Transcript Percents, Proportions & Ratios

th, 7th & 8thGeometry
•6Coordinate
Grade
• Transformations
Benchmark
• Triangles
Related
Skills
:
Presented by:
CATHY JONES
Secondary Math Instruction Specialist
Center for Mathematics and Science Education
Arkansas NASA Education Resource Center
346 N. West Avenue, Room 202
Fayetteville, Arkansas 72701
(479) 575-3875
(479) 575-5680 (FAX)
e-mail: [email protected]
http://www.uark.edu/~k12 info/
Part I…Lessons & Activities
Divisibility Rules: AIMS Marvelous Multiplication & Dazzling Division…Clearing
the Table
Percent of Increase & Decrease: ETA Versatiles…Percents, Proportions &
Ratios
Walch Publisher Real Life Math…How Much is School
Worth? - Bigger, Stronger, and Faster - CDs
Ratios: Domino Ratios and ETA Versatiles…Percents, Proportions & Ratios
Writing Algebraic Equations: ETA Versatiles…Sequences & Equations Algebra & Functions
Geometric Properties: I have Who Has Shapes - Property List of
Quadrilaterals – Score the Shapes Bell Ringer
Similar Figures: AIMS Proportional Reasoning…Rectangular Ratios
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Write
the rule.
Find the…
Multiples
of 2
-orNumbers
Divisible
by 2
Numbers
divisible
by 2
must
end in
an even
number.
Find the patterns and rules for other numbers, including 4, 6, and 9.
Domino Ratios
Car
$5
Football
$6
Doll
$4
Game
$2
Jump Ropes
$3
Puzzle
Free
Top
$1
Find the domino that shows the ratio of the
price of the car to the price of the doll. If
needed, find another domino to show it in
simplest form.
Name: ___________________________________
DOMINO RATIOS
Football
$6
Car
$5
Game
$2
Doll
$4
Top
$1
Jump Rope
$3
Puzzle
Free
Find the domino and draw it correctly that shows the ratios as stated below.
If needed, find another domino to show it in simplest form.
1.
The price of the car compared to the price of the doll.
2. The price of the game compared to the price of the football.
3. The price of the puzzle compared to the price of the jump
rope.
4. The price of the doll compared to the price of the football.
5. The price of the car compared to the price of the puzzle.
6. The price of the top compared to the price of the puzzle.
7. The price of the game and the doll together compared to the
price of the jump rope.
8. The price of the top compared to the difference in the prices
of the jump rope and game.
9. The difference in the prices of the football and the game
compared to the sum of the price of two tops.
10. The sum of the price of the three lowest priced toys
compared to the price of the highest priced toy.
Name: ________________________________________
Property List for Quadrilaterals
On the shape worksheets list as many properties you can
think of. Each property listed must be true for all the shapes
on the sheet.
Use the words “at least” to describe how many of
something.
Ex: “Rectangles have at least 2 lines of symmetry.” Could
they have more? Think about it!
Use sticky note pads to check for right angles, compare side
length, and to draw straight lines. Use mirrors to check for
symmetry.
Name: ________________________________________
SCORE EACH FIGURE
Every triangle is worth 3 points.
Every parallelogram is worth 4 points.
Triangles: ______
Triangles: ______
Triangles: ______
Parallelogram: ______
Parallelogram: ______
Parallelogram: ______
Be ready to explain your reasoning.
Part II…Lessons & Activities
Transformations: Triangles & Transformations
Measurement and Conversions: The Queen’s Gold
Area & Perimeter: Mayan Pyramids – EQUALS Get it
Together…Polygons
Measurement (distance): AIMS Fabulous Fractions…Slide
Ruler Fractions
Area & Perimeter of Irregular Shapes: Learning
Resources Dot Paper Geometry…Geoboards
Probability: What’s the Probability?
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Rectangular Ratios
From AIMS Proportional Reasoning
How can you prove that two
rectangles are similar?
We will look at “families” of similar
shapes, finding the common
characteristics…including nesting,
graphing, and equivalent ratios.
Similar Figures
Where do children see similar
figures?
How do adults use similar figures?
To find similar rectangles sort them
into to look-a-like shapes….different
in size, but the same shape.
Test by lining them up with one vertex
of each rectangle on top of the other.
Do the opposite vertices form a
straight line?
Find Similar Figures
Cut out the rectangles on the
RECTANGLE RATIO sheets
Group those that look-a-like.
Arrange them on the grid
paper…SILIMAR OR NOT?
Draw the line showing similarity.
Repeat for all sets of look-a-likes.
Draw a different colored line showing
similarity for each set.
Find Similar Figures
Complete the RECTANGULAR
RATIOS record sheet.
Make ratios comparing width to length. Are
those from look-a-like sets equivalent?
