comparing wasty wally to enviro joe - the learning...
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Comparing Wasty Wally to Enviro JoE Name: __________________________________________________________
appEndix a1 linear systems grade 10 mathematics, applied (mFm2p)
Differentiated Instruction Teaching and Learning Examples 2009 Ontario Ministry of Education—Student Success/Learning to 18 Implementation, Training and Evaluation Branch 1.
The average Canadian generates approximately 800 kg of garbage per year. Joe is 25 years old when he decides to reduce the amount of garbage he produces. Wally is 16 and he doesn’t care about how much garbage he produces.
Getting to Know JoeHeight: 190 cmWeight: 80 kgAge: 25Nickname: Enviro JoeFavourite Food: NachosAnnual Garbage Production: 800 kg
Getting to Know WallyHeight: 165 cmWeight: 70 kgAge: 16Nickname: Wasty WallyFavourite Food: ShrimpAnnual Garbage Production: 800 kg
a) the past is full of waste…How much garbage has Enviro Joe produced in his life so far? How much garbage has Wasty Wally produced in his life so far?
B) Joe is a changed man!Enviro Joe has decided to decrease his waste production by increasing his recycling, composting regularly and buying products that use less packaging. He now generates 50% less garbage per year. If Joe, a changed man, and Wally, stuck in his ways, both live to be 85, how much garbage will they each produce in their lifetime?
C) Wally catches up…How long will it take for Wasty Wally to catch up to Enviro Joe, the changed man, in terms of garbage production? And how much will they each have produced by that point?
Solve this problem, in as many ways as you can, using any of the tools available to you.
garBagE Bag Cut-outs For Comparing Wasty Wally to Enviro JoE
appEndix a2 linear systems grade 10 mathematics, applied (mFm2p)
2.Differentiated Instruction Teaching and Learning Examples 2009 Ontario Ministry of Education—Student Success/Learning to 18 Implementation, Training and Evaluation Branch
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3.
linEar systEms assEssmEnt ChECklist (page 1 of 2)
appEndix B linear systems grade 10 mathematics, applied (mFm2p)
This checklist may be used as a pre-assessment for this Differentiated Instruction Teaching/Learning Example and to help the teacher differentiate according to readiness throughout the lesson.
LegendN—This student is not at the entry point for this unit and will need additional support to be successful.A—This student is at the entry point for this lesson. B—This student is beyond the entry point and will need additional challenges.
student name Conn
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Differentiated Instruction Teaching and Learning Examples 2009 Ontario Ministry of Education—Student Success/Learning to 18 Implementation, Training and Evaluation Branch
4.
linEar systEms assEssmEnt ChECklist (page 2 of 2)
appEndix B linear systems grade 10 mathematics, applied (mFm2p)
student name Conn
ecti
ng: C
an c
reat
e a
mod
el (a
lgeb
raic
, gr
aphi
cal,
num
eric
al,
etc.
) for
a li
near
rel
atio
n
Conn
ecti
ng: M
akes
co
nnec
tion
s be
twee
n th
e po
int
of in
ters
ecti
on a
nd
a re
al w
orld
con
text
Refl
ecti
ng:
Refl
ects
on
ef
fect
iven
ess
of g
raph
ical
so
luti
ons
to li
near
sy
stem
s (B
can
pro
pose
al
tern
ativ
e st
rate
gies
)
Refl
ecti
ng: J
udge
s th
e re
ason
able
ness
of
his
or
her
resu
lts
Com
mun
icat
ing:
Exp
lain
s an
d ju
stifi
es s
olut
ions
or
ally
, vis
ually
and
/or
in
wri
ting
Brief notes/Comments
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Differentiated Instruction Teaching and Learning Examples 2009 Ontario Ministry of Education—Student Success/Learning to 18 Implementation, Training and Evaluation Branch
5.
ChoiCE Board (Column 1): ChoosE your oWn advEnturE
appEndix C1 linear systems grade 10 mathematics, applied (mFm2p)
Differentiated Instruction Teaching and Learning Examples 2009 Ontario Ministry of Education—Student Success/Learning to 18 Implementation, Training and Evaluation Branch
Cut each card along the solid line and fold along the broken line to make choice cards.
Column 1, Card a You’ve organized a fundraiser for Free The Children by selling T-shirts and hoodies. Janessa has sold 12 hoodies and 8 T-shirts, raising a total of $248. Suhaila sold 7 hoodies and 14 T-shirts, raising a total of $217. How much do T-shirts and hoodies cost?
Column 1, Card BAnayis and Dexter are big fans of The Fractal Guy, and they want to spend the day watching the show. They have the following discussion: Anayis: The Fractal Guy is on all day, you just have to find the channel it’s on! Dexter: Yeah, yeah, but then we’d have to watch commercials all day. It would take, like, 30 minutes for each episode. If we watch my DVDs it will only take 22 minutes per episode. Anayis: Yeah, but your DVDs are at home and it would take an hour to get them. We might as well start right now instead of wasting an hour.
How long would it take for them to watch the same amount of The Fractal Guy using either plan?
Column 1, Card C Arun and Hal are both downloading a 35 Mb (megabyte) video from the Internet. Hal’s computer downloads at 7 Mbps (megabytes per second) and Arun’s downloads at 5 Mbps. If Arun gets 3 Mb downloaded before Hal gets started, how long will it take for Hal’s downloading to catch up to Arun’s?
shopping with
arunhal
the download dash
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Becoming a Couch potato
6.
