Proportional Reasoning: Focus on Sense-Making
-
Upload
chris-hunter -
Category
Education
-
view
230 -
download
1
Transcript of Proportional Reasoning: Focus on Sense-Making
![Page 1: Proportional Reasoning: Focus on Sense-Making](https://reader031.fdocuments.net/reader031/viewer/2022021922/5884e0301a28ab4b778b5e69/html5/thumbnails/1.jpg)
Proportional Reasoning:Focus on Sense-Making
Chris Hunter Numeracy Helping Teacher
Surrey Schools
![Page 2: Proportional Reasoning: Focus on Sense-Making](https://reader031.fdocuments.net/reader031/viewer/2022021922/5884e0301a28ab4b778b5e69/html5/thumbnails/2.jpg)
twitter:@ChrisHunter36
email:[email protected]
the goods:reflectionsinthewhy.wordpress.com/bcamt2016
![Page 4: Proportional Reasoning: Focus on Sense-Making](https://reader031.fdocuments.net/reader031/viewer/2022021922/5884e0301a28ab4b778b5e69/html5/thumbnails/4.jpg)
Representation: Bar Model
2:40
2/3
![Page 5: Proportional Reasoning: Focus on Sense-Making](https://reader031.fdocuments.net/reader031/viewer/2022021922/5884e0301a28ab4b778b5e69/html5/thumbnails/5.jpg)
Representation: Bar Model
2:40
2/3
1:20 1:20
1/3
![Page 6: Proportional Reasoning: Focus on Sense-Making](https://reader031.fdocuments.net/reader031/viewer/2022021922/5884e0301a28ab4b778b5e69/html5/thumbnails/6.jpg)
Representation: Bar Model
4:00
1
1:20 1:20
1/3
1:20
![Page 7: Proportional Reasoning: Focus on Sense-Making](https://reader031.fdocuments.net/reader031/viewer/2022021922/5884e0301a28ab4b778b5e69/html5/thumbnails/7.jpg)
![Page 8: Proportional Reasoning: Focus on Sense-Making](https://reader031.fdocuments.net/reader031/viewer/2022021922/5884e0301a28ab4b778b5e69/html5/thumbnails/8.jpg)
Big Idea(s)
Compete
ncies Content
![Page 9: Proportional Reasoning: Focus on Sense-Making](https://reader031.fdocuments.net/reader031/viewer/2022021922/5884e0301a28ab4b778b5e69/html5/thumbnails/9.jpg)
Big Idea(s)
Compete
ncies
ratios rates
proportions unit price percent coupons
Content
![Page 10: Proportional Reasoning: Focus on Sense-Making](https://reader031.fdocuments.net/reader031/viewer/2022021922/5884e0301a28ab4b778b5e69/html5/thumbnails/10.jpg)
Big Idea(s)
Compete
ncies
ratios rates
proportions unit price percent coupons
Content
Proportional reasoning helps us make sense of multiplicative
relationships.
![Page 11: Proportional Reasoning: Focus on Sense-Making](https://reader031.fdocuments.net/reader031/viewer/2022021922/5884e0301a28ab4b778b5e69/html5/thumbnails/11.jpg)
Big Idea(s)
Compete
ncies
ratios rates
proportions unit price percent coupons
Content
Proportional reasoning helps us make sense of multiplicative
relationships.
