Quick Start Expectations
Teaching Target:
I can use rep-tiles to see the effect of scale factor on
side lengths, angles, perimeter, and area.
Packet HW:
1) Inv . 3-4 pg. 4 – Similar Rectangles
2) Math XL – 30 mins this week
Warm-Up
135⁰
45⁰
135⁰
45⁰
45⁰
d
d
45⁰
135⁰
135⁰
For each of the following
angle measures, find the
measure of its
supplementary angle.
video
Multiple squares form a larger square.
Multiple hexagons do NOT form a larger hexagon.
How do rep-tiles show that
the scale factors and areas of
similar quadrilaterals and triangles are related?
As a table group work on Inv. 3-4 p. 2-3:
Not similar
Similar!
Scale factor: 3
Similar!
Scale factor: 2
Similar!
Scale factor: 2
nine copies
original
9 in²
15 in²
scale factor x scale factor = area
scale factor = 3
81 ÷ 9 = 9 in²
15 x 9 = 135 in²
3 x 3 = 9 ut²
4 cm²
9 cm²
scale factor x scale factor = area
scale factor = 5
4 x 25 = 100 cm²
225 cm²
225 ÷ 25 = 9 cm²
5 x 5 = 25 ut²
Similar!
Scale factor: 2
Not similar
Not similar
Similar!
Scale factor: 2
Packet HW:
1) Inv . 3-4 pg. 4 – Similar Rectangles
2) Math XL – 30 mins this week
Additional practice:
scale factor 2
scale factor 1
original
four copies
Each side length of the larger is twice the length of the
corresponding side of the smaller triangle. (2 x 1 = 2 )
The perimeter of the larger is twice the perimeter of the
smaller (for a scale factor of 2).
(2 x 4 = 8 ut )
The area is 4 times the area of the original because four of the
smaller triangles fit into the larger triangle. (2² x 1 = 4 ut²)
This is also the square of the scale factor.
original
scale factor 1
The side lengths of the new rep-tile A is twice
(2x) the corresponding sides of the original.
(2 x 1 = 2)
A
B
scale factor 2
scale factor 4
B is four times (4x) the
corresponding sides of the original.
(4 x 1 = 4)
And is twice (2x) the sides of A.
(2 x 2 = 4)
For this example:
side length: The scale factor (4) times the corresponding
4
side length of the small rectangle (1) (4 x 1 = )
perimeter: The perimeter of the large rectangle is the scale factor (4)
16 ut times the perimeter of the small rectangle (4) (4 x 4 = )
angles: Angles of all similar figures are congruent, no matter what
(same) the scale factor is.
area: The square of the scale factor (4²)
16 ut² times the area of the small rectangle (1). (4² x 1 = )
Sketch these figures. Then Sketch
try to form a rep-tile out of each.
Yes! All rectangles & parallelograms
have copies that can fit together to
make a larger shape that is similar
to the original.
Can you form a rep-tile out of each of these shapes?
original
parallelogram
non-rectangular parallelogram
four copies
trapezoid
p. 54
Sketch one of these figures. Then try to form a rep-tile.
Yes! All triangles (right,
isosceles, and scalene) have
copies that can fit together to
make a larger, similar triangle.
Can you form a rep-tile out of each of these shapes?
A scalene triangle and rep-tile
scale factor 1
scale factor 2
Each side length of the larger triangle is twice the length of the
corresponding side of the smaller triangle.
(2 x 1 = 2 )
The perimeter of the larger triangle is twice the perimeter of the
smaller triangle (for a scale factor of 2).
(2 x 3 = 6 ut )
The area is 4 times the area of the original because four of the
smaller triangles fit into the larger triangle. This is also the square of
the scale factor.
(2² x 1 = 4 )
scale factor 1
scale factor 2
2. Find the scale factor
of the largest rep-tile.
scale factor 4
side length: The scale factor (4) times the side lengths of the smaller
triangle (1) .
4
(4 x 1 = )
perimeter: The scale factor (4) times the perimeter of the smaller
12 ut triangle (3).
(4 x 3 = )
angles:
The same!
area: The square of the scale factor (4²)
(4²
x
1
=
)
times
the
area
of
the
smaller
triangle
(1).
16 ut²