GISSV Elementary School Mathematics Curriculum, Grade 1

Transcription

1 GISSV Elementary Schl Mathematics Curriculum, Grade 1 Cntent Skills The student is able t Methds f scial interactin, methdlgies and media Crss-disciplinary aspects Relatinship t the schl prgram Learning area: Arithmetic Intrductin t numbers up t 20 Intrductin t peratins Cnceptualize and understand whle numbers up t 20 in a diversity f situatins and a variety f illustratins. Use varius methds t illustrate numbers, and use their psitinal ntatin system. Demnstrate rientatin (cmpare, srt, illustrate) within the number series. Describe and explain numerical frms, relatinships and prperties. Navigate the fllwing cncepts: predecessr / successr greater than / less than even / dd duble / half Create, describe and explain structures. Describe, carry frward, independently develp, systematically change number sequences and patterns. Establish cnnectin between actin, peratin and ntatin. Illustrate and describe Selectin guided by tpic Individual, partner and grup wrk Class discussin Presentatin Weekly wrk plan Wrkshp Statin wrk Seminar Games Rle playing Prjects Crafts Painting, drawing Bks, stries Nn-fictin texts Cmputers Phts Smartbard Chalkbard Mind map Wrksheet Selectin guided by tpic German: Stries Nn-fictin texts Pems English: Stries Nn-fictin texts Pems Art: Theme-based creatin with varius materials Music: Sngs NuG: Daily rutine Seasns The clck Water My schl

2 Mental math Oral and partially written math practical situatins (additin, subtractin). Describe and use the cnnectins between the basic calculatin peratins. Identify and apply math benefits. Cnduct the basic tasks f additin and subtractin in numerical rder up t 20 based n memry. Slve additin and subtractin tasks. Apply basic tasks t analgus tasks. Describe mathematical appraches; cmpare and cntrast with each ther. Describe and apply calculatin strategies. Describe, extend, independently develp and systematically mdify patterns and interrelatinships in structured task sequences. Identify, explain and crrect calculatin errrs. Slve equatins and inequalities. Learning assessments Visual materials: - clred linking cubes - reversible clred tiles / chips - natural materials - flat glass clred pebbles ( Muggle stnes) - everyday bjects - clck - multi-shape gemetric tiles - matchbxes - mirrrs Tables / charts Diagrams / graphs Number line Sprts: Games

3 Ding math in cntext Slve practical and prblembased tasks while applying heuristic prcedures. Assign calculatin tasks t practical situatins; frmulate meaningful questins and answer them. Slve simple cmbinatrial Open t the wrld

4 Intrductin t varius quantities and measurements Hw t deal with quantities and measurements peratins thrugh trial and errr. Gather and use infrmatin frm tables, charts and utlines. Test results fr plausibility. Cmpare, measure, rganize, describe and present bjects r prcesses with the aid f randm and standardized units f measurement. Read, set and recrd the time f day / hurs n the clck t the full hur, and express in varius ways. Pay with mney and change mney. Cmpare, rder and illustrate mnetary amunts. State units in eur and cent, and als give the hur, day, mnth, year. Calculate using quantities in practical and prblem tasks. Learning area: Quantities Open t the wrld Open t the wrld Intrductin t spatial relatins Describe spatial psitin and tpgraphy (abve, belw, inside, utside, right, left). Orient neself within a space; describe and retrace pathways Gemetry

5 Dealing with planes Shw and identify shapes (quadrilateral, rectangle, square, triangle, circle). Differentiate shapes based n their prperties. Place, stack, display, fld, cut-ut, disassemble and re-assemble shapes. Place, describe, extend and independently develp gemetric patterns. Symmetries Indicate if shapes are symmetrical. Determine and plt axes f symmetry. Present symmetrical figures.

