Notizen
Geometry
Inhalt der Notizen (4)
Seite 1
395-397
Measurement and Geometry connection
·
Closely
interconnected in every day life
·
Finding area
of hexagon/triangles (without formula)
·
Moving an
item of furniture (size, weight etc)
·
How much
paint to cover room (volume, shape, size)
·
Landscaping
(size, shape etc)
448-455
·
Properties,
relationships and measurement of points, lines, curves and surfaces
·
3 sub
strands:
o
Shape
o
Location and
transformation
o
Geometric
reasoning
·
Vital for
navigators, engineers, artists, landscapers, builders
·
Language
allows discussion of concepts and helps form ideas in mind
·
Discussion –
connect symbols, actions, words, pictures
·
Discussion –
make links, relate to experience, assign features to symbols and names
·
Word origin
develops shape understanding
·
Visual
geometry – spatial awareness – reading maps, drawing pictures, moving objects
·
Formal
geometry – used in measurement, wrong or right answers, science, technology etc
Van Hiele levels of geometric development
1.
Visualization
– recognized and named without mentioning properties
2.
Analysis – notice
properties, distinguish between types
3.
Informal
deductions – relationships between properties and shapes
4.
Formal
deductions – reason abstractly and use logic
5.
Rigour –
Analytical reasoning and application
Ways of Working
·
Visualizing
spatial arrangements – reading map, jigsaws, net to 3D, imagining and
estimating
·
Communicating
orally and written – discussing and describing properties
·
Drawing and
making models – making, drawing, sketching, cutting out
·
Thinking
logically – differences and similarities, classifying and sorting, picking
relevant properties
·
Apply
concepts and knowledge – making, designing, planning, marking ground
496-499
Paper folding
·
Children can
use geometric understanding to predict results if paper is cut, folded or
transformed.
·
Eg. A square
was folded and hole punched as per image, what would it look like unfolded?
Egg puzzles
·
Pattern
blocks form an egg shape when all joined together (mix of curved and straight
edges) and children can make them in to a variety of bird images
Tangram
·
7 pieces
called ‘tans’ which form a square
·
Can be used
for matching shapes
·
Use
templates to create images
·
Children can
pick which can be made when presented with multiple tangram pics
Seite 2
455-467
2D shapes
·
Have length
and width
·
Grouped by
side attribute
o
Straight
lines – polygon
o
Curves
o
Straight
lines and curves
·
Also:
o
Closed – all
lines meet
o
Not closed –
not all lines meet
o
Simple –
lines don’t cross
o
Not simple –
lines do cross
·
Also:
o
Concave – interior
angle greater than 180
o
Convex –
interior angles 180 or less
Polygons
Poly = many Gons= angles
·
Regular -
angles are the same
·
Irregular –
angles are different
·
Difficulties
o
Not
recognizing different sizes as being same shape
o
Different
examples of same shape (eg. regular and irregular quadrilaterals)
o
Different
orientations are still same shape
o
Only
recognizing stereotype of the shape
Triangles
3 angles – total 180
·
Scalene – no
equal sides or angles
·
Isosceles –
2 equal sides and angles
·
Equilateral
– 3 equal sides and angles, 60 each
·
Acute angle
– less than 90
·
Obtuse angle
– more than 90
·
Right angle – exactly 90
·
Difficulties
o
Right angle
is seen as half a triangle
o
Right angle
with a left orientation is a left angles
o
Chevron or
arrow is confused with triangle
o
Orientation
issues
Quadrilaterals
4 sides
·
Sum of angles
is 360
·
Closed shape
with 4 sides
·
Oblong/rectangle
o
All right
angles
·
Square
o
Right angles
with equal length sides
·
Rhombus
o
2 obtuse
angles
o
2 right
angles
o
Equal sides
o
Diagonals at
right angles (they add up to 180)
·
Kite
o
Angles less
than 180
o
Adjacent
sides equal
o
Diagonals at
right angles (they add up to 180)
·
Arrowhead
o
Adjacent
sides equal
o
One angle
greater than 180
·
Parallelogram
o
Opposite
sides equal
o
2 sets
parallel lines
·
Difficulties
o
Sterotyped
views
o
Diamond is
not a math term, it’s a rhombus or turned square
o
Not
understanding orientation doesn’t affect (may think rectangle has parallel line
to bottom of page)
Geoboards
·
Equally
spaced rows of nails
·
Use rubber
bands
·
Can quickly
make and experiment with 2d shapes
·
Use dot
paper to record
Angles
·
The amount
of turn
·
Full turn is
360
·
Straight
line is 180
·
When line
intersects straight line, deduct known angle from 180 to find unknown
·
Opposite
angles are equal
·
Triangle =
180
·
Quadrilateral
= 360
·
Can work out
other shapes by seeing how many triangles fit in it (eg. 3 triangles fit in
pentagon so 180 x 3 = 540 degrees)
468-469
Circles, ellipses, ovals
·
Curved line
·
Everyday objects
like coin, wheel, football field, jar lids
·
Circumference
– length around circle
·
Radius –
length from center to outside
·
Centre –
middle point
·
Diameter –
length from one side to other
·
Ellipse – 2
fixed points with major and minor axis of symmetry
·
Oval – one
axis of symmetry
·
Difficulties
o
Football
‘oval’ is an ellipse
o
Circles are
described as round rather than circular
429-431
Angles
1.