ChoiCE Board (Column 2): ChoosE your oWn advEnturE
appEndix C2 linear systems grade 10 mathematics, applied (mFm2p)
Differentiated Instruction Teaching and Learning Examples 2009 Ontario Ministry of Education—Student Success/Learning to 18 Implementation, Training and Evaluation Branch
Cut each card along the solid line and fold along the broken line to make choice cards.
Column 2, Card aTwo cities, Statsville and Newtonville, are competing against one another to build the world’s tallest building.Statsville has already started building its tower. It’s already 230 m tall, and they are building at a rate of 4 metres per week.Newtonville is beginning construction today, and they estimate that they can build at a rate of 7 metres per week.When will Newtonville’s tower catch up to Statsville’s tower? Will they be taller than the CN tower, which is 588 m tall, at that point?
Column 2, Card BHannah and Fran are racing downhill. Hannah is on skis and Fran is on her snowboard. Hannah starts off 2,200 m from the bottom of the hill and she is descending at a rate of 7 metres per second. Fran starts off 1,800 metres from the bottom of the hill and she is descending at a rate of 5 metres per second.How long will it take for Hannah to pass Fran? How far from the bottom will they be at that point?
Column 2, Card CPerry and Todd are organizing a carnival to raise money for the Heart and Stroke Foundation at their school. They are responsible for purchasing supplies for the party. They buy a total of 180 items at the store, including balloons that cost 5¢ each and streamers that cost 30¢ each. Perry and Todd spend a total of $25.25. How many balloons and how many streamers did they buy?
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a race to be the tallest
a race to the Bottom
a race for the heart
7.
linEar systEms Exit Cards
appEndix d linear systems grade 10 mathematics, applied (mFm2p)
Differentiated Instruction Teaching and Learning Examples 2009 Ontario Ministry of Education—Student Success/Learning to 18 Implementation, Training and Evaluation Branch
Exit Card—summary of discussion Name: ________________________________________________________________________________
Today, I was really good at: ___________________________________________________________________________________________________________________________________________________________________
I think I need more help with: _______________________________________________________________________________________________________________________________________________________________
Solving a linear system graphically is not always the best way because: ____________________________________________________________________________________________________________
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Exit Card—summary of discussion Name: ________________________________________________________________________________
Today, I was really good at: ___________________________________________________________________________________________________________________________________________________________________
I think I need more help with: _______________________________________________________________________________________________________________________________________________________________
Solving a linear system graphically is not always the best way because: ____________________________________________________________________________________________________________
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8.
tiEr 1 assignmEnt: CrEatE a QuEstion (page 1 of 2) Name: ______________________________________________________
appEndix E linear systems grade 10 mathematics, applied (mFm2p)
Differentiated Instruction Teaching and Learning Examples 2009 Ontario Ministry of Education—Student Success/Learning to 18 Implementation, Training and Evaluation Branch
Match the graph on the left with the answer starter on the right and complete the answer. Then create a question that would result in that answer. Consider the examples on pages 1 and 2 as you determine the graphs and answer starters that match.
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Answer: It will be cheaper at Joe’s after _________________________________________________________________
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JoeJosephine
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Answer: They will pass each other after __________________________________________________________________
9.
tiEr 1 assignmEnt: CrEatE a QuEstion (page 2 of 2) Name: ______________________________________________________
appEndix E linear systems grade 10 mathematics, applied (mFm2p)
Differentiated Instruction Teaching and Learning Examples 2009 Ontario Ministry of Education—Student Success/Learning to 18 Implementation, Training and Evaluation Branch
Match the graph on the left with the answer starter on the right and complete the answer. Then create a question that would result in that answer.Consider the examples on pages 1 and 2 as you determine the graphs and answer starters that match.
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Answer: Joe will earn $ ______________________ before he starts earning overtime.
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Joe’s Gaming WarehouseArchie’s Arcade
Question:
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Answer: Joe will have to work for _______________________________ in order to break even.
tiEr 2 assignmEnt: CrEatE a QuEstion Name: __________________________________________________________
appEndix F linear systems grade 10 mathematics, applied (mFm2p)
10.Differentiated Instruction Teaching and Learning Examples 2009 Ontario Ministry of Education—Student Success/Learning to 18 Implementation, Training and Evaluation Branch
Muddled Mr. Middleton has lost most of his magnificent mathematics lesson on solving linear systems. The only things he can find are the graphs that would result from solving the problems that are given below. He’s even lost his labels!
Your task is to help Mr. Middleton create his lesson by:
a) Adding a scale to the graph
b) Writing the equations that represent the two linear relations given on the graph
c) Writing a word question that would result in the given equations
d) Adding axis labels and a title to the graphs
Question #2Question #1
tiEr 3 assignmEnt: CrEatE a QuEstion Name: __________________________________________________________
appEndix g linear systems grade 10 mathematics, applied (mFm2p)
11.Differentiated Instruction Teaching and Learning Examples 2009 Ontario Ministry of Education—Student Success/Learning to 18 Implementation, Training and Evaluation Branch
Create a real-life word question that can be solved using a linear system of equations and solve it graphically. Your answer should include both the question and the solution.
Question:
Solution: