Download Angles and Polygons

Name: ________________________________________
Date:________________
Soccer Goalies
Prediction: In soccer, when a team shoots a penalty shot, the goalie must stand on the goal line
to defend. But, during other times, the goalie can come out as far as he or she wants. Why do
you think soccer rules require a goalie to stand ON the goal line for penalty kicks? Do you think
there is an advantage if a goalie moves closer to the ball?
__________________________________________________________________
__________________________________________________________________
__________________________________________________________________
Data Collection: Each member of your team will shoot the ball from the marked spot 5 times
for each distance the goalie is standing. Record the fraction of shots made for each person from
each distance. Note: a “shot made” means it does not hit the “goalie” and is between or touching
the “goal” posts. See below for a diagram of what you will be doing outside.
Name
Fraction of shots
made with goalie
on goal line
Fraction of shots
made with goalie
12 feet out from
goal line
Fraction of shots
made with goalie
24 feet out from
goal line
Group Totals
Goal Line
Goalie
Goalie
Goalie
Shooting
Location
.
Goalie on Goal Line
.
Goalie 12 ft. out from Goal Line
IMP Activity: Soccer Goalies
.
Goalie 24 ft. out from Goal Line
1
AP S1
Analysis Questions
1. From which distance the goalie was from the goal line did your team score the least fraction
of goals? Write an inequality to show which fraction was the smallest.
2. From which distance the goalie was from the goal line did your team score the greatest
fraction of goals? Write an inequality to show which fraction was the largest.
3. Why do you think your team had a higher fraction of the goals go “in” from that distance?
Use the pictures from the page before to SHOW what path the ball could have followed to make
a goal in EACH of the three scenarios.
__________________________________________________________________
__________________________________________________________________
4. Describe what is different about the path a ball could have followed to score a goal in each of
the three scenarios.
__________________________________________________________________
__________________________________________________________________
__________________________________________________________________
__________________________________________________________________
In math terms, we call the representation of the difference between the paths a ball could
take to score an Angle. What do you think the term angle means? Explain in words and
with a picture.
Words:
_______________________________________________________________________
_______________________________________________________________________
Picture:
IMP Activity: Soccer Goalies
2
AP S2
Name:________________________________________________Date:____________________
Lines and Line Segments
Reference Set #1: Parallel Lines vs. Intersecting Lines
Examples of Pairs of Parallel Lines/Segments
Non-Examples of Pairs of Parallel
Lines/Segments (Examples of Intersecting
Lines)
Draw two more examples of parallel lines or line Draw two more examples of Intersecting Lines
or segments.
segments.
List three places in the real world where you see
a pair of parallel lines.
Use your own words to describe what a pair of
parallel lines is.
1)
2)
3)
Draw a picture of a figure with parallel lines.
!
IMP Activity: Lines & Segments
AP S3
Reference Set #2: Perpendicular Lines
Examples of Pairs of Perpendicular
Lines/segments
Non-Examples of
Pairs of Perpendicular Lines/segments
Draw two more examples of perpendicular
lines/segments.
Draw two more examples of non-perpendicular
lines/segments.
List three places in the real world where you see
a pair of perpendicular lines.
Use your own words to describe what a pair of
perpendicular lines is.
1)
2)
3)
Draw a picture of a figure with perpendicular lines.
!
IMP Activity: Lines & Segments
2
AP S4
Reference Set #3: Lines, Rays and Line Segments
Examples of Lines
Examples of Rays
Examples of Line Segments
Draw two more examples of
Lines.
Draw two more examples of
Rays.
Draw two more examples of
Line Segments.
Use your own words to
describe what a line is.
Use your own words to describe
what a ray is.
Use your own words to
describe what a line segment is.
How are lines, line segments and rays the same?
How are lines, line segments and rays different?
!
IMP Activity: Lines & Segments
3
AP S5
C
B
A
!
IMP Activity: Lines & Segments
6
AP S6
D
E
F
!
IMP Activity: Lines & Segments
7
AP S7
G
H
I
!
IMP Activity: Lines & Segments
8
AP S8
M
L
K
J
!
IMP Activity: Lines & Segments
9
AP S9
O
N
P
!