6 GISSV Elementary Schl Mathematics Curriculum, Grade 2 Cntents Skills The student is able t Methds f scial interactin, methdlgies and media Crss-disciplinary aspects Relatinship t the schl prgram Learning area: Arithmetic Intrductin t numbers up t 100 Cnceptualize and understand numbers 1 thrugh 100 in a diversity f situatins and a variety f illustratins. Use varius methds t illustrate numbers, and use their psitinal ntatin system. Demnstrate rientatin (cmpare, srt, illustrate) within the number series. Describe and explain numerical frms, relatinships and prperties. Navigate the fllwing cncepts: - predecessr / successr - greater than / less than - even / dd - duble / half - cunting by fives - cunting by tens Create, describe and explain structures. Describe, carry frward, independently develp, systematically change number sequences and patterns. Establish cnnectin between Selectin guided by tpic Individual, partner and grup wrk Class discussin Presentatin Weekly wrk plan Wrkshp Statin wrk Seminar Games Rle playing Prjects Crafts Painting, drawing Bks, stries Nn-fictin texts Cmputers Phts Smartbard Chalkbard Mind map Wrksheet Learning assessments Selectin guided by tpic German: Stries Nn-fictin texts Pems English: Stries Nn-fictin texts Pems Art: Theme-based creatin with varius materials Music: Sngs NuG: The year The clck The weather My schl and my surrundings Sprts: Games

7 Intrductin t peratins actin, peratin and ntatin. Illustrate and describe (and vice versa) practical situatins in mathematics (additin, subtractin, multiplicatin and divisin). Describe and use the cnnectins between the basic calculatin peratins. Identify and apply math benefits. Identify and explain the inslvability f tasks. Mental math Cnduct the basic tasks f additin, subtractin, multiplicatin and divisin in numerical rder up t 100 based n memry. Oral and partially written math Slve additin and subtractin tasks. Apply basic tasks t analgus tasks. Describe mathematical appraches; cmpare and cntrast with each ther. Describe and apply calculatin strategies. Describe, extend, independently develp and systematically mdify patterns Visual materials: - clred linking cubes - reversible clred tiles / chips - natural materials - flat glass clred pebbles ( Muggle stnes) Everyday bjects - matchbxes - tables / charts - diagrams / graphs - number line - scale Materials fr individualized learning: Lgic LÜK Ruler Measuring tape City maps Site maps Mazes / labyrinths Standardized slids Open t the wrld

8 and interrelatinships in structured task sequences. Identify, explain and crrect calculatin errrs. Slve equatins and inequalities. Assess and verify results by mental cmputatin. Ding math in cntext Slve practical and prblembased tasks while applying heuristic prcedures. Assign calculatin tasks t practical situatins; frmulate meaningful questins and answer them. Slve simple cmbinatrial peratins thrugh trial and errr. Gather and use infrmatin frm tables, charts and utlines. Test results fr plausibility. Open t the wrld Learning area: Quantities Intrductin t varius quantities and measurements Cmpare, measure, rganize, describe and present bjects r prcesses with the aid f randm and standardized units f measurement. Estimate lengths and time perids. Open t the wrld Learning area: Gemetry

9 Intrductin t spatial relatins Describe spatial psitin and tpgraphy (abve, belw, inside, utside, right, left). Orient neself within a space and n maps; describe and retrace pathways Open t the wrld Dealing with slids Draw and identify slids, and describe and differentiate their prperties. Frm slids and build with slids.

10 Cntent GISSV Elementary Schl Mathematics Curriculum, Grade 3 Skills The student is able t Frms f scial interactin, methdlgies and media Crss-disciplinary aspects Relatinship t the schl prgram Cncepts f whle numbers (integers) Numbers up t 1,000 Learn abut numbers up t 1,000 Cmprehend numbers up t 1,000, and hw t present them in different ways Cmpare and srt numbers up t 1,000 Learning area: Arithmetic dealing with numbers and symbls Cmprehend numbers up t 1,000 in different situatins and in varius illustratins. Identify, bundle and exchange amunts. Present definitive, graphic and symblic depictins f numbers up t 1,000,000. Describe and explain the representatin f numbers with the aid f the psitinal ntatin system. Split the numbers. Read and write numbers up t ne thusand. Srt, cmpare numbers (<, >, =). Frm and extend numerical sequences. Rund numbers. Describe interrelatinships in numerical sequences, and extend these sequences. Individually develp, mdify and describe Learning and visualizatin tls (e.g., dt images n the hundred table, thusand strip, number line) Assessment tests (Thuringian Cmpetency Tests) Selectin guided by tpic German: Stries Nn-fictin texts Pems English: Stries Nn-fictin texts Pems Art: Theme-based creatin with varius materials Music: Sngs

