Transcript Week-6-Nets-3d-shapes-and

WUPA
Multiply using the grid
method.
Learning Objective
Read and plot coordinates in all
quadrants
DEFINITION
Grid – A pattern of horizontal
and vertical lines, usually
forming squares.
DEFINITION
Coordinate grid – a grid used to locate
a point by its distances from 2
intersecting straight lines.
6
5
4
3
2
1
00 1 2 3 4 5 6
DEFINITION
x axis – a horizontal number line
on a coordinate grid.
0 1 2 3 4 5 6
x
HINT
x ‘is a cross’
(across )
0 1 2 3 4 5 6
x
DEFINITION
y axis – a vertical number line on
a coordinate grid.
y
6
5
4
3
2
1
0
DEFINITION
Coordinates – an ordered pair of
numbers that give the location of a
point on a grid. (3, 4)
6
5
(3,4)
4
3
2
1
00 1 2 3 4 5 6
HINT
The first number is always the x or first letter
in the alphabet. The second number is
always the y the second letter in the
alphabet. 6
5
(3,4)
4
3
2
1
00 1 2 3 4 5 6
HOW TO PLOT ORDERED PAIRS
Step 1 – Always find the x value
first, moving horizontally
y
6
5
(2, 3)
4
3
2
1
00 1 2 3 4 5 6 x
HOW TO PLOT ORDERED PAIRS
Step 2 – Starting from your new
position find the y value by moving
vertically
6
(2, 3) 5
4
(2,3)
y 3
2
1
00 1 2 3 4 5 6 x
HOW TO FIND ORDERED PAIRS
Step 1 – Find how far over horizontally
the point is by counting to the right
y
6
5
(5, 4)
4
3
2
1
00 1 2 3 4 5 6 x
HOW TO FIND ORDERED PAIRS
Step 2 – Now count how far vertically
the point is by counting up
y
6
5
(5,4)
4
3
2
1
00 1 2 3 4 5 6 x
WHAT IS THE ORDERED PAIR?
(3,5)
y
6
5
4
3
2
1
00 1 2 3 4 5 6
x
WHAT IS THE ORDERED PAIR?
(2,6)
y
6
5
4
3
2
1
00 1 2 3 4 5 6
x
WHAT IS THE ORDERED PAIR?
(4,0)
y
6
5
4
3
2
1
00 1 2 3 4 5 6
x
WHAT IS THE ORDERED PAIR?
(0,5)
y
6
5
4
3
2
1
00 1 2 3 4 5 6
x
WHAT IS THE ORDERED PAIR?
(1,1)
y
6
5
4
3
2
1
00 1 2 3 4 5 6
x
WUPA
Find a Percentage of
a number
Learning Objective
Read and plot coordinates in all
quadrants
*
*When the number lines are extended into
the negative number lines you add 3 more
quadrants to the coordinate grid.
y
3
2
1
0
x
-1
-2
-3
-3 -2 -1 0 1 2 3
*
* If the x is negative you move
to the left of the 0. x = -2
y
3
2
1
0
-1
-2
-3
-3 -2 -1 0 1 2 3
x
*
* If the y is negative you move
down below the zero.y = -3
y
3
2
1
0
-1
-2
-3
-3 -2 -1 0 1 2 3
x
*
* Step 1 - Plot the x number
first moving to the left when
the number is negative.
(-3,
-2)
3
y
2
1
0
x
-1
-2
-3
-3 -2 -1 0 1 2 3
*
* Step 2 - Plot the y number
moving from your new position
down 2 when the number is
y
negative.3
2
(-3, -2) 1
0
x
-1
-2
-3
-3 -2 -1 0 1 2 3
*
* When x is positive and y is
negative, plot the ordered pair
in this manner. y
3
2
(2, -2) 1
0
-1
-2
-3
-3 -2 -1 0 1 2 3
x
*
* When x is negative and y is
positive, plot the ordered pair
in this manner. y
(-2, 2)
3
2
1
0
x
-1
-2
-3
-3 -2 -1 0 1 2 3
*
(-3, -3)
y
3
2
1
0
-1
-2
-3
-3 -2 -1 0 1 2 3
x
*
(-1, 2)
y
3
2
1
0
x
-1
-2
-3
-3 -2 -1 0 1 2 3
*
(1, -1)
y
3
2
1
0
x
-1
-2
-3
-3 -2 -1 0 1 2 3
*
(2, -2)
y
3
2
1
0
x
-1
-2
-3
-3 -2 -1 0 1 2 3
*
(-3, -2)
y
3
2
1
0
x
-1
-2
-3
-3 -2 -1 0 1 2 3
Coordinates Keywords & Rules
y
Y Axis and
positioning
vertical
10
Use brackets
(?,?) and
(4,8)
remember
X first
FIRST
QUADRANT Y next
9
8
7
6
5
SECOND
QUADRANT
4
3
2
1
-10 -9
-8 -7
-6 -5
-4 -3 -2
-1
0
1
2
3
4
5
6
7
8
9
-1
-2
-3
ORIGIN
THIRD
QUADRANT
-4
-5
-6
FOURTH
QUADRANT
10
x
X Axis and
positioning
horizontal
-7
-8
33
-9
-10
Mr D. Pay
YOUR TASK!
