~ ame: __,__}1~.JAd=,------ \ .. I .J"".,.. 1

(l.&.\ -u Test Date: )J'/ €'Q\n c,., u. ~

e Unit 3A: Proportionality Test Study Guide

Unit Rates:

1. If Mark uses 3 ~ tablespoons of coffee to 2. Andre took a trip from Boston, I 4 Massachusetts to Paris, France. The plane

make 10 cups of coffee, how much would he need to make one cue of coffe~?

took 6 ~ hours to go 3,669 ! miles. How far 3 5

L!. .:. 10 I( ' F

~ +I,~,,

.. did the plane travel in 1 hour? lsso.'ii 'rlilcj )

+b,.p ,., I 17 31.f '\

,t 2.0 ~ 4 . :i ' to 3 - = p,iltS ~ , oo =I I h l&W° j

= :. -

(.~ 1..9 ~ /0 : I I coA=. :

~ ~ o :. :!:!. I I

L how- ,. . , 3. A standard bathtub holds 70 gallons of 4. Mackenzie ran the Olympic marathon of

water. On average, it takes 7 ~ minutes to 26 ~ miles in a time of 5 ! hours. How far 2 5 5

drain a bathtub. How many gallons of did she run in the first hour?

water go down the drain each minute?

"'70 -~ 1110 af ~ I I ss "1~ • 4 f,!. I •

~ ... , ~ -: - 'ii'~ , ;g ,..i 'l "i C}• :. 1., ~Plild 4~"'' ~ 2. ... ;..........:- P1i\t5 I~•

-= ·- \'4S' -~ - ... 1 15:.~ :.

... \ . , ..; . r • -:. ru" I ,•,un !"\In \ . h ol.U"'

=-- f ~.. \ h ~__. 2. . s n :. ~

5 . •

5. Tiana's car travelled 111 miles on~ of a 6. Joey entered a hot dog eating competition. 8 In 3 ~ minutes, he ate 30 ~ hot dogs. How

tank of gas. How far will she be able to go 4 2

on a full tank of ~as? many hot dogs did he eat in one minute?

1 cg,h ho "dJ'j 1

UI ;... ?, V,f ' . v~c,,.,; ' lPI . 1l, :;IM'1 r:+ ... !"lil~ - ' . ~

3'~' ·~, 'i:" " If To Oj i ,.

~ -- -= - •" ~ ~)

::: or - I 1 M ;1

aa~ I ,,.s 19~+.A~ - .. " • ,c;; I M;I\ -- -: - )',i -n . -r:r -: --;; 'i s \

Proportionality:

.NuMBER TOTAL 8. Find a real-world example of a proportional I

OF Hot.IRS COST{$) RATIO~ y relationship.

I

X

~ 1 $75 , l;tO f,O

2 $120 --~ - I

3 $165 ~ ~ns~..1 wil\ \/~ 3

4 $210 210 How could that relationship be changed to become -'f non-proportional?

5 $255 ,,,, -6 ---- I

7. Fill in the missing ratio values. I I Is the table proportional?

Explain why or why not: NP be ~ -ti,«. lM'\~ r~ ,.s

l'I.~ ~ . .......

1

~-------A 9.

3

2 t: 0 V

l.S ii .. {2

1

0.5

0

0 2 3 ~ . s 6

Number of Ice Cream Bars

a. Is this a proportional graph? Why or why not? )'e~; ori~i ", lintN""

b. fill in the table for the graph

X. IJ~i,., :tC4."'-"'

D

l ~

3 ·

4 5"

. o., c.c1.+- . c. What is the unit rate (include labels)?~ -: t i<a. u-,., \,c,,r-

d. Write the equati?n relating cost to number o ice crl,!am bars purchased. 10.

y .~ Cot+

0 o .5

l , . 5

ol_,

~ -5

Fill in the missing amounts of quarts and gallons. Then find the ratio for the number of quarts (y) to the number of gallons (x) .

Gal (x) I 2 4 5 10 ~ 25 30 4S 100 X Quarts (y) Lt 8 / tp .:lo 4-0 80 too J ,t) 180 'lo- y

' Ratio l:'. !i .! IC, 2,o ~ ~ 100 /1,0 18') 'J!!_ ~ - - - - 46 I 4 " s 10 'Z.0. ZS' 10 ,., )( X

'>!1_ I

I . What docs the i ratio tell us'J CeY\.~ ~ pnpol""+tMolt'~ '"' Q\.l.Ar,b per j'J\bV\

2. Write an equation to show how to find the number of quarts in any number of gallons.

Y ~ "1X [Y ~ tXj ov-[Y~ 4x ~ Determine which of the following graphs represent proportional relationships. Circle the appropriate response.

