> ` @jbjb ;~dd(hhhhDDDf&f&f&f&&,^2b'b'b'b'(---]]]]]]],^_Ra]D-/----]/hhb'(]///-hVb'D(]/XT6hhhh-]//'WDZV'ћf&.CX"Z$]0,^eX@b/@bDZ/D"f&f& Math Unit Overview
Lesson #TopicObjectives/Learning Outcomes
(From Math Makes Sense)Activities
(What students will do)MaterialsAssessment/Criteria1Introduction
Geometry in ArtStudents recognize translations, reflections, and rotations.
Students describe various geometric figures.Students look at the images of Eschers art in their textbook and copies on the board. They answer questions based on his tessellating patterns. They will describe how the figures have been moved around in the picture.
(Math Makes Sense)Images of Eschers art (in txtbk)
Teaching Tessellating Art
Participation2TranslationsWhen a figure moves in a straight line, without turning, it is being translated.
A translation is described by the number of squares moved left or right, up or down.
A figure and its translation image are congruent and face the same direction
A translation arrow shows how a figure has been moved.Students choose a pattern block, place it on grid paper and trace it. They slide the block in a straight line and trace the block again. Their partner writes down how it moved. Take turns moving and describing. Students share their descriptions with the class and we work on a few examples together.
(Math Makes Sense)
Students will work in pairs for the following activity. Each student draws an image in the bottom left hand corner of their grid paper. They label the points. They then translate that shape to a new spot and draw it there. They continue this, using at least 4 different translations until they reach the top of the page. They do not show it to their partner. Students count how many squares they moved the reference point and write it beside each translation. Next, the students draw the beginning figure for their partner on a new sheet and trade sheets. Partner 1 describes the movements necessary to reach the top. They compare sheets and then switch. We discuss problems encountered as a class. Plastic square
Grid paper
Pattern Blocks
Grid paper
Square dot paperParticipation
Question for understanding when circulating
Completion marks for homework3RotationsA figure that turns around a point is being rotated.
A rotation is described by the direction of the turn (clockwise or counter-clockwise), the fraction of the turn, and the turn centre.
A figure and its rotation image are congruent, and face different ways if the rotation is less than 1 complete turn.Students draw a figure on their grid paper, in the centre. They use tracing paper to draw a congruent figure. Using their compass point they turn the figure to a new position. Students share their answers with the class and we will discuss how the descriptions for translations are different from rotations.
(Math Makes Sense)Grid paper
Pattern blocks
Compass
Tracing paperParticipation
Question for understanding when circulating
Completion marks for homeworkLesson #TopicObjectives/Learning Outcomes
(From Math Makes Sense)Activities
(What students will do)MaterialsAssessment/Criteria4ReflectionsA figure and its reflection image are congruent, and face opposite ways.
A mirror line can be vertical, horizontal, or at any in-between position.
A figure and its reflection image are the same distance from the mirror line.Students work in pairs to practice working with reflections. One student draws a line in the middle of the dot paper and their partner draws the figure in the mirror line. They will use a Mira to check if their shape is correct. They will take turns drawing figures and their images.
Discuss activity as a class; draw several images and ask students to work in their groups to explain how to flip them make sure everyone knows before putting up your hand!
(Adapted from Math Makes Sense)
Students will create a symmetrical (quilt) design on square dot paper by translating, rotating and reflecting shapes. They will have four quadrants. They will use a variety of transformations and colour in the quilt pattern. (From Symmetrical Quilt Design website)Square dot paper
Grid paper
Ruler
MirasParticipation
Question for understanding when circulating
Completion marks for homework
All four quadrants are symmetrical; image and colour use is symmetrical; a variety of transformations are used;5Line SymmetryA line of symmetry divides a figure into two congruent parts.
A symmetrical figure has one or more lines of symmetry.
A figure that is not symmetrical has no lines of symmetry.Students work individually with the pattern blocks and paper to determine how many lines of symmetry each one has. They will compare their answers with a partner and we will discuss as a class.
(Adapted from Math Makes Sense)
Students will work in partners to determine where the line of symmetry or more are found in the image. There may be images which are not symmetrical. We will review the answers as a class.