Use multiple strategiesto solve problems
Communicate in a variety of waysto explain and justify ideas
![Page 12: Proportional Reasoning: Focus on Sense-Making](https://reader031.fdocuments.net/reader031/viewer/2022021922/5884e0301a28ab4b778b5e69/html5/thumbnails/12.jpg)
Big Idea
Students will understand that • Thinking about how quantities are related using multiplication is essential for solving a wide variety of
problems • Ratios, rates, and percent make comparisons easy; one term is made the same
Curricular Competencies Content
Students will be able to: • choose correct and efficient strategies • monitor progress to completion of task and make
necessary adjustments along the way • propose and consider or critique alternative
strategies • share mathematical ideas–not just steps!–needed to
solve problems (verbal & written) • present work that is clear and easy to follow • effectively use tables, equations, etc. to support
conclusions or arguments
Students will know that: • two equivalent ratios represent the same
relationship • ratio tables list equivalent ratios in an organized way • a rate represents an infinite number of equivalent
ratios • a unit rate (or price) is an equivalent rate where one
term is “1” • a proportion is an expression of the equivalence of
two ratios • proportion problems can be solved by looking for
scale factors within or between ratios • a percent is a fanatical comparison to 100
Big Idea(s)
Compete
ncies
ratios rates
proportions unit price percent coupons
Content
Proportional reasoning helps us make sense of multiplicative
relationships.
Use multiple strategiesto solve problems
Communicate in a variety of waysto explain and justify ideas
![Page 13: Proportional Reasoning: Focus on Sense-Making](https://reader031.fdocuments.net/reader031/viewer/2022021922/5884e0301a28ab4b778b5e69/html5/thumbnails/13.jpg)
Use l
ogic
and p
atter
ns to
solve
puzz
les an
d play
game
s
Use r
easo
ning a
nd lo
gic to
explo
re, a
nalyz
e, an
d app
ly ma
thema
tical
ideas
Estim
ate re
ason
ably
Demo
nstra
te an
d app
ly me
ntal m
ath st
rateg
ies
Use t
ools
or te
chno
logy t
o exp
lore &
crea
te pa
ttern
s &
relat
ionsh
ips, &
test
conje
cture
s
Mode
l math
emati
cs in
conte
xtuali
zed e
xper
ience
s
Apply
mult
iple s
trateg
ies to
solve
prob
lems i
n both
ab
strac
t and
conte
xtuali
zed s
ituati
ons
Deve
lop, d
emon
strate
, and
apply
math
emati
cal
unde
rstan
ding t
hrou
gh pl
ay, in
quiry
, and
prob
lem
solvi
ng
Visu
alize
to ex
plore
math
emati
cal c
once
pts
Enga
ge in
prob
lem-so
lving
expe
rienc
es th
at ar
e co
nnec
ted to
plac
e, sto
ry, cu
ltura
l pra
ctice
s, an
d pe
rspec
tives
relev
ant to
loca
l Firs
t Peo
ples
comm
unitie
s, the
loca
l com
munit
y, &
other
cultu
res
Use m
athem
atica
l voc
abula
ry &
langu
age t
o con
tribute
to
mathe
matic
al dis
cuss
ions
Expla
in an
d jus
tify m
athem
atica
l idea
s and
decis
ions
Comm
unica
te ma
thema
tical
think
ing in
man
y way
s
Repr
esen
t math
emati
cal id
eas i
n con
crete,
picto
rial, a
nd
symb
olic f
orms
Refle
ct on
math
emati
cal th
inking
Conn
ect m
athem
atica
l con
cepts
to ea
ch ot
her a
nd to
oth
er ar
eas a
nd pe
rsona
l inter
ests
Use m
athem
atica
l arg
umen
ts to
supp
ort p
erso
nal
choic
es
Incor
pora
te Fir
st Pe
oples
wor
ldview
s and
persp
ectiv
es
to ma
ke co
nnec
tions
to m
athem
atica
l con
cepts
A B C D E F G H I J K L M N O P Q R
perfect squares and cubes 1square and cube roots 2
percents less than 1 and greater than 100 (decimal & fractional %) 3numerical proportional reasoning (rates, ratio, proportions, & %) 4
operations with fractions (addition, subtraction, multiplication, division, & order of operations) 5
discrete linear relations (extended to larger numbers, limited to integers) 6
expressions- writing and evaluating using substitution 7two-step equations with integer coefficients, constants, and solutions 8
surface area and volume of regular solids, including triangular and other right prisms and cylinders 9
Pythagorean theorem 10construction, views, and nets of 3D objects 11
central tendency 12theoretical probability with two independent events 13
financial literacy — best buys 14
Big
Idea
s
*Number represents, describes, and compares the quantities of ratios, rates, and percents.
