One-,
description
Transcript of One-,
![Page 1: One-,](https://reader038.fdocuments.us/reader038/viewer/2022102522/56814326550346895daf90a3/html5/thumbnails/1.jpg)
One-,Two-,
Three-Dimensional Shapes
Duane B. Karlin
CEP 811
June 12, 2011
![Page 2: One-,](https://reader038.fdocuments.us/reader038/viewer/2022102522/56814326550346895daf90a3/html5/thumbnails/2.jpg)
What is DIMENSION?
Dimension is a measure in one direction.
What is GEOMETRY?
Geometry is the study of shapes.
Geometric figures can have one, two, or three dimensions.
![Page 3: One-,](https://reader038.fdocuments.us/reader038/viewer/2022102522/56814326550346895daf90a3/html5/thumbnails/3.jpg)
What is DIMENSION?
Dimension is a measure in one direction.
What is GEOMETRY?
Geometry is the study of shapes.
Geometric figures can have one, two, or three dimensions.
Ready to try Question 8 again?
![Page 4: One-,](https://reader038.fdocuments.us/reader038/viewer/2022102522/56814326550346895daf90a3/html5/thumbnails/4.jpg)
MEASUREMENTS can be in U.S. STANDARD or METRIC.
U.S. STANDARD: inches, feet, yards, miles
METRIC: meter, decimeter, centimeter, millimeter
12 inches = 1 foot3 feet = 1 yard1,760 yards = 1 mile
1 meter = 10 decimeters = 100 centimeters = 1,000 millimeters
U.S. STANDARD conversions are trickier to memorize because they do not have a common converting number.
METRIC conversions are easier to understand because they are multiples of 10.
![Page 5: One-,](https://reader038.fdocuments.us/reader038/viewer/2022102522/56814326550346895daf90a3/html5/thumbnails/5.jpg)
READY TO LEARN ABOUT…
One-dimensional shapes?
Two-dimensional shapes?
Three-dimensional shapes?
Or are you ready to TEST YOUR KNOWLEDGE?
![Page 6: One-,](https://reader038.fdocuments.us/reader038/viewer/2022102522/56814326550346895daf90a3/html5/thumbnails/6.jpg)
One-dimensional shapes are measured in only one direction.
This is defined as the LENGTH.
LINES are a one-dimensional shape.
One-Dimensional Shapes
![Page 7: One-,](https://reader038.fdocuments.us/reader038/viewer/2022102522/56814326550346895daf90a3/html5/thumbnails/7.jpg)
One-dimensional shapes are measured in only one direction.
This is defined as the LENGTH.
LINES are a one-dimensional shape.
One-Dimensional Shapes
Ready to try Question 1 again?
![Page 8: One-,](https://reader038.fdocuments.us/reader038/viewer/2022102522/56814326550346895daf90a3/html5/thumbnails/8.jpg)
Two-Dimensional ShapesTwo-dimensional shapes can be measured in two directions.
Their measurements are LENGTH (or BASE) and WIDTH (or HEIGHT).
Click on a shape or capital word to learn more.
The distance around is PERIMETER.
The enclosed space is AREA.
Want a hint about INTERIOR ANGLES?
![Page 9: One-,](https://reader038.fdocuments.us/reader038/viewer/2022102522/56814326550346895daf90a3/html5/thumbnails/9.jpg)
Quadrilateral means “four-sided” shape.
A Triangle is a “three-sided” shape.
An Octagon is an “eight-sided” shape.
Ready to try Question 9 again?
![Page 10: One-,](https://reader038.fdocuments.us/reader038/viewer/2022102522/56814326550346895daf90a3/html5/thumbnails/10.jpg)
CIRCLERadius
Diameter
CircumferenceCenter
![Page 11: One-,](https://reader038.fdocuments.us/reader038/viewer/2022102522/56814326550346895daf90a3/html5/thumbnails/11.jpg)
CENTER
Center
CENTER: the middle of a circle. It is the same distance from the center to any point on the circle.
![Page 12: One-,](https://reader038.fdocuments.us/reader038/viewer/2022102522/56814326550346895daf90a3/html5/thumbnails/12.jpg)
DIAMETER
Diameter
DIAMETER: a line segment that passes through the center of a circle and has its endpoints on opposite sides of the circle.
