line segmentcurriculum.hempfieldsd.org/mathematics/03. grade 3/math expressions parent resources...
TRANSCRIPT
© H
ou
gh
ton
Mif
flin
Har
cou
rt P
ub
lish
ing
Co
mp
any
GeometryReason with shapes and their attributes.
Lesson 97 CC.3.G.1 Describe Plane Shapes . . . . . . . . . . . . . . . .193Lesson 98 CC.3.G.1 Describe Angles in Plane Shapes . . . . . . . . . . .195Lesson 99 CC.3.G.1 Identify Polygons . . . . . . . . . . . . . . . . . . .197Lesson 100 CC.3.G.1 Describe Sides of Polygons . . . . . . . . . . . . . .199Lesson 101 CC.3.G.1 Classify Quadrilaterals . . . . . . . . . . . . . . . .201Lesson 102 CC.3.G.1 Draw Quadrilaterals . . . . . . . . . . . . . . . . .203Lesson 103 CC.3.G.1 Describe Triangles . . . . . . . . . . . . . . . . . .205Lesson 104 CC.3.G.1 Problem Solving • Classify Plane Shapes . . . . . .207Lesson 105 CC.3.G.2 Relate Shapes, Fractions, and Area . . . . . . . . . .209
→
vii
1
endpoints
point
line
line segment
ray
CC.3.G.1
© H
ou
gh
ton
Mif
flin
Har
cou
rt P
ub
lish
ing
Co
mp
any
Name
You can use math words to describe plane shapes.
an exact position or location
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 An open shape does not startends at the same point. 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.
line line segment
2.
point ray
3.
closed shapeopen shape
4.
closed shapeopen shape
Write whether the shape is open or closed.
5. 6. 7. 8.
Describe Plane ShapesOBJECTIVE Identify and describe attributes of plane shapes.
LESSON 97
open closed closed open
Geometry 193
1
CC.3.G.1
© H
ou
gh
ton
Mif
flin
Har
cou
rt P
ub
lish
ing
Co
mp
any
Name
Write how many line segments the shape has.
1.
line segments
2.
line segments
3.
line segments
4.
line segments
Write whether the shape is open or closed.
5. 6.
Problem Solving 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?
4 6
8 5
open closed
Add a fourth line segment, so the
shape starts and ends at the same
point. closed
194 Lesson 97
Describe Plane Shapes
1
right angle
right angle
greater than aright angle
greater than aright angle
less than aright angle
CC.3.G.1
© H
ou
gh
ton
Mif
flin
Har
cou
rt P
ub
lish
ing
Co
mp
any
Name
There are different types of angles.
A right angle formsa square corner.
Some angles are less than a right angle.
Some angles are greater than a right angle.
Look at this shape. Describe the angles.
There are 2 right angles.
There are 2 angles greater than a right angle.
There is 1 angle less 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.
1. 2. 3.
Write how many of each type of angle the shape has.
4.
right
less than a right
greater than a right
5.
right
less than a right
greater than a right
6.
right
less than a right
greater than a right
Describe Angles in Plane ShapesOBJECTIVE Describe angles in plane shapes.
LESSON 98
less than a right angle
greater than a right angle right angle
4
0
0
1
0
5
0
2
2
Geometry 195
1
CC.3.G.1
© H
ou
gh
ton
Mif
flin
Har
cou
rt P
ub
lish
ing
Co
mp
any
Name
Use the corner of a sheet of paper to tell whether the angle isa right angle, less than a right angle, or greater than a right angle.
1. 2. 3.
Write how many of each type of angle the shape has.
4.
right
less than a right
greater than a right
5.
right
less than a right
greater than a right
6.
right
less than a right
greater than a right
Problem Solving 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?
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.
less than a right angle
4
0
0
0
0
5
2
0
4
right anglegreater than a
right angle
6 sides, 6 angles Aimee; Possible explanation: all the
angles are greater than a right angle.
196 Lesson 98
Describe Angles in Plane Shapes
1
CC.3.G.1
© H
ou
gh
ton
Mif
flin
Har
cou
rt P
ub
lish
ing
Co
mp
any
Name
You can identify and name polygons by the number of sides and angles they have.
3 sides
3 angles
triangle
4 sides
4 angles
quadrilateral
5 sides
5 angles
pentagon
6 sides
6 angles
hexagon
8 sides
8 angles
octagon
10 sides
10 angles
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.
sides
angles
2.
sides
angles
Identify PolygonsOBJECTIVE Identify polygons by the number of sides they have.
LESSON 99
5
5
4
4
pentagon quadrilateral
Geometry 197
1
CC.3.G.1
© H
ou
gh
ton
Mif
flin
Har
cou
rt P
ub
lish
ing
Co
mp
any
Name
Is the shape a polygon? Write yes or no.