IMP Activity: Lines & Segments
10
AP S10
Name: ________________________________________ Date:________________
How Does That Spaghetti Intersect?
Part 1: Intersecting Lines: Find all the ways two pieces of spaghetti (lines or line segments)
can be glued down to the same piece of paper. After experimenting, glue down 5 of the ways
you found that you think represent most of the options. Describe what each one represents in
words (e.g., they make a narrow opening at the top).
IMP Activity: How Does That Spaghetti Intersect?
1
AP S11
Part 2: Intersecting Rays: You will now use your spaghetti to investigate all the ways in which
two rays can intersect when sharing a common endpoint. Use two pieces of spaghetti to
represent your two rays and try to find all the ways the two rays can meet to share their endpoint.
Glue down 5 examples you think illustrate most of the options and describe, in words, what each
one represents (e.g., they make perpendicular lines).
IMP Activity: How Does That Spaghetti Intersect?
2
AP S12
Part 3: Sorting Rays that share a common endpoint.
Use the pairs of rays your teacher passes out and sort them into 2 groups: a group that has a
common feature and a group that does not. Try to come up with at least 2-3 ways to sort the
rays. Record the rule you used to sort below each one.
Sort 1
Group 1: Feature/ Rule
Group 2 (Does not have feature)
______________________________________
Sort 2
Group 1: Feature/ Rule
Group 2 (Does not have feature)
______________________________________
Sort 3
Group 1: Feature/ Rule
Group 2 (Does not have feature)
______________________________________
IMP Activity: How Does That Spaghetti Intersect?
3
AP S13
Angle: An angle is formed when two rays share a common endpoint.
Describe what an angle is in your own words and draw a picture (or a few) to show this.
Words:
_______________________________________________________________________
_______________________________________________________________________
Picture:
Part 4: Drawing all possible angles
Begin by gluing down one ray (piece of spaghetti) so that the endpoint is on the point drawn
below. Use your second ray to build and trace all possible angles you can form with this second
piece of spaghetti and the ray (spaghetti) glued down.
Ray 1- glued to
paper
Observation Time!
What shape is made by all possible angles formed by the two rays? _______________________
Draw this shape onto the picture you made above.
IMP Activity: How Does That Spaghetti Intersect?
4
AP S14
Part 5: Defining Fractions and Angles
As you discovered above, all possible angles lie within a circle. Look at the circle below and use
your definition of a fraction to determine what the angle representing ONE of the equal parts is
called.
Defining Fractions:
Start with one whole (the circle) and divide it into ________ equal pieces. We’re talking about 1
of those _________ each pieces when we name the fraction _____________.
Degrees (°): If the angle formed by the two rays represents
1
of the circle, we say this
360
angle measures 1 degree (1°).
IMP Activity: How Does That Spaghetti Intersect?
5
AP S15
Practice Time
1
ths of the circle. Use fraction addition to show what this angle
360
represents. Use degrees to show how many total degrees (°) this angle would be. Recall that
1
= 1 degree (°).
360
1. An angle opens 3
Fractions: _________ + ____________ + ____________ = __________
Degrees: __________ + ____________ + ____________ = __________
1
ths of the circle. Use fraction addition to show what this angle
360
represents. Use degrees to show how many total degrees (°) this angle would be. Recall that
1
= 1 degree (°).
360
2. An angle opens 5
Fractions: ______ + _________ + _________ + _______ + _______ = __________
Degrees: ______ + _________ + _________ + _______ + _______ = __________
1
ths of the circle. Use fraction multiplication to show what this angle
360
represents. Use degrees to show how many total degrees (°) this angle would be. Recall that
1
= 1 degree (°).
360
3. An angle opens 15
Fractions: _________ • ____________ = __________
Degrees: __________ • ____________ = __________
1
ths of the circle. Use fraction multiplication to show what this
360
angle represents. Use degrees to show how many total degrees (°) this angle would be. Recall
1
that
= 1 degree (°).
360
4. 1. An angle opens 45
Fractions: _________ • ____________ = __________
Degrees: __________ • ____________ = __________
IMP Activity: How Does That Spaghetti Intersect?
6
AP S16
Shapes to Sort
IMP Activity: How Does That Spaghetti Intersect?