![Page 13: One-,](https://reader038.fdocuments.us/reader038/viewer/2022102522/56814326550346895daf90a3/html5/thumbnails/13.jpg)
RADIUSRadius
RADIUS: a line segment with one endpoint at the center of a circle and the other endpoint on the circle.
![Page 14: One-,](https://reader038.fdocuments.us/reader038/viewer/2022102522/56814326550346895daf90a3/html5/thumbnails/14.jpg)
CIRCUMFERENCE
Circumference
CIRCUMFERENCE: the distance around a circle.
![Page 15: One-,](https://reader038.fdocuments.us/reader038/viewer/2022102522/56814326550346895daf90a3/html5/thumbnails/15.jpg)
CIRCUMFERENCE = 2πr
π = 3.14
r = radius
CIRCUMFERENCE, instead of PERIMETER, is used to measure the distance around a CIRCLE.
3 inches
C = 2 x 3.14 x 3
C = 6.28 x 3
C = 18.84
CIRCUMFERENCE = 18.84 inches
![Page 16: One-,](https://reader038.fdocuments.us/reader038/viewer/2022102522/56814326550346895daf90a3/html5/thumbnails/16.jpg)
AREA of a CIRCLE is the INTERIOR space.
AREA = πr2
3 inches
3 inchesA = 3.14 x 32
A = 3.14 x 3 x 3
A = 3.14 x 9
A = 28.26
AREA = 28.26 square inches
![Page 17: One-,](https://reader038.fdocuments.us/reader038/viewer/2022102522/56814326550346895daf90a3/html5/thumbnails/17.jpg)
TRIANGLE
3 sides
3 interior angles
The sum of the 3 interior angles always equal 180°.
The prefix “TRI-” means 3.
INTERIOR means inside.
![Page 18: One-,](https://reader038.fdocuments.us/reader038/viewer/2022102522/56814326550346895daf90a3/html5/thumbnails/18.jpg)
BASE
HEIGHT
AREA of a TRIANGLE = ½ BASE (b) x HEIGHT (h)
A = ½b x h
(6 inches)
(6 inches)
A = ½ x 6 x 6
A = 3 x 6
A = 18 square inches
This formula works for ALL TRIANGLES.
![Page 19: One-,](https://reader038.fdocuments.us/reader038/viewer/2022102522/56814326550346895daf90a3/html5/thumbnails/19.jpg)
Equilateral Isosceles Scalene
Right Acute Obtuse
6 types of TRIANGLES.
Click on a shape to learn more, or learn about AREA.
![Page 20: One-,](https://reader038.fdocuments.us/reader038/viewer/2022102522/56814326550346895daf90a3/html5/thumbnails/20.jpg)
EQUILATERAL TRIANGLE
All interior angles equal 60°.
All three sides are the same length.
(60° + 60° + 60° = 180°)
60°
60°60°
![Page 21: One-,](https://reader038.fdocuments.us/reader038/viewer/2022102522/56814326550346895daf90a3/html5/thumbnails/21.jpg)
ISOSCELES TRIANGLE
Two sides are equal.
The angles opposite of the equal sides are also equal.
REMEMBER: the sum of the interior angles will always equal 180° in a triangle.
![Page 22: One-,](https://reader038.fdocuments.us/reader038/viewer/2022102522/56814326550346895daf90a3/html5/thumbnails/22.jpg)
SCALENE TRIANGLE
All three sides are different lengths.
All interior angles are different, but they still equal 180°.
![Page 23: One-,](https://reader038.fdocuments.us/reader038/viewer/2022102522/56814326550346895daf90a3/html5/thumbnails/23.jpg)
SCALENE TRIANGLE
All three sides are different lengths.
All interior angles are different, but they still equal 180°.
Ready to try Question 6 again?
![Page 24: One-,](https://reader038.fdocuments.us/reader038/viewer/2022102522/56814326550346895daf90a3/html5/thumbnails/24.jpg)
RIGHT TRIANGLE
One angle, opposite the longest side, measures 90°. It is signified by the ☐ symbol.
![Page 25: One-,](https://reader038.fdocuments.us/reader038/viewer/2022102522/56814326550346895daf90a3/html5/thumbnails/25.jpg)
ACUTE TRIANGLE
All 3 interior angles are less than 90°. Equilateral triangles are
an example of an acute triangle, but not all acute triangles are equilateral triangles.