Whole class investigation: Pairs plot the following coordinates on
grids:
( -3, -7), (3,5), (0, -1), (1, 1), (-2, -5), (5,9), (-1, -3), (2,3).
Join al l the points, what do you notice?
Choose three of the points and add 3 to each of the x
coordinates.
Chose these three new points to each other using a different
coloured pencil. Try subtracting three and drawing the new points
from x coordinates. What happens if you subtract three from the y
and x coordinates?
36
Coordinates in 4 Quadrants.
y
10
-5,9
a
b
9
-8,9
6
-10,4
d
-7,4
d
a
-10,-1
d
-10,-5
-8 -7
a
-5,6
c
-6 -5
b
7 d
4
b
2
-1
0
-1,2
e
-6,-8
d
-4,-10
c
1
-3,-5
a
3
-2
4,-3
-3
-4
-5
-6
8
2
-8
c
-9
-10
-1,-10
4
a
5
6
7
a
7,-1
7,-6
b
0,-6
-7
c
2,-9
c
6,4 b
2
1,0
-1
-6,-1
c
1
10,7
1,4
3
-4 -3 -2
-6,-5
a
b
1
d
6
5
a 8,10
2,7
8
7
5
c
-6,2
-10 -9
-2,6
Mr D. Pay
4
d
b
6,-9
8,4
8
9
10
What are the
vertex
coordinates of
x each shape?
b 10,-1
3
c
10,-6
WUPA
Find fractions of
numbers
Learning Objective
Recognise parallel and perpendicular faces
and edges on 3.D shapes
Rehearse the terms polyhedron, tetrahedron
and begin to use dodecahedron.
What is the difference between a 2D shape
and 3D shape?
Which 3D shapes can you name?
CUBE
Can you think of any objects which are the shape of
a cube?
CUBOID
Can you think of any objects which are the shape of a
cuboid?
SPHERE
Can you think of any objects which are shape of a sphere?
CONE
Can you think of any objects which are the shape of a cone?
CYLINDER
Can you think of any objects which are the shape of a
cylinder?
SQUARE BASED
PYRAMID
TRIANGULAR PRISM
What is a Polyhedron?
Polyhedrons
Non-Polyhedrons
Do you notice a difference?
Polyhedrons
Non-Polyhedrons
Polyhedrons
 A solid that is bounded by polygons with straight
meeting faces.
 There are two main types of solids:
Prisms
and
Pyramids
Face
 The polygons that make up the sides of a polyhedron
Edge
 A line segment formed by the intersection of 2 faces
Vertex
 A point where 3 or more edges meet
Name the Polyhedron and find
the number of Faces, Vertices,
and Edges
a.
b.
c.
a.
b.
F=5
V=5
E=8
c.
F=5
V=6
E=9
F=8
V = 12
E = 18
a.
b.
F=5
V=5
E=8
c.
F=5
V=6
E=9
F=8
V = 12
E = 18
Does anybody see a pattern?
Euler’s Theorem
F+V=E+2
Euler’s Theorem
F+V=E+2
Example:
Euler’s Theorem
F+V=E+2
Example:
F = 6, V = 8, E = 12
Euler’s Theorem
F+V=E+2
Example:
F = 6, V = 8, E = 12
6 + 8 = 12 +2
Euler’s Theorem
F+V=E+2
Example:
F = 6, V = 8, E = 12
6 + 8 = 12 +2
14 = 14
Example: Use Euler’s Theorem to
find the value of n
Faces: 5
Vertices: n
Edges: 8
Example: Use Euler’s Theorem to
find the value of n
Faces: 5
Vertices: n
Edges: 8
F+V=E+2
5+n=8+2
5 + n = 10
n=5
WUPA
Divide using Chunking.
Visualise 3.D shapes from
2.D drawings and identify
different nets for a closed
cube.
NET 1
NET 2
NET 3
NET 4
NET 5
NET 6
NET 7
NET 8
YOUR TASK!
Draw the net of an open cube using five squares.
What other arrangements of five squares will also make a net
which we can fold to make an open cube?
Explore different arrangements.
Cut them out to check they do indeed fold to create an
open cube.
Nets of cubes
Solutions – There are 11 in total