*Computational fluency and flexibility extend to operations with fractions.
*Discrete linear relationships can be represented in many connected ways and used to identify and make generalizations.
*The relationship between surface area and volume of 3D objects can be used to describe, measure, and compare spatial relationships.
*Analyzing data by determining averages is one way to make sense of large data sets and enables us to compare and interpret.
Cont
ent
Grade 8 Math Curricular CompetenciesReasoning and Analyzing Understanding and Solving Communicating and Representing Connecting and Reflecting
@JudyLarsen3
![Page 14: Proportional Reasoning: Focus on Sense-Making](https://reader031.fdocuments.net/reader031/viewer/2022021922/5884e0301a28ab4b778b5e69/html5/thumbnails/14.jpg)
Jeff Marc
$75 $60 $45Peter Liljedahl
Chris
![Page 15: Proportional Reasoning: Focus on Sense-Making](https://reader031.fdocuments.net/reader031/viewer/2022021922/5884e0301a28ab4b778b5e69/html5/thumbnails/15.jpg)
BUY TWO PAIRS,GET ONE PAIR FREE!
3rd pair must be of equal or lesser value
![Page 16: Proportional Reasoning: Focus on Sense-Making](https://reader031.fdocuments.net/reader031/viewer/2022021922/5884e0301a28ab4b778b5e69/html5/thumbnails/16.jpg)
Jeff Marc
? ? ?
Chris
![Page 17: Proportional Reasoning: Focus on Sense-Making](https://reader031.fdocuments.net/reader031/viewer/2022021922/5884e0301a28ab4b778b5e69/html5/thumbnails/17.jpg)
Jeff Marc
$45 $45 $45
h/t Carley Brockway
Chris
![Page 18: Proportional Reasoning: Focus on Sense-Making](https://reader031.fdocuments.net/reader031/viewer/2022021922/5884e0301a28ab4b778b5e69/html5/thumbnails/18.jpg)
Jeff Marc
$60 $45 $30
Chris
![Page 19: Proportional Reasoning: Focus on Sense-Making](https://reader031.fdocuments.net/reader031/viewer/2022021922/5884e0301a28ab4b778b5e69/html5/thumbnails/19.jpg)
Chris Jeff Marc
$56.25 $45.00 $33.75
![Page 20: Proportional Reasoning: Focus on Sense-Making](https://reader031.fdocuments.net/reader031/viewer/2022021922/5884e0301a28ab4b778b5e69/html5/thumbnails/20.jpg)
![Page 21: Proportional Reasoning: Focus on Sense-Making](https://reader031.fdocuments.net/reader031/viewer/2022021922/5884e0301a28ab4b778b5e69/html5/thumbnails/21.jpg)
![Page 22: Proportional Reasoning: Focus on Sense-Making](https://reader031.fdocuments.net/reader031/viewer/2022021922/5884e0301a28ab4b778b5e69/html5/thumbnails/22.jpg)
Jeff Marc
$150 $90 $60
Chris
![Page 23: Proportional Reasoning: Focus on Sense-Making](https://reader031.fdocuments.net/reader031/viewer/2022021922/5884e0301a28ab4b778b5e69/html5/thumbnails/23.jpg)
MARS
![Page 24: Proportional Reasoning: Focus on Sense-Making](https://reader031.fdocuments.net/reader031/viewer/2022021922/5884e0301a28ab4b778b5e69/html5/thumbnails/24.jpg)
Rod Ratios
What is the ratio of this pair of Cuisenaire Rods? How do you know? How many pairs can you find with the same ratio?
