Download Ordered Pairs - Hempfield Curriculum

Geometry
→ Graph points on the coordinate plane to solve real-world and
mathematical problems.
Lesson 94
Lesson 95
Lesson 96
CC.5.G.1
CC.5.G.2
CC.5.G.2
Ordered Pairs . . . . . . . . . . . . . . . . . . . .187
Graph Data . . . . . . . . . . . . . . . . . . . . .189
Line Graphs . . . . . . . . . . . . . . . . . . . . .191
→ Classify two-dimensional figures into categories based on
their properties.
Lesson 97
Lesson 98
Lesson 99
CC.5.G.3
CC.5.G.3
CC.5.G.3
. . . . . . . . . .193
. . . . . . . . . .195
. . . . . . . . . .197
. . . . . . . . . .199
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Lesson 100 CC.5.G.4
Polygons . . . . . . . . . . . . .
Triangles . . . . . . . . . . . . .
Problem Solving • Properties of
Two-Dimensional Figures . . . . .
Quadrilaterals . . . . . . . . . .
vii
Name
LESSON
94
1
Ordered Pairs
CC.5.G.1
OBJECTIVE Graph and name points on a coordinate grid using ordered pairs.
A coordinate grid is like a sheet of graph paper bordered at the left
and at the bottom by two perpendicular number lines. The x-axis is
the horizontal number line at the bottom of the grid. The y-axis is the
vertical number line on the left side of the grid.
An ordered pair is a pair of numbers that describes the location of a
point on the grid. An ordered pair contains two coordinates, x and y.
The x-coordinate is the first number in the ordered pair, and
the y-coordinate is the second number.
(x, y)
(10, 4)
Plot and label (10, 4) on the coordinate grid.
To graph an ordered pair:
y-axis
• Start at the origin, (0, 0).
• Think: The letter x comes before y in the
alphabet. Move across the x-axis first.
• The x-coordinate is 10, so move 10 units right.
• The y-coordinate is 4, so move 4 units up.
• Plot and label the ordered pair (10, 4).
10
9
8
7
6
5
4
3
2
1
1 2 3 4 5 6 7 8 9 10
x-axis
Use the coordinate grid to write an ordered
pair for the given point.
1. G
3. J
(3, 4)
(4, 6)
2. H
(8, 10)
4. K
(1, 2)
Plot and label the points on the coordinate grid.
5. A (1, 6)
6. B (1, 9)
7. C (3, 7)
8. D (5, 5)
9. E (9, 3)
10. F (6, 2)
Geometry
y-axis
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0
(10, 4)
11
10 B
9
8
7 A
6
5
4
3
K
2
1
0
H
C
J
G
D
F
E
1 2 3 4 5 6 7 8 9 10 11
x-axis
187
Name
1
Ordered Pairs
CC.5.G.1
Use Coordinate Grid A to write an ordered pair
for the given point.
2. B (5, 7)
4. D (9, 3)
3. C (4, 8)
5. E (3, 4)
Coordinate Grid A
y-axis
1. A (2, 3)
6. F (6, 5)
10
9
8
7
6
5
4
3
2
1
0
C
B
F
E
D
A
1 2 3 4 5 6 7 8 9 10
x-axis
Plot and label the points on Coordinate Grid B.
Coordinate Grid B
9. O (8, 7)
10. M (2, 1)
11. P (5, 6)
12. Q (1, 5)
10
9
8
7
6
Q
5
R
4
3
2
M
1
0
Problem Solving
6 units
188
y-axis
13. Which building is located at (5, 6)?
14. What is the distance between Kip’s
Pizza and the bank?
N
1 2 3 4 5 6 7 8 9 10
x-axis
Port Charlotte
Use the map for 13–14.
Price Slicer Mart
O
P
10
9
8
7
6
5
4
3
2
1
0
Kip’s Pizza
bank
Price Slicer Mart
School
Post office
1 2 3 4 5 6 7 8 9 10
x-axis
Lesson 94
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8. R (0, 4)
y-axis
7. N (7, 3)
Name
1
Graph Data
LESSON
95
CC.5.G.2
OBJECTIVE Collect and graph data on a coordinate grid.
