G r a d e 6 M a t h e m a t i c s. Shape and Space

Transcription

1 G r a d e 6 M a t h e m a t i c s Shape ad Space

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3 Grade 6: Shape ad Space (Measuremet) (6.SS.1, 6.SS.2) Edurig Uderstadig(s): All measuremets are comparisos. The uit of measure must be of the same ature as the property of the object beig measured. May geometric properties ad attributes of shapes are related to measuremet. Geeral Learig Outcome(s): Use direct or idirect measuremet to solve problems. Specific Learig Outcome(s): 6.SS.1 Demostrate a uderstadig of agles by idetifyig examples of agles i the eviromet classifyig agles accordig to their measure estimatig the measure of agles usig 45º, ad 90º, ad 180º as referece agles determiig agle measures i degrees drawig ad labellig agles whe the measure is specified [C, CN, ME, V] 6.SS.2 Demostrate that the sum of iterior agles is 180º i a triagle 360º i a quadrilateral [C, R] Achievemet Idicators: Provide examples of agles foud i the eviromet. Classify a set of agles accordig to their measure (e.g., acute, right, obtuse, straight, reflex). Sketch 45º, 90º, ad 180º agles without the use of a protractor, ad describe the relatioship amog them. Estimate the measure of a agle usig 45º, 90º, 180º as referece agles. Measure, usig a protractor, agles i various orietatios. Draw ad label a agle i various orietatios usig a protractor. Describe the measure of a agle as the measure of rotatio of oe of its sides. Describe the measure of a agle as the measure of a iterior agle of a polygo. Explai, usig models, that the sum of the iterior agles of a triagle is the same for all triagles. Explai, usig models, that the sum of the iterior agles of a quadrilateral is the same for all quadrilaterals. Shape ad Space 3

4 Prior Kowledge Studets may have had experiece with the followig: Dividig 3-digit umerals by 1-digit umerals Solvig oe-step sigle-variable equatios, ad problems ivolvig these equatios, usig whole umbers oly Addig ad subtractig 1-, 2-, ad 3-digit umerals with aswers to 1000 Related Kowledge Studets should be itroduced to the followig: Demostratig ad explaiig the meaig of preservatio of equality, cocretely, pictorially, ad symbolically Backgroud Iformatio A agle is the space betwee two rays or lie segmets that are joied at a commo poit. There are may differet sizes of agles, some are small ad some are large. Agles ca be see by observig differet geometric shapes as well as the eviromet aroud us. Agles are measured i degrees usig a protractor. Grade 6 is the first year studets are formally learig about agles ad agle measures. This year, studets will lear to measure agles usig a protractor, recogize referece agles (45º, 90º, ad 180º), ad estimate measures of agles usig the referece agles. Look at referece agles show below: Grade 6 Mathematics: Support Documet for Teachers

5 Based o these agles, studets will be able to recogize whether a agle is smaller tha 45º (see agle A below), betwee 45º ad 90º (see agle B below), betwee 90º ad 180º (see agle C below), or bigger tha 180º (see agle D below) agle A agle B 135 agle C 210 agle D Based o the agle measure, studets will lear to ame ad classify agles as acute (betwee 0º ad 90º, such as agles A, B, ad referece agle 45º above), right (90º, such as referece agle 90º above), obtuse (betwee 90º ad 180º, such as agle C above), straight (180º, such as referece 180º above), ad reflex (betwee 180º ad 360º, such as agle D above). Studets will also lear to idetify examples of agles foud i the eviromet, such as the space betwee the ceilig ad the wall, the space betwee the groud ad a lamp post, or the space betwee two braches o a tree. Measurig iterior agles of polygos will reveal some iterestig geometric rules. Studets will lear that the sum of iterior agles is 180º i a triagle the sum of iterior agles is 360º i a quadrilateral square trapezoid rectagle parallelogram rhombus irregular quadrilateral Shape ad Space 5

6 Mathematical Laguage agle acute agle degree iterior agle polygo quadrilateral reflex agle straight agle triagle Learig Experieces Assessig Prior Kowledge BLM 5 8.9: Cetimetre Grid Paper Orgaizatio: Idividual/whole class 1. Distribute to each studet the cetimetre grid paper from BLM Ask studets to use the cetimetre grid to draw the followig: a) Four kids of polygos with 2 cm sides each b) Four kids of polygos with 3 cm sides each c) Four kids of polygos with 4 cm sides each 3. Ask them to write the ame of the polygo iside each shape. 4. Ask studets to write iside each polygo the umber of sides it has. 5. Have oe studet draw oe of his or her polygos o the board. 6. With a piece of paper, cover most of the polygo, leavig oly oe agle visible, ad say to the studets: This is a agle. Who could come to the board ad show aother agle? 7. Have studets poit out differet agles iside the polygo. 8. Draw each agle separately, ext to the polygo. 6 Grade 6 Mathematics: Support Documet for Teachers

7 9. Discuss agles. Ask studets questios such as the followig: a) Are all of these agles the same? b) What is the same? c) What is differet? 10. Tell studets to cout the umber of agles they fid i each polygo, ad write the umber iside each polygo. 11. Discuss the relatioship betwee the umber of sides ad the umber of agles Observatio Checklist Observe studets resposes to determie whether they ca do the followig: r Costruct differet kids of polygos (i.e., triagle, quadrilateral, petago, ad hexago). r Costruct polygos give measure of sides. r Name polygos accordig to the sides that they have. r Recogize agles. r Recogize the relatioship betwee sides ad agles of a polygo. Suggestios for Istructio Provide examples of agles foud i the eviromet. BLM 5-8.2: Cocept Descriptio Sheet #1 Orgaizatio: Whole class/small group/idividual 1. Have a class discussio o the cocept of agles. Have studets aswer questios, such as the followig: a) What are agles? b) Where ca you fid agles? c) Are all agles the same? 2 Distribute to each studet a copy of BLM 5-8.2: Cocept Descriptio Sheet #1. Shape ad Space 7