11 numerical sequences accrding t a pattern. Differentiate dd and even numbers. NuG: Depends n the subject Sprts: Games Intrductin t peratins Arithmetic Enhance understanding f additin, subtractin, multiplicatin and divisin Multiply and divide in tw steps Establish a link between an everyday situatin, the assciated arithmetic peratin and the symblic ntatin. Illustrate practical situatins in crrespnding arithmetic exercises, and vice versa: describe the arithmetic exercises that apply t the practical situatin. Explain cnnectins between the basic peratins, and use them when calculating. Describe the benefits, rules and strategies f mathematics; describe cnfrmance t a set pattern and apply this when calculating. Identify and explain the inslvability f Learning and visualizatin tls (e.g., hundreds chart, hundreds fields, thusands field, number line)

12 tasks. Mental math Arithmetic Mentally cmpute numbers up t 1,000 in basic numerical ratis Perfrm the basic tasks f all basic calculatin peratins by memry. Use individual calculatin prcesses Verbal and infrmal written arithmetic Arithmetic Infrmal written arithmetic Slve tasks invlving all fur basic arithmetic peratins, either verbally r infrmally in writing. Describe the calculatin prcesses; cmpare and cntrast with each ther. Describe verbal and infrmal written arithmetic strategies, and apply them flexibly. Describe and extend patterns in structured task sequences. Identify, explain and crrect calculatin errrs. Slve equatins and inequalities by trial and errr, based n mental deliberatin f the cntent. Estimate and verify results by making a mental calculatin. Learning assessment: Determine the student s current level Use individual calculatin prcesses Cnduct a variety f exercises using infrmal written methds Written arithmetic Arithmetic Explain the stepwise strategy t slve Learning

13 Written arithmetic the fur basic calculatin peratins, using examples f each task. Perfrm the written algrithms f the fur basic arithmetic peratins (additin and subtractin in tw t three steps; multiplicatin and divisin using base ten numerals and remainders). D a rugh estimate fr the written arithmetic exercises and duble-check yur estimate. assessment: Determine the student s current level Use individual calculatin prcesses Practice infrmal written methd in a variety f ways Arithmetic in cntext Practical situatins Develp practical situatins and hw t represent them Develp and apply slutins Find slutin prcesses Develp practical situatins and hw t represent them. Slve cmplex practical exercises. Deduce relevant data frm texts, illustratins (diagrams, tables, sketches) and verbalize them. Find and frmulate mathematical prblems frm practical situatins. Cmpare varied practical tasks and describe changes. Fr practical tasks, decide whether an estimate calculatin suffices. Describe functinal relatinships within practical tasks; illustrate accrdingly and slve crrespnding tasks. Describe functinal relatinships presented in tables. Deduce and illustrate data frm/in tables, diagrams and ther related frmats Create calculatin pictures Identify and highlight critical infrmatin in texts Students relate t pertinent real life situatins (e.g., the csts f a class field trip) Open t the wrld

14 Slve cmbinatrial tasks thrugh systematic apprach as well as the use f apprpriate illustratins. Interpret illustratins. Using simple randm experiments, estimate, cmpare and justify the chances f winning (e.g., when spinning a wheel f frtune, tssing dice r flipping a cin) by taking an experimental apprach r by mental deliberatin f the cntent. Describe results f randm experiments by using: certain; pssible/likely; impssible. Write dwn calculatin steps in prper rder. Test results fr plausibility. Travel brchures; price lists; catalgues Math practice cards fr prblem slving Using sizes/cncepts f size, and handling mney Using cncepts f size Sizes Cmpare, measure and rganize bjects r prcedures frm real life using Length arbitrary units and standard units; describe and present results. Weight Estimate and review units, using suitable representatives as a tl. Time Mney Apply the prcesses fr estimating and measuring Measure bjects r prcesses prperly and precisely Select and use measuring tls Open t the wrld