10
AP S17
Name _________________________________________________________________ Date __________________________ Stacking & Labeling Angles Part 1:Stacking Predict: The largest angle below is Angle ______ because _____________________ ______________________________________________________________________________________ Angle A Angle C Angle B Task 1: Cut out Angles A, B, and C from the extra page by cutting carefully along the straight lines. Task 2: Line up a corner (vertex) of Angle A with the center of the circle. Glue Angle A in the circle. Task 3: Glue Angle B in the circle, stacking it on top of Angle A. Line up the corner (vertex) of Angle B with the corner (vertex) of Angle A. Then, glue Angle C in the circle, stacking it on top of Angle B. Line up the corner (vertex) of Angle C with the corner (vertex) of Angle B. Analysis: 1) What do you notice about angles A, B, and C? __________________________________________________________________________________________ 2) Was your prediction correct? Why or why not? __________________________________________________________________________________________ 3) What is the same about angles A, B, and C? __________________________________________________________________________________________ 4) What is different about angles A, B, and C? __________________________________________________________________________________________ Big Idea: Angles that are equal in measure can be represented by pictures with different length __________________. AP S18
Task 2: Sorting With your group, sort the angles in your envelope into different piles based upon angle measure.. I sorted my angles ___________________________________________________________________ _________________________________________________________________________________________ _________________________________________________________________________________________ What would happen if you stacked and glued the angles from the individual groups on top of one another?________________________________________________________________________ __________________________________________________________________________________________ Task 3: Circle Time How many degrees are in a circle? __________________ What fraction of the circle do angles A, B and C represent? _______________ How many degrees do angles A, B & C represent? _____________ Use fractions to show your calculation: Big Idea: We call an angle measuring 90° a right angle. We show angle is a right angle by drawing a small box in the corner of the angle as shown below. Task 4: Classifying the angles you sorted in Task 2 For each “group” of angles you sorted in task 2, describe them as being a right angle, less than a right angle or greater than a right angle. Glue one angle from each group below and record the name you gave that group. Big Idea: We call an angle measuring greater than 90°, an obtuse angle. We call an angle measuring less than 90°, an acute angle, Label each group glued above as right, obtuse or acute. AP S19
Angles for Task 1: Stacking Angle A Angle A Angle B Angle C Angles for Task 1: Stacking Angle B Angle C IMP Activity: Stacking & Labeling Angles 3 AP S20
center IMP Activity: Stacking & Labeling Angles 4 AP S21
Angles for Task 2: Sorting
33°
10°
120° IMP Activity: Stacking & Labeling Angles 8 AP S22
90°
IMP Activity: Stacking & Labeling Angles 9 AP S23
IMP Activity: Stacking & Labeling Angles 10 AP S24
Name: ________________________________________ Date:________________
Doing a 180
Task 1: Your team will be assigned a starting ray (shown in the
picture below)and a direction in which you must perform a turn.
Use string or a meter stick to represent the starting ray, and then
have a student model the turn with their body. Record what the
angle formed by your body and the original ray looks like on your page below.
1: Open Counter Clockwise
1
turn
4
Team 2: Open Clockwise
1
turn
4
Team 3: Open Clockwise
1
turn
4
1
turn
2
1
turn
2
1
turn
2
3
turn
4
3
turn
4
3
turn
4
Full turn
Full turn
Full turn
4: Open Counter Clockwise
1
turn
4
Team 5: Open Clockwise
1
turn
4
Team 6: Open Clockwise
1
turn
4
1
turn
2
1
turn
2
1
turn
2
3
turn
4
3
turn
4
3
turn
4
Full turn
Full turn
Full turn
Question: Does the direction in which the angle opens affect its measure? Why or why not?
___________________________________________________________________________
IMP Activity: Doing a 180
1
AP S25
Task 2: Labeling the Angles with Degrees
Recall: How many degrees are in a circle? ________________
1
1. How many degrees are there in a quarter ( ) turn of a circle? ____________
4
1
Show your math below and label all the turns above with degrees.
4
1
2. How many degrees are there in a half ( ) turn of a circle? ____________
2
1
Show your math below and label all the turns above with degrees.
2
3
3. How many degrees are there in a three-quarter ( ) turn of a circle? ____________
4
3
Show your math below and label all the turns above with degrees.
