Gr.8 Fractions - SGDSBMathLearningPartners

Transcription

Contents of Grade Level Planning Supports
Paget#:
Fractions
Pizza and Cake
Fraction Frenzy (Pre-Unit Anenment)
Differentiating Instruction Based on Diagnostic Aue..ement
PartB Problems
Multiplying - zero to One and Beyond!
Modelling with Area
Simply Using Symbols
• Fraction Action Game
Mixed Models
Let's Share
Juat One Plene
TIPS Resources
• See Section 2 "Fractiona" aection
Connecting to Composites
Summative Task
98
102
107
123
126
127
129
131
133
136
138
141
142
Lesson Outline: Fractions
Grade 8
BIGPI~RE
•
same conceptual fbundation as
ope
•
•
•
•
use
den
•
•
rel,resell1 cl()mpo!;ite numbers as products
a DletlJl'",
division
use patterning to de:tenuirl.e
fractions can
a fraction:
area:
aemonstrate Drof1ciency in opentti()ns
up to two trl;l\;ti<ms;
a calculator
in problem "nlvin,y
28
Parts Problems
•
a fractional
•
a
•
fractions are
•
TIPS Section
-" Grade (:\
Queens Printer for Onlario. 2004
(modified by HCDSB)
96
•
patterning to develop the 'invert~and~multiply
dividio!! two fractions.
Pf'!l(,ti".. dividing
rate
esources from TIPS continuum on fractions to
36
TIPS Seelion
'-'''+'H;;''''
Grade e
Queen's PrInter
Ontario, 2004
numbers as products of
common multiples.
common
(modmed by HeeSB)
Gradel
Dncr;il!tlQn
Mlttria..
•
• $leIJ!xillrd,
Activate and assess
• (flIetion tlrcle,
• chan paper
• flIlIrker>
• £lIM:!£>.
~
lmall Group! -+ Ordering fraction!
Students may IJse
a (:l!Ilculator to
each
to iii
decimal
As math class time begins distribute fraction cards
find
same
Tm<:tl(ftlS in order and
Two
with the same colour scI of Irac·ltorls
the
used.
two
tW()
for
other group.
imHp! 7 f'rtJII!tdol1
Each group
a summary of their strslteg les.
CuJ"rinlu. Expeda~rvatioulA'-'1 Notes;
•
Action.
Students use their
knowledae of
lIMit (kogp! 7 Modeling Fradoot
Set up multiple stations of the two activities.
Stu,dents we)rk in
groups at one ofthe stations
Studerllts prepare
time then
on
determine
common
denominators
C.rrkulu. EqMdatioulO_rvatioulAueedotal Notes: Assess
•
CoMoIldate
Debrief
Sludents to review
the factors of
composite
numbers, slllhey
reduce fracllons,
JYI!!II elm 7 DJH.w!Jim
Use the chart !)aper solutions to COIIS()llida:le Ul1de,rstklnctimg:
I)
can have dillf'erent
exrtressed in different ways,
eX~tressed with commcmr()!' actdlltio'lt
rl 1
11
5) Fractions can be reduced when numerator and denominator share a common
than 1
to the Minds On
to discuss how to use common del1011rlll1ators
and
(0, ,and 1) when cOfllpar'ing IT'dC:tlOfIS.
Home Activit! or.Furth!f CIMlr90m Consolidation
To
tor next day's ll.'Ssessment task, make a graftiti sheet
rel'l:lember about rrac'ti.OfIS, Ccmsider inCI11dini.g:
a) temtino]logy
b) how to
e) how to rel1resent
on a number line
TIPS Section 3
Grade a
Queen's Prinlerlor
2004
(modified by HeDSEl
you
98
26"1: Fraction Cards
Cut into vertical strips, This produces sufficient cards for four classes.
7
~
6
6
~
5
7
5
SecliQn
Grade 8
Queen's Printer for Ontario, 2004
(modifted by HeeS8)
99
26.2: Fraction Stations
Pizza Pieces
1. Use circular fraction pieces to create a model for a pizza that has been cut into pieces. On
chart paper:
a) Draw the model.
b) Write an equation for the model.
c) Show that the equation is true,
is true.
Write the equation.
1
1
1
1
2
4
6
12
-+ + +
11 1 1
-+ + +
2 4 6 12
6
3 2
1
+
i2 12 12
6 3 2 1
-+-+
12
12
I
Create different models using the same procedure,
Different models might have.
a smallnumber offraction pieces
b) a large number offraction pieces
c) allfmction pieces the same
d) some fraction pieces the same
TfPS Section
~. Grade
and some pieces ofdifferent size
(m,H:litll:ld by HCOBRI
100
26..2: Fraction Stations
Pieces of Cake
1. Create a geoboard model for one whole cake that has been cut into pieces. On chart paper:
a) draw the model;
b) write an equation for the model;
c) show that the equation is true.
