Multiple Representations Of Linear Relationships, Grades 7-8
Multiple Representationsof Linear Relationships,Grades 7-8Sana BrennanRegion 4 ESCwww.esc4.netSBrennan@esc4.net713.744.4401Want the latest buzz fromRegion 4 Mathematics?Visit us online!http://bit.ly/1uklEvMFor Handouts:QR Codehttp://bit.ly/1aNWJGPPermission to copy classroom-ready materialsgranted to attendees of this session. 2015 Region 4 Education Service CenterAll rights reserved.
(A) represent linearrelationships using verbaldescriptions, tables, graphs, andequations that simplify to theform y mx b.(7) Expressions, equations, andrelationships. The student appliesmathematical process standardsto represent linear relationshipsusing multiple representations.The student is expected to:(C) determine the constant ofproportionality (k y/x) withinmathematical and real-worldproblems.(B) represent linear non-proportionalsituations with tables, graphs, andequations in the form of y mx b,where b 0.(E) solve problems involving directvariation.A) represent linear proportionalsituations with tables, graphs, andequations in the form of y kx.(B) write linear equations intwo variables in variousforms, including y mx b, Ax By C, andy - y1 m(x - x1), given onepoint and the slope and giventwo points(D) write and solve equationsinvolving direct variation.(2) Linear functions,equations, and inequalities.The student applies themathematical processstandards when usingproperties of linear functionsto write and represent inmultiple ways, with andwithout technology, linearequations, inequalities, andsystems of equations. Thestudent is expected to:Algebra IIntroduction to the Revised Mathematics TEKS: Vertical Alignment Chart Grade 5 – Algebra I(A) identify independent anddependent quantities fromtables and graphs.(6) Expressions, equations,and relationships. The studentapplies mathematical processstandards to use multiplerepresentations to describealgebraic relationships. Thestudent is expected to:((A) compare two rulesverbally, numerically,graphically, and symbolicallyin the form of y ax ory x a in order todifferentiate between additiveand multiplicativerelationships.A) represent constant rates ofchange in mathematical and realworld problems given pictorial,tabular, verbal, numeric,graphical, and algebraicrepresentations, including d rt.Grade 7Grade 8Applying Multiple Representations for Foundations of Functions(4) Proportionality. The(4) Proportionality. The student(5) Proportionality. The studentstudent applies mathematicalapplies mathematical processapplies mathematical processprocess standards to developstandards to represent and solvestandards to use proportional andan understanding ofproblems involving proportionalnon-proportional relationships toproportional relationships inrelationships. The student isdevelop foundational concepts ofproblem situations. Theexpected to:functions. The student is expected to:student is expected to:Grade 6 2013 Texas Education Agency. All Rights Reserved 2013(D) recognize the differencebetween additive andmultiplicative numericalpatterns given in a table orgraph.(C) generate a numericalpattern when given a rule inthe form y ax or y x aand graph.(4) Algebraic reasoning. Thestudent applies mathematicalprocess standards to developconcepts of expressions andequations. The student isexpected to:Grade 516
(A) calculate, using technology,the correlation coefficientbetween two quantitativevariables and interpret thisquantity as a measure of thestrength of the linear association.(4) Linear functions, equations,and inequalities. The studentapplies the mathematical processstandards to formulate statisticalrelationships and evaluate theirreasonableness based on realworld data. The student isexpected to:(5) Proportionality. The student appliesmathematical process standards to useproportional and non-proportionalrelationships to develop foundationalconcepts of functions. The student isexpected to:(C) contrast bivariate sets of data thatsuggest a linear relationship with bivariatesets of data that do not suggest alinear relationship from a graphicalrepresentation.(D) use a trend line that approximatesthe linear relationship between bivariatesets of data to make predictions.(G) identify functions using sets ofordered pairs, tables, mappings, andgraphs.(H) identify examples ofproportional and nonproportional functions that arise frommathematical and real-world problems.(C) write linear equations in twovariables given a table of values,a graph, and a verbal description.(2) Linear functions, equations,and inequalities. The studentapplies the mathematical processstandards when using propertiesof linear functions to write andrepresent in multiple ways, withand without technology, linearequations, inequalities, andsystems of equations. Thestudent is expected to:(I) write an equation in the formy mx b to model a linear relationshipbetween two quantities using verbal,numerical, tabular, and graphicalrepresentations.(F) distinguish between proportional andnon-proportional situations using tables,graphs, and equations in the form y kx or y mx b, where b 0.5) Proportionality. The student appliesmathematical process standards to useproportional and non-proportionalrelationships to develop foundationalconcepts of functions. The student isexpected to:Algebra IIntroduction to the Revised Mathematics TEKS: Vertical Alignment Chart Grade 5 – Algebra I(B) write an equation thatrepresents the relationshipbetween independent anddependent quantities from atable.(C) represent a given situationusing verbal descriptions, tables,graphs, and equations in the formy kx or y x b.(7) Expressions, equations, andrelationships. The student appliesmathematical process standards torepresent linear relationships usingmultiple representations. The studentis expected to:Grade 7Grade 8Applying Multiple Representations for Foundations of Functions(6) Expressions, equations, andrelationships. The student appliesmathematical process standardsto use multiple representations todescribe algebraic relationships.The student is expected to:Grade 6 2013 Texas Education Agency. All Rights Reserved 2013Grade 517
Name:Date:Designing a Fairy Swimming PoolAmber has created a Fairy Garden and wants to add a swimming pool. The pool will be rectangularand surrounded by colorful border made of square tiles. The pictures below show the three smallestpools Amber can build.Pool 1Pool 2Pool 31. On grid paper, draw Pool 4 & Pool 5. How many tiles are needed for each of these pools?2. Talk with your partner about any patterns or observations about the first five pools thatmight help you describe larger pools. Record the highlights of your discussion below:3. Without constructing it, describe a method for finding the total number of tiles that wouldbe needed to build Pool 50.4. Write a rule that could be used to determine the number of tiles, x, needed for any pool.Explain how your rule relates to the visual representation of the pools.5. Write a different rule that could be used to determine the number of tiles needed for anypool. Explain how this new rule relates to the visual representation of the pools.Adapted from: National Council of Teachers of Mathematics. (2001). Navigating through Algebra in Grades 6-8. Reston:National Council of Teachers of Mathematics.