![Page 26: One-,](https://reader038.fdocuments.us/reader038/viewer/2022102522/56814326550346895daf90a3/html5/thumbnails/26.jpg)
OBTUSE TRIANGLE
One interior angle in an obtuse triangle is greater than 90°.
![Page 27: One-,](https://reader038.fdocuments.us/reader038/viewer/2022102522/56814326550346895daf90a3/html5/thumbnails/27.jpg)
QUADRILATERALS
The prefix “QUAD-” means 4, as in a 4-sided figure or shape.
Click on a shape to learn more.
![Page 28: One-,](https://reader038.fdocuments.us/reader038/viewer/2022102522/56814326550346895daf90a3/html5/thumbnails/28.jpg)
PERIMETER of any shape is calculated by adding the sides together.
PERIMETER = distance around a shape
3 inches
3 inches
3 inches 3 inches
PERIMETER = 3 + 3 + 3 + 3
P = 12 inches
![Page 29: One-,](https://reader038.fdocuments.us/reader038/viewer/2022102522/56814326550346895daf90a3/html5/thumbnails/29.jpg)
AREA of a QUADRILATERAL is calculated by multiplying the Length (or Base) by the Width (or Height).
AREA = square units it takes to fill a shape
3 inches
3 inches
AREA = 3 x 3
A = 9 square inches
1 inch
1 inch
1 inch
1 2 3
4 5 6
7 8 9
![Page 30: One-,](https://reader038.fdocuments.us/reader038/viewer/2022102522/56814326550346895daf90a3/html5/thumbnails/30.jpg)
SQUARE
All 4 sides are equal and parallel.
Parallel means the lines always maintain the same distance apart.Parallel lines will never touch.
All interior angles equal 90°.
REMEMBER: A square is a rectangle, but a rectangle is not a square!
![Page 31: One-,](https://reader038.fdocuments.us/reader038/viewer/2022102522/56814326550346895daf90a3/html5/thumbnails/31.jpg)
SQUARE
REMEMBER: A square is a rectangle, but a rectangle is NOT a square!
Ready to try Question 7 again?
![Page 32: One-,](https://reader038.fdocuments.us/reader038/viewer/2022102522/56814326550346895daf90a3/html5/thumbnails/32.jpg)
RECTANGLE
Opposite sides are equal and parallel.
All interior angles equal 90°.
![Page 33: One-,](https://reader038.fdocuments.us/reader038/viewer/2022102522/56814326550346895daf90a3/html5/thumbnails/33.jpg)
RHOMBUS, or DIAMOND
A special type of PARALLOGRAM. All 4 sides are equal and parallel.
Interior angles equal 90°.
![Page 34: One-,](https://reader038.fdocuments.us/reader038/viewer/2022102522/56814326550346895daf90a3/html5/thumbnails/34.jpg)
PARALLELOGRAM
Opposite sides are equal and parallel.
Opposite angles are equal.
![Page 35: One-,](https://reader038.fdocuments.us/reader038/viewer/2022102522/56814326550346895daf90a3/html5/thumbnails/35.jpg)
TRAPEZOID
Has one pair of parallel sides.
![Page 36: One-,](https://reader038.fdocuments.us/reader038/viewer/2022102522/56814326550346895daf90a3/html5/thumbnails/36.jpg)
Area = ½ x (b1 + b2) x h
AREA OF A TRAPEZOID = ½ x (BASE 1 + BASE 2) x HEIGHT
15 inches
10 inches
5 inches
A = ½ x (15 + 10) x 5
A = ½ x (25) x 5
A = 12.5 x 5
AREA = 62.5 square inches
![Page 37: One-,](https://reader038.fdocuments.us/reader038/viewer/2022102522/56814326550346895daf90a3/html5/thumbnails/37.jpg)
Area = ½ x (b1 + b2) x h
AREA OF A TRAPEZOID = ½ x (BASE 1 + BASE 2) x HEIGHT
15 inches
10 inches
5 inches
A = ½ x (15 + 10) x 5
A = ½ x (25) x 5
A = 12.5 x 5
AREA = 62.5 square inches
Ready to try Question 2 again?