Example:
Draw the modeL
Write the equation.
Show that the equation is true.
1 1 1 1
+
+ +
8 8 8 8 2
1 1 1 1 1
+ + +-+
8 8 8 8 2
4 1
==
+
8 2
1
1
k
......
-+')
')
Create different models using the same procedure.
Different models might have:
a) a small number ofpieces
a large number ofpieces
the same size for allpieces
d) some pieces ofthe same size and some pieces ofdifferent size
TIPS Section
Grade 8
Queen'$ Printer for Ontario, 2004
(m()dified by HCDSB)
101
Grade 8
PtlCdRl9n
•
MlHrJiIi
• manipulatives
• chart paper
• markers
• calculators
• 13LM 27.1
Assess
AHMament
SmI" Grgun :Z Pm It Onl
Post Graffiti sheets with the fbllowing
1) Show
ways to find
w
2~.3 + II2
Show different ways to find 2 2 I I
3
w
3) List fraction
Show smne
and me:anltlgs.
slU,dents work in small
move to
sheets. ~.lrCU!lHe
assessment for
At
•
Actionl
Manipulative!>
available at aach
on a number
IndiYklual:z A!UHm!nt
Review instructitms with students
1<11l)wledl.!e of
27J}.
$tat1l:m:
bk:!ekIL
circles, geoboards,
rufers
Check that sheets
contain correct
information,
the
CW'l'lett.lum ExpeeUUouIPaper..peKH AsHameut!Rubne:
•
Consolidate
Debrief
students'
learning.
Individual ~
RefI!ction
Students reflect on their answers to
8.
Home AdVItY or FUrtb!f: C._room COnIQlidation
Think of different contexts fi:)r questions that can also be """"""",,.,,,1
expr,esskm: 6
TIPS Section
Grade 8
the
".-
Printer for Ontario, 2004
(modifIed by
102
27.. 1: Fraction Frenzy: Pre.. .Unit Assessment
Name:
Date:
Instructions:
1 Answer all of the questions as completely as possible,
2. Your answers will be assessed for understanding, communication, and
correctness.
3. If you think you can explain your reasoning much better by talking or by
showing something to me, draw a speaker symbol beside the question.
Speaker
.-,,,..,
IUit;,~l'J
<»)
If you need me to read something to you, show me the sign language
symbol for R
5, If you need manipulatives, show me the sign language symbol
forM.
6, You may use a calculator for any part of this assessment
1
<
A circle is divided into four parts as shown in the diagram.
One of the parts is shaded.
Which fraction of the whole circle is shaded?
Give reasons for your answe
a) one~quarter
(b)) less than one~quarter
TIPS SeClkm 3 - Grade 8
(modified
(1J)
c) more than one-quarter
by Hens B)
103
27.. 1: Fraction Frenzy: Pre-Unit Assessment (continued)
2. a) Use the diagram to convince Robyn that
3 of a chocolate cake is equivalent to 12 of the cake.
5
b) Could you convince Robyn that
~
is equivalent to
~:
without using a diagram?
Justifyyour answer:
I
3,
Put a checkmark
in the one column that best describes the given number.
Between 0 and
1
~
2
Between
1
')
and 1
Greater titan 1
6
i)
11
61
Explain your answer for -',
83
Section
- Grade 8
(modified by HOOSB)
104
27.1: Fraction Frenzy: Pre-Unit Assessment (continued)
4, Sue, lila, and Mel Ling jog on a track every morning,
Sue jogs
7
8:
Lila jogs
5 km and Mei Ling jogs .3 !km.
6
2
a) Use the number line to represent the distance that each person jog.s,
I
S~~ I
I
L\~V.I
o
1
2
3
~Yl,;~~
I4
b) How much farther does Mei Ling jog every morning than Sue? Showyour work:
How much farther does Mei Ling jog than Lila in one week? Showyour wor*:
::
5,
a) ')_ 1 +
Showyour
2
4 1 'J.3
""
4
-
- .,"
')
t+
TIPS Section 3 - Grade
Queen's Printer for Onlario, 2004
(modified by HCDSB)
Page 106
27.. 1: Fraction Frenzy: Pre-Unit Assessment (continued)
Both Jay and Ali save a fraction of their weekly allowances.
Compare the fractions to determine who saves the largest fraction of their
allowance each week.
Jay's
Fraction
Ali's
Fraction
Explanation
,J t;..y
Week
1
W~k
Week
3
I
4
11
3
11
"'l
"'l
7
8
10
11
9
j
saves the largest fraction.
I know this because,.,
saves the largest fraction.
this because ..