Graph the data on the coordinate grid.
Plant Growth
Plant Growth
1
2
3
4
Height (in inches)
4
7
10
11
Height (in inches)
y-axis
12
End of Week
• Choose a title for your graph and label it.
You can use the data categories to name
the x- and y-axis.
• Write the related pairs of data as ordered pairs.
( 1 , 4 ), ( 2 , 7 )
(
3
10
,
), (
4
11
,
10
8
6
4
2
0
1
)
2
3
4
5
6
x-axis
End of Week
• Plot the point for each ordered pair.
Graph the data on the coordinate grid. Label the points. Check students’ graphs.
1.
2.
Distance of Bike Ride
Time (in minutes)
30
60
90
120
Time (in minutes)
15
30
45
60
Distance (in miles)
9
16
21
27
Total Pages
1
3
9
11
Write the ordered pair for each
point.
Write the ordered pair for each
point.
(
30 ,
9
), (
60 ,
16
)
(
15
,
1
), (
30 ,
3
)
(
90 ,
21
), (
120 ,
27
)
(
45 ,
9
), (
60
11
)
Geometry
Total Pages
y-axis
30
25
20
15
10
5
0
20
40
60
80
100
x-axis
Time (in minutes)
,
Bianca’s Writing Progress
Distance of Bike Ride
Distance (in miles)
y-axis
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Bianca’s Writing Progress
120
14
12
10
8
6
4
2
0
5 10 15 20 25 30 35 40 45 50 55 60
x-axis
Time (in minutes)
189
Name
1
Graph Data
CC.5.G.2
Graph the data on the coordinate grid.
1.
Outdoor Temperature
Outdoor Temperature
1
Temperature (°F) 61
3
5
65
7
71
75
y
9
77
a. Write the ordered pairs for each point.
(1, 61), (3, 65), (5, 71), (7, 75), (9, 77)
b. How would the ordered pairs be different
if the outdoor temperature were recorded
every hour for 4 consecutive hours?
Temperature (°F)
Hour
80
70
60
50
40
30
20
10
x
0
1
2
3
4 5 6 7 8 9 10
Time (hours)
Possible answer: There would be
4 ordered pairs; the ordered pairs would record the outdoor temperature
at Hours 1, 2, 3, and 4.
2.
Possible graph is shown.
Windows Repaired
Windows Repaired
1
2
3
4
5
Total Number Repaired
14
30
45
63
79
a. Write the ordered pairs for each point.
(1, 14), (2, 30), (3, 45), (4, 63), (5, 79)
b. What does the ordered pair (2, 30)
tell you about the number of
windows repaired?
y
Total Number of Windows
Day
80
70
60
50
40
30
20
10
0
x
1
2
3
4
5 6 7
Days
8 9 10
Possible answer: After 2 days, a total
of 30 windows had been repaired.
190
Lesson 95
© Houghton Mifflin Harcourt Publishing Company
Problem Solving
Name
LESSON
96
1
Line Graphs
CC.5.G.2
OBJECTIVE Analyze and display data in a line graph.
A line graph uses a series of line segments to show how a set of data
changes over time. The scale of a line graph measures and labels the data
along the axes. An interval is the distance between the numbers on an axis.
Average Monthly High Temperature
in Sacramento, California
Use the table to make a line graph.
• Write a title for your graph. In this
example, use Average Monthly
High Temperature in Sacramento.
Month
Temperature (˚F)
Jan.
Feb.
53
60
Mar. April
65
71
May
80
• Draw and label the axes of the line
graph. Label the horizontal axis Month.
Write the months. Label the vertical axis Temperature (°F).
• Choose a scale and an interval. The range is 53–80,
so a possible scale is 0–80, with intervals of 20.
• Write the related pairs of data as ordered pairs:
(Jan, 53); (Feb, 60); (Mar, 65); (April, 71); (May, 80).
1. Make a line graph of the data above.
2. Make a line graph of the data in the
table.
80
60
40
20
0
Average Low Temperature
in San Diego, California
Month
Temperature (°F)
Jan.
Feb.
Mar.
April
May
Month
Use the graph to determine between
which two months the least change in
average high temperature occurs.
Mar.
April
May
June
July
51
51
60
62
66
Average Low Temperature
in San Diego
Temperature (ºF)
Temperature (ºF)
© Houghton Mifflin Harcourt Publishing Company
Average Monthly High
Temperature in Sacramento
70
65
60
55
50
45
0
March
April
May
June
July
Month
Use the graph to determine between
which two months the greatest change
in average low temperature occurs.
February and March
Geometry
April and May
191
Name
1
Line Graphs
CC.5.G.2
Use the table for 1–5.
Hourly Temperature
Time
Temperature (˚F)
10 A.M.
11 A.M.
12 noon
1 P.M.
2 P.M.
3 P.M.
4 P.M.
8
11
16
27
31
38
41
1. Write the related number pairs for the hourly
temperature as ordered pairs.
(10, 8); (11, 11); (12, 16); (1, 27); (2, 31);
(3, 38); (4, 41)
2. What scale would be appropriate to graph
the data?
?flicpK\dg\iXkli\
Possible interval: 5
4. Make a line graph of the data.
Possible graph is shown.
,'
+,
+'
*,
*'
),
)'
(,
('
,
'
5. Use the graph to find the difference in temperature
between 11 A.M. and 1 P.M.
(' (( () (
) * +
8%D% 8%D% effe G%D% G%D% G%D% G%D%
K`d\
16°F
Problem Solving
6. Between which two hours did the
least change in temperature occur?
7. What was the change in
temperature between 12 noon
and 4 P.M.?
Between 10 A.M. and 11 A.M. and
between 3 P.M. and 4 P.M.
192
25°F
Lesson 96
© Houghton Mifflin Harcourt Publishing Company
3. What interval would be appropriate to graph
the data?
K\dg\iXkli\`eñ= Possible scale: 0 to 50
Name
LESSON
97
1
Polygons
CC.5.G.3
OBJECTIVE Identify and classify polygons.
A polygon is a closed plane figure formed by
three or more line segments that meet at
points called vertices. You can classify a
polygon by the number of sides and the
number of angles that it has.
Polygon
Congruent figures have the same size and
shape. In a regular polygon, all sides are
congruent and all angles are congruent.
Classify the polygon below.
How many sides does this polygon have?
Sides
Angles
Vertices
Triangle
3
3
3
Quadrilateral
4
4
4
Pentagon
5
5
5
Hexagon
6
6
6
Heptagon
7
7
7
Octagon
8
8
8
Nonagon
9
9
9
Decagon
10
10
10
5 sides
5 angles
How many angles does this polygon have?
Name the polygon. pentagon
no
Are all the sides congruent?
no
Are all the angles congruent?
© Houghton Mifflin Harcourt Publishing Company
So, the polygon above is a pentagon. It is not a regular polygon.
Name each polygon. Then tell whether it is a regular polygon
or not a regular polygon.
1.
K
2.
>
P
3.
?
L
<
=
J
quadrilateral;
not a regular
polygon
Geometry
O
M
L
4.
N
E
K
F
J
G
I
H
I
triangle;
not a regular
polygon
pentagon;
regular
polygon
octagon;
regular
polygon
193
Name
1
Polygons
CC.5.G.3
Name each polygon. Then tell whether it is a
regular polygon or not a regular polygon.
2.
1.
4 sides, 4 vertices, 4 angles means it is
a quadrilateral . The sides are not
all congruent, so it is
quadrilateral; regular
not regular .
3.
4.
octagon; not regular
6.
triangle; regular
pentagon; not regular
Problem Solving
7. Sketch nine points. Then, connect
the points to form a closed plane
figure. What kind of polygon did
you draw?
Check students’ drawings;
nonagon.
194
8. Sketch seven points. Then, connect
the points to form a closed plane
figure. What kind of polygon did you
draw?
Check students’ drawings;
heptagon.
Lesson 97
© Houghton Mifflin Harcourt Publishing Company
5.
hexagon; regular
Name
1
Triangles
LESSON
98
CC.5.G.3
OBJECTIVE Classify and draw triangles using their properties.
You can classify triangles by the length of their sides and
by the measure of their angles. Classify each triangle.
Use a ruler to measure the side lengths.
Use the corner of a sheet of
paper to classify the angles.
• equilateral triangle
All sides are the same
length.
• acute triangle
All three angles are acute.
• isosceles triangle
Two sides are the same
length.
• obtuse triangle
One angle is obtuse. The
other two angles are acute.
• scalene triangle
All sides are different
lengths.
• right triangle
One angle is right. The other
two angles are acute.
Classify the triangle according to its side lengths.
It has two congruent sides.
The triangle is an isosceles triangle.
© Houghton Mifflin Harcourt Publishing Company
Classify the triangle according to its angle measures.
It has one right angle.
The triangle is a right triangle.
Classify each triangle. Write isosceles, scalene, or equilateral.
Then write acute, obtuse, or right.
1.
2.
9 mi
78°
14 mi
66°
scalene; acute
10 m
equilateral; acute
5.
Geometry
10 m
4m
5 in.
15 mi
isosceles; obtuse
3.
5 in.
36°
4.
5 in.
isosceles; acute
6.
scalene; right
isosceles; right
195
Name
1
Triangles
CC.5.G.3
Classify each triangle. Write isosceles, scalene, or equilateral.
Then write acute, obtuse, or right.
1.
2.
8 mm
118°
6 mm
37°
53°
10 mm
42 in.
None of the side measures are equal.
So, it is
scalene
angle, so it is a
3.
. There is a right
right
4.
50 cm
15 cm
isosceles
triangle.
22°
.`e%
),`e%
)+`e%
50 cm
isosceles
obtuse
acute
scalene
right
5. sides: 44 mm, 28 mm, 24 mm
angles: 110°, 40°, 30°
scalene
obtuse
6. sides: 23 mm, 20 mm, 13 mm
angles: 62°, 72°, 46°
scalene
acute
Problem Solving
7. Mary says the pen for her horse is an
acute right triangle. Is this possible?
Explain.
196
8. Karen says every equilateral triangle is
acute. Is this true? Explain.
No. It can be right or acute,
Yes. All the angles in an equilateral
but not both.
triangle are acute.
Lesson 98
© Houghton Mifflin Harcourt Publishing Company
A triangle has sides with the lengths and angle measures given.
Classify each triangle. Write scalene, isosceles, or equilateral.
Then write acute, obtuse, or right.
Name
LESSON
99
1
Problem Solving • Properties of
Two-Dimensional Figures
CC.5.G.3
OBJECTIVE Solve problems using the strategy act it out.
A
Haley thinks hexagon ABCDEF has 6 congruent sides, but she
does not have a ruler to measure the sides. Are the 6 sides
congruent?
Read the Problem
What do I need to find?
I need to determine if sides
AB, BC, CD, DE, EF, and FA
6
sides and 6 congruent
angles.
How will I use the
information?
act it out by tracing
I will
© Houghton Mifflin Harcourt Publishing Company
the figure and then folding
the figure to match all
the sides to see if they are
congruent .
F
C
E
D
Solve the Problem
Trace the hexagon and cut out the shape.
Step 1 Fold the hexagon to match the sides AB
and ED, sides FE and FA, and sides CD
and CB.
have the same length.
What information do I need
to use?
The figure is a hexagon with
B
F
A
C
E
D B
The sides match, so they are congruent.
Step 2 Fold along the diagonal between B
and E to match sides BA and BC, sides AF
and CD, and sides EF and ED. Fold along
the diagonal between A and D to match
sides AF and AB, sides FE and BC, and
sides DE and DC.
Step 3 Use logic to match sides AB and CD, sides
AB and EF, sides BC and DE, and sides DE
and FA.