Students will use a square of paper, and following my directions, create shapes with one line of symmetry, two lines and possibly six lines of symmetry. We will create them one at a time; students will show them to the people at their group and then hold them up for the class to see. This will show them that there are many shapes possible with varying numbers of lines of symmetry. (Adapted from Snowflakes )Grid paper
Square dot paper
Pattern blocks
Tracing paper
Scissors
Miras
Geoboards & Geobands
Square construction, white or origami paperParticipation
Question for understanding when circulating
Completion marks for homework
Students create shapes with 1-2-6 lines of symmetryLesson #TopicObjectives/Learning Outcomes
(From Math Makes Sense)Activities
(What students will do)MaterialsAssessment/Criteria6Strategies ToolkitGuess and check is a good strategy to use when solving a problem with more than one possible solution.Students work individually and choose two pattern blocks that are the same and one that is different. They arrange the blocks to make a shape with only one line of symmetry. They trace the figure and draw a dotted line to show where the line of symmetry is found. Students will share their figures with the class on the overhead.
Students repeat the activity in small groups using pentominoes. We will then discuss the results as a class.
(Adapted from Math Makes Sense)Pattern blocks
(Overhead) pentominoes
Miras
Grid paperParticipation
Question for understanding when circulating
Completion marks for homework.7Exploring TilingA tiling pattern covers a surface with figures.
A tiling pattern has no gaps or overlaps.
A tiling pattern with all figures congruent is a tessellation.
Tessellation pictures can be created by repeating the same pattern several times.Students choose a pattern block to create their own tiling image. They try to cover a piece of paper with copies of the block so that there are no gaps. They will explain how they could make the pattern using different transformations and then repeat with a different block. We will then discuss the results as a class.
(Adapted from Math Makes Sense)
Read A Cloak for the Dreamer to the class. Students will look for examples of tessellating in the book. They will identify which shapes tessellate and which ones dont in the book; students will come up with reasons why that might be.
(Adapted from Quilting: Lets finish the pattern)
Students create their own imaginary cloak using construction paper and one or two tessellating shapes (From A Cloak for the Dreamer)
Students create their own picture by tessellating a shape. They will colour in the images; if it looks like a person or animal, they may then draw features. (Art class period)
(Adapted from Math Art p. 67)Pattern blocks
Square & triangular dot paper
Tracing paper
Grid paper
Scissors
Congruent square tiles
A Cloak for the Dreamer
Tessellation patterns
Lightweight cardboard
Construction paper
Crayons/coloured pencilsParticipation
Question for understanding when circulating
Completion marks for homework
One or two shapes used; minimum of two colours; entire page is covered with shapes
Art tessellations contain no gaps or spaces.
They are coloured in one colour per imageLesson #TopicObjectives/Learning Outcomes
(From Math Makes Sense)Activities
(What students will do)MaterialsAssessment/Criteria8Coordinate GridsAn ordered pair is used to describe the position of a point on a grid.
When the numbers in an ordered pair are large, a scale is used on the grid.Students work in pairs to explore grid work. They will draw and label a grid and then draw a figure on the grid. With their partner they describe the figure so someone else can draw it without seeing it & write down their description. They then trade with another pair and try and follow their directions to duplicate the shape. Students will share examples with the class. (From Math Makes Sense)
Students will plot dots on a grid using points that I give them and then join the lines to create a variety of shapes (starting at the origin etc). We will begin with simpler shapes and then move in to more complicated shapes. We will discuss the difficulties in plotting points as a class. (Adapted from the IRP)Grid paper
RulersParticipation
Question for understanding when circulating
Completion marks for homework.
All vertices are where two grid lines meet; descriptions of shapes are accurate9Show What you Know Review for TestStudents have an understanding of the concepts covered in the previous classes.
Students can explain the process they used to solve problems
Students will review previous lessons by working in small groups to solve problems that I ask them. We will discuss the answers as a class before students complete the practice questions individually in preparation for the test.
After marking their work, students will receive class time to prepare for the test. I will have more practice questions so students may focus on areas where they had particular trouble, before the test. (Extra practice questions may come from Pic-A-Puzzle)Square dot paper
Triangular grid paper
Miras
Tracing paper
Pattern blocksParticipation
Question for understanding when circulating
Mark homework (practice questions)10Unit TestStudents will work individually to complete the unit test. I expect this to take more than one math period so the test will be given in two sections. Tracing paper
Square dot paper
Students answered the questions correctly and were able to explain their thinking (where required).
Assessment:
Participation: For all lessons I will be looking for participation in the class discussions and in the activities the students are performing. For the most part, this will take the form of an informal evaluation where I may check their name off on a class list if they answer questions or are actively involved in their pair/group work.