Look at the lines you drew on the graphs.
Compare the points, width over length,
where the lines crossed through the
vertices. Are these the same as you found
on the record sheet?
What’s the common name for the ratio of
these lines?
ACTIVITY
Use only transformations
of a triangle to make the
star.
Can you use…..
Reflections?
Rotations?
Translations?
Name: ________________________________
ACTIVITY: Measure, draw, and cut out ONE triangle with angles of 36o, 18o and 126o. Use this triangle as a pattern and cut
out the number of triangles needed for the entire star.
1. What are the lengths of each of the sides of your triangle?
________ ________ _______
2. Find someone’s triangle whose sides are different than yours. Compare the measurements. If the triangles all have the
same angles but different side lengths what relationship do they have? Discuss your findings.
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_________________________________________________________________________________________________________
3. Using as many transformations of the triangle as possible, make the star. Describe the transformations you used. Could
you use the following transformations? Explain. Be specific as to what line or point it is being reflected over, or the
point and degree of rotation, as well as the direction of translation.
Reflection: _______________________________________________________________________________________________
___________________________________________________________________________________________________________________________________________________________
Rotation: _________________________________________________________________________________________________
__________________________________________________________________________________________________________
Translation: _______________________________________________________________________________________________
_________________________________________________________________________________________________________
The Queen had set aside gold to pay her
children's allowance. She had a bag that
weighed 12 oz and another that weighed
11 oz. She had a third bag that weighed
13 oz . How many pounds of gold will she
be giving to her children?
Step 1: What does the problem ask you Step 2: What information is need but
not stated in the problem?
to find?
A. The number of ounces of gold
A. Weight of each bag of gold.
altogether.
B. How many ounces are in a pound.
B. The bag that weighed the most.
C. The amount of money the Queen
C. The amount the second bag weighed.
has.
D. The number of pounds of gold
D. Number of children the Queen has.
altogether.
Step 3: Select the correct expression(s).Step 4: Select the correct solution.
A.
B.
C.
D.
(12 + 11 + 13)16
12/16 + 11/16 + 13/16
16/(12 + 11 + 13)
(12 + 11 + 13)
16
Use the scales to verify your answer.
A. 36 lb
B. 36 oz
C. 2.25 lb
D. 2 ¼ oz
Mayan Pyramids
Polygons
The temple-pyramids were one
of the Mayans most impressive
achievements. The massive
stone structures were built in
the heart of Mayan cities.
The pyramids were built in layers of walls on top of one
another. Each wall was smaller than the one below it.
The top of the pyramid was a temple for the priests to go
and communicate to the Gods.
The outside was covered with a thick layer of mud
(stucco). When the mud dried is was painted in bright
colors.
Pyramid 1
Use the blocks to make a pyramid that is 3 walls high and has
a temple on top.
The bottom wall should have 5 blocks on each side.
What is the perimeter of each wall?
Bottom: _____ Middle: _______ Top: ______
What is the area of the base of the pyramid? _____
The temple on the top is made of 4 blocks, what is its
perimeter? ______ area? _____
Pyramid 2
Use the blocks to make a pyramid with a base wall
that is 6 units by 6 units and is two units tall.
What is the perimeter and are of the base?
Perimeter _______ Area _______
There are 4 walls and all are the same height. Each
one has a width and length of one unit less than the
one below it.
The height of the temple is double the height of a
wall and is 2 units wide on each side.
Make a table that shows the Perimeter and Area (as if
it had a floor) inside of each wall and the temple.
Pyramid 3
Use the blocks to make a pyramid that is 3 walls high and has
a temple on top.
The bottom wall has a perimeter of 48 cm.
Each of the next walls are 8 cm less than the one below it.
The temple on top is 6 cm by 6 cm by 6 cm.
Use a table of other method and determine the decrease in the
area (as if there was a floor) and perimeter for each level.
Show and explain your work
Pyramid 4
A pyramid is 3 walls high. Each wall is 1 block tall and 1
block thick. The base wall has 4 blocks on each side, the
next has 3, and the next has 2 on each side.
Build a pyramid that is similar, but double in size.
The temple on the original pyramid is only 1 block.
Make sure the new temple is also similar, but double in size.
Describe what had to be done to make the double pyramid.
____________________________________________________
____________________________________________________
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Use prior
knowledge
to make a
prediction.
Conduct an
experiment
to find the
probability.
If you throw a 10-sided polyhedral dice 100 times, what are the
Theoretical and Experimental probabilities of rolling a 7?
Think about it…state your Theoretical probability. _________
Do the experiment…organize your data…find your Experimental
probability. __________
Is everyone’s answer the same? _____
Would averaging all the results give us a better answer? _____
Try it, state your outcome and explain your reasoning.
______________________________________________________
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