15 Dealing with sizes Sizes Cmpare size data Cnvert size data Use these units: millimeter, centimeter, meter, kilmeter and cmpare with ft, yard and mile fr length data. Secnd, minute, hur, a.m., p.m. fr time data. Kilgram, gram fr weights. Eur/cent, dllar/cent fr mnetary units. Determine time perids (bth in 12-hur and 24-hur cycles), als using arrw pictures. Calculate and present the lengths f the day. Read the units, plt, rund t the next unit, extend. Create apprximate cmparisns between German and American units. State sizes using varius units and different methds f ntatin, including the cmma-based ntatin methd. Use frmulatins t describe fractinal sizes (e.g., quarter-hur; half-meter). prperly Ruler, straightedge, dmeter Scale Clck, stpwatch Apply the prcesses fr estimating and measuring Measure bjects r prcesses prperly and precisely. Select and use measuring tls prperly Create arrw pictures Ruler, straightedge, dmeter Scale Clck, stpwatch Open t the wrld Gemetry: Wrking in space and plane

16 Cncept f space Spatial experience and cncept f space Read maps and plans; describe rutes Read scale flr plans, ther plans and maps Using visualizatin, repsitin slids and plane figures, and predict the utcme. Orient neself within a space and find ne s lcatin n plans. Read scale flr plans, maps, plans. Describe rutes; trace rutes. Create a basic, scale flr plan / site plan. When slving gemetric tasks, apply strategies (such as checking thrugh trial and errr; drawing; finding examples). Example: Prepare twn map r hiking maps within an expanded area, sketching in the pathways Open t the wrld Dealing with planes Gemetric figures Planes Slids Identify, label and describe quadrangles, squares, rectangles as well as triangles fund in the surrundings, in pictures and in drawings. Identify, label and describe slids (spheres, cubes, rectangular frms, cylinders, pyramids, cnes) in the surrundings, in pictures and in drawings. Differentiate planes based n their prperties. Assign planes and slids t ne anther. Describe slids by using crners, edges and planes. Use drawing and wrk tls prperly (triangle and circle). When slving gemetric tasks, apply strategies (such as checking thrugh trial and errr; drawing; finding examples). Mdeling planes/surfaces, flding, kneading, Open t the wrld

17 Symmetry Axisymmetry Draw axisymmetric figures Check figures fr mirrr symmetry Differentiate relatinships between planes. Place, stack, display, fld, cut ut, disassemble and re-assemble shapes (e.g., the tangram). Measure the lengths f the sides f planes. Reprduce, refine and describe regularities in symmetrical patterns (e.g., rnamental strips with gemetric patterns). Describe and cntrast cube structures, and build accrding t plan. Indicate whether r nt planes r figures are axisymmetric. Determine and plt axes f symmetry. Psitin and draw axisymmetric shapes. pinning. Use a triangular prtractr prperly When slving gemetric tasks, apply strategies (such as checking thrugh trial and errr; drawing; finding examples) Utilize the gebard Drawing Draw gemetric shapes Draw and measure Draw distances, planes, shapes and symmetric patterns freehand and with drawing tls (triangular prtractr and circle). Becme familiar with drawing and wrk tls (ruler and circle), and

18 lines and distances Learn hw t use a ruler Draw varius shapes with given units f area r scpe. use them prperly Open t the wrld Experiment with circles Draw freehand

19 GISSV Elementary Schl Mathematics Curriculum, Grade 4 Cntent Skills The student is able t... Frms f scial interactin, methdlgies and media Crss-disciplinary aspects Relatinship t the schl prgram Cncepts f whle numbers (integers) Subject area: Arithmetic dealing with numbers and symbls Numbers up t 1,000,000 Learn abut numbers up t 1,000,000 Cmprehend numbers up t 1,000,000, and hw t present them in different ways Cmprehend numbers up t 1,000,000 in different situatins and in varius presentatins. Identify, bundle and exchange amunts. Present definitive, graphic and symblic depictin f numbers up t 1,000,000. Describe and explain the representatin f numbers with the aid f the psitinal ntatin system. Split the numbers. Read and write numbers up t ne millin. Learning and visualizatin tls (e.g., dt images n the hundred tables, thusand strips, thusand fields, millimeter squares n millimeter paper, number line)