"
10
7, a) Deb drew this picture to represent one whole:
Draw a picture to represent 7 of Deb's whole:
6
b) Chi drew these five hearts to represent one whole:
Draw a picture to represent I I of Chi's whole:
2
-
8. Answer one of the follOWing questions clearly using mathematics vocabulary.
a) Describe how fractions are used in the kitchen.
b) I am most like a fraction when I .
I am not yet comfortable with fractions because .. ,
d) I always enjoy working with fractions because ...
TIPS Section
- Grade 8
Queen's Printer for Ontano. 2004
(modified by HeeSB)
Page 106
on
8
nl!::u"tru""JQ,til"
QIIcriRlon
Develop pre~R4J ••tte bowWce aad skiDs aeeded to be Jlleeepful m
wo,ldal with fnadio.. to:
II
model
fractions
create equivalent
symbolically
re~lreSetlt rractiorlS on II nmnk"r
......11
• chart plIper
• milrkers
• ffllctlrm circles
• mien
• t\LMsl ,I to I
ANenment
BLM 1,I)on
one-quarter" is the correct
pre~pared tQ share the
Use the Prior
Anessment
resipO'rlSEtS to pair
stulden,tll with
mixed readiness
levels,
The diagram in
quel.tion 1
illUis/rstt!!!!! on!!! out
of four pieces;
however, onequarter of 111 whole
is one of tour
parts of the
This is a very
llubtle difference.
•
Actionl
PI'" ~ !tJ.r9UH'
Distribute one response sheet (BLM I
tbr each
EXlplain that
station has ibur student eXI~ml)lal"S
response sheet Their
is to discuss the eXlmllJlal'S
"'Teate a
that is
than any
eXl~mtllar's,
finished at One
move to ",nt,I!;,!>r
After
response and
Set up two !lets of
auestionls on
stalions as
described in ElLM
1,f,
are
their task at each of the four stations
their individual task.
Students need 10
know thai thliiY wi!!
be
Curmulum ExpeemdoMlObseMflltmuIMeutal
questions
Each student in
the pair needs to
take resporlsfbillty
for their own
Individual -+ Practice
Students choose whether
wht) feel
need more I)racll(~e
who are
in
choose to
wilh the
4
in W(lfK:llnll
on BLMl A,
CumeulBm ElpeetatIDbslObservaUouIMeBml Note:
Refer 10 Th/nk
•
Consolloate
Debrief
Who'. ct_ -+ Refl.ction
Guide a discussion about revising and
observations about the
and
solutions, Discuss students'
of the eXt~mr)lllr solLltltlnS.
LI!srt!tcy*
Mathematics.
Reviling and
Hime ActiviD' or Further Classroom Co_liIatto..
Reflect on the learning goals at each stati(m. Identify
don't undetsttmd and/or concepts that you
to hrnf',i,,,.
TIPS Section 3 - Grade 8
Queen's Printer for OnllMio, 2004
you still
(modified by HeDSB)
107
Additional Observations and Plans for Differentiation
(Teacher)
1, Throughout this unit, ask students to compare fractions.
a) Build "benchmark" skills. When a fraction response is given, ask students
whether the fraction is closer to 0, one~half or one.
Adjust benchmarks to reflect the two closest whole numbers that the fraction is
between, For example, for a response of 3
1
8
,ask if the fraction is closer to
1
3, 3-,
or 4.
')
b) Build opportunities to further develop comparison strategies:
comparing two fractions with the same denominator
comparing two fractions with the same numerator
comparing fractions when both the numerator and denominator differ by one
2, During the Minds On section of some lessons, do further work to develop conceptual
understanding (and then proficiency) on converting between improper and mixed
fraction forms.
Fraction circle pieces or pattern blocks could be used, For example, give a student
or group of students 13, one~sixth fraction circle pieces so they can demonstrate
both 13 and 2 1. Calculators could also be used to practise and self-check
6
6
conversions.
Suggested Questions for Home Activity or Minds On:
a) How many different ways can you explain how to change 3 5 to an improper
8
fraction?
b) How many different ways can you explain how to change
17 to a mixed number?
~,
3. Continue to ask students to represent fractions with pictures and a variety of
concrete models.
4. Ask questions to determine that students know how one whole is defined for each
fraction question.
TIPS Section 3
Grade 8
Queen's Printer for
2004
(modified by HCDS8)
108
1
(]J)
1, A circle is divided into four parts as shown in the diagram,
One of the parts is shaded,
Which fraction of the whole circle is shaded?
Give reasons foryour answer.
a) one-quarter
TIPS Section :3 - Grade 8
less than one-quarter
more than one-quarter
(modified by HenSe)
109
1.2: Pair Response Sheet
2. a) Use the gil/en diagram to convince Robyn that
5
is equivalent to
of a
~
the cake.
20
.
b) Convince Robyn that
~
is equivalent to
:: without using a diagram.
Justifyyour answer,
3.