4
4. How many degrees are there in a full turn in a circle? ____________
Show your math below and label all the full turns above with degrees.
5. What does it mean for someone to do a “180”? Explain in words and with a picture.
Words: _______________________________________________________________
____________________________________________________________________
Picture:
6. Professional snowboarders can do a trick called a “720”. What do you think this means?
Explain in words and with a picture.
Words: _______________________________________________________________
____________________________________________________________________
Picture:
IMP Activity: Doing a 180
2
AP S26
Task 3: Benchmark Angles
In addition to a 90°, a 180°, and a 270° angle, there are other common angles we use in math.
1. Fold your 90° angle in half (2 equal parts).
a) How many degrees is this angle? ________________
b) Show the math you used to determine this.
c) What fraction of the circle does this angle represent?
d) Show the math you used to determine this.
e) Trace this new angle onto page 1 for each of the “teams” in the same box that shows the 90°
turn and label this as a fraction and with degrees.
2. Fold your 90° angle into thirds (3 equal parts).
a) How many degrees is this angle? ________________
b) Show the math you used to determine this.
c) What fraction of the circle does this angle represent?
d) Show the math you used to determine this.
e) Trace this new angle onto page 1 for each of the “teams” in the same box that shows the 90°
turn and label this as a fraction and with degrees.
Benchmark Angles: Common angles we use to estimate or compare angles.
Draw a sketch of each benchmark angle below.
90°
45°
IMP Activity: Doing a 180
30°
180°
270°
3
AP S27
Name: ________________________________________
Date:________________
Building a Protractor
Task 1: Starting with each ray below and your 90° angle, draw a sketch (and label near the end
of the ray) of the following angles: 30°, 45°, 90°, 180°, 270°. Be precise in your drawing.
Opening up from a ray pointing to the right
0° or _____°
Opening up from a ray pointing to the left.
0° or _____°
IMP Activity: Building a Protractor
1
AP S28
Task 2: Using your pictures above, estimate the measure (in degrees) of each angle shown
below. Record the estimate in the Estimate 1 column and also list if the angle is acute, right or
obtuse.
Angle
Estimate 1
Estimate 2
Actual
1.
2.
3.
4.
5.
6.
IMP Activity: Building a Protractor
2
AP S29
7.
8.
9.
10.
Task 3:
Predict: How can we be more precise in our estimates? _________________________________
_____________________________________________________________________________
Your teacher will now give you a 10° angle. What fraction of the circle is a 10° angle? _______
Use your ten degree angle to add more detail to your drawings on page 1. Beginning at 0°,
sketch a ray to represent each 10° angle and label the angles at the end of the ray in increments
of 10. When you are done, you should have a picture labeled from 0° to 360° counting by 10’s.
Repeat the same process for the picture opening up from a ray pointing to the left (you will have
to begin with your angle by the 0°!)
IMP Activity: Building a Protractor
3
AP S30
Task 4: Estimation #2
Using what you have built on page 1 to be more precise in measuring angles, estimate the
measure of each of the 10 angles from task 2 and record your new (or the same if you have not
modified your original estimate) estimate.
Task 5: Building the rest of the protractor
Predict: How can we be more precise in our estimates? _________________________________
_____________________________________________________________________________
Go back to each of the pictures you were drawing on page 1.
Draw a circle to represent the path the opening ray will follow as it slowly turns. This circle
should be marked and show every 10°. Label every 5° with a dash and a number and then use
small tick marks to divide each 10° into 1° increments. Do this for both models on page 1.
You have now built a protractor.
What do you think a protractor is? __________________________________________________
______________________________________________________________________________
What is a protractor used for? _____________________________________________________
_____________________________________________________________________________
Task 6: Your teacher will now give you a protractor built to be precise to the nearest 1°. Try to
use this protractor to measure the 10 angles from pages 2-3 and record what you think the exact
measurement is in the final column (note: your final measurement should be CLOSE to your
estimates; if not, look at how you are using the protractor!).