The sides match, so they are congruent.
1. Justin thinks square STUV has
4 congruent sides, but he does not
have a ruler to measure the sides. Are
the sides congruent? Explain.
Possible answer: Yes. A square by
2. Esther knows octagon OPQRSTUV
has 8 congruent angles. How can
she determine whether the octagon
has 8 congruent sides without using
a ruler?
definition has 4 congruent sides.
Possible answer: She could trace
If he folds the square in half both
the octagon, cut it out, and fold
ways and along both diagonals,
the figure to match the sides.
then the sides will match.
Geometry
197
Name
1
Problem Solving • Properties
of Two-Dimensional Figures
CC.5.G.3
Solve each problem.
1. Marcel thinks that quadrilateral ABCD at the right
has two pairs of congruent sides, but he does not
have a ruler to measure the sides. How can he
show that the quadrilateral has two pairs of
congruent sides?
A
B
D
C
He can fold the quadrilateral in half both ways. If both sets of
sides match, then they are congruent.
2. If what Marcel thinks about his quadrilateral is
true, what type of quadrilateral does he have?
3. Richelle drew hexagon KLMNOP at the right. She
thinks the hexagon has six congruent angles.
How can she show that the angles are congruent
without using a protractor to measure them?
rectangle
K
P
L
M
O
N
Possible answer: She can fold the hexagon in
half five different ways to show that the angle
at vertex K matches the angle at each other vertex.
S
© Houghton Mifflin Harcourt Publishing Company
4. Jerome drew a triangle with vertices S, T, and U.
He thinks ∠TSU and ∠TUS are congruent. How
can Jerome show that the angles are congruent
without measuring the angles?
T
U
Possible answer: He can fold the triangle in half
along a line from vertex T to check if ∠TSU and ∠TUS
match exactly. If they do, then the two angles are congruent.
5. If Jerome is correct, what type of triangle did
he draw?
isosceles
198
Lesson 99
Name
LESSON
100
1
Quadrilaterals
OBJECTIVE Classify and compare quadrilaterals using their properties.
CC.5.G.4
You can use this chart to help you classify quadrilaterals.
quadrilateral
4 sides
parallelogram
quadrilateral
opposite sides are parallel
opposite sides are congruent
rectangle
parallelogram
4 right angles
2 pairs of perpendicular sides
trapezoid
quadrilateral
exactly one pair of parallel sides
rhombus
parallelogram
4 congruent sides
square
rhombus
rectangle
Classify the figure.
The figure has 4 sides, so it is a quadrilateral. The figure
has exactly one pair of parallel sides, so it is a trapezoid.
© Houghton Mifflin Harcourt Publishing Company
quadrilateral, trapezoid
Classify the quadrilateral in as many ways as possible. Write quadrilateral,
parallelogram, rectangle, rhombus, square, or trapezoid.
1.
2.
quadrilateral, parallelogram,
rectangle
3.
quadrilateral
4.
quadrilateral, trapezoid
Geometry
quadrilateral, parallelogram
199
Name
1
Quadrilaterals
CC.5.G.4
Classify the quadrilateral in as many ways as possible. Write quadrilateral,
parallelogram, rectangle, rhombus, square, or trapezoid.
1.
2.
It has 4 sides, so it is a quadrilateral .
None of the sides are parallel, so there
quadrilateral,
parallelogram, rhombus
is no other classification..
4.
3.
quadrilateral,
parallelogram
quadrilateral,
parallelogram, rectangle
6.
quadrilateral, trapezoid
quadrilateral, trapezoid
Problem Solving
7. Kevin claims he can draw a
trapezoid with three right angles. Is
this possible? Explain.
8. “If a figure is a square, then it is a
regular quadrilateral.” Is this true or
false? Explain.
True. All 4 angles and all 4 sides
200
No. If there are 3 right angles, the
of a square are congruent. That
last angle is a right angle also, and
means that a square is regular and a
that is a rectangle, not a trapezoid.
quadrilateral.
Lesson 100
© Houghton Mifflin Harcourt Publishing Company
5.