20 Cmpare and srt numbers up t 1,000,000 Cncepts f peratins Read and illustrate numbers using a different numeric system (Rman numerals) Srt, cmpare numbers (<, >, =). Frm and extend numerical sequences. Rund numbers. Describe interrelatinships in numerical sequences, and extend these sequences. Individually develp, mdify and describe numerical sequences accrding t a pattern. Differentiate dd and even numbers. Arithmetic Enhance understanding f additin, subtractin, multiplicatin and divisin Establish a link between an everyday situatin, the assciated arithmetic peratin and the symblic ntatin. Cmpute numbers up t 1,000,000. Illustrate practical situatins in crrespnding arithmetic exercises, and vice versa describe the arithmetic exercises that apply t the practical situatin. Explain cnnectins between the basic peratins, and use them when calculating. Describe the benefits, rules and strategies f mathematics; describe cnfrmance t a set pattern and apply Learning and visualizatin tls (e.g., hundred table, thusand field, number line) Open t the wrld

21 Mental math Arithmetic Mentally cmpute numbers up t 1,000,000 in basic numeric ratis this when calculating (cmmutativity, multiplicatin peratr (pint) befre divisin peratr (slash)). Identify and explain the inslvability f tasks. Hw t use a calculatr. Perfrm the basic tasks f all basic calculatin peratins by memry. Use individual calculatin prcesses Verbal and infrmal written arithmetic Arithmetic Infrmal written arithmetic Slve tasks invlving all fur basic calculatin peratins, either verbally r infrmally in writing. Describe the calculatin prcesses; cmpare and cntrast with each ther. Describe verbal and infrmal written arithmetic strategies, and apply them flexibly. Describe and extend patterns in structured task sequences. Identify, explain and crrect calculatin errrs. Slve equatins and inequalities by trial and errr, based n mental deliberatin Learning assessment: Determine the student s current level Use individual calculatin prcesses Practice infrmal written methd in a variety f ways

22 f the cntent. Estimate and verify results by making a mental calculatin. Written arithmetic Arithmetic Written arithmetic Explain the stepwise strategy t slve the fur basic calculatin peratins, using examples f each task. Perfrm the written algrithms f the fur basic arithmetic peratins (additin: up t three addends; subtractin: up t tw subtrahends; multiplicatin: multiple factrs; divisin: single-digit and imprtant tw-digit divisrs (10, 12, 20) with remainder). D a rugh estimate fr the written arithmetic exercises and duble-check yur estimate. Learning assessment: Determine the student s current level Use individual calculatin prcesses Practice infrmal written methd in a variety f ways Check results by mental calculatin Arithmetic in cntext Practical situatins Develp practical situatins and hw t represent them. Slve cmplex practical exercises. Deduce and illustrate data frm/in tables, NuG: Depending n

23 Develp practical situatins and hw t represent them Develp and apply slutins Find slutin prcesses Deduce relevant data frm texts, illustratins (diagrams, tables, sketches) and verbalize them. Find and frmulate mathematical prblems frm practical situatins. Cmpare varied practical tasks and describe changes. Fr practical tasks, decide whether an estimate calculatin suffices. Describe functinal relatinships within practical tasks; illustrate accrdingly and slve crrespnding tasks. Describe functinal relatinships presented in tables. Slve cmbinatrial tasks thrugh systematic apprach as well as the use f apprpriate illustratins. Interpret illustratins. Using simple randm experiments, estimate, cmpare and justify the chances f winning (e.g., when spinning a wheel f frtune, tssing dice r flipping a cin) by taking an experimental apprach r by mental deliberatin f the cntent. Describe results f randm experiments by using: certain; pssible/likely; impssible. Write dwn calculatin steps in prper rder. Test results fr plausibility. diagrams and ther related frmats Create calculatin pictures Identify and highlight critical infrmatin in texts Students relate t pertinent real life situatins (e.g., the csts f a class field trip) Travel brchures; price lists; catalgues Math practice cards fr prblem slving subject matter and prject Open t the wrld