8 3 Tell studets to write the word agle iside the oval, ad complete the sheet, doig the followig: a) Describe the characteristics of a agle. b) Provide examples of agles. c) Provide examples of o-agles. d) Draw pictures of agles. 4 Tell studets to discuss with their group members the agles they ca fid a) i the classroom b) i their homes c) o the playgroud 5 Have studets record their examples of agles i their jourals. Observatio Checklist Observe studets resposes to determie whether they ca do the followig: r Describe the characteristics of a agle. r Provide examples of agles. r Provide examples of o-agles. r Draw pictures of agles. r Provide examples of agles foud i the classroom. r Provide examples of agles foud i their homes. r Provide examples of agles foud o the playgroud. 8 Grade 6 Mathematics: Support Documet for Teachers

9 Suggestios for Istructio Classify a set of agles accordig to their measure (e.g., acute, right, obtuse, straight, reflex). Provide examples of agles foud i the eviromet. BLM 6.SS.1.1: Agles Orgaizatio: Whole class/idividual 1. Draw a right agle o the board ad write right agle uder it. 2. Tell studets to look aroud the classroom to spot some right agles. 3. Discuss the examples of right agles they spotted i the classroom. 4. Draw a straight agle o the board ad write straight agle uder it. 5. Tell studets to look aroud the classroom to spot some straight agles. 6. Discuss the examples of straight agles they spotted i the classroom. 7. Discuss other agles ad ame them. 8. Ask studets to draw examples of acute, obtuse, ad reflex agles o the board. 9. Distribute a copy of BLM 6.SS.1.1, ad ask studets to write the ame of each agle iside it. 10. Discuss their classificatios. Observatio Checklist Observe studets resposes to determie whether they ca do the followig: r Recogize a right agle. r Recogize a straight agle. r Recogize a acute agle. r Recogize a obtuse agle. r Recogize a reflex agle. r Provide examples of agles foud i the eviromet. Shape ad Space 9

10 Suggestios for Istructio Sketch 45º, 90º, ad 180º agles without the use of a protractor, ad describe the relatioship amog them. Provide examples of agles foud i the eviromet. BLM 6.SS.1.2: Referece Agles Orgaizatio: Whole class/idividual 1. Place o the overhead projector a trasparecy of BLM 6.SS Draw two vertical lies o the chalkboard i order to create three sectios. 3. Write o the top part of the first sectio 45º, secod sectio 90º, ad third sectio 180º. The say to the studets Look aroud the classroom ad fid possible examples of each agle. 4. Have a class discussio about the possible examples for each agle. 5. Ask for three voluteers (oe for each sectio) to record possible examples of each agle, ad sketch the agle (without a protractor). 6. Discuss the relatioship amog the three agles ad their importace (referece agles). 7. Tell studets to sketch a 45º, 90º, ad 180º agle without a protractor, ad describe the relatioship amog these three agles i their jourals. Observatio Checklist Check studets replies to determie whether they ca do the followig: r Provide a example of a 45º agle. r Provide a example of a 90º agle. r Provide a example of a 180º agle. r Sketch a 45º agle without a protractor. r Sketch a 90º agle without a protractor. r Sketch a 180º agle without a protractor. r Describe the relatioship amog these three (45º, 90º, 180º) agles. 10 Grade 6 Mathematics: Support Documet for Teachers

11 Suggestios for Istructio Estimate the measure of a agle usig 45º, 90º, 180º as referece agles. Measure, usig a protractor, agles i various orietatios. BLM 6.SS.1.1: Agles BLM 6.SS.1.2: Referece Agles Orgaizatio: Idividual 1. Distribute to each studet a copy of BLM 6.SS Place a trasparecy of the BLM 6.SS.1.2 o the overhead projector. 3. Tell studets to use the referece agles to estimate the measure of each agle o their paper, ad write the estimated measure ext to the agle. 4. Ask a few studets to read out loud their estimated measures of each agle. 5. Say Take out your protractors, measure each agle, ad record the agle measuremet ext to the agle. 6. Whe they complete their work, ask studets to record the differece betwee the measured agle ad its estimate. 7. Let studets kow that, with practice, their estimates ca get quite close to the actual agle measuremet. Observatio Checklist Check studets replies to determie whether they ca do the followig: r Use the referece agles to estimate the measure of a agle. r Estimate the measure of a acute agle, usig 45º ad 90º agles as referece agles. r Estimate the measure of a obtuse agle, usig 90º ad 180º agles as referece agles. r Estimate the measure of a reflex agle, usig a 90º agle as a referece agle. r Use a protractor to measure agles i stadard positio. r Use a protractor to measure agles i various orietatios. Shape ad Space 11

12 Suggestios for Istructio Draw ad label a agle i various orietatios usig a protractor. poster-sized paper protractor pecil Orgaizatio: Groups of four 1. Seat studets i groups of four. 2. Distribute a large poster-sized paper to each group. 3. Say to the class: a) I wat each of you to choose a agle measure. Make sure that the umber of degrees you choose is ot the same as the agle chose by ay of the other three members i your group. b) Use your protractor to draw your agle o the poster-sized paper i frot of you. c) The, usig the same agle measure, draw the agle i three other orietatios. d) Label each agle (write the agle measure iside the agle). 4. Have oe member of each group place the paper (completed work) o the board. 5. Ask studets to have a class discussio o what they have observed about agles i various orietatios. Observatio Checklist Check studets replies to determie whether they ca do the followig: r Use a protractor to measure a agle. r Draw a agle. r Replicate a agle. r Draw a agle i various orietatios. 12 Grade 6 Mathematics: Support Documet for Teachers

13 Suggestios for Istructio Describe the measure of a agle as the measure of rotatio of oe of its sides. Orgaizatio: Whole class 1. Say ad demostrate the followig to the class: a) Today s activity will be a live demostratio of a agle measure. It will ivolve some physical activity o your part. b) I wat everyoe to stad up facig me. Stad with your feet together ad preted your feet are the two sides of a agle. c) Now, keepig your heels together, rotate your left foot so that you make a agle. (Demostrate). d) How big of a agle ca you make without movig your right foot ad without fallig? e) Now, make a zero degree agle by rotatig your left foot back to a feet together positio. (Demostrate). f) Show the perso ext to you a variety of agles you ca make by keepig your heels together ad rotatig your right foot. g) Thaks for the great participatio. Now, go back to your seats. 2. Discuss the umber of agles ad the kids of agles that studets made with their feet. 3. Tell studets to describe i their jourals what happes to the measure of a agle whe you rotate oe of its sides. Observatio Checklist Check studets replies to determie whether they ca do the followig: r Follow directios. r Make a agle usig their feet. r Make a variety of agles usig their feet. r Associate the chage i measure of a agle with the rotatio of its side. Shape ad Space 13