![Page 38: One-,](https://reader038.fdocuments.us/reader038/viewer/2022102522/56814326550346895daf90a3/html5/thumbnails/38.jpg)
HINT! Remember, the number of degrees in any geometric shape is 180 x (N – 2), where “N” is equal to the number of sides.
So, with a PENTAGON, 5-sided shape, we would write: 180 x (5 – 2) = 180 x 3 = 540, so the number of degrees in a PENTAGON is 540°.
An OCTAGON, 8-sided shape, has 180 x (8 – 2) = 180 x 6 = 1080°.
A HEXAGON, 6-sided shape, has 180 x (6 – 2) = 180 x 4 = 720°.
![Page 39: One-,](https://reader038.fdocuments.us/reader038/viewer/2022102522/56814326550346895daf90a3/html5/thumbnails/39.jpg)
HINT! Remember, the number of degrees in any geometric shape is 180 x (N – 2), where “N” is equal to the number of sides.
So, with a PENTAGON, 5-sided shape, we would write: 180 x (5 – 2) = 180 x 3 = 540, so the number of degrees in a PENTAGON is 540°.
An OCTAGON, 8-sided shape, has 180 x (8 – 2) = 180 x 6 = 1080°.
A HEXAGON, 6-sided shape, has 180 x (6 – 2) = 180 x 4 = 720°.
Ready to try Question 10 again?
![Page 40: One-,](https://reader038.fdocuments.us/reader038/viewer/2022102522/56814326550346895daf90a3/html5/thumbnails/40.jpg)
SHAPES WITH MORE THAN 4 SIDES
Click on a shape to learn more.
![Page 41: One-,](https://reader038.fdocuments.us/reader038/viewer/2022102522/56814326550346895daf90a3/html5/thumbnails/41.jpg)
PENTAGONNo parallel sides.
All 5 sides can be equal, but they don’t have to be.
Interior angles all equal 540°.
The prefix “PENTA-” means 5.
If each side is equal, then each interior angle equals 108°.
![Page 42: One-,](https://reader038.fdocuments.us/reader038/viewer/2022102522/56814326550346895daf90a3/html5/thumbnails/42.jpg)
PENTAGONNo parallel sides.
The prefix “PENTA-” means 5.
Ready to try Question 5 again?
![Page 43: One-,](https://reader038.fdocuments.us/reader038/viewer/2022102522/56814326550346895daf90a3/html5/thumbnails/43.jpg)
AREA of a PENTAGON
Divide the pentagon into 5 equal triangles.
Divide those triangles in half.
You now have 10 right angle triangles.
The formula for finding the area of a triangle is A = ½ b x h
A = ½ x 3 x 5
A = 1.5 x 5
A = 7.5
But this is only the area for one triangle, so we need to multiply this number by the total number of triangles within the pentagon.
A = 7.5 x 10
AREA = 75 square inches
BASE = 3 inches
HEIGHT = 5 inches
![Page 44: One-,](https://reader038.fdocuments.us/reader038/viewer/2022102522/56814326550346895daf90a3/html5/thumbnails/44.jpg)
HEXAGON
Parallel sides are opposite each other.
The prefix “HEXA-” means 6.
Interior angles all equal 720°.
3 pairs of parallel sides.
If each side is equal, which they do not have to be, then each interior angle equals 120°.
![Page 45: One-,](https://reader038.fdocuments.us/reader038/viewer/2022102522/56814326550346895daf90a3/html5/thumbnails/45.jpg)
OCTAGON
The prefix “OCTA-” means 8.
Interior angles all equal 1080°.
4 pairs of parallel sides.
Parallel sides are opposite each other.
If each side is equal, which they may or may not be, then each interior angle equals 135°.
![Page 46: One-,](https://reader038.fdocuments.us/reader038/viewer/2022102522/56814326550346895daf90a3/html5/thumbnails/46.jpg)
Three-Dimensional Shapes
Three-dimensional shapes are measured in three directions:
length, width, and height.
Three-dimensional shapes also have FACES, VERTICES, and EDGES.
Click on a shape or capital word to learn more.
![Page 47: One-,](https://reader038.fdocuments.us/reader038/viewer/2022102522/56814326550346895daf90a3/html5/thumbnails/47.jpg)
FACES
FACES refers to the sides of a shape.
In this example, the CUBE has 6 faces, but we can only see 3.
REMEMBER: In a three-dimensional shape, you may not always be able to see all of the faces (sides) of the shape.