Questioning for understanding: While I circulate to observe students working in groups, I will ask questions to see what level of understanding they have. Questions could be How is the original figure the same or different from figures A and B? How do you know if the figure and the reflected image match? I will use a number system or a key (i.e. 1 does not understand concept yet, 2 grasps some elements of the concept and 3 fully understands concept)
Completion marks for homework: Students self-mark their homework. As I circle the room asking for the answers, I will mark down whether they were able to provide an answer or not (if incorrect, I will return to them later). This is the system my sponsor teacher uses so I will be following her lead for this.
Presently, I have not had the opportunity to discuss further assessment strategies with my sponsor teacher. I would like to incorporate the use of math journals as I believe this will be a unit where they would be especially helpful in creating a deeper understanding.
Resources:
Britton, J. and Britton, W. Teaching Tessellating Art. Dale Seymour Publications. USA:1992
Bruce, A. Symmetrical Quilt Designs & Patterns Using Dot Paper. HYPERLINK "http://www.adrianbruce.com/Symmetry/quilt/quilt.html" http://www.adrianbruce.com/Symmetry/quilt/quilt.html. Viewed March 13, 2007.
Dyer, M. et al. Quilting: Lets finish the pattern. HYPERLINK "http://www.nsa.gov/teachers/ms/geom16.pdf" http://www.nsa.gov/teachers/ms/geom16.pdf. Viewed March 10, 2007.
Friedman, A. A Cloak for the Dreamer. Scholastic Inc. New York: 1994.
Ford Brunette, C. Math Art: Projects and Activities Grades 3-5. Scholastic: 1997.
Math Makes Sense 5. Unit 7: Transformational Geometry. Teachers Guide.
Ministry of Education. Integrated Resource Package: Grade 5. Transformations
Schadler, R and Seymour, D. Pic-A-Puzzle. Creative Publications Inc. Palo Alto: 1970.
Snowflakes. HYPERLINK "http://www.montessoriworld.org/Handwork/foldingp/snowflak.html" http://www.montessoriworld.org/Handwork/foldingp/snowflak.html. Viewed March 13, 2007.
Van de Walle, J and Folk, S. Elementary and Middle School Mathematics. Pearson Education Canada Inc. Toronto: 2005.
Prior Knowledge Needed:
Students can recognize translations, reflections, and rotations
Students are able to describe various geometric figures
PLOs:
recognize motion as a slide ( HYPERLINK "http://www.bced.gov.bc.ca/irp/mathk7/appfs_z.htm" \l "translation" translation), a turn ( HYPERLINK "http://www.bced.gov.bc.ca/irp/mathk7/appfp_r.htm" \l "rotation" rotation), or a flip ( HYPERLINK "http://www.bced.gov.bc.ca/irp/mathk7/appfp_r.htm" \l "reflection" reflection)
recognize tessellations created with regular and irregular shapes in the environment
cover a surface using one or more tessellating shapes
create and identify tessellations using regular HYPERLINK "http://www.bced.gov.bc.ca/irp/mathk7/appfp_r.htm" \l "polygon" polygons
plot whole number, ordered number pairs in the first HYPERLINK "http://www.bced.gov.bc.ca/irp/mathk7/appfp_r.htm" \l "quadrant" quadrant with HYPERLINK "http://www.bced.gov.bc.ca/irp/mathk7/appff_j.htm" \l "interval" intervals of 1, 2, 5, and 10
identify a point in the first quadrant using HYPERLINK "http://www.bced.gov.bc.ca/irp/mathk7/appfk_o.htm" \l "ordered" ordered pairs
Topic: Transformational Geometry
Grade Level: 5
Big Ideas:
Translations, reflections and rotations are transformations.
A line of symmetry divides a figure into 2 congruent parts, so that one part fits exactly onto the other part when the figure is folded along the line of symmetry.
A figure may be transformed repeatedly to create a tiling pattern.
A figure tessellates when congruent copies of it cover a surface with no gaps or overlaps.
An ordered pair can be used to describe the location of a point on a grid.