14 Suggestios for Istructio Describe the measure of a agle as the measure of rotatio of oe of its sides. a variety of craft materials scissors Orgaizatio: Pairs 1. Let studets kow that they will be makig their ow protractors usig what they kow about agles. 2. Have them work i pairs to formulate a pla for how they are goig to make their protractor. 3. Ask them to documet the steps they take, makig specific referece to referece agles ad rotatio. 4. Allow studets to costruct a protractor. 5. Have the studets all measure the same agles from the classroom usig their protractors (i.e., the edge of a desk, the bidig ad edge of a three-rig bider). 6. Facilitate a class discussio about the studets protractors. Observatio Checklist Check studets replies to determie whether they ca do the followig: r Reaso mathematically. r Apply their kowledge about referece agles. r Apply their kowledge about rotatio. r Measure agles usig a protractor. 14 Grade 6 Mathematics: Support Documet for Teachers

15 Suggestios for Istructio Describe the measure of a agle as the measure of a iterior agle of a polygo. protractor ruler pecil Orgaizatio: Whole class/idividual 1. Draw four distict agles o the board (e.g., 30º, 45º, 90º, ad 120º). 2. Measure each agle usig a protractor. 3. Write the measure of each agle iside it. 4. Have a discussio o agles ad agle measures. 5. Draw a triagle (i.e., choose oe of the agles you drew o the board ad coect its two adjacet sides by a third lie segmet, creatig a side opposite to the agle). See example below. or agle triagle... etc. 6. Ask studets the followig: a) What happeed to the agle? b) Did the agle measure chage? 7. Ask a studet to measure the agle that was made ito a iterior agle of a triagle. 8. Discuss iterior agles of a polygo. 9. Ask oe of the studets to come up to the board ad draw a polygo, but ot a triagle, usig aother oe of the agles. 10. Ask studets to predict the measure of the agle, which is ow a iterior agle. 11. Ask a differet studet to come up to the board ad measure that particular iterior agle. Shape ad Space 15

16 12. Ask studets what would happe to the other two agles if they were made ito iterior agles. 13. Discuss the measure of agles as the measure of a iterior agle of a polygo. 14. Tell studets to do the followig: a) Draw a agle i their jourals. b) Describe the measure of the agle as the measure of a iterior agle of a polygo of their choice. Observatio Checklist Check studets replies to determie whether they ca do the followig: r Sketch a agle (approximate size). r Measure a agle with a protractor. r Kow what a iterior agle of a polygo is. r Describe the measure of a agle as the measure of a iterior agle of a polygo. Suggestios for Istructio Explai, usig models, that the sum of the iterior agles of a triagle is the same for all triagles. BLM 6.SS.1.3: Sum of Iterior Agles of a Triagle straws pipe cleaers scissors protractor pecil Orgaizatio: Whole class/four groups 16 Grade 6 Mathematics: Support Documet for Teachers

17 1. Pre-cut straws to the followig legths: 6 cm, 9 cm, 12 cm, ad 15 cm. It would be helpful if you could have a differet colour for each legth, such as red, gree purple, ad white. 2. For each group, you will eed the followig: a) two straws of each: 6 cm (red) 15 cm (white) b) four straws of each: 9 cm (gree) 12 cm (purple) 3. Distribute to each group the 12 pre-cut straws ad 12 pipe cleaers. 4. Distribute to each studet a copy of BLM 6.SS Tell studets to do the followig: a) Separate the straws ito four piles accordig to size (colour). b) Slightly bed each pipe cleaer. c) Take oe red straw, oe purple straw, ad oe white straw d) Use the pipe cleaers to joi two straws together. e) You will eed three bet pipe cleaers to joi the three straws ad form a triagle. f) Usig three differet legths of straws will make a scalee triagle. g) Measure each agle of the scalee triagle. h) O BLM 6.SS.1.3, mark scalee uder Triagle Name. i) Write the measure of each iterior agle uder Iterior Agle Measures. j) Add up the measure of the three iterior agles ad write the sum uder Sum of Iterior Agles of Triagle. 6. Place o the overhead projector a trasparecy copy of BLM 6.SS Ask studets for iformatio to record uder each headig. 8. Discuss the results they got by measurig the iterior agles of the scalee triagle. 9. Tell studets to use oe gree straw, oe purple straw, ad oe white straw to costruct a right triagle. 10. Tell studets to record the ame, each agle measure, ad sum of iterior agles of the right triagle o the BLM sheet. 11. Tell studets to use three gree straws to make a equilateral triagle, ad the two purples ad oe red straw to make a isosceles triagle. 12. Have them record the results of each triagle. Shape ad Space 17

18 13. Discuss the results they got by measurig the iterior agles of the other three triagles. For example, compare the a) iterior measures of each triagle to the iterior measures of the scalee triagle b) sum of the iterior measures of each triagle to the sum of the iterior measures of the scalee triagle c) iterior measures of each triagle to the iterior measures of the other triagles d) sum of the iterior measures of each triagle to the sum of the iterior measures of the other triagles 14. Tell studets to write i their jourals what they observed about how differet measures of the iterior agles of a triagle ifluece the sum of the iterior agles of a triagle. Observatio Checklist Check studets replies to determie whether they ca do the followig: r Follow istructios. r Costruct a model. r Measure iterior agles of a triagle accurately. r Explai, usig models, that the sum of the iterior agles of a triagle is 180º. r Explai, usig models, that the sum of the iterior agles of a triagle is the same for all triagles. Suggestios for Istructio Explai, usig models, that the sum of the iterior agles of a quadrilateral is the same for all quadrilaterals. BLM 6.SS.1.4: Sum of Iterior Agles of a Quadrilateral BLM 6.SS.2.3: Sides for Flexible Quadrilaterals protractor scissors pecil small bider rigs (safety pis or paper clips will also work) Orgaizatio: Whole class/small groups 18 Grade 6 Mathematics: Support Documet for Teachers