![Page 48: One-,](https://reader038.fdocuments.us/reader038/viewer/2022102522/56814326550346895daf90a3/html5/thumbnails/48.jpg)
VERTEX (singular), or VERTICES (plural)
A VERTEX is where two or more points meet; a corner.
This example of a RECTANGULAR PRISM has 8 VERTICES.
Once again, not every VERTEX may be visible in a three-dimensional shape.
![Page 49: One-,](https://reader038.fdocuments.us/reader038/viewer/2022102522/56814326550346895daf90a3/html5/thumbnails/49.jpg)
VERTEX (singular), or VERTICES (plural)
A VERTEX is where two or more points meet; a corner.
This example of a RECTANGULAR PRISM has 8 VERTICES.
Ready to try Question 4 again?
![Page 50: One-,](https://reader038.fdocuments.us/reader038/viewer/2022102522/56814326550346895daf90a3/html5/thumbnails/50.jpg)
EDGES
The EDGE of a shape is the line where two surfaces meet.
This CYLINDER has 2 EDGES.
![Page 51: One-,](https://reader038.fdocuments.us/reader038/viewer/2022102522/56814326550346895daf90a3/html5/thumbnails/51.jpg)
CUBE
The CUBE has 6 sides, 8 vertices, and 12 edges.
To find the SURFACE AREA of a CUBE, find the area of one side (L x W), and then multiply by the total number of sides (6). Remember to count all the hidden sides!
3 inches
3 inches
3 inches
SURFACE AREA = (L x W) x 6
= (3 x 3) x 6
= 9 x 6
SURFACE AREA = 54 square inches
SURFACE AREA is the measurement we would use to cover the outside of the shape, like a wrapped package.
![Page 52: One-,](https://reader038.fdocuments.us/reader038/viewer/2022102522/56814326550346895daf90a3/html5/thumbnails/52.jpg)
CUBE
To find the VOLUME of a shape, use this formula: Length x Width x Height.
VOLUME is the amount of space a three-dimensional shape occupies.
VOLUME = L x W x H
4 inches
4 inches
4 inches
VOLUME = 4 x 4 x 4
VOLUME = 64 cubic inches
HINT: “CUBIC” measurement is used with volume because 64 equal-sized cubes would fit into the shape.
![Page 53: One-,](https://reader038.fdocuments.us/reader038/viewer/2022102522/56814326550346895daf90a3/html5/thumbnails/53.jpg)
SPHERETo find the SURFACE AREA of a sphere, use this formula:
SURFACE AREA = 4πr2
8 inches
DIAMETER = 8 inches, so the RADIUS equals 4 inches.
= 4π42
= 4π(4 x 4)
= 4π(16)
=12.56 x 16
SURFACE AREA = 200.96 square inches
Ready to learn about the VOLUME of a SPHERE?
![Page 54: One-,](https://reader038.fdocuments.us/reader038/viewer/2022102522/56814326550346895daf90a3/html5/thumbnails/54.jpg)
SPHERE
8 inches
To calculate the VOLUME of a SPHERE, things get a little tricky.
VOLUME = 4/3 πr3
= 4/3 π (4 x 4 x 4)
= 4/3 x π x 64
= 4.187 x 64
VOLUME = 267.95 cubic inches
The RADIUS is half of the DIAMETER, so half of 8 is 4.
![Page 55: One-,](https://reader038.fdocuments.us/reader038/viewer/2022102522/56814326550346895daf90a3/html5/thumbnails/55.jpg)
CYLINDER
2 inches
6 inches
A CYLINDER is actually two circles (one on the top and one on the bottom) and a rectangle in the middle.
If we cut the middle and lay it flat, it would form a rectangle.
Click on the dotted line to see what the cylinder would look like if it was “dissected.”
![Page 56: One-,](https://reader038.fdocuments.us/reader038/viewer/2022102522/56814326550346895daf90a3/html5/thumbnails/56.jpg)
To see the CYLINDER in this shape makes calculating the SURFACE AREA easier to understand.
SURFACE AREA = 2πr2 + 2πrh
CYLINDER
The formula looks confusing, but it is simply finding the surface area of two circles and one rectangle.
2 inches
6 inches
The circumference of the circle actually forms the base of the rectangle.
= 2π22 + 2π2 x 6
= 2π4 + 2π12
= 6.28 x 4 + 6.28 x 12
= 25.12 + 75.36
SURFACE AREA = 100.48 square inches
![Page 57: One-,](https://reader038.fdocuments.us/reader038/viewer/2022102522/56814326550346895daf90a3/html5/thumbnails/57.jpg)
CYLINDER
Ready to try Question 3 again?
3 faces
![Page 58: One-,](https://reader038.fdocuments.us/reader038/viewer/2022102522/56814326550346895daf90a3/html5/thumbnails/58.jpg)
CYLINDER
To calculate the VOLUME of a CYLINDER, use this formula: V = πr2h
2 inches
6 inchesV = π x 22 x 6
V = π x 4 x 6
V = π x 24
V = 75.36 cubic inches
![Page 59: One-,](https://reader038.fdocuments.us/reader038/viewer/2022102522/56814326550346895daf90a3/html5/thumbnails/59.jpg)
RECTANGULAR PRISM The RECTANGULAR PRISM has 6 sides, 8 vertices, and 12 faces.
To calculate the SURFACE AREA or VOLUME or the RECTANGULAR PRISM, use the same formula as you would for the CUBE.
![Page 60: One-,](https://reader038.fdocuments.us/reader038/viewer/2022102522/56814326550346895daf90a3/html5/thumbnails/60.jpg)
TEST YOUR KNOWLEDGE OF SHAPES
QUESTION 1
How many dimensions does a line have?
ONE TWO THREE AS MANY AS IT NEEDS
![Page 61: One-,](https://reader038.fdocuments.us/reader038/viewer/2022102522/56814326550346895daf90a3/html5/thumbnails/61.jpg)
QUESTION 2
Which of the following formulas would be used to calculate the area of a trapezoid?
A = ½ B x H
A = L x W
A = ½ (Base 1 + Base 2) x Height
A = πr2
![Page 62: One-,](https://reader038.fdocuments.us/reader038/viewer/2022102522/56814326550346895daf90a3/html5/thumbnails/62.jpg)
QUESTION 3
How many faces does a cylinder have?
Three Two Five Eight
![Page 63: One-,](https://reader038.fdocuments.us/reader038/viewer/2022102522/56814326550346895daf90a3/html5/thumbnails/63.jpg)
QUESTION 4
On a three-dimensional shape, what is it called where two or more points meet?
Face Vertex Mystery Party
![Page 64: One-,](https://reader038.fdocuments.us/reader038/viewer/2022102522/56814326550346895daf90a3/html5/thumbnails/64.jpg)
QUESTION 5
How many parallel sides are on a pentagon?
5 3 2 0
![Page 65: One-,](https://reader038.fdocuments.us/reader038/viewer/2022102522/56814326550346895daf90a3/html5/thumbnails/65.jpg)
QUESTION 6
Which of these figures is a scalene triangle?
![Page 66: One-,](https://reader038.fdocuments.us/reader038/viewer/2022102522/56814326550346895daf90a3/html5/thumbnails/66.jpg)
QUESTION 7
True or false? A square is a rectangle and a rectangle is a square.
TRUE FALSE
![Page 67: One-,](https://reader038.fdocuments.us/reader038/viewer/2022102522/56814326550346895daf90a3/html5/thumbnails/67.jpg)
QUESTION 8
What is geometry?
The study of numbers.
The study of shapes.
An example of counting.
What the acorn said when it grew up.
![Page 68: One-,](https://reader038.fdocuments.us/reader038/viewer/2022102522/56814326550346895daf90a3/html5/thumbnails/68.jpg)
QUESTION 9
If I had a quadrilateral, two octagons, and a triangle, how many sides would I have?
19 23 25 15
![Page 69: One-,](https://reader038.fdocuments.us/reader038/viewer/2022102522/56814326550346895daf90a3/html5/thumbnails/69.jpg)
QUESTION 10
WHICH FORMULA WILL HELP ME FIGURE OUT HOW MANY DEGREES ARE IN ANY GIVEN GEOMETRIC SHAPE?
180 x (number of sides - 2)
½ Base x Height x the number of sides
2πr
add the number of sides together
![Page 70: One-,](https://reader038.fdocuments.us/reader038/viewer/2022102522/56814326550346895daf90a3/html5/thumbnails/70.jpg)
EXCELLENT!