Region 4 Education Service CenterAll rights reserved.
Pool Models for DisplayPool 1Pool 2Pool 3Pool 1Pool 2Pool 3Adapted from: National Council of Teachers of Mathematics. (2001). Navigating through Algebra in Grades 6-8. Reston:National Council of Teachers of Mathematics.
Date:Ask your partner to checkyour equation, and signhis/her name if they agree. Region 4 Education Service CenterAll rights reserved.Use your predicted rule tocomplete this table. Ask yourpartner to verify theinformation in yourcompleted table. Revise yourprediction, if needed, andrecord your final answer.Without showing yourpartner, choose one card.Enter the equation into agraphing calculator andaccess the table.DirectionsSignature:Signature:2015y x 12100y x 4x 5I think mypartner’s rule is: 5x102 2x2y-intercept:Slope:4yy10y x y x I think mypartner’s rule is:y-intercept: 1xyyAsk your partner for the y-values basedon his/her equation to complete thetable below. Use the completed table todetermine the slope and y-intercept ofyour partner’s rule.Ask your partner for the y-values basedon his/her equation to complete thetable below. Use the completed table todetermine the slope and y-intercept ofyour partner’s rule.Slope:Challenge 2Challenge 1Cut apart the Rule Cards, mix them up, and place them face down on the desk between you and a partner. Complete Challenge 1 byfollowing the directions below. Then each of you will draw a new card and repeat the process for Challenge 2.Guess My Rule ChallengeName:Gather My CluesCheck My PredictionEquation
Rule CardsCut along the bold dotted lines. Four sets of cards are provided. y 2x 5 3 x 4y y 4x 13x 621y x 425y x 24 y 2x 5y 3 x 4 y 4x 13x 621y x 425y x 24 y 2x 5 3 x 4y y 4x 13x 621y x 425y x 24 y 2x 5y 3 x 4 y 4x 13x 621y x 425y x 24 y y y y Region 4 Education Service CenterAll rights reserved. 5 x 8y y 1x2y 5 x 8y 1x2 5 x 8y y 1x2y 5 x 8y 1x2
Sana Brennan Region 4 ESC www.esc4.net SBrennan@esc4.net 713.744.4401 Permission to copy classroom-ready materials granted to attendees of this session.
Linear Growing Patterns Representations Sorting Activity (printable) Students will: sort different representations of linear growing patterns into matching groups 1.5.2 Assessment Demonstration Linear Growing Patterns Representations Pattern Building (printable) Students will: represent lin
Multiple Linear Regression Linear relationship developed from more than 1 predictor variable Simple linear regression: y b m*x y β 0 β 1 * x 1 Multiple linear regression: y β 0 β 1 *x 1 β 2 *x 2 β n *x n β i is a parameter estimate used to generate the linear curve Simple linear model: β 1 is the slope of the line
Chapitre I. Les fonctions L des représentations d’Artin et leurs valeurs spéciales1 1. Représentations d’Artin1 2. Conjectures de Stark complexes4 3. Représentations d’Artin totalement paires et Conjecture de Gross-Stark11 4. Et les autres représentations d’Artin?14 5. Représentations d’
SKF Linear Motion linear rail INA Linear SKF Linear Motion Star Linear Thomson Linear linear sysTems Bishop-Wisecarver INA Linear Pacific Bearing Thomson Linear mecHanical acTuaTors Duff-Norton Joyce/Dayton Nook Industries Precision mecHanical comPonenTs PIC Design Stock Drive Product
mx b a linear function. Definition of Linear Function A linear function f is any function of the form y f(x) mx b where m and b are constants. Example 2 Linear Functions Which of the following functions are linear? a. y 0.5x 12 b. 5y 2x 10 c. y 1/x 2 d. y x2 Solution: a. This is a linear function. The slope is m 0.5 and .
MA 575: Linear Models MA 575 Linear Models: Cedric E. Ginestet, Boston University Multiple Linear Regression Week 4, Lecture 2 1 Multiple Regression 1.1 The Data The simple linear regression setting can be extended to the case of pindependent variables, such that we may now have the followi
Feeny Math Resources Linear Functions Linear Functions Linear Functions Linear Functions Linear Functions Which of the following is a solution to the linear function in the graph? A. (1,1) B. (5,3) C. (
Sep 25, 2007 · A linear program is an optimization problem where all involved functions are linear in x; in particular, all the constraints are linear inequalities and equalities. Linear programming is the subject of studying and solving linear programs. Linear programming was born during the second World
