09 51 • [email protected] • www. entsoe.eu Inertia and Rate of Change of Frequency (RoCoF) 1. Executive Summary ............................................................................................................... 3 2. Introduction and Aim of the Document ................................................................................... 4 3. Definitions .............................................................................................................................. 6 3.1 Inertia ................................................................................................................................. 6 3.2 Rate of Change of Frequency (RoCoF) .............................................................................. 8 3.3 Centre of Inertia .................................................................................................................. 9 4. Impact of Inertia on Power Systems ..................................................................................... 11 4.1 Frequency and Voltage Control of Generators .................................................................. 11 4.2 Stability ................................................................................................................................. 12 4.3 Protection Equipment ......................................................................................................