(From Math Makes Sense Unit 7 Teachers Guide)
________________________________________________
ik=?J>?A$&%\&]&_&**--../]0^0v4w44444!5"5d5мzjh~bh
6CJUaJh~bh
6CJ\aJh~bh
66CJaJh
6h~bh
65CJaJh~bh
6CJaJ&jh
6CJUaJmHnHsH uh~bCJaJh~b5CJaJ&jh~bCJUaJmHnHsH uh~bh~b5aJ/ )/Ldo$$M&`#$/Ifa$gd
6
gd
6
.@[HHH4
&F$M&`#$/Ifgd
6$$M&`#$/Ifa$gd
6kd$$Ifֈ&.F7C
6`Mx62:4a/
?YZh$M&`#$/Ifgd
6
&F$M&`#$/Ifgd
6hikx [HH44
&F$M&`#$/Ifgd
6$$M&`#$/Ifa$gd
6kd$$Ifֈ&.F7C
6`Mx62:4a k
<
&F$M&`#$/Ifgd
6
<=?I~[HH44
&F$M&`#$/Ifgd
6$$M&`#$/Ifa$gd
6kd$$Ifֈ&.F7C
6`Mx62:4ay+I
&F$M&`#$/Ifgd
6
IJSYv[OOOOOOOO$$Ifa$gd
6kd$$If.ֈ&.F7C
6`Mx62:4a 'qbVVIIIII
&F$Ifgd
6$$Ifa$gd
6kd$$If%ֈ&.;7"=t62:4a34 $Ifgd
6
&F$Ifgd
6+f(HbVVIIIII
&F$Ifgd
6$$Ifa$gd
6kdc$$Ifֈ&.;7"=t62:4aH+9e
&F$Ifgd
6 *>bVVVVVVVV$$Ifa$gd
6kd:$$Ifֈ&.;7"=t62:4a >?ATsbVVIIIII
&F$Ifgd
6$$Ifa$gd
6kd$$If<ֈ&.;7"=t62:4a#$&UI$$Ifa$gd
6kd$$Ifֈ&.;7"=t62:4a
&F$Ifgd
6&7g" b!!p""'###$"$0$;$D$[$\$t$u$$$$$ $Ifgd
6
&F$Ifgd
6$$Ifa$gd
6$$%%%&%'%(%{%|%%% $Ifgd
6
&F$Ifgd
6
%%%%&&&&>&H&\&bVVVVVVVV$$Ifa$gd
6kd$$If`ֈ&.;7"=t62:4a \&]&_&p&&'()bVVIIII
&F $Ifgd
6$$Ifa$gd
6kd$$If<ֈ&.;7"=t62:4a))))*6***Hkda $$Ifb
ֈ&.;7"=t62:4a
&F$Ifgd
6
&F$Ifgd
6****;+<+",%-6-L-R-`-o-}---
&F$Ifgd
6
&F$Ifgd
6
&F
$Ifgd
6 $Ifgd
6
&F$Ifgd
6$$Ifa$gd
6-----r...bVVM@@@
&F$Ifgd
6 $Ifgd
6$$Ifa$gd
6kd8
$$Ifֈ&.;7"=t62:4a..........USSSSSSkd$$Ifֈ&.;7"=t62:4a
&F$Ifgd
6 .../]0^00212g3v4w4444455h6i66677K7L77777gd
6d5e5f55555#6$6%6N6O6v66667778L8M8N888889959t9u9999999":#:.:/:::;:::ƴƨƨƨƖƨƒƆƆs$h~bh
60J>*B*CJaJphh~bh
65CJaJh
6#jLh~bh
6CJUaJh~bh
66CJaJ#j/
h~bh
6CJUaJh~bh
6CJaJh~bh
60JCJaJjh~bh
6CJUaJ#jh~bh
6CJUaJ-78899959u9999:Q;;<======>>>Q??
&Fgd
6
&F
gd
6
&Fgd
6gd
6:::::::::;;<<<
<C<D<<<<<<<<<<<9=:============?@@h~bh
65CJaJh
6h~bh
6CJaJjh~bh
6CJUaJ$h~bh
60J>*B*CJaJph*??????@@@@gd
6^gd
6 9&P1h0:p
6= /!S"S#$%$$If!vh555}
55+5N#vN#v+#v#v}
#v#v:V
6`Mx6555C555/2:4
$$If!vh555}
55+5N#vN#v+#v#v}
#v#v:V
6`Mx6,555C555/2:4
$$If!vh555}
55+5N#vN#v+#v#v}
#v#v:V
6`Mx6,555C555/2:4
$$If!vh555}
55+5N#vN#v+#v#v}
#v#v:V.
