Transcript Stretching and Shrinking Number Two Similar Figures

Investigations
For 6th, 7th, and 8th grades
Project commitment
• D level: part one of investigation and do two
“Connections” problems completed with all
criteria (strategy shown how to solve the
problem and picture models/manipulative
models representing the problem and
answer) Up to 11 points
• As a class choose the two problems, so we
can compare strategies and answers.
Project commitment
• C level: D level plus part two of investigation and do four
“Connections” problems completed with all criteria Up
to 13 points
• As a class choose two more Connection problems to add
to the two we already chose, so we can compare
strategies and answers.
• You and team members are creating math
presentations to share strategies and solutions for each
section. We have 2-3 weeks per unit. See rubric for
how I will assess your project work.
Attention: as we move through investigations, you must
have notes complete for each section before being allowed
to move on to the next section in the investigation.
Project commitment
• B level: C level plus part three of investigation,
two problems from “Applications” and four
“Connections” problems completed with all
criteria Up to 15 points (Group chooses the two
Application problems.)
• A level: B level plus part four of investigation (if
available), two problems from “Applications” ,
four problems from “Connections”, and two
problems from “Extensions” completed with all
criteria Up to 17 points (Independent choice for
Extension problems)
Project commitment
• Sign up for what level you plan to go for as we begin
investigation.
• You are also expected to complete a word wall
project for each investigation unit. Comparing and
Scaling is 6th grade. Stretching and Shrinking is 7th
grade. Thinking with Mathematical Models is 8th
grade. Label your word wall on the back with the
appropriate unit that your word belongs to with your
S.A.N.D.
7th grade
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Investigation 2 Opener
7th grade
Launch 2.1: “Drawing Wumps”
• Goals: Use algebraic rules
to produce similar figures
on a coordinate grid. Focus
student attention on both
lengths and angles as
criteria for similarity.
Contrast similar figures with
non-similar figures.
Four in a Row
7th grade
Launch 2.1: “Drawing Wumps”
• How many of you know how to
play tic-tac-toe?
• How many do you need in a
row to win?
• Today, we will play a different
game of tic-tac-toe. You will
need four in a row to win.
• We’ll play the left side of the
class against the right side of
the class. The left side can go
first and tell me the
coordinates. 
Four in a Row
7th grade: Four in a Row Coordinates must be equal
to or less than the absolute value of 4.
7th grade
Continue with 2.1 Launch
• Supposed to have video of
the Mug Wumps…
•
http://teachingtechie.typepad.com/learning/2010/04/th
e-wumps-add-new-family-membersdid-you-ever-thinksimilarity-was-this-much-fun-in-math-class.html
• Explore questions A-C.
• http://www.geogebratube.o
rg/student/m22093
….
7th grade
Continue with 2.1 Launch
• The points for Zug are found
from the points for Mug.
The rule is (2x,2y). What do
you think this rule tells us to
do to a Mug point to get a
Zug point? 
• What do the other rules tell
you to do for Lug, Bug, and
Glug?
Explore
Go through your table and
compute the new value of the
x and y for each point.
Remember that you are always
starting with Mug’s x- and ycoordinates. Then locate the
points and connect them in
sets as you did for Mug.
7th grade
2.1 Summarize
Students should be prepared to
share neatly formed Wumps
under the document camera.
(We should share this with the
8th graders to cover some
concepts that we may have
missed last year.)
…
• How would you describe to
a friend the growth of the
figures that you drew?
• Which figures seem to
belong to the Wump family
and which do not?
• Are Lug and Glug related?
Did they grow into the same
shape?
7th grade
2.1 Summarize
In earlier math units in CMP,
we learned that both angles
and the lengths of edges help
determine the shape of a
figure. How do the
corresponding angles of the
five Wumps compare?
…
7th grade
2.1 Summarize
Now let’s look at the
corresponding lengths for the
five figures. Are the lengths
related? Are some of them
related and others not?
How do the lengths in similar
Wumps compare?
Hint: a tool we can use is our
tracing paper to compare the
Wumps
…
7th grade
Launch 2.2: “Hats Off to the
Wumps”
• Goals: Understand the role
multiplication plays in
similarity relationships.
Understand the effect on
the image if a number is
added to the x- and ycoordinates.
Wumps are looking for hats!
7th grade
Explore 2.2: “Hats Off to the
Wumps”
• Use computers (maybe) and
graph paper option on
smart notebook to draw
hats. Must have rules for
Mug’s hat figured out.
Use computers today?
• Go to edmodo.com to post a
rule that makes a hat that is
not similar to Mug’s hat.
Your rule should be unlike
any other student’s rule!
(Prove your rule with your
hat compared with Mug’s
hat on paper graph paper.)
7th grade
Explore 2.2: “Hats Off to the
Wumps”
• What rule would you give
the largest possible image
on the grids provided?
• Make up a rule that would
place the image in another
quadrant.
Tips
• Cut out a hat and move it
on the grid where you want
it to go. Trace it. Explore
how the coordinates
changed from the original
position.