Alan, Barry and Cusam jog on a track every morning.
Alan jogs 7 km, Barry jogs 2
8
5
6
km and Cusam jogs
I .
2
- km.
a) Use the number line to represent the distance that
person jogs.
I
I
I
I
o
1
2
3
~
4
How much farther does
Section:3
Grade
Queens Printer for Ontano, 2004
(mcidifll~d
by HCDSBj
110
1
1. In diagrams a, b, and c, the same square is divided into pieces of different shapes,
For each of the diagrams below, state whether the shaded portion
whole square. Give reasons foryour answer.
c)
b)
a)
one-sixteenth of the
b
The diagram shows the top of a piece of cheese that is divided into 4
equal pieces. Shade three-eights of the <.llll"fl:.lt"'&:.
a) Use the diagram to convince Kelly that: of a pi.zza is equivalent to
l~
of a pizza.
b) Convince Kelly that: is eqUivalent to 6 without using a diagram.
~
15
Justifyyour answer.
I
SectJon:3
Grade 8
Queens Printer for Ontario, 2004
(modified by HCDSB)
1
1
4,
George, Nicky and Tula need ribbon for wrapping gifts.
7
George needs 3 m, Nicky needs 1 m. and Tula needs
4
8
.
2 m of ribbon.
3
a) Use the number line to 8ccumtel,vrepresent the amount of ribbon
that each person needs.
E:l<.t,(~t
rJ;L¥'''\,,(, ",\v..
It I
o
1
I
,
I
,v'I
2
3
~
4
b) How much more ribbon does Tula need than Nicky?
Show your work
nps Section 3 -
Grade 8
(modified by
Page 112
1,,4: Fraction Challenges
Challenge 1
is
two different ways to
1
is ll<Jt
is
I
-- +
5
Challenge 2
After a class pizza party! it is Jody1s job to determine how to
equally share the remaining pizza from four groups among eight
students who are still hungry.
The four groups report that they have the following amounts of pizza left
over:
5 .
8
pizza
Show at least two different ways to determine how much pizza each of the
eight students
Showyour work.
-; ,} I
TiPS Secilon
~
Grade
{modified by HeDSB)
13
1.. 5: Student Exemplars (Teacher)
~n.uuction./8ugg
..tion.
1, Make two sets of each of the student exemplars on the next pages, Consider mounting the
two identical sets, Set A and Set B, on two different colours of paper.
2, Set up 8 stations - four for Set A and four for Set B, Place one set of exemplars for one
question at each station as well as any manipulatives or tools the students may find useful,
e.g., rulers for question 4a.
3. Pair a student who demonstrated stronger responses in the prior learning assessment with a
student who demonstrated weaker responses.
4. Instruct each pair of students to visit each of the four stations in Set A or each of the four
stations in Set B. At each station, students discuss the four exemplars, then create and
record a correct solution that integrates words and symbols, Their goal is to create a
solution that is better than any of the exemplars. Instruct students that each partner needs to
be able to explain the solutions they submit.
TIPS Section
Grade
Queen'$ Printer for Ontario, 2004
(modified by HCDSB)
114
1.5: Student Exemplars
cher) (conlnued)
Station 1
the
riianrl:tm
to r:rU"I\ilnr:tl>
that
12
:1
5
Learning Goal - to model equivalent fractions
Station 1
2.
Question 2a Exam
Use the
5
dja~tram
to conVlm;e
,
12
IS
t(J
I'
{}.
Learning Goal - to model equivalent fractions
TIPS SecHon:3
Grade
Queen's Printer tor Ont..rlo, 2004
(ffiooifteid by HCDSSj
115
1.5: Student Exemplars (Teacher) (continued)
Question 2a ExamDle 3
Station 1
2<
Usethl!!
:3
dislgrslm to eonviru,e
a<
5
is eQuivalent to
1~ of the cake.
Learning Goal - to model equiva.lent fractions
Station 1
Question 2a Examele 4
2,
a) Use the
3
5
dialillralm to
a cllOco!ate
t"'..... n\iin"'lIl
IS eQUivalent to
12
Learning Goal - to model. equivalent fractions
Queen's Pnnler for Ontario, 2004
(modified by HeDSEl)
116
1,,5: Student Exemplars (Teacher) (continued)
Station 2
Question 2b ExamDle 1
Could you convine;e
that
3 .
:;
to
IS
12
,
without
a diagram?
your answer.
~
Learning Goal - to create equivalent fractions symbolically
Station 2
Question 2b Examele 2
oj Could you convlflC~
thai
3 .
is
5
to
I
without
20
a dia(;ranl?
your answer.
Queen"s Printer for Ontario. 2004
(modified by HCDS8)
117
Station 2
3 .
,5
IS
12
(0
.
without
a diagram?
answer.
Question 2b Exam
Station 2
3 .
