Answers to Parent Pages L97-L105

Transcription

Geometry
→ Reason with shapes and their attributes.
97
98
99
100
101
102
103
104
105
CC.3.G.1
CC.3.G.1
CC.3.G.1
CC.3.G.1
CC.3.G.1
CC.3.G.1
CC.3.G.1
CC.3.G.1
CC.3.G.2
Describe Plane Shapes . . . . . . . . . .
Describe Angles in Plane Shapes . . . . .
Identify Polygons . . . . . . . . . . . . .
Describe Sides of Polygons . . . . . . . .
Classify Quadrilaterals . . . . . . . . . .
Draw Quadrilaterals . . . . . . . . . . .
Describe Triangles . . . . . . . . . . . .
Problem Solving • Classify Plane Shapes
Relate Shapes, Fractions, and Area . . . .
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© Houghton Mifflin Harcourt Publishing Company
Lesson
Lesson
Lesson
Lesson
Lesson
Lesson
Lesson
Lesson
Lesson
vii
Name
LESSON
97
1
Describe Plane Shapes
CC.3.G.1
OBJECTIVE Identify and describe attributes of plane shapes.
You can use math words to describe plane shapes.
point
an exact position or location
line
endpoints
line segment
ray
a straight path that goes in two directions without end
points that are used to show segments of lines
part of a straight line and has 2 endpoints
part of a straight line that has 1 endpoint and
continues in one direction
A plane shape is a shape on a flat surface. It is formed by points that make
curved paths, line segments, or both. Plane shapes can be open or closed.
A closed shape starts and
ends at the same point.
An open shape does not start
and end at the same point.
Look at this plane shape called a triangle.
It is a closed shape.
It has 3 line segments.
The line segments meet at the endpoints.
Circle all the words that describe the shape.
1.
2.
line
line segment
3.
point
ray
4.
closed shape
open shape
closed shape
open shape
Write whether the shape is open or closed.
6.
5.
open
Geometry
7.
closed
8.
closed
open
193
Name
1
Describe Plane Shapes
CC.3.G.1
Write how many line segments the shape has.
2.
1.
4
line segments
3.
6
line segments
5
line segments
4.
8
line segments
Write whether the shape is open or closed.
5.
6.
open
closed
7. Carl wants to show a closed
shape in his drawing. Show and
explain how to make the drawing
a closed shape.
8. The shape of a fish pond at a park
is shown below. Is the shape open
or closed?
Add a fourth line segment, so the
shape starts and ends at the same
point.
194
closed
Lesson 97
Problem Solving
Name
LESSON
98
1
Describe Angles in Plane Shapes
CC.3.G.1
OBJECTIVE Describe angles in plane shapes.
There are different types of angles.
A right angle forms
a square corner.
Some angles are less
than a right angle.
Look at this shape.
Describe the angles.
right angle
Some angles are greater
than a right angle.
greater than a
right angle
There are 2 right angles.
less than a
right angle
There are 2 angles
greater than a right angle.
There is 1 angle less than
a right angle.
right angle
greater than a
right angle
Use the corner of a sheet of paper to tell whether the angle is a
right angle, less than a right angle, or greater than a right angle.
2.
1.
less than a
right angle
3.
greater than a
right angle
right angle
Write how many of each type of angle the shape has.
4.
5.
6.
4
right
1
right
0
right
0
less than a right
0
less than a right
2
less than a right
0
greater than a right
5
2
Geometry
195
Name
1
Describe Angles in Plane Shapes
CC.3.G.1
Use the corner of a sheet of paper to tell whether the angle is
a right angle, less than a right angle, or greater than a right angle.
2.
1.
less than a
right angle
3.
greater than a
right angle
right angle
Write how many of each type of angle the shape has.
4.
5.
6.
4
right
0
right
2
right
0
less than a right
0
less than a right
0
less than a right
0
greater than
a right
5
greater than
a right
4
greater than
a right
7. Jeff has a square piece of art
paper. He cuts across it from one
corner to the opposite corner
to make two pieces. What is the
total number of sides and angles
in both of the new shapes?
6 sides, 6 angles
8. Kaylee tells Aimee that the shape
of a stop sign has at least one
right angle. Aimee says that
there are no right angles. Who is
correct? Explain.
Aimee; Possible explanation: all the
angles are greater than a right angle.
196
Lesson 98
Problem Solving
Name
LESSON
99
1
Identify Polygons
CC.3.G.1
OBJECTIVE Identify polygons by the number of sides they have.
You can identify and name polygons by the number of sides
and angles they have.
3 sides
3 angles
4 sides
4 angles
5 sides
5 angles
triangle
quadrilateral
pentagon
6 sides
6 angles
8 sides
8 angles
10 sides
10 angles
hexagon
octagon
decagon
Describe and name this shape.
Describe and name this shape.
It has 4 sides.
It has 6 sides.
It has 4 angles.
It has 6 angles.
It is a quadrilateral.
It is a hexagon.
Write the number of sides and the number
of angles. Then name the polygon.
1.
2.
5
sides
4
sides
5
angles
4
angles
pentagon
Geometry
quadrilateral
197
Name
1
Identify Polygons
CC.3.G.1
Is the shape a polygon? Write yes or no.
2.
1.
no
yes
3.
4.
no
no
Write the number of sides and the number
of angles. Then name the polygon.
6
sides
4
sides
6
angles
4
angles
hexagon
6.
5.
quadrilateral
Problem Solving
7. Mr. Murphy has an old coin that
has ten sides. If its shape is a
polygon, how many angles does
the old coin have?
10 angles
198
8. Lin says that an octagon has
six sides. Chris says that it has
eight sides. Whose statement
is correct?
Chris’s statement
Lesson 99
Name
LESSON
100
1
Describe Sides of Polygons
CC.3.G.1
OBJECTIVE Determine if lines or line segments are intersecting, perpendicular, or parallel.
There are different types of line segments in polygons.
• Intersecting lines are lines that cross
or meet. Intersecting lines form angles.
• Perpendicular lines are intersecting
lines that cross or meet to form right angles.
• Lines that appear never to cross or meet and
are always the same distance apart are
parallel lines. They never form angles.
A
B
C
Which shape or shapes appear to have parallel sides? A
Which shape or shapes appear to have perpendicular sides? A, B
Which shape or shapes appear to have intersecting sides? A, B, C
Look at the dashed sides of the polygon. Tell if they
appear to be intersecting, perpendicular, or parallel.
Write all the words that describe the sides.
2.
1.
parallel
Geometry
3.
intersecting,
perpendicular
intersecting
199
Name
1
Describe Sides of Polygons
CC.3.G.1
Look at the dashed sides of the polygon. Tell if they
appear to be intersecting, perpendicular, or parallel.
Write all the words that describe the sides.
2.
intersecting,
perpendicular
parallel
4.
3.
5.
6.
intersecting,
perpendicular
intersecting
7.
8.
parallel
intersecting
parallel
9.
intersecting,
perpendicular
intersecting
1.
Problem Solving
Use shapes A–D for 10–11.
10. Which shapes appear to have parallel sides?
A
A, C, D
11. Which shapes appear to have perpendicular
sides?
B, C
200
B
C
D
Lesson 100
Name
LESSON
101
1
Classify Quadrilaterals
OBJECTIVE Describe, classify, and compare quadrilaterals based on their sides and angles.
CC.3.G.1
You can classify quadrilaterals by their sides and by their angles.
square
rectangle
2 pairs of opposite sides
that are parallel
2 pairs of opposite sides that
are parallel
4 sides that are of
equal length
are of equal length
4 right angles
4 right angles
trapezoid
rhombus
1 pair of opposite sides that
are parallel
are parallel
lengths of sides could be
the same.
4 sides that are of equal
length
How can you classify the quadrilateral?
It has only 1 pair of opposite sides that are parallel.
The lengths of all 4 sides are not equal.
So, the quadrilateral is a trapezoid.
Circle all the words that describe the quadrilateral.
1.
Geometry
2.
