Download 3 gr Geometry, time Study Guide

Study Guide
3 gr Geometry, time
01/21/2010
Symmetry - A
A symmetric figure is one that can be folded in half so that the two halves match exactly (or are the same size
and shape). The letter "A" is a symmetrical figure. It can be folded in half evenly. It does not change
appearance when held to a mirror.
One artistic way to help the student understand symmetry is for you to draw half of a simple shape (such
as a square, circle, triangle, or heart) on a piece of paper and have the student draw the other half. Fold
the paper on the halfway line and compare to see if both sides match.
In the following figures, the dotted lines are lines of symmetry.
Time - C
At this level, students should be able to tell time. In addition, they should be familiar with how to add and
subtract time.
It is recommended that students use an actual clock (non-digital) when learning to tell time. Set the
hands at different positions and have the student tell the time.
In addition, ask the student to add or subtract time from the clock. For example, if the clock is set at
5:15, what time will it be in two hours? (Answer = 7:15)
Lines
A line is a straight path extending in both directions with no endpoints. Students must identify sets of lines,
such as parallel lines.
It is important for the student to understand the different types of lines.
Intersecting lines are lines that meet or cross. Intersecting lines have only one point in common.
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A diagonal is a line segment that joins two vertices of a polygon, but is not a side of the polygon. For
example, each of the four corners of a rectangle are labeled (ABCD).
A diagonal goes through the middle of the rectangle, connecting either BD or AC.
Parallel lines are lines in the same plane that do not intersect. Parallel lines have no points in common.
Perpendicular lines are two lines that intersect and form right angles. Perpendicular lines have only one
point in common.
Horizontal lines run parallel to the horizon (left-right).
Vertical lines run perpendicular to the horizon (up-down).
Figures - B
Students must identify various geometric figures.
A creative method for improving this skill is to help the student draw the geometric figures commonly
studied in this grade. After he or she has drawn all the figures, develop a series of flash cards. On one
side of the card, draw the figure. On the other side, write the name of the figure. The following are
figure definitions to help you get started:
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Cylinder - a solid with two bases that are congruent circles
Sphere - a solid with all points at a fixed distance from the center
Cone - a solid with one circular face and one vertex
Pyramid - a solid with one face that is a polygon and three (or more) faces that are triangles with a
common vertex
Cube - a rectangular prism with six congruent square faces
Example 1: How many triangles are there in this figure?
Step 1: Count the obvious triangles - the outside of the figure is one triangle and there are 6 obvious
triangles inside the figure.
Step 2: Count the triangles in the figure that are not obvious. (see diagrams below)
Step 3: Count the total number of triangles.
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1 + 6 + 2 + 2 + 2 = 13
Answer: There are 13 triangles in the figure.
Identify Squares and Rectangles
This skill requires students to distinguish between squares and rectangles. Students may be asked to determine
which picture has a square or rectangle in it, to determine the number of squares or rectangles in a figure, or to
identify the set of figures that contains the appropriate number of squares and/or rectangles. The definitions
below will help the student learn the differences between squares and rectangles.
A rectangle is a closed four-sided figure in which the opposite sides are parallel (they will never
intersect or cross) and congruent (exactly the same length), and all four angles are congruent (exactly the
same measure).
Examples of Rectangles:
A square is a closed four-sided figure in which the opposite sides are parallel and all four sides are
exactly the same length. Although a square is technically a type of rectangle, students at this level
typically do not consider squares to be rectangles.
Examples of Squares:
Example 1:
Which set has one square?
A. is not the correct answer. There are two squares in answer choice A.
B. is not the correct answer. There are three squares in answer choice B.
C. is the correct answer. There is exactly one square in answer choice C.
D. is not the correct answer. There are no squares in answer choice D.
Example 2:
How many squares are in the figure?
Step 1: There are four squares in the middle and there is one square above each rectangle, for a total of
six squares so far.
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Step 2: The four squares in the middle combine to make one large square.
Answer: There are 7 squares in the figure.
Example 3:
Which picture has a square in it?
A. is the correct answer. There is a square on the space man's chest.
B. is not the correct answer. There are no squares or rectangles in this picture.
C. is not the correct answer. There are rectangles in the spaceship, but no squares.
D. is not the correct answer. There is a rectangle at the base of the satellite dish, but there are no
squares.
A fun activity that will reinforce the skill of recognizing squares and rectangles is to take a walk around
the neighborhood, park, or mall. Have the student point out squares and rectangles that are visible as he
or she is walking around. Help the student verify that the shapes he or she points out are actually
squares or rectangles.
Geometric Figures - B
Geometric figures are figures that are used when discussing and studying geometry. Geometric figures can
include plane figures, angles, lines, points, and segments. Plane figures are closed two-dimensional geometric
figures. Examples of plane figures are squares, rectangles, triangles, circles, ovals, diamonds, and
parallelograms. The examples below will help the student recognize the different ways in which geometric
figures can be displayed.
Rectangles:
A rectangle is a closed four-sided figure in which the opposite sides are parallel (they will never
intersect or cross) and congruent (exactly the same length), and all four angles are congruent (exactly the
same measure).
Examples of Rectangles:
Squares:
A square is a closed four-sided figure in which the opposite sides are parallel and all four sides are
congruent. Although a square is technically a type of rectangle, students at this level typically do not
consider squares to be rectangles.
Examples of Squares:
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Triangles:
A triangle is a closed three-sided figure.
Examples of Triangles:
Ovals:
An oval is an oblong curved figure that is similar to the shape of an egg.
Examples of Ovals:
Circles:
A circle is a closed curve in which every point is equally distant from a fixed point, the center.
Examples of Circles:
Diamonds:
A diamond is a closed four-sided figure in which two inner angles are obtuse (larger than 90º ) and the
other two inner angles are acute (less than 90º ).
Examples of Diamonds:
Parallelograms:
A parallelogram is a closed four-sided figure in which the opposite sides are parallel and congruent.
Although squares, rectangles, and diamonds are all types of parallelograms, students at this level
typically do not make these considerations. Students at this level generally consider parallelograms to
look like the examples below.
Examples of Parallelograms:
Points:
A point is a single spot that shows location only.
Example of a Point:
Lines:
A line is a geometric figure formed by an infinite set of points that form a straight path extending in
opposite directions. A line is drawn with an arrow on each end to show that it continues forever in both
directions.
Examples of Lines:
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Line Segments:
A line segment is the part of a line that is between any two points on the line. Line segments have
definite end points and do NOT continue in both directions forever.
Examples of Line Segments:
Rays:
A ray is a geometric figure formed by an infinite set of points that form a straight path extending in one
direction. A ray continues in one direction forever.
Examples of Rays:
Angles:
An angle is a geometric figure formed by two lines or line segments that meet at a single point or by two
rays that begin at the same point.
Examples of Angles:
It is important to note that lines, line segments, rays, and angles NEVER contain curves.
Once the student is familiar with these geometric figures, he or she should be able to identify them when
given a group of geometric figures to choose from.
Example 1:
Which group of shapes has a circle and a square?
A. is not the correct answer. There is a circle, but there is no square.
B. is not the correct answer. There is a square, but there is no circle.
C. is not the correct answer. There is a square, but there is no circle.
D. is the correct answer. There is a square and a circle.
Example 2:
Choose the ray.
A. is not the correct answer. This is an angle.
B. is not the correct answer. This is a curve.
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C. is the correct answer. This is a ray.
D. is not the correct answer. This is a line segment.
One way to reinforce these concepts is to cut index cards in half, then draw a geometric figure on one
half of the card and write the corresponding name on the other half of the card. Shuffle the cards, place
them on a flat surface, and have the student match them up. This can easily be made into a game by
timing how long it takes the student to match them all up.
Similar Figures - A
Similar figures are figures that have the same shape, but not necessarily the same size.
Imagine that you have reduced or enlarged a figure in a photocopy machine - the figure has the same
shape, but not the same size. The figures below are similar figures (they have exactly the same shape,
but they are different sizes).
The figures below are NOT similar because they are not exactly the same shape.
The following are ways to determine that figures are NOT similar:
• The figures are the same height, but different widths.