IS
5
12
to --
WIUlUU\
answer
a diatlral11?
t
TIPS Secllol1 3 .~ Grade 8
(modified by HCDSB)
W3
1.5: Student Exemplars (Teacher) Ccontinued)
Station 3
4.
i .
li 3t
I I 11~I.l
J•
twt..~
1
2
"-"73
4
Learning Goal - to represent fractions on a number line
Station 3
Question 4a Example 2
4
3I
Learning Goal - to represent fractions on a number line
TIPS Section:3
Grade
Queer($ Printer for Ontario, 2004
(modified by
Hl
Station 3
on a
4.
1
':;
. km and
vV;'d!H
·km,
dllslalnc:e thaI each
nti;r,u,\n
learnino Goal - to reDresent fractions on a number line
Station 3
Question 4a Example 4
on a
,5
-6
km
each
10 reoresent
nti;rcor.M
Could anything
be added to this
solution to make
Learnina Goal - to reDresent fractions on a number line
TIPS Section
_. Grade B
(modified by
Page 120
Station 4
Learning Goal - to subtract fractions
Question 4b
Station 4
c_~_
1
c::::>
Page 121
1..5: Student Exemplars (Teacher) (continued)
Station 4
Question 4b Example 3
does
jog every mtlrnlnn
Show
work,
Question 4b Examole 4
Station 4
dMI Cuum
every momlng that Alln? Show yout'. woric,
TIPS Section
- Grade
(modmed by HeDSB)
122
f
Gradel
28: Parts Problems
RlHdItMm
..
Use manipulatives
s)'lnbols t()
•
MatIdaII
• fractioll circles,
blockll,
the multiplication
linb,
nnmher and a frnl~tional qmtntity
paper
• chart
• 13LM 2!11
Asuumem
pa'rlIblff ~ IIYNDI' Rnpontp
Students share
to the previous
responses,
whether
Home Activity: Record and
problem is well connected to
Responses!
1) 6 boltles are
the COfnplJltatiioil,
fliledwith
water, How
•
Actionl
I_"
OfOlPl ~ Modelling
W'.
fun
otwater
are there in
to!al?
mlRIRV'."
Students choose one ()fthe IXlsted problems and represet
explain
t() find the answer
a fHf'lfiAr..nl manipu!:ative,
repl'esent the
Sttldems rellon to
gmup,
Currieuill,m E:s:pedatkuwObHrvationlADeedocai Notes, Cireu!;ate,
reflt~ctivle QIJesltimls at elleh group, Determine if each
one whole every other repres,ent;ati<:~IHh~pelnds
manipula'tive~s, Sltudl~nts
2)
walked
ofa km, Kerl
walked 6 times
as far How far
did Kerl walk?
!lb9JI Cfw ~ QtmontDtion
Help students understand that multiplicaHol1 prclbll:~ms
number
Dem()nstrnte 6 4
4 identical
of 6
The total is 24 Vl)J~;\;t;:"
Reore:Setlt one whole
with 4 'riMarl",
Put 4
for the solution and discuss
the
is
and
one he:"a!ilonai
~
into each
the answer is
Write
Further discuss
!O 4,
Palra ~ Practice
Students works in oairs on BLM 28.1,
•
C'omlolldate
o.brief
Whole Cfw :7 Dl8cu-mR
Compare these
5 3,5
,5 3 em, What is the same lind what is
different when you calculate answers to these
the Syl111bclls?
Summarize student
on
a whole
by a fractional
Include
on
and
fbrms (nroner !o
iml::rroper and vice
Home AetMt! or Further ClanroomCoRsolidation
Create and solve five questions that involve a whole number multiplied
TIPS Sectlon:3
Grade 8
Queen's Prinler tor Onlarlo, 2004
(modified by HCDSBj
a
123
28..1: Parts Problems
1
Determine a solution to each of the following problems. Show a manipulative representation
as well as a symbolic solution.
Problem
"/'L'~j'R
a) Dave ate'" 2 of a mini
5
pizza. John ate 3 times
as much,
How many mini pizzas
did John eat?
Here's my solution:
::.'
~
i
b) Farrell spent::' of an
4
hour doing homework
every night for 8 nights
a row,
How many hours did
he spend on
homework?
~
D
One whole is represented
by:
•
xg
..-:"'I
'i
---
Here's my solution:
2, Calculate:
7 5
6
5
b)
7
to
14
"J
I~
TIPS Section 3 Grade
Queen's Priolsrior Onlario, 2004
(modified by
124
GradeS
result ofmultiplying a number a fraction between (l and I
with the result
a nurnber
a number srreater than I
.,...."
• Allee in
W(lllderllllltl story
• HLM29.!
_ _ment
in the
Carroll was a
expmm that you are
to
•
Action!