1. 2.
3. 4.
Write the number of sides and the number of angles. Then name the polygon.
5.
sides
angles
6.
sides
angles
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?
8. Lin says that an octagon has six sides. Chris says that it has eight sides. Whose statement is correct?
no yes
no no
6
6
4
4
hexagon quadrilateral
10 angles Chris’s statement
198 Lesson 99
Identify Polygons
1
A B C
CC.3.G.1
© H
ou
gh
ton
Mif
flin
Har
cou
rt P
ub
lish
ing
Co
mp
any
Name
There are different types of line segments in polygons.
• Intersecting lines are lines that crossor meet. Intersecting lines form angles.
• Perpendicular lines are intersectinglines 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.
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.
1. 2. 3.
Describe Sides of PolygonsOBJECTIVE Determine if lines or line segments are intersecting, perpendicular, or parallel.
LESSON 100
parallelintersecting,
perpendicular intersecting
Geometry 199
1
A
B
C
D
CC.3.G.1
© H
ou
gh
ton
Mif
flin
Har
cou
rt P
ub
lish
ing
Co
mp
any
Name
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.
1. 2. 3.
4. 5. 6.
7. 8. 9.
Problem SolvingUse shapes A–D for 10–11.
10. Which shapes appear to have parallel sides?
11. Which shapes appear to have perpendicular sides?
parallelintersecting,
perpendicular intersecting
intersecting
parallel
intersecting, perpendicular
intersecting
parallel
intersecting, perpendicular
A, C, D
B, C
200 Lesson 100
Describe Sides of Polygons
1
CC.3.G.1
© H
ou
gh
ton
Mif
flin
Har
cou
rt P
ub
lish
ing
Co
mp
any
Name
You can classify quadrilaterals by their sides and by their angles.
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. 2. 3.
Classify QuadrilateralsOBJECTIVE Describe, classify, and compare quadrilaterals based on their sides and angles.
LESSON 101
2 pairs of opposite sides that are parallel
2 pairs of opposite sides that are of equal length
4 right angles
2 pairs of opposite sides that are parallel
4 sides that are of equal length
4 right angles
1 pair of opposite sides that are parallel
lengths of sides could be the same.
2 pairs of opposite sides that are parallel
4 sides that are of equal length
square
rhombus
trapezoid
square
rectangle
quadrilateral
square
rectangle
rhombus
square rectangle
rhombustrapezoid
Geometry 201
1
CC.3.G.1
© H
ou
gh
ton
Mif
flin
Har
cou
rt P
ub
lish
ing
Co
mp
any
Name
Circle all the words that describe the quadrilateral.
1. 2. 3.
Use the quadrilaterals below for 4–6.
4. Which quadrilaterals appear to have no right angles?
5. Which quadrilaterals appear to have 4 right angles?
6. Which quadrilaterals appear to have 4 sides of equal length?
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?
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?
square
rectangle
rhombus
trapezoid
square
rectangle
rhombus
trapezoid
square
rectangle
rhombus
trapezoid
A B C ED
B, D, and E A and C B, C, and D
square rhombus
202 Lesson 101
Classify Quadrilaterals
1
© H
ou
gh
ton
Mif
flin
Har
cou
rt P
ub
lish
ing
Co
mp
any
Name
CC.3.G.1
Use grid paper to draw a quadrilateral.
Step 1 Use a ruler to draw line segments. Connect A to B.
Step 2 Connect B to C.
Step 3 Connect C to D.
Step 4 Connect D to A.
Write the name of your quadrilateral.
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
4. 2 pairs of opposite sides that are parallel
Draw QuadrilateralsOBJECTIVE Draw quadrilaterals.
LESSON 102
rhombus
AD
C
B
rectangle square
For 1–4, possible drawings are shown.
Geometry 203
1
© H
ou
gh
ton
Mif
flin
Har
cou
rt P
ub
lish
ing
Co
mp
any
Name
CC.3.G.1
Draw a quadrilateral that is described. Name the quadrilateral you drew.
1. 4 sides of equal length
2. 1 pair of opposite sides that are parallel
Draw a quadrilateral that does not belong. Then explain why.
3.
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.
5. Victor drew a quadrilateral with no right angles and 4 sides of equal length. What quadrilateral could Victor have drawn?
square
square or rectangle rhombus
trapezoid
Possible explanation: I drew a trapezoid. It has only 1 pair of
opposite sides that are parallel. The 3 quadrilaterals shown
have 2 pairs of sides that are parallel.
For 2-3, check students’ drawings. Possible drawings are shown.
204 Lesson 102
Draw Quadrilaterals
1
© H
ou
gh
ton
Mif
flin
Har
cou
rt P
ub
lish
ing
Co
mp
any
Name
You can describe a triangle by its types of angles.