• The figures are the same width, but different heights.
• One figure is wide and short, while the other figure is tall and skinny (as in the case above).
Example 1:
Which two shapes are similar?
Solution:
A. is not the correct answer. The first triangle is short and wide, while the second triangle is tall and
skinny.
B. is the correct answer. The shape of the triangles is the same and they are different sizes.
C. is not the correct answer. The triangles appear to be the same width, but they are different heights,
so the triangles are not exactly the same shape.
D. is not the correct answer. The triangles appear to be close to the same height, but one triangle is
much skinnier than the other. Therefore, the triangles are not the same shape.
Example 2:
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Choose the pair of similar shapes.
Solution:
A. is not the correct answer. The hexagons appear to be close to the same height, but one is much
skinnier than the other. Therefore, the hexagons are not exactly the same shape.
B. is not the correct answer. One of the flowers is fatter and the other is longer. Therefore, the flowers
are not exactly the same shape.
C. is the correct answer. The shape of the ovals is the same, and they are different sizes.
D. is not the correct answer. The rectangles appear to be the same width, but one rectangle is much
taller than the other. Therefore, the rectangles are not exactly the same shape.
Try the following activity to help reinforce this skill. Cut out different shapes, some that are similar
and others that are not. Mix up the shapes and have the student choose the similar figures. This could
be made into a game in which each person gets a turn to choose a pair of similar figures. Another
activity might involve taking a picture of a cartoon character, drawings of miscellaneous shapes, or other
images to a local copy store. Use the reduction or enlargement feature to change the size of each image
in several different ways. The results will be figures that are similar to the originals.
Identify Shapes in Real World Figures
Plane figures are two-dimensional geometric figures. Students need to be able to identify squares, rectangles,
triangles, circles, ovals, and diamonds by sight and to identify the word names of the figures. In this skill,
students will be asked to find geometric shapes in real world figures. The examples below will help the student
recognize the different ways in which these shapes can be displayed.
Rectangles:
A rectangle is a closed four-sided figure in which the opposite sides are parallel (they will never
intersect or cross) and congruent (exactly the same length), and all four angles are congruent (exactly the
same measure).
Examples of Rectangles:
Squares:
A square is a closed four-sided figure in which the opposite sides are parallel and all four sides are
congruent. Although a square is technically a type of rectangle, students at this level typically do not
consider squares to be rectangles.
Examples of Squares:
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Triangles:
A triangle is a closed three-sided figure.
Examples of Triangles:
Ovals:
An oval is an oblong curved figure that is similar to the shape of an egg.
Examples of Ovals:
Circles:
A circle is a curve in which every point is equally distant from a fixed point, the center.
Examples of Circles:
Diamonds:
A diamond is a closed four-sided figure in which two inner angles are obtuse (larger than 90º ) and the
other two inner angles are acute (less than 90º ).
Examples of Diamonds:
Students will be required to identify these shapes in real world diagrams for this skill. There are three
types of problems. The first involves several real world figures and asks the student to identify the
figure that contains one of the shapes listed above. The second involves matching a real world diagram
to its simplified geometric shape. The third involves naming the geometric shape that makes some part
of the diagram. Examples of these three types of problems are provided below.
Example 1:
In which picture can you find a triangle?
Solution:
The envelope, diagram D, is the only diagram with a triangle. Diagrams A and B contain rectangles
and diagram C contains circles, but none of these have any triangles.
Answer: Diagram D contains a triangle.
Example 2:
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The package is most like which shape?
Answer: The package is most like the prism in answer (B).
Example 3:
The door on the microwave is _______________ .
A. a rectangle
B. an oval
C. a triangle
D. a circle
Answer: A. The door on the microwave is a rectangle.
An activity that will help students learn this skill is to draw circles, squares, rectangles, triangles, and
diamonds on index cards. Then have the student go through a magazine or book, or look around the
surroundings to try to identify each of the shapes in at least one real world setting. For example, the
student could see a circle in the face of a clock in the house, a rectangle in the shapes of the drawers in
the kitchen, and an oval in the face of a favorite cartoon character.
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