Reference:
SeflS(}of
Fractions, R8/10$,
use matheltrlalrlcs
2002
P..... -7 "A" IDIn: to "I"
SLM 29.1
as an overhead
transparency.
Yearbook.
Display tile first row ofBLM 29, I on an
Ask Partner A to answer the
f61lovvinlaquestion to Panner B:
If Alice was 120 em tall and drank from a
that will make her 1/2
will her new height be'?
B to
the answer to the whole class,
row of the chart and record
responses on the
Leanml SkWBIObsenradoDJMeutal Note:
Whole CIm -7 Disc_Ion
Discuss what mathematical opel
and the
bottle fraction to _
.
_
(artsw'er: multiplication) Students answer additional qUI~sti,(ms in which a
number is multiplied mixed number, Students estimate fill answer
caJcuJiiitulg it
2 and multiolication bv:
bv 3 and
etc,
If students think
that the operation
is division, a.sk:
• Would Allce 00
taHer or shorter
after
•
this
Dofgeta
shorter
Currieulum Expe.::taUousiOmen'atioDJMeutal
",,,,,i,,,*,,
umier:,Iarlilir,g Ihal
•
COMofida.
Debriof
Classroom poster
TIPS Section 5 Who is Correct
Pal... -7 Reflection
Students individually answer the
on the
Hila if carret'I:) In
share responses, Discuss to form a
group response wilh
than I results in a product that is
than
". _ . a !lumber
the
number. Mi,lltipl'vitllg a number that is between () and I results in
number,
a oroduct that is smaller than the
Home ActivitY or Fyrther Cia_room Conao'ldation
For cach ofti,c expressions determine if the answer "viii be larger or smaller
than the first number. Create a word
fhr each ofthe eXI)re~;sic!ns.
Calculate the llnswer. Show your work
al 4
Section
,m
Grade 8
3
4
2
3
8
c}
6
(modlfled by
15
MLAJ1o>t:\\
Consider
some stw:lenls
fraction circles or
strips to use at
home.
125
5..4 . 1: Alice Grows and Shrinks
120cm
-21
~OCfY\
120 em
1
3
~o U\1
<.;~oAer
120cm
1
6
aDeM
~ho\~er
120 em
5
6
\DDGIY\
sho,\u-
2
1
~~O(rn
t4\\er
11
~ODCf¥)
-taHer
120cm
3
120 em
6
do
~at pa~~ ~:tice
\t
~reo.\e-
'S~O\\t: r
::~Uffl1:gAJ~::b:rOf12;j;Y a7:41kr,
""II
one
I
-the
-flew
f\lAfI'Ih/J'
jeh
6jj er
..
t~/I O\~If\Cl \
29.1: Alice Grows and Shrinks
Magic Bottle
em) After
~D(M
120 em
2
120em
~DCff\
1
3
aO
120 em
120em
Ctl\
\ODc~
120em
~aOCf\l
120em
aooc~
TiPS Section :3 - Grade
Queens Printer lor OntarIO, 2004
(modified by HenSe)
126
•
fractions where both fractions are
between 0
I,
M •••mem
Pal... -7 Credng Modt..
Display a question:
'h. (I)ke
ate 2
Sample Models:
, "t
was left over from the Mad Hatter's Tea
flow much
whole
did
eat'?
3
stwients create II plc Loriai
1
•
Action.
Alice
that
used to solve
WJmIt CIm -7 Dl8cygton
Students share responses for the Minds On
Discuss which
Inodel.s be easy to use
models were e'dsiest to lise. Would any
to find an answer to a Question like: 2 x 14? Make the pr()bl,em
17
of
had
as a
15
model fbI" multiplying fractions, Draw this model:
how this re(~tarlgular m()del can be
.
to show that 2 3 6. Discussion should lead to
understanding that the multiplication
can be
the
and width of a
and the
product
the area
the
model fbI' multiplication of whole numbers with
Further
a virtual
~ ChoQse
Index ~ Choose
&
you are now
to use an area mode! for the multiplication of
two fractions.
The length of the
rectangle is 3 units
and the width is :2
units, so the area
Is 3 x 2 which
6 square
Whole Clau -7 PreMntation
Use a
projection unit to access the site:
-? Choose Index -? Choose
MJmbt'/:r &'
1'3·5tMode!
with students
your actions,
illtii1LlllillllJ11i!Jk~Qlli!!!J:'llU!l!:~!};1!!!rm::Y..t!!!!ll!
F'rtJt'fi<ms -
several
•
Consollda.te
Debrief
w
Pal... -7 Invedgation U$ing Compute...
In pairs, students work with virtual manipulatives f~)r fractions ofl,ecltangles,
( ) n e i s the
,. one
is the "recorder," Partners
mles tl,r each
Students
their solutions and submit them fbI" assessment at the end of the
que~sti(:ms to further
ofthe area model.
modelled
an overhead
a marker but
using the Internet
allows lime for
many more
examples.