24 Using sizes / cncepts f size, and handling mney Using cncepts f size Sizes Vlume measurements; liter/milliliter as units f measure Cmpare, measure and rganize bjects r prcedures frm real life using arbitrary units and standard units that relate t mass and vlume; describe and present results. Learn hw t handle the units I and ml (liter and milliliter). Apply fractins and decimal fractins (e.g., ¼ l, ½ l, ¾ l). Estimate mass and vlume using crrespnding representatins. Apply the prcesses fr estimating and measuring Measure bjects r prcesses prperly and precisely. Select and use measuring tls prperly Recipes in children s ckbks Prductin f drinks NuG: Nature and technlgy: Water Open t the wr Dealing with sizes Sizes Cmpare size data Cnvert size data Use these units: - kilmeter (km) fr length - secnd (s) fr time perids - kilgram (kg), gram (g), tn (t) fr mass data - liter (l) and milliliter (ml) fr vlume data State sizes using varius units and different methds f ntatin, including Apply the prcesses fr estimating and measuring Measure bjects r prcesses prperly and precisely Select and use measuring tls prperly NuG: Nature and technlgy: water Individual in space and time: hw t use maps Individual in space and time: the slar system Open t the wr

25 Determine the measurement number and measuring unit f a size r dimensin the cmma-based ntatin methd. Use frmulatins t describe fractins f measurements (e.g., quarter-hur; halfmeter). Sprts: Running; jumping; thrwing Cncepts f space Gemetry: Wrking in space and plane Spatial experience and cncept f space Read maps and plans; describe rutes Read scale flr plans, ther plans and maps Using ne s imaginatin, repsitin slids and plane figures, and predict the utcme. Orient neself within a space and find ne s lcatin n plans. Read scale flr plans, maps, plans. Describe rutes; trace rutes. Create a basic, scale flr plan / site plan. When slving gemetric tasks, apply strategies (such as checking thrugh trial and errr; drawing; finding examples). Example: Prepare twn plan r hiking maps within an expanded area, sketching in the pathways NuG: Individual in space and time: hw t use maps Art: Graphic materials, printed materials, written materials Planes, slids, space Open t the wrld Dealing with planes

26 Gemetric figures Scale and surface area Symmetry Identify, label and describe quadrangles (trapezid, parallelgram, rhmbus and deltid) and triangles (right angle, equilateral and issceles triangle) in surrundings, in pictures and in drawings. Describe the prperties f planes, using pint, segment and mid-pint f the circle; radius and diameter; right angle. Differentiate planes based n their prperties. Differentiate relatinships between planes. Place, stack, display, fld, cut ut, disassemble and re-assemble shapes (e.g., the tangram). Reprduce, refine and describe regularities in symmetrical patterns (e.g., rnamental strips with gemetric patterns). Cmpare the cntent f a plane by dividing it. Determine scpe f planes. Differentiate between cntent and scpe f planes. Enlarge and lessen planes. Use drawing and wrk tls prperly (triangle and circle) When slving gemetric tasks, apply strategies (such as checking thrugh trial and errr, drawing, finding examples). Mdeling planes/surfaces, flding, kneading, pinning. Art: Planes, slids, space

27 Axisymmetry and radial (rtatinal) symmetry Draw axisymmetric shapes Check shapes fr mirrr symmetry Becme familiar with rtatinally symmetric shapes; independently prduce and test shapes fr rtatinal symmetry Demnstrate whether r nt planes r shapes are axisymmetric. Determine and plt axes f symmetry. Psitin and draw axisymmetric shapes. Rtate basic shapes as instructed; discver prperties f radial symmetry. Lcate radial symmetry in the surrunding envirnment. Use a triangular prtractr prperly When slving gemetric tasks, apply strategies (such as checking thrugh trial and errr; drawing; finding examples). Utilize the gebard Place and enhance rtatinally symmetric shapes and draw them n quadrille paper Cnduct quarterrtatin, halfrtatin Wind wheels, parasls, etc. Art: Planes, slids, space Open t the wrld Drawing Draw gemetric shapes Draw distances, planes, shapes and symmetric patterns freehand and with drawing tls (triangular prtractr and circle). Draw varius shapes with given units f Prperly use drawing and wrk tls (triangular prtractr and circle) Art: Planes, slids, space

28 Draw and measure lines and distances Learn hw t use a triangular prtractr and circle area r scpe. Draw circles with given radius r diameter. Determine radius and diameter. Illustrate lines that are parallel and hrizntal t each ther by using the triangle. Example: Draw lines parallel and hrizntal t each ther; create right angles, circles, arcs, patterns Open t the wrld Learn hw t draw with a triangular prtractr and circle Draw freehand