19 1. Have studets seated i small groups. 2. Distribute to each studet a copy of BLM 6.SS.2.2 ad BLM 6.SS Tell studets to do the followig: a) Take BLM 6.SS.2.3. b) Cut the strips of paper alog the lies. You should have 16 strips of paper large 2. 1 medium small c) Use a hole-pucher to puch holes o each ed of the strips of paper. d) Separate the strips of paper ito four piles accordig to the followig classificatios: parallelogram P1, parallelogram P2, trapezoid T1, ad trapezoid T2. e) Joi two strips of paper by liig up the holes ad puttig a rig through the holes. The, usig the same method, joi to them the third ad the fourth strip of paper to form the four sides of each quadrilateral. f) Measure each agle of the parallelogram P1 without movig the sides of the model. g) O your sheet BLM 6.SS.2.2, mark parallelogram P1 uder the Name of Quadrilateral. h) Write the measure of each iterior agle uder Iterior Agle Measures. i) Add up the measure of the four iterior agles ad write the sum uder Sum of Iterior Agles of Quadrilaterals. 4. Write o the board parallelogram P1. 5. Tell studets to discuss with their group members their agle measures ad the sum of their iterior measures. 6. Ask a few studets to record o the board their agle measures ad the sum of their iterior measures. 7. Discuss with the class the results they got by measurig the iterior agles of parallelogram P1 ad how some results may be similar or differet from other studets results. 8. Tell studets to do the followig: a) Measure the iterior agles of the other three quadrilaterals. b) Record the measure of each iterior agle. c) Record the sum of the measures of each quadrilateral. Shape ad Space 19

20 9. Discuss the results they got by measurig the iterior agles of the other three quadrilaterals. For example: compare the followig: a) Iterior measures of each quadrilateral to the iterior measures of the parallelogram P1 b) Sum of the iterior measures of each quadrilateral to the sum of the iterior measures of the parallelogram P1 c) Iterior measures of each quadrilateral to the iterior measures of the other quadrilaterals d) Sum of the iterior measures of each quadrilateral to the sum of the iterior measures of the other quadrilaterals 10. Tell studets to write i their jourals what they observed about how differet measures of the iterior agles of a quadrilateral ifluece the sum of the iterior agles of a quadrilateral. Observatio Checklist Check studets replies to determie whether they ca do the followig: r Follow istructios. r Costruct a model. r Measure iterior agles of a quadrilateral accurately. r Explai, usig models, that the sum of the iterior agles of a quadrilateral is 360º. r Explai, usig models, that the sum of the iterior agles of a quadrilateral is the same for all quadrilaterals. 20 Grade 6 Mathematics: Support Documet for Teachers

21 Grade 6: Shape ad Space (Measuremet) (6.SS.3) Edurig Uderstadig(s): All measuremets are comparisos. There is o direct relatioship betwee perimeter ad area. Perimeter, area, ad volume are measurable properties of objects. The uits of measure must be of the same ature as the property beig measured. Geeral Learig Outcome(s): Use direct or idirect measuremet to solve problems. Specific Learig Outcome(s): 6.SS.3 Develop ad apply a formula for determiig the perimeter of polygos area of rectagles volume of right rectagular prisms [C, CN, PS, R, V] Achievemet Idicators: Explai, usig models, how the perimeter of ay polygo ca be determied. Geeralize a rule for determiig the perimeter of polygos. Explai, usig models, how the area of ay rectagle ca be determied. Geeralize a rule for determiig the area of rectagles. Explai, usig models, how the volume of ay right rectagular prism ca be determied. Geeralize a rule for determiig the volume of right rectagular prisms. Solve a problem ivolvig the perimeter of polygos, the area of rectagles, or the volume of right rectagular prisms. Prior Kowledge Studets may have had experiece with the followig: Demostratig a uderstadig of multiplyig 2-digit umerals by 2-digit umerals to solve problems Demostratig a uderstadig of divisio of 2-digit umerals by 3-digit umerals Usig perimeter or area or both (whole umbers) to desig ad costruct differet rectagles ad draw coclusios Demostratig a uderstadig of measurig legth Shape ad Space 21

22 Demostratig a uderstadig of volume Idetifyig ad sortig quadrilaterals Describig orally ad i writig the rule for patter Demostratig a uderstadig of area of regular ad irregular 2-D shapes Describig ad costructig rectagular ad triagular prisms Demostratig a uderstadig of perimeter of regular ad irregular shapes Addig ad subtractig 1-, 2-, ad 3-digit umerals with aswers to 1000 Related Kowledge Studets should be itroduced to the followig: Explaiig ad applyig the order of operatios, excludig expoets Represetig geeralizatios arisig from umber relatioships Backgroud Iformatio Perimeter, area, ad volume are ot of the same ature; therefore, they do ot use the same uits of measuremet. Perimeter is the distace aroud a shape, ad it is measured i liear uits such as kilometres (km), metres (m), cetimetres (cm), ad millimetres (mm). Area is the amout of surface a shape covers, ad it is measured i square uits such as square kilometres (km²), square metres (m²), square cetimetres (cm²), ad square millimetres (mm²). Volume is the amout of space a object occupies or, if the object is hollow, the amout of space iside the object (capacity). Volume is measured i cubic uits such as cubic metres (m³), cubic cetimetres (cm³), ad cubic millimetres (mm³). Whe give either perimeter, or area, or both, studets i Grade 5 leared to: (a) desig ad costruct differet rectagles; (b) draw coclusios. They also demostrated a uderstadig of volume by: (a) selectig ad justifyig referets for cm³ ad m³ uits; (b) estimatig volume by usig referets for cm³ ad m³; (c) measurig ad recordig volume (cm³ ad m³ ); ad (d) costructig rectagular prisms for a give volume. I Grade 6, studets will lear through their activities to develop ad apply a formula for determiig the (a) perimeter of polygos; (b) area of rectagles; ad (c) the volume of right rectagular prisms. 22 Grade 6 Mathematics: Support Documet for Teachers

23 Mathematical Laguage cetimetre millimetre kilometre height legth width perimeter area volume polygo rectagle right rectagular prism Learig Experieces Assessig Prior Kowledge BLM 5-8.9: Cetimetre Grid Paper ruler pecil scissors tape Orgaizatio: Idividual 1. Tell studets that you wish to assess their uderstadig of perimeter ad area of rectagles ad also their uderstadig of volume of rectagular prisms. 2. Distribute to each studet a copy of BLM Tell studets to draw two rectagles: a) Oe with a 14 cm perimeter ad mark P = 14 cm iside it. b) Oe with a 24 cm² area ad mark A = 24 cm² iside it. Shape ad Space 23

24 4. Circulate to check that studets chose a correct rectagle for each sceario. 5. Costruct a rectagular prism that has a 60 cm³ volume. 6. Circulate to check that studets chose a correct rectagular prism. Observatio Checklist Observe studets resposes to determie whether they ca do the followig: r Use a give perimeter to fid the dimesios of a rectagle. r Use a give area to fid the dimesios of a rectagle. r Divide two-digit umerals by oe-digit umerals. r Draw a rectagle. r Use a give volume to fid the dimesios of a rectagular prism. r Costruct a rectagular prism. Suggestios for Istructio Explai, usig models, how the perimeter of ay polygo ca be determied. geoboard elastic bad pegs Orgaizatio: Whole class/small group/idividual 1. Distribute to each studet: a) 1 geoboard b) 6 pegs c) 1 elastic bad 2. Say the followig to the studets: a) Use the geoboard, elastic bad, ad ay umber of pegs you wat to make a polygo. b) Aalyze your polygo to determie its perimeter. 24 Grade 6 Mathematics: Support Documet for Teachers

25 c) Write i your otebook how you determied the perimeter of your polygo. d) Use your geoboard, elastic bad, ad pegs to make a differet polygo. e) Aalyze your ew polygo to determie its perimeter. f) Write i your otebook how you determied the perimeter of your ew polygo. g) Use your geoboard, elastic bad, ad pegs to make two more types of polygos, ad go through the same process. h) Aalyze the otes you wrote about how to determie the perimeter of each polygo. i) Write i your otebook how you would determie the perimeter of ay polygo. j) Repeat the process for regular polygos. 3. Discuss together what studets foud out about determiig the perimeter of ay polygo. Observatio Checklist Check studets replies to determie whether they ca do the followig: r Costruct a polygo usig a geoboard, elastic bad, ad pegs. r Determie the perimeter of a polygo. r Add legths together. r Explai how they determied the perimeter of a polygo. Shape ad Space 25

26 Suggestios for Istructio Geeralize a rule for determiig the perimeter of polygos. collectio of polygos (both regular ad irregular) BLM 6.SS.3.1: Polygo Collectio: Set 1 5, with the polygos cut out ad placed i evelopes Orgaizatio: Four or five groups 1. Distribute a differet collectio of polygos to each group. 2. Tell studets to do the followig: a) Sort the polygos by their umber of sides. b) Estimate ad the measure the perimeter of each polygo. c) Ca you fid a shortcut or rule for fidig the perimeter of polygos? d) Exchage your polygo collectio with aother group. e) Verify that the shortcut or rule you developed works for other polygos. f) Report to the class how your group calculated the perimeters, icludig the shortcut (or rule) you foud. g) Discuss similarities or differeces amog your fidigs. Observatio Checklist Check studets replies to determie whether they ca do the followig: r Sort polygos by the umber of their sides. r Estimate the perimeter of a polygo. r Measure the perimeter of a polygo. r Explai the shortcut or rule for fidig the perimeter of a polygo. 26 Grade 6 Mathematics: Support Documet for Teachers

27 Suggestios for Istructio Explai, usig models, how the area of ay rectagle ca be determied. geoboard elastic bad pegs Orgaizatio: Whole class/idividual 1. Distribute the followig to each studet: a) 1 geoboard b) 1 elastic bad c) 4 pegs 2. Say the followig to the studets: a) Use the geoboard, elastic bad, ad the four pegs to make a rectagle. b) Aalyze your rectagle to determie its area. c) Write i your otebook how you determied the area of your rectagle. d) Use your geoboard, elastic bad, ad pegs to make a differet rectagle. e) Aalyze your ew rectagle to determie its area. f) Write i your otebook how you determied the area of your ew rectagle. g) Use your geoboard, elastic bad, ad pegs to make two more types of rectagles, ad go through the same process. h) Aalyze the otes you wrote about how to determie the area of each rectagle. i) Write i your otebook how you would determie the area of ay rectagle. 3. Discuss together what studets foud out about determiig the area of ay rectagle. Observatio Checklist Check studets replies to determie whether they ca do the followig: r Costruct a rectagle usig a geoboard, elastic bad, ad pegs. r Determie the area of a rectagle. r Explai how they determie the area of a rectagle. Shape ad Space 27

28 Suggestios for Istructio Geeralize a rule for determiig the area of rectagles. square tiles or a geoboard Orgaizatio: Groups 1. Distribute square tiles or a geoboard to each group. 2. Tell studets to do the followig: a) Make a collectio of rectagles. b) Look for shortcuts that ca be used i determiig area. c) Determie the area of each rectagle. d) Draw each rectagle o grid paper. e) Record each rectagle s dimesios o grid paper. f) Record the area of each rectagle iside it. g) Exchage collectios with aother group. h) Verify that the shortcut or rule you developed works for other rectagles. i) Report to the class how your group calculated the area, icludig ay shortcut (or rule) you may have foud. Observatio Checklist Check studets replies to determie whether they ca do the followig: r Costruct differet rectagles. r Determie the area of differet rectagles. r Measure the sides of a rectagle. r Use multiplicatio facts. r Fid a shortcut or rule for fidig the area of a rectagle. r Explai the shortcut or rule for fidig the area of a rectagle. 28 Grade 6 Mathematics: Support Documet for Teachers

29 Suggestios for Istructio Explai, usig models, how the volume of ay right rectagular prism ca be determied. Geeralize a rule for determiig the volume of right rectagular prisms. ceticubes Orgaizatio: Small groups 1. Tell studets to: a) Make right rectagular prisms whose volumes are 48 cm³, 36 cm³, 28 cm³, 21 cm³, ad 12 cm³. b) Make a table, such as the oe below. c) Record each prism s dimesios area of its base volume Width i cm Legth i cm Area of Base i cm 2 Height i cm Volume i cm 3 d) Explai i your jourals how the volume of each of these right rectagular prisms was foud. e) Discuss with your group members how a prism s dimesios are related to its area ad volume. f) Explai i your jourals how the volume of ay right rectagular prisms ca be foud. g) Write a shortcut method or rule to be used to calculate volume of ay right rectagular prism. h) Verify your shortcut rules by predictig the volume of a right rectagular prism that is 4-cm wide by 3-cm log by 10-cm high. i) Build the prism usig ceticubes ad cout the umber of cubes. The cout should match the volume calculated by your rule. j) Share your coclusios with the class. Shape ad Space 29

30 Observatio Checklist Check studets replies to determie whether they ca do the followig: r Costruct a right rectagular prism usig ceticubes, give a specific volume. r Calculate dimesios of a right rectagular prism, give a specific volume. r Fid a shortcut or rule for fidig the volume of a right rectagular prism. r Explai the shortcut or rule for fidig the volume of a right rectagular prism. Suggestios for Istructio Explai, usig models, how the volume of ay right rectagular prism ca be determied. Geeralize a rule for determiig the volume of right rectagular prisms. ceticubes Orgaizatio: Small groups 1. Have a class discussio about volume ad right rectagular prisms. Be sure everyoe uderstads before you move o. 2. Preset studets with the followig problem: A grocery store chai is opeig up a ew store i Stoewall, MB. They are give very specific istructios as to how to place each shelf so that all of the items will fit. The page about juice boxes has a small tear i the bottom ad some iformatio seems to be missig. 30 Grade 6 Mathematics: Support Documet for Teachers

31 The maager does ot wat the owers to doubt his abilities, so he has the stockig clerks try to figure out the height that the shelf should be. They ca record their iformatio i the table below: Width i cm Legth i cm Area of Base i cm 2 Height i cm Volume i cm 3 3. Have studets explai i their jourals how the volume relates to the width, legth, area of base, ad height of their right rectagular prisms. Ask them to use this relatioship to determie the volume of a juice box that is 5 cm log by 3 cm wide by 6 cm tall. Observatio Checklist Check studets replies to determie whether they ca do the followig: r Costruct a right rectagular prism usig ceticubes, give a specific volume. r Fid a shortcut or rule for fidig the volume of a right rectagular prism. r Explai the shortcut or rule for fidig the volume of a right rectagular prism. Shape ad Space 31

32 Suggestios for Istructio Solve a problem ivolvig the perimeter of polygos, the area of rectagles, or the volume of right rectagular prisms. BLM 6.SS.3.2: Dolly Made a Garde Orgaizatio: Idividual 1. Distribute to each studet a copy of BLM 6.SS Tell studets to do the followig: a) Read the problem carefully. b) Name the polygo. c) Explai how they will fid the perimeter of Dolly s garde. d) Solve the perimeter problem of Dolly s garde. 3. Discuss with the class the polygo created by Dolly. 4. Ask a studet to write the ame of the polygo o the board. 5. Have a studet tell the class how he or she foud the perimeter of Dolly s garde. 6. Ivite commets by other studets. 7. Ask a studet to write his or her solutio o the board. 8. Discuss the results with the class. Observatio Checklist Check studets replies to determie whether they ca do the followig: r Recogize ad ame a polygo. r Explai how they will fid the perimeter of a polygo. r Solve the perimeter of a polygo. 32 Grade 6 Mathematics: Support Documet for Teachers

33 Suggestios for Istructio Solve a problem ivolvig the perimeter of polygos, the area of rectagles, or the volume of right rectagular prisms. BLM 6.SS.3.3: David s Playroom A poster-sized paper Orgaizatio: Small group 1. Distribute to each studet a copy of BLM 6.SS.3.3 ad a poster-sized paper. 2. Tell studets to do the followig: a) Read the problem carefully. b) Name the quadrilateral. c) Explai how they will fid the area of David s playroom. d) Solve the area problem of David s playroom. 3. Discuss with the class the quadrilateral created by David. 4. Ask each group to use the poster-sized paper to do the followig: a) Write the ame of the quadrilateral o top of the poster paper. b) Draw the shape of David s playroom. c) Write dow how they foud the area of David s playroom. d) Write their solutio to the problem ivolvig the area of David s playroom. 5. Place each poster o the board. 6. Discuss the results with the class. Observatio Checklist Check studets replies to determie whether they ca do the followig: r Recogize ad ame a quadrilateral. r Explai how they will fid the area of a quadrilateral. r Solve the area of a quadrilateral. Shape ad Space 33

34 Suggestios for Istructio Solve a problem ivolvig the perimeter of polygos, the area of rectagles, or the volume of right rectagular prisms. BLM 6.SS.3.4: Peter s Toy Box Orgaizatio: Idividual 1. Distribute to each studet a copy of BLM 6.SS Tell studets to do the followig: a) Read the problem carefully. b) Create a chart based o the problem. c) Explai how you will fid the volume of Peter s toy box. d) Solve the volume problem of Peter s toy box. 3. Discuss with the class the dimesios of Peter s toy box. 4. Write the dimesios o a overhead trasparecy. 5. Have a studet tell the class how he or she foud the volume of Peter s toy box. 6. Ask if ayoe has a differet explaatio. 7. Ask a studet to write his or her solutio o the board. 8. Discuss the results with the class. Observatio Checklist Check studets replies to determie whether they ca do the followig: r Create a chart based o a problem. r Explai how they will fid the volume of a right rectagular prism. r Solve a problem ivolvig the volume of a right rectagular prism. 34 Grade 6 Mathematics: Support Documet for Teachers

35 Grade 6: Shape ad Space (3-D Objects ad 2-D Shapes) (6.SS.4, 6.SS.5) Edurig Uderstadig(s): Shapes are distiguished by their properties Geeral Learig Outcome(s): Describe the characteristics of 3-D objects ad 2-D shapes, ad aalyze the relatioships amog them. Specific Learig Outcome(s): 6.SS.4 Costruct ad compare triagles i differet orietatios, icludig scalee isosceles equilateral right obtuse acute [C, PS, R, V] 6.SS.5 Describe ad compare the sides ad agles of regular ad irregular polygos. [C, PS, R, V] Achievemet Idicators: Sort a set of triagles accordig to the legth of the sides. Sort a set of triagles accordig to the measures of the iterior agles. Idetify the characteristics of a set of triagles accordig to their sides or their iterior agles. Sort a set of triagles ad explai the sortig rule. Draw a triagle (e.g., scalee). Replicate a triagle i a differet orietatio ad show that the two are cogruet. Sort a set of 2-D shapes ito polygos ad o-polygos, ad explai the sortig rule. Demostrate cogruece (sides to sides ad agles to agles) i a regular polygo by superimposig. Demostrate cogruece (sides to sides ad agles to agles) i a regular polygo by measurig. Demostrate that the sides of a regular polygo are of the same legth ad that the agles of a regular polygo are of the same measure. Sort a set of polygos as regular or irregular ad justify the sortig. Idetify ad describe regular ad irregular polygos i the eviromet. Shape ad Space 35

36 Prior Kowledge Studets may have had experiece with the followig: Desigig ad costructig differet rectagles Idetifyig ad sortig quadrilaterals accordig to their attributes Demostratig a uderstadig of area of regular ad irregular 2-D shapes Describig ad costructig rectagular ad triagular prisms Demostratig a uderstadig of lie symmetry Sortig regular ad irregular polygos accordig to the umber of sides Related Kowledge Studets should be itroduced to the followig: Demostratig a uderstadig of agles Performig a combiatio of trasformatios o a sigle 2-D shape, ad drawig ad describig the image Backgroud Iformatio A polygo is a closed plae figure formed by three or more lie segmets. The simplest polygo is a triagle. There are regular polygos ad irregular polygos. A regular polygo is a polygo i which all sides ad all agles are cogruet. See examples below triagle quadrilateral petago hexago A irregular polygo is a polygo whose sides ad agles are ot all cogruet. See examples below triagle quadrilateral petago hexago 36 Grade 6 Mathematics: Support Documet for Teachers

37 A triagle is a polygo with three sides ad three agles. Triagles are sorted accordig to their sides ad agles. A scalee triagle is a triagle with o cogruet sides ad o cogruet agles. Example: A isosceles triagle is a triagle with at least two cogruet sides ad two cogruet agles. Example: A equilateral triagle is a triagle with three cogruet sides ad three cogruet agles. Example: C A B Shape ad Space 37

38 A right triagle is a triagle with oe right agle. Examples: A obtuse triagle is a triagle cotaiig oe obtuse agle (greater tha 90º ad less tha 180º). Example: A acute triagle is a triagle i which all three agles are acute (greater tha 0º ad less tha 90º). Example: A C B Whe two figures have the same shape ad size, they are cogruet. Examples: Two sides (lie segmets) are cogruet if they are the same legth. Two agles are cogruet if they have the same measure. 38 Grade 6 Mathematics: Support Documet for Teachers

39 Mathematical Laguage acute cogruet equilateral hexago isosceles obtuse petago polygo right scalee square triagle Learig Experieces Assessig Prior Kowledge BLM 5-8.9: Cetimetre Grid Paper ruler protractor pecil Orgaizatio: Idividual 1. Distribute to each studet a copy of BLM Ask studets to use the cetimetre grid to draw the followig: a) Oe triagle usig a ruler ad protractor. b) Oe quadrilateral usig a ruler ad protractor. 3. Tell studets to do the followig: a) Mark each iterior agle of each shape with a differet letter of the alphabet. b) Name each iterior agle of each polygo accordig to its measure. Shape ad Space 39

40 4. Circulate to check that studets do the followig: a) Draw the correct shape. b) Write the correct ame for each agle. Observatio Checklist Observe studets resposes to determie whether they ca do the followig: r Draw a triagle usig a ruler ad protractor. r Draw a quadrilateral (e.g., square, rectagle, parallelogram, trapezoid, or other irregular quadrilateral) usig a ruler ad protractor. r Recogize iterior agles i a polygo. r Mark iterior agles i a polygo. r Name iterior agles of a polygo accordig to their measure (e.g., acute, right, obtuse, straight, reflex). Suggestios for Istructio Sort a set of triagles accordig to the legth of the sides. scissors ruler BLM 6.SS.4.1: Cards of Triagles #1 BLM 6.SS.4.2: Sortig of Triagles Accordig to the Legth of the Sides Orgaizatio: Whole class/pairs 1. Distribute to each pair a copy of BLM 6.SS.4.1, ad to each studet a copy of BLM 6.SS Have the studets cut the cards of triagles i BLM 6.SS.4.1 so they get eight cards (that is, four cards per studet). 40 Grade 6 Mathematics: Support Documet for Teachers

41 3. Tell studets to do the followig: a) Measure all three sides of each triagle. b) O your copy of BLM 6.SS.4.2, mark dow the ame of the triagle legth of each side how may sides have the same legth that is, 3 sides have the same legth 2 sides have the same legth No sides are the same legth c) Discuss the results with your parter. d) Copy your parter s results oto your sheet. e) Sort the triagles accordig to the umber of sides that have the same legth (3, 2, oe). 4. Have a class discussio o sortig triagles accordig to the legth of the sides. 5. Tell studets to write i their jourals their observatios o sortig triagles accordig to the legth of the sides. Observatio Checklist Observe studets resposes to determie whether they ca do the followig: r Measure the sides of a triagle. r Compare triagles accordig to the legth of the sides. r Sort triagles accordig to the legth of the sides. Shape ad Space 41