![Page 71: One-,](https://reader038.fdocuments.us/reader038/viewer/2022102522/56814326550346895daf90a3/html5/thumbnails/71.jpg)
Oops! Why don’t you try that one again?
Or click here for help!
![Page 72: One-,](https://reader038.fdocuments.us/reader038/viewer/2022102522/56814326550346895daf90a3/html5/thumbnails/72.jpg)
EXCELLENT!
![Page 73: One-,](https://reader038.fdocuments.us/reader038/viewer/2022102522/56814326550346895daf90a3/html5/thumbnails/73.jpg)
Oops! Why don’t you try that one again?
Or click here for help!
![Page 74: One-,](https://reader038.fdocuments.us/reader038/viewer/2022102522/56814326550346895daf90a3/html5/thumbnails/74.jpg)
EXCELLENT!
![Page 75: One-,](https://reader038.fdocuments.us/reader038/viewer/2022102522/56814326550346895daf90a3/html5/thumbnails/75.jpg)
Oops! Why don’t you try that one again?
Or click here for help!
![Page 76: One-,](https://reader038.fdocuments.us/reader038/viewer/2022102522/56814326550346895daf90a3/html5/thumbnails/76.jpg)
EXCELLENT!
![Page 77: One-,](https://reader038.fdocuments.us/reader038/viewer/2022102522/56814326550346895daf90a3/html5/thumbnails/77.jpg)
Oops! Why don’t you try that one again?
Or click here for help!
![Page 78: One-,](https://reader038.fdocuments.us/reader038/viewer/2022102522/56814326550346895daf90a3/html5/thumbnails/78.jpg)
EXCELLENT!
![Page 79: One-,](https://reader038.fdocuments.us/reader038/viewer/2022102522/56814326550346895daf90a3/html5/thumbnails/79.jpg)
Oops! Why don’t you try that one again?
Or click here for help!
![Page 80: One-,](https://reader038.fdocuments.us/reader038/viewer/2022102522/56814326550346895daf90a3/html5/thumbnails/80.jpg)
EXCELLENT!
![Page 81: One-,](https://reader038.fdocuments.us/reader038/viewer/2022102522/56814326550346895daf90a3/html5/thumbnails/81.jpg)
Oops! Why don’t you try that one again?
Or click here for help!
![Page 82: One-,](https://reader038.fdocuments.us/reader038/viewer/2022102522/56814326550346895daf90a3/html5/thumbnails/82.jpg)
EXCELLENT!
![Page 83: One-,](https://reader038.fdocuments.us/reader038/viewer/2022102522/56814326550346895daf90a3/html5/thumbnails/83.jpg)
Oops! Why don’t you try that one again?
Or click here for help!
![Page 84: One-,](https://reader038.fdocuments.us/reader038/viewer/2022102522/56814326550346895daf90a3/html5/thumbnails/84.jpg)
EXCELLENT!
![Page 85: One-,](https://reader038.fdocuments.us/reader038/viewer/2022102522/56814326550346895daf90a3/html5/thumbnails/85.jpg)
Oops! Why don’t you try that one again?
Or click here for help!
![Page 86: One-,](https://reader038.fdocuments.us/reader038/viewer/2022102522/56814326550346895daf90a3/html5/thumbnails/86.jpg)
EXCELLENT!
![Page 87: One-,](https://reader038.fdocuments.us/reader038/viewer/2022102522/56814326550346895daf90a3/html5/thumbnails/87.jpg)
Oops! Why don’t you try that one again?
Or click here for help!
![Page 88: One-,](https://reader038.fdocuments.us/reader038/viewer/2022102522/56814326550346895daf90a3/html5/thumbnails/88.jpg)
EXCELLENT!
![Page 89: One-,](https://reader038.fdocuments.us/reader038/viewer/2022102522/56814326550346895daf90a3/html5/thumbnails/89.jpg)
Oops! Why don’t you try that one again?
Or click here for help!
![Page 90: One-,](https://reader038.fdocuments.us/reader038/viewer/2022102522/56814326550346895daf90a3/html5/thumbnails/90.jpg)
CONGRATULATIONS!
Your knowledge of shapes is out of this world!
Finished? Return HOME or RAISE YOUR HAND for the teacher!