@robertkaplinsky
![Page 25: Proportional Reasoning: Focus on Sense-Making](https://reader031.fdocuments.net/reader031/viewer/2022021922/5884e0301a28ab4b778b5e69/html5/thumbnails/25.jpg)
Proportional Problem Types:(1) missing-value, and (2) comparison
![Page 26: Proportional Reasoning: Focus on Sense-Making](https://reader031.fdocuments.net/reader031/viewer/2022021922/5884e0301a28ab4b778b5e69/html5/thumbnails/26.jpg)
Split Time
@ddmeyer
![Page 27: Proportional Reasoning: Focus on Sense-Making](https://reader031.fdocuments.net/reader031/viewer/2022021922/5884e0301a28ab4b778b5e69/html5/thumbnails/27.jpg)
Split Time
What’s the first question that comes to your mind? What’s a guess that’s too low? What’s a guess that’s too high? Write down your estimate. What information would be helpful to know here?
![Page 28: Proportional Reasoning: Focus on Sense-Making](https://reader031.fdocuments.net/reader031/viewer/2022021922/5884e0301a28ab4b778b5e69/html5/thumbnails/28.jpg)
Split Time
![Page 29: Proportional Reasoning: Focus on Sense-Making](https://reader031.fdocuments.net/reader031/viewer/2022021922/5884e0301a28ab4b778b5e69/html5/thumbnails/29.jpg)
Split Time
![Page 30: Proportional Reasoning: Focus on Sense-Making](https://reader031.fdocuments.net/reader031/viewer/2022021922/5884e0301a28ab4b778b5e69/html5/thumbnails/30.jpg)
Representation: Ratio Table
metres 400
seconds 75
![Page 31: Proportional Reasoning: Focus on Sense-Making](https://reader031.fdocuments.net/reader031/viewer/2022021922/5884e0301a28ab4b778b5e69/html5/thumbnails/31.jpg)
Representation: Ratio Table
metres 400 40
seconds 75 7.5
![Page 32: Proportional Reasoning: Focus on Sense-Making](https://reader031.fdocuments.net/reader031/viewer/2022021922/5884e0301a28ab4b778b5e69/html5/thumbnails/32.jpg)
Representation: Ratio Table
metres 400 40 80
seconds 75 7.5 15
![Page 33: Proportional Reasoning: Focus on Sense-Making](https://reader031.fdocuments.net/reader031/viewer/2022021922/5884e0301a28ab4b778b5e69/html5/thumbnails/33.jpg)
Representation: Ratio Table
metres 400 40 80 160
seconds 75 7.5 15 30
![Page 34: Proportional Reasoning: Focus on Sense-Making](https://reader031.fdocuments.net/reader031/viewer/2022021922/5884e0301a28ab4b778b5e69/html5/thumbnails/34.jpg)
Representation: Double Number Line
seconds
400
75
0
0
40 80 160
7.5 15 30
metres
![Page 35: Proportional Reasoning: Focus on Sense-Making](https://reader031.fdocuments.net/reader031/viewer/2022021922/5884e0301a28ab4b778b5e69/html5/thumbnails/35.jpg)
![Page 36: Proportional Reasoning: Focus on Sense-Making](https://reader031.fdocuments.net/reader031/viewer/2022021922/5884e0301a28ab4b778b5e69/html5/thumbnails/36.jpg)
![Page 37: Proportional Reasoning: Focus on Sense-Making](https://reader031.fdocuments.net/reader031/viewer/2022021922/5884e0301a28ab4b778b5e69/html5/thumbnails/37.jpg)
![Page 39: Proportional Reasoning: Focus on Sense-Making](https://reader031.fdocuments.net/reader031/viewer/2022021922/5884e0301a28ab4b778b5e69/html5/thumbnails/39.jpg)
Carnival Tickets
What questions do you have?
@robertkaplinsky
![Page 40: Proportional Reasoning: Focus on Sense-Making](https://reader031.fdocuments.net/reader031/viewer/2022021922/5884e0301a28ab4b778b5e69/html5/thumbnails/40.jpg)
![Page 41: Proportional Reasoning: Focus on Sense-Making](https://reader031.fdocuments.net/reader031/viewer/2022021922/5884e0301a28ab4b778b5e69/html5/thumbnails/41.jpg)
![Page 42: Proportional Reasoning: Focus on Sense-Making](https://reader031.fdocuments.net/reader031/viewer/2022021922/5884e0301a28ab4b778b5e69/html5/thumbnails/42.jpg)
![Page 43: Proportional Reasoning: Focus on Sense-Making](https://reader031.fdocuments.net/reader031/viewer/2022021922/5884e0301a28ab4b778b5e69/html5/thumbnails/43.jpg)
![Page 44: Proportional Reasoning: Focus on Sense-Making](https://reader031.fdocuments.net/reader031/viewer/2022021922/5884e0301a28ab4b778b5e69/html5/thumbnails/44.jpg)
What do you notice?