This triangle has 1 right angle.
This triangle has 1 angle greater than a right angle.
This triangle has 3 angles less than a right angle.
You can describe a triangle by the number of sides of equal length.
This triangle has 0 sides of the same length.
This triangle has 2 sides of the same length.
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.
4. No sides are equal in length.
2. One angle is greater than a right angle.
5. Two sides are equal in length.
3. Three angles are less than a right angle.
6. Three sides are equal in length.
Describe TrianglesOBJECTIVE Describe and compare triangles based on the number of sides that have
equal length and by their angles.
CC.3.G.1LESSON
103
•
••
•
•
•
•
•
•
•
••
Geometry 205
1
© H
ou
gh
ton
Mif
flin
Har
cou
rt P
ub
lish
ing
Co
mp
any
Name
Use the triangles for 1–3. Write A, B, or C.Then complete the sentences.
1. Triangle has 3 angles less than a right angle and
appears to have sides of equal length.
2. Triangle has 1 right angle and appears to have
sides of equal length.
3. Triangle has 1 angle greater than a right angle
and appears to have sides of equal length.
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?
Problem Solving 5. Matthew drew the back of his
tent. How many sides appear to be of equal length?
6. Sierra made the triangular picture frame shown. How many angles are greater than a right angle?
CC.3.G.1
A B C
B
3
Kathy KellyKyle
Kathy
2 sides 0 angles
C
A
0
2
206 Lesson 103
Describe Triangles
1
CC.3.G.1
© H
ou
gh
ton
Mif
flin
Har
cou
rt P
ub
lish
ing
Co
mp
any
Name
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.
What types of polygons are in both circles?
Read the Problem Solve the Problem
What do I need to find? What is true about all polygons in the circle labeled Quadrilaterals?
What is true about all polygons in the other circle?
Which polygons are in the section where the circles overlap?
So, and are in the section where the circles overlap.
What information do I need to use?
The circles are labeled
How will I use the information?
1. Brad drew the Venn diagram at the right. What type of shapes are in the section where the circles overlap?
Problem Solving • Classify Plane ShapesOBJECTIVE Solve problems by using the strategy draw a diagram to classify plane shapes.
LESSON 104
what types of polygons are They all have 4 sides.
They all have sides of equal length.
shapes that are quadrilaterals and that
have 4 sides that are of equal length
a square a rhombus
in both circles
Quadrilaterals and Polygons
with All Sides of Equal Length
I will describe the shapes in the
section where the circles overlap
QuadrilateralsPolygons with All
Sides of Equal Length
TrianglesPolygons with Right Angles
triangles that have 1 right angle
Geometry 207
1
CC.3.G.1
© H
ou
gh
ton
Mif
flin
Har
cou
rt P
ub
lish
ing
Co
mp
any
Name
Solve each problem.
1. Steve drew the shapes below. Write the letter of each shape where it belongs in the Venn diagram.
2. Janice drew the shapes below. Write the letter of each shape where it belongs in the Venn diagram.
3. Beth drew the shapes below. Write the letter of each shape where it belongs in the Venn diagram.
A B C
DE
C, DA B, E
Triangle Right Angle
Right AngleAll Sides of
Equal Length
A, B, C D
A B C
D EB,C,
E
PerpendicularSides
Parallel Sides
A, D
A B
C D
208 Lesson 104
Problem Solving • Classify Plane Shapes
1
© H
ou
gh
ton
Mif
flin
Har
cou
rt P
ub
lish
ing
Co
mp
any
Name
CC.3.G.2
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.
Each part is 1 __ 6 of the whole shape’s area.
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.
1. 4 equal parts
Each part is of the whole shape’s area.
2. 8 equal parts
Each part is of the whole shape’s area.
Relate Shapes, Fractions, and AreaOBJECTIVE Partition shapes into parts with equal areas and express the area
as a unit fraction of the whole.
LESSON 105
Possible drawings are shown.
1 __ 8 1 __
4
Geometry 209
1
© H
ou
gh
ton
Mif
flin
Har
cou
rt P
ub
lish
ing
Co
mp
any
Name
CC.3.G.2
Draw lines to divide the shape into equal parts that show the fraction given.
1.
1 __ 3
2.
1 __ 8
3.
1 __ 2
Draw lines to divide the shape into parts with equal area. Write the area of each part as a unit fraction.
4.
4 equal parts
5.
6 equal parts
6.
3 equal parts
Problem Solving7. 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.
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 __ 4 1 __
6 1 __
3
1 __3 1 __
8
Possible drawings are shown.
Possible drawings are shown.
Possible drawings are shown.
210 Lesson 105
Relate Shapes, Fractions, and Area