Students can use
this interactive sile
for further pracltce
(J)!Jl!;;:L!JJ!illbl!lW..J~<!JdlL!11Y1!J~m~~t~lli~tl.J)1!!lJ).
Lamillg SkiIUIStaymg Oil TaskiClueeldUt:
students to lnt,erpret msl:ruc:l!c,ns.
Home Aetivity or Further CI..-room ConeolldatiQn
Show this website to someone and explain a solution. If Internet access is 110t
aV{IHable a1 home consider
the local library or share a Dictorial model
ofmulti[)lying fractions
the ret:lal1111e model.
TIPS Sect!on 3 - Grade 8
Queerf$ PrInter for Onlario, 2004
(modified by HCDSB)
Page 127
30.1: What's My Share?
There is part of one rectangular pizza left over from Friday night's
supper.
The first column in the chart shows the fraction of the left~over pizza that
you get to eat The second column shows the fraction of one pizza that
is left over.
Complete the chart. (The first row is already complete.)
Your share of the I Fraction of pizza
I that i. left over
left overs
2
3
1
')
k
4
5
1
3
3
4
-5
Picture solution
I-
Do you get to eat
more or I... than
one-half of a full
pizza?
Your share as a
fraction of the
whole pizza
I
1
2
Of
6
3
I
Less
')
Create more questions, Record solutions.
TIPS Section 3 ~ Grade 8
Queen's Printer for Ontarfo. 2004
(modified by HeOSEl)
128
D~y~~':~i~~y Using SY~~~~~~~ __~.m~m~ "~~,,"".""~_"._""""""_""""""
••
Il!Isr.IItkm
•
MttltiiPly two
where both
""
"
~_
G~~~_8
Mlttrtlfe
• nne set ofllllmber
cards for every
Ibllr stlldenlS
• BLM 3U
are between 0 and 1
Att• •sment
small Group' (4) ~ Game
Students play Fraction Action. (BLM 31.1)
Currieulum ExpeetatwasJObservatiouJMental Note:
common
•
Actloni
and
for
calculators to
compare fractions.
Imllvidal :t MeHle' maIDa
., "
Ask: WInch fractton
IS
3
4
_. or
WBltbe
2
3
will
1
or smaller than . :
4
or
?
smaller than - ? Students individually determine an answer to the pr(~b!t:m,
3
Carrieu1um E1peetatioulQtdzlRahrie:
nJr undiersl:andmg.
WboI! CIm :t DiHwIon
Some students may have done a sYl100clhc
Connect to their symbolic
responses te) the rectamrular mtldeJ.
3 2
niscuss each number in the SYl1illxlllc
x"
4 3 solution.
6
Where do we see "0" in the area model?
12
Where do we see" 12" in
area model?
:::: 1
etc.
2
Whole CII. ~ Brainstorm
Advise students that they will be
in small groups on some prclblle:tllSL
Brainstorm ,t list
to do when
and when
with
frru:ti(1lns, e.g., ask
What is one
inlhis
and how can I
model it?
See Think
Cross-
Small Group' ~ Problem Solving
Students solve teflcher~prepared problems that involve the nrc,dlt"!
fractions
less than
fhr salad dn:ssllng
rCCluirt:s 2/5 cup of
Eila's thinks she needs
l/3 of
How much vinPfmr
for her
•
Consolidate
Debrief
Whole Clan -7 Cia" Jgyrnal
ft)r someone who is
Guide the development of a class journal
eXf,lalintflg how to find fraction
symbolically
Home ActivItY or Further CIM_room Consolidation
Create and solve fraction questions that involve the product ofl.wo fra,cti<)fls
that are less than otle whole. Record any
you still have
the
multiplication of fractions. Share your response,
TIPS Section
Grade 8
(modified by HCDSBl
129
31 . 1: Fraction Actionl
Instructions:
1, Two pairs of students form a group of
four.
Which fraction
is larger?
2. Each group of four students needs one
set of cards,
3. One player deals the entire set into two
equal stacks of cards, numbers down.
Each pair gets one of the stacks.
4. Each person turns over one card from
their team's stack.
5. Each pair forms a fraction by using the
smaller card as the numerator and the
larger card as the denominator.
6. The pair with the largest fraction claims all
of the cards and puts them on the bottom
of their stack, The other pair may
challenge the claim and check using a
calculator, but if the pair loses the
challenge, two cards are given to the
other team,
7< If a tie occurs, the tie cards are put back
into the middle of each pair's
8, Play can continue until one team has all
the cards or until time is called<
TIPS Section 3
Grade 8
2
•
A
3
A
2
005
o
500
{modified by
•
3
•
7
00
000
00
7
Page
Gradel
P!udRl9n
.....'I!