What do you wonder?
![Page 45: Proportional Reasoning: Focus on Sense-Making](https://reader031.fdocuments.net/reader031/viewer/2022021922/5884e0301a28ab4b778b5e69/html5/thumbnails/45.jpg)
“Best use of textbooks ever.”
![Page 46: Proportional Reasoning: Focus on Sense-Making](https://reader031.fdocuments.net/reader031/viewer/2022021922/5884e0301a28ab4b778b5e69/html5/thumbnails/46.jpg)
![Page 47: Proportional Reasoning: Focus on Sense-Making](https://reader031.fdocuments.net/reader031/viewer/2022021922/5884e0301a28ab4b778b5e69/html5/thumbnails/47.jpg)
![Page 48: Proportional Reasoning: Focus on Sense-Making](https://reader031.fdocuments.net/reader031/viewer/2022021922/5884e0301a28ab4b778b5e69/html5/thumbnails/48.jpg)
![Page 49: Proportional Reasoning: Focus on Sense-Making](https://reader031.fdocuments.net/reader031/viewer/2022021922/5884e0301a28ab4b778b5e69/html5/thumbnails/49.jpg)
M
athChallenge
25#
Answer:Good Grape should have the strongest grape taste.
Ratios are fractions that compare two or morequantities. Shoppers use ratios to compare prices;cooks use them to adjust recipes. Architects and
designers use ratios to create scale drawings.
Figure This! If all grape juice concentrates are the same strength, which recipe would you
expect to have the strongest grape taste?
???
?
GR
APE JUICE JUNG
LE
Hint: For each recipe think about how much watershould be used with 1 cup (c.) of concentrate,or how much concentrate should be used with
1 cup of water.
Which tastes
JUICIER
NCTM
![Page 50: Proportional Reasoning: Focus on Sense-Making](https://reader031.fdocuments.net/reader031/viewer/2022021922/5884e0301a28ab4b778b5e69/html5/thumbnails/50.jpg)
Which city is “selfier”?
Anaheim, California Milan, Italy
![Page 51: Proportional Reasoning: Focus on Sense-Making](https://reader031.fdocuments.net/reader031/viewer/2022021922/5884e0301a28ab4b778b5e69/html5/thumbnails/51.jpg)
reflectionsinthewhy.wordpress.com/wncp-virtual-file-cabinetMore Missing-Value & Comparable Comparison Problems
![Page 52: Proportional Reasoning: Focus on Sense-Making](https://reader031.fdocuments.net/reader031/viewer/2022021922/5884e0301a28ab4b778b5e69/html5/thumbnails/52.jpg)
@robertkaplinsky
![Page 53: Proportional Reasoning: Focus on Sense-Making](https://reader031.fdocuments.net/reader031/viewer/2022021922/5884e0301a28ab4b778b5e69/html5/thumbnails/53.jpg)
Curricular Competencies RevisitedBig Idea(s)
Compete
ncies
ratios rates
proportions unit price percent coupons
Content
Proportional reasoning helps us make sense of multiplicative
relationships.
![Page 54: Proportional Reasoning: Focus on Sense-Making](https://reader031.fdocuments.net/reader031/viewer/2022021922/5884e0301a28ab4b778b5e69/html5/thumbnails/54.jpg)
Curricular Competencies RevisitedBig Idea(s)
Compete
ncies
ratios rates
proportions unit price percent coupons
Content
Proportional reasoning helps us make sense of multiplicative
relationships.
?