• Use different colors for the
transformations you
represent on your graphs.
7th grade
2.2 Summarize
2.2 Continued
• Are the images similar to the
original? Why or why not?
• Next question: What rule
would make a hat with the line
segments 1/3 the length of
Hat 1’s line segments?
• Next question: What happens
to a figure on a coordinate grid
when you add or subtract from
its coordinates? _E_O_A_ION
Next question: What rule would
make a hat the same size as Hat 1
moved up 2 units on the grid?
Next question: What rule would
make a hat with line segments twice
as long as Hat 1’s line segments and
move 8 units to the right?
Next question: Describe a rule that
moves Hat 1 and does not produce a
similar figure.
7th grade
2.2 Summarizing continues
• What effect does the rule
(5x-5,5y+5) have on the
original hat?
• What about the rule
(1/4x,4y-5/6)
2.2 Continued
• Make up a rule that will
shrink the figure, keep it
similar and move it to the
right and up.
• Check for understanding:
Do the above procedure at
edmodo.com. Post your
idea! We will check it out.

7th grade
2.3 “Mouthing Off and Nosing
Around”
• Goals: Develop more
formal ideas of the meaning
of similarity, including the
vocabulary of scale factor.
Understand the relationship
of angles, side lengths,
perimeters, and areas of
similar polygons.
Launch
7th grade
2.3 Launch
• What does the 0.15
represent?
• What does the 2.50
represent?
Okay, you are applying for jobs
at the boat house and the
manager will check your ability
to see if you can be trusted to
calculate correct rental
charges. (next slide)
Scale Factor:
• The number that the side
lengths of one figure can be
multiplied by to give the
corresponding side lengths
of the other similar figure
7th grade
2.3 Launch
• Using the hats from 2.2,
answer these questions:
• How does Zug’s hat compare
with Mug’s hat?
• How do the perimeters
compare between Mug and
Zug?
• Do these patterns apply for
Mug to Bug? For Mug to
Glug? For Mug to Lug?
• Use two similar hats and ask
the students to compare the
lengths. See scale factor.
Scale Factor:
• The number that the side
lengths of one figure can be
multiplied by to give the
corresponding side lengths
of the other similar figure
7th grade
2.3 Launch
• The challenge is to use
criteria of corresponding
angles and side lengths to
determine which rectangles
(mouths) and which
triangles (noses) are similar.
Correspondence (and I am not
talking letter writing):
• Corresponding angles have
the same measure.
• Corresponding side lengths
from one figure are
multiplied by the same
scale factor.
7th grade
2.3 Explore
Work on problems A-F. Share
strategies and solutions with
details in your Math Tab.
Paint programs vs. Draw
programs
7th grade
2.3 Summarize
I want to grow a new Wump
from Wump I (Mug). The scale
factor is 9. What are the
dimensions and perimeter of
the new Wump’s mouth?
If the scale factor is 75, what
are the measurements of the
new mouth?
Why are the dimensions 300
by 75? What rule would
produce this figure?
*
Why does the perimeter grow
the same way as the lengths of
the sides of a rectangle?
Let’s go the reverse direction.
How cay you find the scale
factor from the original to the
image if you all have are the
dimensions of the two similar
figures?
7th grade
2.3 Summarizing
If the perimeter of the mouth
of a new Wump family
member is 150, what is the
length, width, and area of its
mouth? What scale factor was
used to grow this new Wump
from Mug I ?
Continues…
If the area of the mouth of a
new Wump family member is
576, what are the length and
width of its mouth?
If this makes sense, go to next
slide.
7th grade
2.3 Summarizing
What scale factor is needed to
produce a new mouth
(rectangle) whose perimeter is
5? (Remember the original P =
10.)
Continues…
On grid paper, draw a
quadrilateral (or parallelogram)
that is not a rectangle.
Make a similar quadrilateral using
a scale factor of 2.
Compare the corresponding
lengths of the two figures.
Compare the measures of the
corresponding angles.
How can you decide if two figures
are similar?
7th grade
Launch Extension 29 “Comic
Strip Character”
• Select a drawing of a comic
strip character from a
newspaper or magazine.
• Draw a grid over the figure
with tracing paper or use a
transparent grid.
• Identify the key points on
the figure and then enlarge
the figure by using each of
the rules to the right.
Rules for Dilation
• (2x,2y)
• (x,2y)
• (2x,y)
• Which rule creates a similar
figure?
7th grade
7th grade
• Student presentations for this investigation shared after
two class session spent on final preparations to share.
Spruce up your presentations with color, drawings,
neatness, etc.
• Presentation Days: compare work in your Math Tab to the
presentations presented by student groups. Be prepared to
critique their argument for solving the problems. Teacher
assesses with rubric and checks for reliable valid strategies
and solutions.
• Summative Assessment Piece
• Reflections shared in Reflection Journal
• Check our vocabulary and fill in definitions.
• Check word wall progress.