IMP Activity: Building a Protractor
4
AP S31
Name: ________________________________________ Date:________________
Navigating in the Dark
Navigating Outside
Your group will go outside with a piece of chalk, a protractor and a
meter stick. You will mark a starting point on the ground and then
follow a series of directions to end up at another point. Your team
then must determine what steps to take to get back “home” (to the starting location). These steps
should be detailed enough that someone could follow them in the pitch dark (assuming they
could read the protractor and meter stick!) Assign the following roles in your group: walker,
distance measurer, angle measurer, recorder. The recorder will take a sheet of blank paper to
draw a sketch of the path you took from start until end. Note: it is up to you to decide what path
you would like to take to get back to the start!
Task 1
Step
What to Do
1
From your starting point, walk forward 3 meters.
2
Turn 45° left.
3
Walk forward 1 meter.
4
Turn 45° left.
5
Walk forward 2 meters.
6
Turn 100° left.
7
Walk forward 2 meters
8
9
10
11
12
Task 2
Step
What to Do
1
Walk right 2 meters.
2
Turn 360°
3
Walk forward 2 meters.
4
Turn 90° right
5
Walk forward 1 meter.
6
Turn 45° right.
7
Walk backwards 3 meters.
8
9
10
11
12
Question: Will every group’s picture of the path they took look the same? Why or why not?
___________________________________________________________________________
IMP Activity: Navigating in the Dark
1
AP S32
Navigating a Ship Scenario:
You have been given the all-important task of creating the path for a ship
to take so that it can navigate in the dark safely through many islands.
Navigating a Ship Task:
For the map you’ve been given, determine the path the boat should take to get safely from the
point labeled “here” to the point labeled “there”. Use a protractor and a ruler (measure to the
nearest mm) to determine the path the boat should take to avoid crashing into land. Number and
record the steps on the page provided.
Testing Your Path:
Once your directions are written, trade them with another person at your table (give only the
directions, not the map). With the directions you have been given, draw out the path on a piece
of blank paper. When you think you’ve successfully “navigated” your ship, ask your partner for
the original map. Then overlay your path onto the map to see if you’ve made it safely!
Step
What to Do (include direction, angle, distance, etc)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
Summary Questions
1. Did your ship make it safely? ____________
2. If not, what wentwrong?
___________________________________________________________________________
3. When is it important to be precise in our measurements?
___________________________________________________________________________
IMP Activity: Navigating in the Dark
2
AP S33
Map 1
**Start**
•
**End**
•
IMP Activity: Navigating in the Dark
4
AP S34
Map 2
**End**
•
•
**Start**
IMP Activity: Navigating in the Dark
5
AP S35
Map 3
**Start**
•
•
**End**
IMP Activity: Navigating in the Dark
6
AP S36
Name: ________________________________________ Date:________________
Revisiting Soccer Goalies: Cutting Angles
Opening Question: In soccer, what do you think it means for the goalie to “cut down the
shooter’s angle?” Record your idea with words and a picture below.
__________________________________________________________________
__________________________________________________________________
Picture:
Opening Scenario: While you were at school, your little brother found a 90° from your school
work and decided to cut it as shown by the dotted line below (thankfully he cut through the
vertex).
Is the angle still 90°? _______ Why or why not? _____________________________________
___________________________________________________________________________
Investigation: Each member of your team will begin with a 90° angle. Each of you will choose
to make 1, 2, or 3 cuts through the vertex of your angle. Once cut, measure each “new” angle
with the protractor and record the measure of each angle. Glue the angles back together at the
vertex to show what the sum of the angles should be and then use math to show that the angles
are or are not still equal to 90°.
Angles Glued Together:
Math to show angles still form or no longer form a 90° angle. (Bonus: Use a number bond
to show this!)
_____________________________________________________________________
IMP Activity: Revisiting Soccer Goalies: Cutting Down Angles
1
AP S37
Big Idea Questions
1. How is decomposing an angle (cutting it into smaller angles) similar to decomposing a
number (such a 10 or 90)?
_____________________________________________________________________
_____________________________________________________________________
2. How is it different?
_____________________________________________________________________
_____________________________________________________________________
A Lost Piece I
Your brother thought it was fun to continue cutting your angles when you were gone at school,
but he usually taped them back together so that you never knew. One day, he cut a right angle
into 3 angles (through the vertex of course), but he lost one of the angles. Below are the two
angles he has.