Identify
attribute angle
o
Use
rotagrams, angle arms and wheels – these are dynamic and show turn
o
Angle as a
corner
o
Angle as a
shape
o
Angle as a
measure of turn
2.
Comparing
and ordering angles
o
Direct
comparison by layering
o
Use rotagram
to show turn (bigger or smaller)
3.
Measuring
angles non-standard
o
Fold paper
to show
o
Half turn
o
Quarter turn
o
Estimate the
amount of turn
4.
Measuring
angles using standard
o
Dividing 360
to get:
o
180 half
o
90 quarter
o
Then use
full circle protractor (connect to rotagram)
Difficulties
·
Longer lines
is a bigger angle
·
Different
orientations
·
Left or
wrong angle
·
Half scale
protractor difficult as not sure which direction to follow
417-418
·
Use peg,
rope and chalk to create a circle
·
Highlights constant
distance of the radius
·
Use paper
circle in half to show diameter
·
Circumference
is 3 times longer than diameter
·
3.14 = d x c
·
use pi and
symbol last after relationship established
Seite 3
470-480
3 dimensional solids
·
Have length,
width AND depth
·
3 categories
o
All flat
surfaces
o
All curved
surfaces
o
Combination
of curved and flat
Polyhedron
·
Poly = many
hedron = face
·
All faces
are flat
·
Face
·
Vertex
·
Edge
Platonic solids
·
All faces
are the identical
·
Tetrahedron
– 4 triangles
·
Hexahedron –
6 squares
·
Octahedron –
8 triangles
·
Icosahedron
– 20 triangles
·
Dodecahedron
– 12 pentagons
Pyramids and prisms
·
Prisms – 2
identical, parallel faces joined by rectangles
·
Named for
the shape (pentagonal prism, hexagonal prism)
·
Cut in cross
section to make 2 of the same shape
·
Pyramids – triangles
meeting at common point with shape-based base
Spheres, cylinders, cones
·
Cylinder - 2
flat identical surfaces joined by single curved surface
·
Cones – one
flat surface joined by curved surface that meets at a point
·
Spheres –
completely curved surface
Difficulties
·
Confused
names for 2D and 3D
·
2D sides
confused with 3D faces and edges
·
Difference
between prism and pyramid
·
Not knowing
enough 2D to label the 3D
From 2 dimensional shapes to 3 dimensional solids
·
Need to
visualize 2D to 3D
·
Need to
create 2D from 3D image
·
Sketching
has several conventions
o
Dotted lines
show edges out of sight
o
Front faces
shaded to distinguish from others
o
Vanishing
points to show parallel lines
·
Isometric
paper is for making cubed shapes on paper, allows for straight lines
·
Viewpoints
refer to front, side and top views of 3d shape. Used to visualize
·
Difficulties
o
Cube is a
hexagon- cant see the 3D, think its flat
o
Isometric
clashes with perspective drawing in art
o
Cant
identify hidden cubes when viewed from one angle
o
Cant imagine
other faces of objects when show from one view
Nets
·
Flat version
that shows all edges, angles etc
·
Good to
clearly show how many rather than rotating object
·
Better to
deconstruct than to build
Geoshapes / Polydron
·
Shapes that
click together to form 3D
·
Use to make
the net then connect them to make 3D
502-503
Euler’s rule
Total of faces and vertices is
always two more than the number of edges
Seite 4
481-496
Location
·
Language –
moves from informal (next to, on top of, besides) to formal (left, right,
north, clockwise)
·
Position
·
Arrangement
·
Direction
·
Grids – each
space has a letter, kids can write the co-ordinates to spell their names. Could
draw a path using coordinates
·
·
Maps –
begins simple and progresses to alphanumeric, ordered pairs, cartesian etc
o
Also
includes symbols, compass, scale
o
May confuse
order of pair (x then y)
o
Difference
between grid lines and spots within
Transformation
Translation
·
Slides
across
·
Kids might
only go left to right not in other directions
Reflection
·
Flips over
·
Mirror line
defines where it flips (below, beside)
·
Kids may
just move shape across the line rather than mirroring
Rotation
·
Turns around
·
Centre of
turn defines where it ends up (may be in centre or edge of shape)
Also enlargement, dilation
(smaller), distortion
Tessellation
·
Comes from
small stone square mosaic
·
Uses pattern
to make continuous art
·
Brick drives
are tessellations
·
3 polygons
can tessellate – square, triangles and hexagons
Symmetry
Line symmetry
Test on paper by folding in half
to see if the same. Or hold half up to mirror.
·
Bilateral or
vertical – same on both sides, line down the middle – butterfly or heart
·
Horizontal –
same on top and bottom, line along horizon – use folded paper
·
Diagonal –
right angle triangle
·
Multiple
lines – square has both vertical and horizontal, pentagon has 3
Rotation symmetry
·
When rotated
less than 180, the shape fits within its outline atleast once, like a triangle
Difficulties
·
If the shape
is rotated they may think its not symmetrical (a turned rectangle for example)
·
May think it
is diagonal symmetry when its not, if it was flipped the would not meet up,
they just have the same area
Informationen
- Beschreibung
- 2 Math Year 2 (Geometry) Notiz am Geometry, erstellt von Ashleigh Collins am 28/04/2016.
- Erstellt von
- Ashleigh Collins
- Aufrufe
- 12
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