دليل المعلم Volume 1 الرياضيات للصف التاسع منهج انجليزي Reveal الفصل الثالث 2021 2022
Make sense of problems and persevere in solving them
Mathematically students start by explaining to themselves me meaning of a and looking for entry pomts to its They analyze corstraülts, relationships. and goals. They make conjectures abwt the form and meaNing of the solution and plan a sdutim pathway rather ttun simply "Ito a solutim attempt. They consider analogous and try special cases and simpler forms of me riginal pr±lem in order to gain "bigm into its soutim. They monitor and evaluate their mogress dtange course if necessary. Older studmts might. on the context of the transform algebraic expressions or change the viewing window meir yaphing calculator to get the they need. Mathematically proficient studmts can explaül between equatins. verbal descriptims. tables, and yaphs or draw diayams of important features relatjmstips, graph data and search for regularity or treMs. Yourw students milt rely on cmcrete objects pictures to corueptualize and a MathematicaNy proficient students check their answers to problems using a different method. and they continually ask themselves, -Does this make sense ?- They can the approaches of others to complex and idertify between different
2 Reason abtractty and quantiatively
Matrematjcalty proficient students make sense of quantities and their relationships neem situations. They bring two c«nplementary abilities to bear *wol'ärg wantitative relatimships: the ability to decontextualize—to abstract a given situation and represent it symbolically and maNpulate he representing symbols as if they have a life of treir without necesqrily atten&ng to their refererts—and the abdity to contextwfze. to pause as need diring trp manimjlation in ord« to probe ilto tie referents tie symbols invdved. Quantitative reasming entails habits of a coherent representation of the prchlem at hand: the units inWved. attending to the meanng of quantities. not just how to compute aM knowng md flexiby using Offerent properties of operations md jects
Corstruct viable arguments and critique the reasonil,g of them
Mathematically proficient students mderstand and use stated assumptions and previously eqablished resuts in constructing arguments. They make conjecüres and build a logical progressim of statements to eVore truth of ttpir cmjectures_ Thw are abe to analyze situations by breaking them into cases, can recognize and use counterexamples. They justify their cmclusions. ænmunicate them to and respmd to the arWnents of others. They reasm inåjctively about data. making *usible arguments tret take into account the context frn which the data arose
Mathematically proficient students are also able to compare the effectiveness of two plausible arguments, distinguish correct or reasming frun that which is flawed, and—if there is a flaw in an what it is. Elementary studmts can construct argunmts usirg concrete referents wch as octs, fawü-'gs, diagams, and actims_ Such arguments can make sense and be even thwgh they are not gemralized made formal until later grades. Later. learn to determile domains to which an argument applies. at all grades can listen read ttp arguments of others. decide they make sense, and useful westions to clarify improve the argunents
Mathematica"y students can the mathematics they know to solve. in everyday life. s«iety. the workplace. In early wades. ttüs as simple as writing an addition ewation to descrüe a situatm In rne a student might apply reasoning to a event or analyze a mouen in ttp community. By a studert use Math Integrated II to sdve a or a function to how one wantity imerest anMtpr. Mathematically proficient who can what they are comfortable making assumpbons awoximatms to simplify a complicated situation. realizing that these may later. Tty are able to identity "TVtant wantities in a practical situation aM their relatimships using such as diagrams. two-way taWes, graphs flowcharts and fumuas. They can analyze those relationships mathematically to draw cmclusims. They routinely ntergy« their mathematical results in the cmtext the situatim and reflt on whemer the resuts make sense, imprwing the if it has served its purpose
5 use
Mathemabcalty proficient conseder the available when a math«natical Thse include pencil and cmcrete a ruler. a system, a statistical or dynamic Reveal Math II software Proficient students are sufficiently familiar with for their course to make sound disims wtm each of these might be helpful th the inst to gained and their limitations. For example mathematically proficiert high schml analyze yaphs of functions and seLRions using a graphing calculator. They detect errors Lßing estimatim other mathematical When making mathnatical they krw ttut thndogy can enable them to visualize he
results of assumptions. explore conseqLRnces. and with data. Mathematically proficient stud«lts at variws wade levels are abe to relevant external mathematical resources. such as #tal content a website. and them to Ttpy are aue to tmls to and their of concepts
6 Attend to precisim
Mathematkally proficient stLents try to communcate to They try to use dear defilitjms in discussion with others and in meit own reasoning They state meanülg of the they chmse. includng equal cmsistently and aiaWy. They are careful about units meanne. and labelng axes to clarify the correspondence with quantibes a Ttpy calculate efficiently. runerical answers wih a of precision appropriate the problem context. In elementary grades. students give carefully formulated explanations to each Mher. the time they high they have learned to examirp claims i make exit ot
The Iglite! by Dr. Raj Shah. cdbvate ariosity and challenge students. Use mese in me Launch to your students to a yowth mindset towards mathematics and Use notes for implementation and support for erxouraging stronge
Essential Question
At end ths shodd able to answer the Essertial Ouestim
How can relationsNps in tringles be used in real-wu Sample answer: The relationships he Mferent parts of a can information the triangle in a cmtext example. scxial segmems can opomal
ctnices in design
What Will You Learn
to this have your students rateh item listed. Then, at me end of ttp yma will reminded to haæ ymr students return to these to rate their They should see that their knowledge and skills have increased
DINAH ZIKE
Students write mtes new terms and cmcepts as mey are in each lesson of ttüs Teach Have students construct their Fddable as illustrated. Have studems write an explanation of term cmcept on he awwriate section Of Foldabe wtWe working each lessm. Encowage to exanWes of each term or cmcept on me back of each flap
Wtm to use It Encourage to add to their Foldaue as mey work throu tve module, and to use it to review nmJle test
Launch the Module
Fu this nmje, he Launch he Module video uses architectwe to demonsrate the lßefuhess of and their irtrinsic parts and relationships. StLents learn abwt me use Of for stabiity in arctüectwe