1. What is the measure of the angle he lost? _________
2. Explain how you determined this.
_____________________________________________________________________
_____________________________________________________________________
A Lost Piece II
Your brother is back at his cutting. This time, he cut a 180° into 4 angles (through the vertex of
course), but he again lost one of the angles. Below are the three angles he has.
1. What is the measure of the angle he lost? _________
2. Explain how you determined this.
_____________________________________________________________________
_____________________________________________________________________
IMP Activity: Revisiting Soccer Goalies: Cutting Down Angles
2
AP S38
Angle Puzzles
Your brother got out of control with his angle cutting one day while you and two friends were
outside playing. He cut everyone’s and does not know how to put them back together. Below
are all of the pieces he has. Before he began cutting (through the vertex of each angle), there
was one 90° angle, one 180° angle and one 140° angle.
Put the three original angles back together. Glue the angles and use a math sentence to show that
each set of smaller angles really add up to the sum of the angle from which they were cut.
IMP Activity: Revisiting Soccer Goalies: Cutting Down Angles
3
AP S39
Revisiting the Soccer Goalie
1. What do you think it means for a goalie to “cut down the shooter’s angle?”
__________________________________________________________________
__________________________________________________________________
2. Using the pictures below, draw angles to represent the path the ball could take form the
shooting location to score (the vertex should be on the shooting location).
Scenario 1
Scenario 2
Scenario 3
Goal Line
Goalie
Goalie
Goalie
Shooting
Location
Goalie on Goal Line
Goalie 12 ft. out from Goal Line
Goalie 24 ft. out from Goal Line
3. Find the sum of the two angles representing the paths the ball could take to score in EACH of
the three scenarios above. Use the table below to organize your information.
Scenario 1
Measure Angle 1:
Measure Angle 2:
Sum:
Measure Angle 1:
Scenario 2
Measure Angle 2:
Sum:
Measure Angle 1:
Scenario 3
Measure Angle 2:
Sum:
4. Compare the total angle a shooter could use to make a goal (sum) for each of the three
scenarios. Write a math sentence to show what you see.
5. What does it mean, mathematically, to cut down a shooter’s angle?
__________________________________________________________________
__________________________________________________________________
IMP Activity: Revisiting Soccer Goalies: Cutting Down Angles
4
AP S40
90° Angle for students to use in the Investigation
90° Angle for students to use in the Investigation
90° Angle for students to use in the Investigation
90° Angle for students to use in the Investigation
IMP Activity: Revisiting Soccer Goalies: Cutting Down Angles
7
AP S41
Name: ________________________________________ Date:________________
Sorting Shapes
Sort 1: Sort your shapes into piles based on the number of sides of each polygon. As a group
presents, write a definition for each category of the Polygons and list the letters of the shapes that
meet this criteria.
Triangle: ________________________________________________________________
_________________________________________________________________________
Quadrilateral: _____________________________________________________________
_________________________________________________________________________
Pentagon: ________________________________________________________________
_________________________________________________________________________
Hexagon: ________________________________________________________________
_________________________________________________________________________
Sort 2: Sort the pentagons into 2 piles. Then sort the hexagons into 2 piles. Record a rule for
your sort below and be prepared to share.
Rule for pentagon sort:
___________________________________________________________
_____________________________________________________________________________
Rule for hexagon sort: __________________________________________________________
_____________________________________________________________________________
Shape Q is a regular pentagon. Measure its sides and angles and define what it means for a
pentagon to be regular:
__________________________________________________________________________
Shape R is a regular hexagon. Measure its sides and angles and define what it means for a
hexagon to be regular:
__________________________________________________________________________
IMP Activity: Sorting Shapes
1
AP S42
Sort 3: Take all of your quadrilaterals and sort them into 2 groups: a group that has a key
feature and a group that does not have that key feature. Record the letters of your sort as well as
your rule below.
Quadrilaterals that have this feature: _______________________________________________
Quadrilaterals that do not have this feature: __________________________________________
Feature/Rule: __________________________________________________________________
Sort 4: Find all the quadrilaterals that have NO parallel lines. Record the letters of these shapes.
Note: The name we have for this group is simply the term, quadrilateral
Quadrilaterals with NO parallel lines: _______________________________________________
Sort 5: Sort the quadrilaterals that have parallel lines into those with 1 set of parallel lines and
those with 2 sets and record the letters of each group’s shapes below.