6`Mx6,555C555/2:4
$$If!vh5755i
555#v#v#v#vi
#v#v7:V%t6555=555"/2:4
$$If!vh5755i
555#v#v#v#vi
#v#v7:Vt6,555=555"/2:4
$$If!vh5755i
555#v#v#v#vi
#v#v7:Vt6,555=555"/2:4
$$If!vh5755i
555#v#v#v#vi
#v#v7:V<t6555=555"/2:4
$$If!vh5755i
555#v#v#v#vi
#v#v7:Vt6,555=555"/2:4
$$If!vh5755i
555#v#v#v#vi
#v#v7:V`t6,555=555"/2:4
$$If!vh5755i
555#v#v#v#vi
#v#v7:V<t6555=555"/2:4
$$If!vh5755i
555#v#v#v#vi
#v#v7:Vb
t6,555=555"/2:4
$$If!vh5755i
555#v#v#v#vi
#v#v7:Vt6,555=555"/2:4
$$If!vh5755i
555#v#v#v#vi
#v#v7:Vt6,555=555"/2:4
IDyK5http://www.adrianbruce.com/Symmetry/quilt/quilt.htmlyKjhttp://www.adrianbruce.com/Symmetry/quilt/quilt.htmlDyK*http://www.nsa.gov/teachers/ms/geom16.pdfyKThttp://www.nsa.gov/teachers/ms/geom16.pdfqDyK?http://www.montessoriworld.org/Handwork/foldingp/snowflak.htmlyK~http://www.montessoriworld.org/Handwork/foldingp/snowflak.html@@@NormalCJ_HaJmH sH tH DA@DDefault Paragraph FontRi@RTable Normal4
l4a(k(No List4U@4~b Hyperlink >*ph%
:%
:~ v v v v vJ:! )/Ldo/
?YZhikxk<=?I~ y
+IJSYv'q
34+f(H+9e *>?ATs#$&7g"bp'"0;D[\tu%&'({| & > H \ ] _ p !"####$6$$$$$$;%<%"&%'6'L'R'`'o'}'''''''r(((((((()]*^*0,1,g-v.w.....//h0i00011K1L111112233353u33334Q556777777888Q9999999: :0ʀ00000|8: : : : : : : #v#v|#v$ kj #v#v!#vz z z z z z z z z z z z z z z z z N N N N N N N N N N N N N N
/atid/<
>tc<>tsi0 0 00 00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 00 00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 00 00 0 0 0 0 0 0 0000 00 0 0 0 0 0 00 00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 00
0
0
0
0
0
0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0p`0000000100000000000000000000000 0 00
0
0
0
0
0
0|"g`000 0 0 0 0 0000000_d5:@!;=h <IH>&$%\&)*-..7?@"$%&'()*+,-./0123456789:<>@#)m,V U
*6B
K
AXXXXXXXXXX8@j(
V 1"Z@@@K1V@@1@@1@@1?@@
V 1"Z@@@K1V@@1@@1@@1?@@
V
1"Z@@@K1V@@1@@1@@1?@@
B
V 1"Z@@@K1V@@1@@1@@1?@@
B
S ?:-T@8
t4TL,tTdt
7j&t
j&t8=8C'''L'Q'(11112233: :(....v00L1b1c1111112222: ::::3333336m'zQ`jNrBVU |F?AT#$&7" > H \ ] _ p !##$$$$<%%'o''''''r(((( :@`3:,:@UnknownGTimes New Roman5Symbol3Arial? Courier New;Wingdings"0hmfmf!H "J!S4)
) 3qHX)?~b%Meghan Camposano Math Unit OverviewMegs
Wendy CarrD
Oh+'0 ,
HT
`lt|'&Meghan Camposano Math Unit OverviewMegsegsegsNormalWendy Carr2Microsoft Word 11.0@F#@n@n!
՜.+,D՜.+,Php|
' uH)&Meghan Camposano Math Unit OverviewTitle 8@_PID_HLINKS'Ax<m!1http://www.bced.gov.bc.ca/irp/mathk7/appfk_o.htmordered21http://www.bced.gov.bc.ca/irp/mathk7/appff_j.htm interval01http://www.bced.gov.bc.ca/irp/mathk7/appfp_r.htm quadrant`)1http://www.bced.gov.bc.ca/irp/mathk7/appfp_r.htmpolygontV1http://www.bced.gov.bc.ca/irp/mathk7/appfp_r.htmreflection!1http://www.bced.gov.bc.ca/irp/mathk7/appfp_r.htm rotationy< 1http://www.bced.gov.bc.ca/irp/mathk7/appfs_z.htmtranslation1?http://www.montessoriworld.org/Handwork/foldingp/snowflak.html7*http://www.nsa.gov/teachers/ms/geom16.pdfP5http://www.adrianbruce.com/Symmetry/quilt/quilt.html
!"#$%&'()*+,-./0123456789:;<=>?ABCDEFGIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxy{|}~Root Entry F^
ŖnData
@1TableHbWordDocument;~SummaryInformation(zDocumentSummaryInformation8CompObjXObjectPool^
Ŗn^
Ŗn FMicrosoft Word DocumentNB6WWord.Document.8