3.
square
square
square
rhombus
rectangle
rectangle
trapezoid
quadrilateral
rhombus
201
Name
1
Classify Quadrilaterals
CC.3.G.1
Circle all the words that describe the quadrilateral.
1.
2.
3.
square
square
square
rectangle
rectangle
rectangle
rhombus
rhombus
rhombus
trapezoid
trapezoid
trapezoid
Use the quadrilaterals below for 4–6.
B
4. Which quadrilaterals
appear to have no
right angles?
C
D
E
appear to have 4 right
appear to have 4 sides
angles?
of equal length?
B, D, and E
A and C
B, C, and D
Problem Solving
7. A picture on the wall in Jeremy’s
classroom has 4 right angles,
4 sides of equal length, and
2 pairs of opposite sides that are
parallel. What quadrilateral best
describes the picture?
square
202
8. Sofia has a plate that has
4 sides of equal length, 2 pairs
of opposite sides that are
parallel, and no right angles.
What quadrilateral best describes
the plate?
rhombus
Lesson 101
A
Name
LESSON
102
1
Draw Quadrilaterals
CC.3.G.1
OBJECTIVE Draw quadrilaterals.
Use grid paper to draw a quadrilateral.
Step 1 Use a ruler to draw line segments.
Connect A to B.
B
Step 2 Connect B to C.
Step 3 Connect C to D.
C
A
D
Step 4 Connect D to A.
Write the name of your quadrilateral.
rhombus
For 1–4, possible drawings are shown.
1. Choose four endpoints that
connect to make a square.
2. Choose four endpoints that connect
to make a trapezoid.
Use grid paper to draw a quadrilateral that is described.
Name the quadrilateral you drew.
3. 4 right angles
rectangle
Geometry
4. 2 pairs of opposite sides that
are parallel
square
203
Name
1
Draw Quadrilaterals
CC.3.G.1
Draw a quadrilateral that is described. For 2-3, check students’ drawings.
Possible drawings are shown.
Name the quadrilateral you drew.
1. 4 sides of equal length
2. 1 pair of opposite sides that
are parallel
square
trapezoid
Draw a quadrilateral that does not belong.
Then explain why.
3.
Possible explanation: I drew a trapezoid. It has only 1 pair of
opposite sides that are parallel. The 3 quadrilaterals shown
Problem Solving
4. Layla drew a quadrilateral with
4 right angles and 2 pairs of
opposite sides that are parallel.
Name the quadrilateral she could
have drawn.
square or rectangle
204
5. Victor drew a quadrilateral with
no right angles and 4 sides of
equal length. What quadrilateral
could Victor have drawn?
rhombus
Lesson 102
have 2 pairs of sides that are parallel.
Name
LESSON
103
1
Describe Triangles
OBJECTIVE Describe and compare triangles based on the number of sides that have
equal length and by their angles.
CC.3.G.1
You can describe a triangle by its
types of angles.
You can describe a triangle by the
number of sides of equal length.
This triangle has
1 right angle.
This triangle has
0 sides of the
same length.
This triangle has
1 angle greater
than a right angle.
This triangle has
2 sides of the
same length.
This triangle has
3 angles less than
a right angle.
This triangle has
3 sides of the
same length.
Draw a line to match the description of the triangle(s).
1. One angle is
a right angle.
sides are
• 4. No
equal in length.
•
•
2. One angle is greater
than a right angle.
3. Three angles are
less than a right
angle.
•
•
•
•
5. Two sides are
equal in length.
sides are
• 6. Three
equal in length.
•
•
Geometry
•
•
205
Name
1
Describe Triangles
CC.3.G.1
Use the triangles for 1–3. Write A, B, or C.
Then complete the sentences.
1. Triangle
B
has 3 angles less than a right angle and
3
appears to have
2. Triangle
0
C
B
A
C
sides of equal length.
has 1 right angle and appears to have
3. Triangle
A
has 1 angle greater than a right angle
and appears to have
2
4. Kyle, Kathy, and Kelly each drew a
triangle. Who drew the triangle
that has 1 angle greater than a right
angle and appears to have no sides
of equal length?