Quadrilaterals with exactly 1 set of parallel lines are called trapezoids: ____________________
Quadrilaterals with 2 sets of parallel lines are called parallelograms: ______________________
Sort 6a: Sort the parallelograms into 2 groups, one group where all parallelograms have a right
angle and a group of parallelograms that do not have a right angle. List the letters of the shapes
below.
Parallelograms with a right angle are called rectangles: ________________________________
Parallelograms without a right angle are simply called parallelograms: ___________________
Sort 6a: Sort the parallelograms into 2 groups, one group where all parallelograms have all four
side lengths the same measure and one where the four side lengths are not all the same.. List the
letters of the shapes below.
Parallelograms with four equal side lengths are called rhombi (this is plural for rhombus):
___________________________
Parallelograms without four equal side lengths are simply called parallelograms: _____________
IMP Activity: Sorting Shapes
2
AP S43
Sort 7: Sort the rectangles into 2 groups based upon the lengths of the sides. List the letters of
the shapes below.
Rectangles with 4 equal sides are called squares: _____________________________________
Sort 8: Measure the side lengths (in cm) and angles of each triangle and record the information
in the table below.
Triangle
Side Lengths (cm)
Angle Measures
Type
A
B
C
D
E
F
G
Triangles!!
Right Triangles contain exactly one 90° angle. List which triangles are right triangles:
________
Acute Triangles have all three angle measures less than 90°. List which triangles are acute
triangles: ________
Obtuse Triangles have exactly one angle measure greater than 90°. List which triangles are
obtuse triangles: ________
Equilateral Triangles have all three congruent (equal in measure) side lengths. List which
triangles are equilateral triangles: ________ Bonus: what do you notice about the angles of
equilateral triangles? _________________
Isosceles Triangles have exactly two congruent (equal in measure) side lengths. List which
triangles are isosceles: _______________________ Bonus: what do you notice about the
angles of isosceles triangles? _________________
Scalene Triangles have no congruent (equal in measure) side lengths. List which triangles are
scalene: _______________________
IMP Activity: Sorting Shapes
3
AP S44
A
B
C
D
E
F
IMP Activity: Sorting Shapes
6
AP S45
G
H
I
J
K
L
IMP Activity: Sorting Shapes
7
AP S46
M
N
O
P
IMP Activity: Sorting Shapes
8
AP S47
Q
R
S
T
U
V
IMP Activity: Sorting Shapes
9
AP S48
Name:_____________________________________ Date:____________ Period:__________
Cutting Corners
Directions: Below each shape, write the name of the shape (be as specific as possible).
1)
2)
Directions for making posters:
Begin with your assigned shape. Make 1 straight cut through the shape to get two new shapes. Tape the
2 new shapes on the poster (so it looks like the original shape) and then label the two shapes with a noun
and as many adjectives as you think apply. Continue doing this to the same original shape (beginning
with a new copy each time) to get as many different shapes as possible.
IMP Activity: Cutting Corners©
1
AP S49
Challenge Questions
Directions: Answer each question BOTH in words and with a picture to explain your thinking.
1. Can a triangle have more than 1 obtuse angle? Why or why not?
2. Can a trapezoid be called “right”? Why or why not?
3. Can a triangle have two right angles? Why or why not?
4. Can a right triangle also be isosceles? Why or why not?
5. Can a trapezoid be isosceles? Why or why not?
6. Can an equilateral triangle be obtuse? Why or why not?
IMP Activity: Cutting Corners©
2
AP S50
Ticket Out The Door
Directions: Below each shape, write the name of the shape (be as specific as possible).
1)
IMP Activity: Cutting Corners©
2)
6
AP S51
Starting Shape: Parallelogram
IMP Activity: Cutting Corners©
7
AP S52
Starting Shape: Trapezoid
IMP Activity: Cutting Corners©
8
AP S53
Starting Shape: Rectangle
IMP Activity: Cutting Corners©
9
AP S54
Starting Shape: Triangle
IMP Activity: Cutting Corners©
10
AP S55
Starting Shape: Square
IMP Activity: Cutting Corners©
11
AP S56
Name:______________________________________________ Date:____________
Can You Make What I Have?
