File - 6th Grade Math

2:
" Texa
Esse
Knowledge and gkills
Targeted TEKS •
7.4(D) Solve problems involving,
ratios, rates, and percents, including
multi-step problems involving
percent increase and percent
decrease, and financial lite[acy
problems. Also addresses Z4(A).
Maps have grids to locate cities.The coordinate plane is a type of grid
that is formed when two number lines intersect at their zero points.
The number lines separate the coordinate plane into four regions called
quadrants.
Mathematical Processes
An ordered pair is a pair of numbers, such as (1,2), used to locate or
graph points on the coordinate plane.
7.1 (A); 7.1 (B), 7.1 (C), 7.1 (D)
.
Vo/ab
Vocabulary
coordinate plane
[ Thex'c°°rdinate c°rresp°fÿds !'")ÿ (to a number on the x-axis,
quadrants
1! 2)< .... The y-coordinate correspondSto a nunÿber on the y-axis.
ordered pair
Label the coordinate plane with the terms ordered pair, x-coordinate,
x-coordinate
and y-coordinate.
y-coordinate
y-axis
origin
(4
x-axis
Essential Question ÿ):. _
HOW can you show that two
objects are proportional?
Graph points (2, 3) and (-3, -2) above. Connect the three points
on the coordinate plane. Describe the graph.
J
Which ÿ Mathematical Processes did you use?
Shade the circle(s) that applies.
(ÿ) Apply Math to the Real World.
C) Organize Ideas.
(ÿ) Use a Problem-Solving Model.
C) Analyze Relationships.
(ÿ) SelectTools and Techniques.
(ÿ Justify Arguments.
i
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v
;'
\
(ÿ Use Multiple Representations.
connectED.mcgraw-hill,corn
Lesson 5 Graph Proportional Relationships
159
Another way to determine whether two quantities are proportional is
to graph the quantities on the coordinate plane.If the graph of the two
quantities is a straight line through the origin, then the two quantities
are proportional.
rÿ, ,i ................................................................
- .Linear Relationships ! ÿ
. ..
,'
" ,
Tutor
1. The slowest mammal on Earth is the tree sloth. It moves at a
speed of 6 feet per minute. Determine whether the number of
feet the sloth moves is proportional to the number of minutes
it moves by graphing on the coordinate plane. Explain your
.
reasoning.
table
find
the
Make
a to
number
of feet
for
walk, ed
0, 1,2, 3, and 4 minutes.
..................................................................... 1
: Time (mini . : 0 I 2 3 I 4
Jili
!!;
.%.
'I
Distance (ft): 0 6 12 18 24
,-
Graphthe
ordered pairs
(time, distance) on'the
coordinate plane. Then
connect the ordered pairs.
28
0,I
=
The line passes through the origin
and is a straight line. So, the number
of feet traveled is proportional to the
If,,
24
20
16
12
4
,
/
/
/
/
1 23456
number of minutes.
Time (min)
- Iÿr? Do this problem to find out.
{ÿ.ii
a. James earns $5 an hour babysitting.
• .": Determine whether the amount of
money James earns babysitting is
proportional to the number of hours
he babysits by graphing on the
coordinate plane. Explain your
reasoning in the work Zone.
16ÿ Y---i ...... i---i ...... i ...... i ...... i
14
12
10
8
E 6 ...... i ...... " ...... ! ...... i ...... !------ÿ
4
2
0
=-i---:ÿ ...... ! ...... ! ..... ! ...... i
= ! ,, ,, , xi
I 2 3 4 5 6
Time (h)
rn
t-
•
]:
.... 160 Chapter2 ProportionaIRelationships
0
The cost of renting video games from
Games Inc. is shown in the table,
Determine whether the cost is
• proportional to the number of games
rented by graphing on the coordinate
plane. Explain your reasoning.
Write the two quantities as
ordered pairs (number of
1
3
2
5
3
7
4.
9
games, cost).
The ordered pairs are (1,3),
(2, 5), (3, 7), and (4, 9).
Graph the ordered pairs
on the coordinate plane.
Then connect the ordered
pairs and extend the line
10
9
8
7
'ÿ
to the y-axis.
....
6
5
4
The line does not pass through the
origin. So, the cost of the video
games is not proportional to the
3
2
1
number of games rented.
1 2 3 45x
2
Check The ratios are not constant. 1ÿ 5 ¢"
Number of Games
Goÿ" PrY Do this problem to find out.
b. The table sh6ws the number of Calories an athlete burned
per minute of exercise. Determine whether the number of Calories
burned is proportional to the number of minutes by graphing on
the coordinate plane. Explain your reasoning in the Work Zone.
.14
I/t
li-.Minÿt-es::: I:: ::cal°fiesÿ:i }
0 1 0
a
12
10
...... i ...... i ......
8
O
4
=1 •
l
3
13
I 2 3 4 5
Time (rain)
Tutor
Which batting cage represents a
proportional relationship between
the number of pitches thrown and
Lÿ
J
t
r,
the cost? Explain.