11. 12. 13. i

I

I - 1+ .... .. ... ·,n "

' 7 . 'Ill .._ I

I

.. I

:

I I ,_ I i L

'-~· i--' - ' l ,., ,.,, /<

rt I

: t I\ · t l f , i •

- I ' , ~ ' I ' I ,,

I I I - . •· H- ... + ' ' r

i ! -+- ,_ .... ..L ·f }-..

'--' :

..... ~

,._,._ ~ ~ - 1--i- ·1- I

~ I ,.,

-I I I- - -~ ... +- ! .. I

! j \ ! t ' \

+-~ ,

~ ' • 1 , ; .. , r ~

'-t--i- ! I I - , I I

l l W I ;

. • I I

Proportional on-proportional Proportional non-proportiono

Ob Ori j

It

2

--------14. 15 16.

_::, . _.,,,--

-- .,,, ~-

Proportional non-proportional ~ non-proportional

NUMBER TOTAL RATrO: y

Of'HOURS CosT ($) X

1 $45 45 -I

2 $90 ~- '{!_ 2 - I

3 $135 I 35 '4' -- -3 - I 13'0 'IS

4 $180 - ; -4 , 5 $225 2.2.S'::.

i., -!i I

17. Fill in the missing ratio values. Is the table proportional? Explain why or why not:

f - the v.n;+ ~c...+.( (.en$-+M,+ {Ii r-r~ht\J11

i~ +ht ~G.Jl'\.C., ( 't~) So I ,.

-hu. ~h wt>\J.l.l .ht- 1,'necU"'.

J:'.\, ~ Also 30 ~ -+~ or;e,~I\ ( 01 0).

·2

18. The amount of money Amy has saved is proportional to the number of weeks that have passed. This relationship

is graphed below. a. Identify the unit rate or constant of

proportionality and explain its meaning, related to this context.

f~T ~ twn tto io S""'•~ ~ ,~ b. Explain the meaning of the points, (0, O) and (4,

40), within this context.

(o,o) - ~~ it i~ ~ o, ~ ii fO ("f 140) .. ~ ~ i.t, ~ i~ ~LfO

y Sev ,ngs ( I n dollars )

S>O

60

70

80

50

40

30

20

2 4 6 N umber ~ f V\/eeks x

3

----------------------------- ' r--- ...., ---19. a. Is this a proportional graph?

Why or why not? 700 - --·· l I

I Yes; li'c1wr ~ ()l""io•·f\ 600 ~------- ----- - ---1·-

b. What is the unit rate {include labels)? How do you know?

Y \ ~o c:~\o.-i cJ

x-=- \ ~n0.<-4'-

Cv~ >t ::: I ... -tN. ~r"f \\, ":. I l.O

c. Write the equation for calorics related to number of snacks.

'j~ MX.

d. Where does tht! unit rate show up on the graph? In the equation?

Gl t"D.f> h - ~ he,t'\ X -:. I

500

400 .. • 91 a a

300

200

100

0

l - .. -- --·· { -· -· - , -----,-----1--I

I l- --

I .

I I I --I

i t

0

1

I

I -·· - i

2

£ct,~-\-,()'('\ - y:; ':F ){ ~n;-t..-..::t"c.-

3

Number of Snildts

20.

You can use table, graphs, words or equations to represent and compare proportional 1 . h. D"ffi r ed b 1 re at.Ions 1ps. I crcnt eye 1sts rates arc represent COW.

Words Cyclist A Equation Cyclist C

A cyclist can ride 2./ miles in 2 hours. y =9x ~

Table Cyclist B Graph ,. Cyclist D '

40

Time Hours Distance (miles) 30

0 0 e 20 I 5 C

ci: 2 10 -"' ,o

3 15 0

I I

' I

4

' . J . ~ >

Tinw th~11r<.\

'

5

Put the cyclists in order from fastest to slowest, using math AND words to explain your reasoning.

P>® C . t> . (l 10) 5 n-,~ y::ctx ®' . Th ~ ; ~ ""' - I h

I h

C, 1:> 0~ of

I le

-j I

l I

I

6

It 4