42 Suggestios for Istructio Sort a set of triagles accordig to the measures of the iterior agles. scissors protractor BLM 6.SS.4.3: Cards of Triagles #2 BLM 6.SS.4.4: Sortig of Triagles Accordig to the Measure of the Iterior Agles Orgaizatio: Whole class/pairs 1. Distribute to each pair a copy of BLM 6.SS.4.3, ad to each studet a copy of BLM 6.SS Have studets cut the cards of triagles i BLM 6.SS.4.3 so they get eight cards (that is, four cards per studet). 3. Tell studets the followig: a) Measure all three iterior agles of each triagle. b) O your copy of BLM 6.SS.4.4, mark dow the ame of the triagle the measure of each iterior agle 3. Ask studets to use the measure of the iterior agles to sort their triagles ito groups. Have them explai their sortig rules o the table provided. 4. Discuss the various sortig rules as a class. Through the discussio, ecourage studets to sort the triagles by a) the umber of agles that are equal (3 equilateral, 2 isosceles, oe scalee) b) the type of agles it cotais (oe obtuse obtuse, oe right right, all acute acute) 5. Ecourage correct use of mathematical termiology 6. Ask studets to show their kowledge of differet types of triagles through their choice of a) a joural etry b) a flip book c) a iterview d) a poem e) etc. 42 Grade 6 Mathematics: Support Documet for Teachers

43 Observatio Checklist Observe studets resposes to determie whether they ca do the followig: r Measure iterior agles of a triagle. r Compare triagles accordig to the measure of the iterior agles. r Sort triagles accordig to the measure of the iterior agles. Suggestios for Istructio Idetify the characteristics of a set of triagles accordig to their sides or their iterior agles. ruler protractor BLM 6.SS.4.5: Triagle Idetificatio Orgaizatio: Whole class/idividual 1. Distribute to each studet a copy of BLM 6.SS Tell studets to aalyze the set of triagles. 3. Say to the studets the followig: a) You eed to measure the sides or iterior agles of the triagles. b) Record their measuremets. c) Idetify the characteristics of the set of triagles based o your measuremets. 4. Have a class discussio. 5. Tell studets to write their observatios regardig the idetificatio of the set of triagles i their jourals. Shape ad Space 43

44 Observatio Checklist Observe studets resposes to determie whether they ca do the followig: r Measure the sides of triagles. r Measure the iterior agles of triagles. r Compare triagles accordig to the legth of their sides. r Compare triagles accordig to their iterior agles. r Idetify the characteristics of a set of triagles accordig to their sides or their iterior agles. Suggestios for Istructio Sort a set of triagles accordig to the legth of the sides. Sort a set of triagles accordig to the measures of the iterior agles. Idetify the characteristics of a set of triagles accordig to their sides or their iterior agles. paper pecil ruler protractor grid paper Orgaizatio: Small groups 1. Seat studets i small groups. 2. Had out a grid paper to each studet. 3. Tell studets the followig: a) Each group eeds to make a set of triagles (that is, a group of triagles with similar characteristics). b) Discuss with group members what kid of triagles each perso will make. c) Discuss with group members how may triagles each perso will make. d) Make your triagles. 44 Grade 6 Mathematics: Support Documet for Teachers

45 4. Whe your set of triagles is complete, chage sets with aother group. 5. Idetify the characteristics of the other group s set of triagles accordig to their sides or their iterior agles. Observatio Checklist Observe studets resposes to determie whether they ca do the followig: r Work well as a member of a group. r Costruct a variety of triagles. r Idetify the characteristics of the other group s set of triagles accordig to their sides or their iterior agles. Suggestios for Istructio Sort a set of triagles, ad explai the sortig rule. protractor ruler BLM 6.SS.4.6: Triagle Page Orgaizatio: Whole class/small groups 1. Distribute to each studet a copy of BLM 6.SS Tell studets to do the followig: a) Aalyze the triagles carefully. b) Sort the triagles ad record them i your otebooks. c) Explai your sortig rule i your otebooks. d) Discuss the results with your group members. 3. Have a few studets orally preset their work. 4. Use the presetatios as the basis for a class discussio o the sortig of triagles. 5. Tell studets to write their observatios o sortig triagles i their jourals (e.g., Did everyoe use the same sortig rule? Why? What are the sortig methods some studets used?). Shape ad Space 45

46 Observatio Checklist Observe studets resposes to determie whether they ca do the followig: r Measure the sides of triagles. r Measure the iterior agles of triagles. r Sort triagles accordig to their sides or iterior agles. r Explai the sortig of triagles. Suggestios for Istructio Draw a triagle (e.g., scalee). Replicate a triagle i a differet orietatio ad show that the two are cogruet. protractor ruler a blak sheet of paper pecil Orgaizatio: Idividual 1. Have a class discussio o triagles (e.g., Ca studets ame some triagles ad describe them accordig to their sides or iterior agles?). 2. Distribute to each studet a blak sheet of paper (computer paper is fie). 3. Tell studets to do the followig: a) Draw a triagle usig a ruler ad a protractor. b) Replicate the triagle i a differet orietatio. c) Show that the two triagles are cogruet. 4. Ask a few studets to give a oral presetatio to the class. 46 Grade 6 Mathematics: Support Documet for Teachers

47 Observatio Checklist Observe studets resposes to determie whether they ca do the followig: r Draw a triagle usig a ruler ad protractor. r Measure sides of a triagle accurately. r Measure iside agles of a triagle accurately. r Replicate triagles usig a ruler ad protractor. Suggestios for Istructio Sort a set of 2-D shapes ito polygos ad o-polygos, ad explai the sortig rule. BLM 6.SS.5.1: Polygos or No-polygos? Orgaizatio: Whole class/pairs 1. Distribute to each pair a copy of BLM 6.SS O the board, create two colums. Write the word polygos i oe colum ad the word o-polygos i the other colum. 3. Tell studets to do the followig: a) Aalyze the 2-D shapes i BLM 6.SS.5.1. b) Discuss the 2-D shapes with your parters (e.g., Which colum does each 2-D shape belog to? Why?). c) Copy the chart off the board ito your otebooks. d) Place each 2-D shape i the appropriate colum. 4. Ask a few studets to help you complete the chart o the board. 5. Have a class discussio o the results of the sortig of the 2-D shapes. Shape ad Space 47