\
7
i
j/
1
v
,ÿ " "
_ÿFun CenterI
III
0 1 2 3 4 5 6 7 8 910111213
Number of Pitches
The graph for the Fun Center is
a straight line through the origin. So, the relationship between
the number of the pitches thrown and the cost is proportional.
\
7'
o
U 2
straight line, but it does not pass
through the origin. So, the
relationship is not proportional.
!
.........
II,i
The graph for Softball Plus is a
!:
i
..............
t"
5 ]_SoftballPlus _ ÿ.ÿ
I,
42
The cost of 3-D movie tickets is $12 for 1 ticket, $24 for
2 tickets, and $36 for 3 tickets. Determine whether the cost
is proportional to the number of tickets by graphing on the
36
30
24
coordinate plane. Explain your reasoning. (Examples1 and 2)
Ij
.....................................................................
ÿ
...... ' ...... T ...... 7 ...... i .....
y:
,
:
18
12
6
iii':
..... ilii: ..... ...... ...... ......
X:
12345
Tickets
/1ÿ ',,.
2. The number of books two stores sell after 1, 2, and 3 days
is shown. Which book sale represents a proportional
relationship between time and books? Explain. (Examnle3)
Y
, rl f ! i,I
"iOi°"ia'aie..
i)%
6
i
o
O
/,-'ÿ ÿh Discount Books J
1:o
3
//
x
/.t"
iii]
2
iÿ,,.
Rate Yourself!
4 5 6 7 8
Time {days}
1
:ÿ.ÿ,, Building on the Essential Question How does
graphing relationships help you determine whether the
relationship is proportional or not?
..........................
@ @ ©
Find out online. Use the
Self-Check Quiz.
>.
Check
iii' ,
i
162 Chapter 2 Proportional Relationships
I
I
Name
My Homework
(ÿ Use Multiple Representations Determine whether the relationship
between the two quantities shown in each table are proportional by
graphing on the coordinate plane. Explain your reasoning. (Examples1 and 2)
2OO
.
175
'Week
- ",,u..'cc="m:
Balance ($) "
I
' 125
2
150
3
175
;---! ...... ! ...... i ...... i ...... i ...... i
...... ! ............. i ...... ! ...... i ...... i
150
I&l
125
,- 100
75
50
25
...... i ...... ! ...... i ...... ÿ---:4 .......
:
I,
i
',
:
: x)
1 2 3 4 5
Weeks
400
.
350
Serving I Calories
1
/ '
7O
3
210
5
350
°ÿ
300
250
...... ÿ--i ........... :-i ...... i
o 200
I,j
150
..... +---i---: ...... ! ...... ]----i
100
............ ! .................. i-:
50
!
i
ÿ
i
ix:
1 2 3 4 5 6
Servings
3. The heightof two plants is recorded after 1,2, and 3 weeks
as shown in the graph at the right.Which plants'growth
represents a proportional relationship between time and
height? Explain. (Example3)
9'Y
J
3
iÿD-X
0 1 2 345 6
Time (weeks)
8
Lesson 5 Graph Proportional Relationships 163
t
Use a problem-solving model to solve each problem.
10. Raisins are sometimes sold by the pound.
11. The red line shows the distance traveled for
sho .ws the distance traveled for five minutes
The table below shows the cost for different
five minutes by a giant tortoise.The blue line
by a three-toed sloth. If each animal kept
weights of raisins. Choose the statement
traveling at its same rate for one hour, hoW
below that best describes the appearance
much farther would the tortoise have traveled
of the graph of the relationship between
weight and cost of raisins s°ld' ÿ(ÿ
than the sloth? 1ÿt (ÿ
9istauce Traveled
7O
,- 60
1
(ÿ a straight line that passes through the origin
(]ÿ) a curved line that passes through the origin
(ÿ a curved line that does not pass through
. the origin
0
4
Time3(rain)
ÿ 2
@ a straight line the does not pass through
the origin
13. Jarrod is comparing gym memberships.
Gym A charges $38 per month for
12. The relationship between the side length s of
a square' nal
andrelationship.
the perimeterGiven
P of the
square
is a
that
the side
roportlo
. 4__ e side
Pength of the smaller square is 5 th
length of the larger square, determine the
membership, with no annual fees. Gym B
charges an annual fee of $I 5 and a monthly
membership cost of $35.Which gym charges
more for a yearly membershipÿBy how much
more? Justify your response. ÿ @ (ÿ
perimeter, in centimeterS, of the smaller
square. ÿ%:ÿ 0 (ÿ
7--I
s=Scm
__ÿ ,ÿt.ÿÿ
....
= Measurement and Data @ = Mathematical Proce-ÿ
=Expressions, Equati°ns,andÿelati°nships
= ÿlumberancl Operations ÿ = prop0[ti0nality
. _. n.ÿnrtionalRelati°nships