Kyle
Kathy
Kelly
Problem Solving
5. Matthew drew the back of his
tent. How many sides appear to
be of equal length?
2 sides
206
6. Sierra made the triangular picture
frame shown. How many angles
are greater than a right angle?
0 angles
Lesson 103
Kathy
Name
LESSON
104
1
CC.3.G.1
OBJECTIVE Solve problems by using the strategy draw a diagram to classify plane shapes.
A Venn diagram shows how sets of things
are related. This Venn diagram shows how
quadrilaterals and polygons with all sides of
equal length are related. The shapes in the
section where the circles overlap show
shapes that belong to both groups.
Quadrilaterals
Polygons with All
Sides of Equal Length
What types of polygons are in both circles?
Read the Problem
What do I need to find?
what types of polygons are
in both circles
What information do I need
to use?
The circles are labeled
Solve the Problem
What is true about all polygons in the
circle labeled Quadrilaterals?
They all have 4 sides.
What is true about all polygons in the
other circle?
They all have sides of equal length.
Quadrilaterals and Polygons
Which polygons are in the section where
the circles overlap?
with All Sides of Equal Length
shapes that are quadrilaterals and that
How will I use the information?
have 4 sides that are of equal length
I will describe the shapes in the
a rhombus
So, a square and
are
in the section where the circles overlap.
section where the circles overlap
1. Brad drew the Venn diagram at the
right. What type of shapes are in the
section where the circles overlap?
Triangles
Polygons with
Right Angles
triangles that have 1 right angle
Geometry
207
Name
1
CC.3.G.1
Solve each problem.
1. Steve drew the shapes below. Write the
letter of each shape where it belongs in
the Venn diagram.
Triangle
A
B
C
A
D
Right Angle
B, E
C, D
E
2. Janice drew the shapes below. Write the
the Venn diagram.
All Sides of
Equal Length
Right Angle
B
C
A, B, C
D
D
3. Beth drew the shapes below. Write the
the Venn diagram.
Parallel Sides
B
A
D
208
E
Perpendicular
Sides
C
A, D
B,C,
E
Lesson 104
A
Name
LESSON
105
1
Relate Shapes, Fractions, and Area
CC.3.G.2
OBJECTIVE Partition shapes into parts with equal areas and express the area
as a unit fraction of the whole.
You can separate a plane shape into equal parts to explore
the relationship between fractions and area.
Divide the rectangle into 6 parts with equal area. Write
the fraction that names the area of each part of the whole.
Step 1 Draw lines to divide the rectangle into 6 parts
with equal area. Use the grid to help you.
Step 2 Write the fraction that names each part of the
divided whole.
Think: Each part is 1 part out of 6 equal parts.
__ of the whole shape’s area.
Each part is 1
6
Step 3 Write the fraction that names the whole area.
Think: There are 6 equal parts.
__.
The fraction that names the whole area is 6
6
Draw lines to divide the shape into parts with equal
area. Write the area of each part as a unit fraction. Possible drawings are shown.
1. 4 equal parts
2. 8 equal parts
1
__
4
of
Each part is
the whole shape’s area.
Geometry
Each part is
shape’s area.
1
__
8
of the whole
209
Name
1
Relate Shapes, Fractions, and Area
CC.3.G.2
Draw lines to divide the shape into equal
parts that show the fraction given. Possible drawings are shown.
2.
1.
3.
1
__
1
__
3
1
__
8
2
Draw lines to divide the shape into parts with equal area.
Write the area of each part as a unit fraction. Possible drawings are shown.
5.
6.
6 equal parts
4 equal parts
1
__
1
__
4
Possible drawings are shown.
7. Robert divided a hexagon into
3 equal parts. Show how he
might have divided the hexagon.
Write the fraction that names
each part of the whole you
divided.
1
__
3
210
1
__
3
6
Problem Solving
3 equal parts
8. Show how you might divide the
shape into 8 equal parts. What
fraction names the area of each
part of the divided shape?
1
__
8
Lesson 105
4.

Answers to Parent Pages L97-L105

Transcription

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