In the space below, use your ruler and protractor to draw a single figure that has all of the following
properties:
• The figure is composed of between 4 and 6 lines, rays or segments. (Make sure to label points with
letters)
• The figure includes at least one right angle.
• The figure includes at least one obtuse angle.
• No part of the figure is disconnected from the rest.
• The figure encloses some area.
Below or on the reverse write directions that would tell someone how to draw your figure without
having seen it. Consider using some of the sentence frames provided and the word bank to help you
write your directions. Also make sure to label your vertices with letters!
My Creation
Sentence Frames:
Draw a _____________ line ________ cm long.
Label this point _________________.
From ________________, draw ______________.
Directions for making my figure.
Word Bank
Parallel
Perpendicular
Line
Line Segment
Ray
Point
Vertical
Horizontal
Acute
Obtuse
Right
Intersecting
Angle
Degree
CM/ Inch
Vertex
1.) _________________________________________________________________________________
__
_________________________________________________________________________________
2.) _________________________________________________________________________________
__
_________________________________________________________________________________
3.) _________________________________________________________________________________
__
_________________________________________________________________________________
4.) _________________________________________________________________________________
__
_________________________________________________________________________________
IMP Activity: Can You Make What I Have?
1 AP S57
5.) _________________________________________________________________________________
__
_________________________________________________________________________________
6.) _________________________________________________________________________________
__
_________________________________________________________________________________
7.) _________________________________________________________________________________
__
_________________________________________________________________________________
8.) _________________________________________________________________________________
__
_________________________________________________________________________________
9.) _________________________________________________________________________________
__
_________________________________________________________________________________
10.) ________________________________________________________________________________
__
________________________________________________________________________________
IMP Activity: Can You Make What I Have?
2 AP S58
Name: ________________________________________ Date:________________
Not All Designs Are Created Equal
Task 1: Sort the pictures you have been given into two groups: in one group put all the pictures
have a certain feature and in the other group put the pictures that do NOT share that feature.
Record the letter of the pictures in each group as well as your rule for sorting. Come up with at
least 3 different ways to sort the pictures.
Sort 1: Rule ________________________________________________________________
__________________________________________________________________________
Pictures that fit this rule: _____________________________________
Pictures that do NOT fit this rule: _______________________________
Sort 2: Rule ________________________________________________________________
__________________________________________________________________________
Pictures that fit this rule: _____________________________________
Pictures that do NOT fit this rule: _______________________________
Sort 3: Rule ________________________________________________________________
__________________________________________________________________________
Pictures that fit this rule: _____________________________________
Pictures that do NOT fit this rule: _______________________________
Teacher’s Sort: Rule _________________________________________________________
__________________________________________________________________________
Pictures that fit this rule: _____________________________________
Pictures that do NOT fit this rule: _______________________________
IMP Activity: Not All Designs are Created Equal
1
AP S59
Line of Symmetry: A line that could be drawn through a 2-Dimensional picture or shape
such that the figure can be folded on the line into matching parts.
Task 2: Try to fold the designs in pictures A, C, E, G, I and K along the line of symmetry to
show that the pictures are really symmetrical. Try to do the same thing for the other 6 pictures
and be prepared to show that those pictures are NOT symmetrical.
Task 3: Investigating Polygons for symmetry.
Predict: Which polygons do you think will have a line of symmetry?
_____________________________________________________________________________
_____________________________________________________________________________
_____________________________________________________________________________
You will use the shapes you sorted for the Sorting Shapes lesson to investigate which polygons
have a line of symmetry. After trying to fold the shape to find out if it does have a line of
symmetry, draw a sketch below of the ones that do and show where the line of symmetry is.
IMP Activity: Not All Designs are Created Equal
2
AP S60
Task 4: Drawing the other half
For each shape below, only half of the shape is showing. Assume a line of symmetry was used
to show you just half of the picture. Use this information to draw the other half of the picture.
IMP Activity: Not All Designs are Created Equal
3
AP S61
C
K
A
IMP Activity: Not All Designs are Created Equal
F
B
L
6
AP S62
E
I
D
H
G
IMP Activity: Not All Designs are Created Equal
J
7
AP S63