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Creating mathematical problems related to trees

Creating mathematical problems related to trees. Comenius projekt: More trees , yes please !. Math + problem + imagine = … wait and see. Oh, those fractions !. One day , we ’ve had an experimental way of teaching fractions :. What is the phrase ?

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Creating mathematical problems related to trees

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  1. Creatingmathematicalproblemsrelated to trees Comenius projekt: More trees, yesplease!

  2. Math + problem + imagine =…waitandsee

  3. Oh, thosefractions!

  4. One day, we’ve had anexperimentalwayofteachingfractions: What is thephrase? 1st word: the third fifth ofthe word CEDAR+thesecond fifth ofthe word HRAST+V+thefourth fifth ofthe word JAVOR 2nd word: the fifth sixthofthe word PINIJA+thefourthsixthofthe word SMREKA 3rd word: the third fourthofthe word LIPA+the third eighthofthe word MARELICA+the first fourthof word the VRBA+thesecond third ofthe word BOR Solution: DRVO JE PRVO ( the wood is the first) cedar = cedar; hrast = oak; javor = maple; smreka = spruce; lipa = linden; marelica = apricot; vrba = willow; bor = pine

  5. Studentssaythat it’s easier to learnfractionsifyoumakethosekindoftasks • 1st word: the third fifth ofthe word JAVOR+thesecondfourthofthe word LIPA+thefourth fifth ofthe word HRAST+thesecond third ofthe word BOR+the first sixthofthe word KRUŠKA+ thesecondsixthofthe word TOPOLA • 2nd word: the first third ofthe word DUD+thesecond fifth ofthe word BREZA+the first fourthofthe word VRBA+thesecondfourthofthe word JOHA • 3rd word: the first sixthofthe word PAPAJA+the first fifth ofthe word LIMUN+thesecondninthofthe word BOROVNICA+ the fifth sixthofthe word JAGODA+thesixthsixthofthe word TREŠNJA • 4th word: the first seventhofthe word NARANČA+thesecond third ofthe word CER+the first ninthofthe word MANDARINA+thesixthsixthofthe word SMOKVA Solution: VISOKO DRVO, PLODA NEMA!(talltree, no fruit!) javor = maple; lipa = linden; hrast = oak; bor = pine; kruška = pear; topola = poplar dud= mulberry ; breza = birch; vrba = willow; joha = alder; papaja = papaya; limun = lemon; borovnica = blueberry; jagoda = strawberry; trešnja = cherry; naranča = orange; cer = Turkeyoak; mandarina = tangerine; smokva = fig

  6. Letterbyletter… ________ NE PADA DALEKO OD_______ 1st word: the first twofifthsofthe word JASEN+the first threefifthsofthe word BUKVA+the third fourthofthe word ORAH 2nd word: thelasttwofifthsoftheword HRAST+thelasttwofourthsofthe word GRAB+the first sixthofthe word LUŽNJA+thelastfourthofthe word VRBA Solution: JABUKA NE PADA DALEKO OD STABLA (Anappledoesn’t fall far awayfromthetree) The 2ndand 3rdfifthsofthe word HRAST ____ The 4th fifth ofthe word BREZA ____ The 1stfourthofthe word LIPA ____ The 2nd third ofthe word BOR ____ The 2ndsixthof word SMREKA ____ The 1stseventhof word CVIJEĆE ____ The 2ndfourthof word LIPA ____ Solution: RAZLOMCI (fractions)

  7. Task-it’s like youhave to…mathstory…it’s like fun People who live in Lipa (lindentreeinCroatian) street decided to plantanalleyalongthe street to get more oxygenduringthehotsummers. Ifthe distance betweentwotrees is 2 m, andthe street is 378 m long, how manytrees do theyneed? Solution: (378:2+1)∙2= 380 stabala There are 3 branches on thetreeandoneachbrenchthere are 3 nests, ineach nest there are 2 littlebirds. Howmanylittlebirds are there ? Solution: 3∙3∙2= 18 stabala

  8. Thewalnut problem Filip and his familycut a walnuttreelastyear, at the age of 20. As thewalnuttreereleasessulfur, theycanplantanothertree on that place notuntil at least one tenthofthecentury(1/10century – 2/5 decade) years. Howmanyyearsshouldtheywait to succefullyplantanothertree? Solution: 1/10 century is 10 years, 2/5 decade is 4 years; 10 – 4 = 6 years

  9. Axialsymmetry ??? Ratherconfusing for the fifth grade

  10. Paper, colourinks, scissors…they done miracles working… the first results…

  11. And, intheend…

  12. Withthecamerainthe city on theriver, youcan’t missaxialsymmetrics bytheriver Bosut, wherepeoplelivescontinuously for 9000 years

  13. Enigmatika andmath are related? Heureka!

  14. Thecrosswords working…

  15. Thecrosswordswerethe most popular to do…

  16. Therebuses ‘’’ + ‘ + ‘’’ ‘’’ Solution: JELA (Croatiantree) Solution: JABLAN (Croatiantree)

  17. Theassociation game

  18. A1 B1 C1 A2 B2 C2 A3 B3 C3 Thesolutionof A column Thesolutionof B column Thesolutionof C column Thefinalsolution

  19. It hasfruits It is green There are giftsunder it It has no leavesinthewinter It haslittleneedles Christmas It hasleaves It hasleavesinthewinter There are decorations all over it DECIDUOUS TREE EVERGREEN TREE CHRISTMAS TREE TREE

  20. Pythagoras tree

  21. Yes, treeshelps to understandbetterPythagoreantheorem… • Studentsofthe 8. grade weredrawing some odd, squaredtreeswiththehelpofPythagoreantheorem… • Pythagorean theorem has served us in the construction of one beautiful fractals called Pythagoras tree. Symmetrically Pythagoras tree occurs  that of one side of the square we construct an isosceles right angled triangle. • Boughbybough… • And, those are theresults…

  22. PythagorastreehasmadebydynamicgeometrysoftwareGeoGebra

  23. Rectangulartrianglesleads us to snailandseashell…

  24. Coordinatesystemin a slightlydifferentway

  25. Statistics Myclass’ favouritetree

  26. Poll What’s Yourfavouritetree: • Englishoak • hornbeam • mapletree • elm • willow

  27. Pollresultsbyclasses

  28. Similarityoftriangles

  29. I wonder how tallthattree is?

  30. Hmm, ifTalescoulddefinetheheightofCheopspyramid 2500 years ago, whycouldn’t I calculatetheheightofthistree…

  31. All I need is a woodenstick, measuringtapeand some mathematicalknowledgeaboutthesimilarityoftriangles.

  32. Measuringresults: • Treeshadowlength 15.7 m • Woodenstickheight 0.85 cm • Woodenstickshadowlength 1 m

  33. TREE STICK x 0,85 m 15.7 m 1 m Now I onlyhave to do a littlemath

  34. Treeheight : stickheight = treeshadow : stickshadow x : 0.85 = 15.7 : 1 x = 13.345 m So, thetree is 13.345 m high.

  35. Arrangedbymathteachers :Sandra PernarMirjana JavorMarija Čopčić BanovacandtheirstudentsMarch, 2013.Primaryschool Ivan MazuranicVinkovciRepublicof Croatia

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