• Itllltlipuilltlves
•
tVllfietyl
• BLM 32J
A$sanment
Small GrouDl '% EguiValent FractIon8
Distribute one fraction ard to each student (Bl,M 32, I), Studenits
have equivalent
Small groups
convinl;e someone else that
are equivalent
•
Action!
Curriculum ExpeeiatioDlObservatioBlMeataJ Note: Circulate imd
understtmding in
fhr
group ,,"'.H .,."
J!J!!M Grou.p '% Qi!!?\MfgJ)
Discuss equivalent fractions based on your
from small group
work.
therefore
ImII.GrouIf %I9!JJIUI MeuMdlUl ProrBml
3 ~ (lithese can
I
Students work in small groups to solve the problem:
2
be represented
I
I
cups
2
I
3~
oibread. How much
:2
he use?
Chalhlnge groups who
a correct solutinn to
sollu!.ic>l1s, e.g.,
and fractional Clrctes or squares.
J!J!!M
the answer
cups, picturt~
c" -+ PIKI!fkm
Discuss the limitations of manipulativC$, e.g.. some denominators are ditlicult
to work
whole
require too many m2tnilnll,flth/es.
Establish a need for altemative methods
multiplication so
Tell students
will extend the area
can diSl;OViet
In lata! there are
I
5~·
.
circles.
4
t"rdct.ions (I n1pr'oper)
Give each gmup a diflerent nri\i!ll,'f que~>tkm
f;!C'livilv) E:ach group uses the rectangle
re~lre~;errts its concrete model syrllbl[)Il(~allly
•
COf1$oiidatl'
Debrief
Whole Class ~ P~ons and DI8cUMiona
One group shares its symbolic multiplication and discusses how it connects to
the
of the small gmup
as a whole
class.
the multiplication oftwo
the
are
than two,
Home ActMtY or Further ClHlroom GoJl8Olldation
Tanya is 16 years old and just got her G I driver's license. For every hmlr she
on math at
her parents will
2
her 1 hours ofIPl1ilctil:e
3
')
time. This week
many
2":'
S
on math. Your
ways you can show that
can
is to see how
.., I I
"lOUrs
5
time.
Section
Grade 8
(modified by HCDSB\
131
5.7.1: Equivalent Fractions
10
5
3
6
14
7
4
~
~
8
11
6
~
New
VCTMUU
9
12
21
12
28
-
~
16
22
33
44
~
~
18
24
14
10
~
on
20
~.
~
12
7
-5
15
~
21
15
~
28
~
20
32.1: Equivalent Fractions
1~
5
10
6
15
9
14
21
~
~
3
3
1~
7
4
-
-
1~
6
11
6
22
12
33
18
2
1
5
7
5
14
----10
21
15
Ii
9
5
18
10
27
-
3
1
8
11
-
8
22
16
33
24
5
1
8
13
26
39
4
5
TIPS Section 3 ~" Grade 8
-
-
16
8
Queens Printer
12
8
Ontarjo, 2004
(modified by
H('h<;:P;\
15
-
24
'132
33: Let'. Share
GradeS
~
Mattd*
•
• mtlllipuhltives
• BLM :3:11
Ms.amen!
sma·g BroUM ? SbidnalOld9D!
Students foml small groups to share solutions
one tvoe ofsolution
the
•
AOOOO!
of
small BrouM ~ Pmbltm 8glylna witt MlniRJItativee
Pose the first question on BLM 33.1, Students should have a
of
maJlliptlltltiives available to help them solve the
can use
cailmlators to
the second
Continue
questions 3 and 4,
(Multiple
will be pre1;ent1ed
CumeuJum Expeetatiou/ObJervatkJulABtedotal:
l.:ircllh:Ue"
spel~ifk students which
could
the
Plillhare ~ Rtftlction
Students highlight words in the four problems that
this
as
one that can be solved
division. and share their responses Wilh another
•
Consollda.
Debrief
the length
or Wldllloftl
reetlmgle lI:ivelllhe
area
lIunil rllte
Conslck:lr
an overfu.tad of
BlM and reveal
the questlons one
at a
Whole ClaR ~ Di&UUign
Discuss each
four
as represerltati 1.e
ofdivision
pr()bl1em. Discuss how
a problem "il1"ml,[>'f
strat:egy that
find usef\J! when fractions are
e.g., the
que~stkm could become: A
.
to sItar" ,>t'IJ'ifll,IV
knows that 12 2 can be used to
then this
can be transferred to
that:3
d
5
can be used to
solve the
Home Activity or Further Clmroom Con$Olidatton
Number Problems: Find a number to replace the que~stl(m mark.
Record
that you used.
3x ?
5
M\;·",t""rv
I
Hatve samples of
other "dlvi$ion"
problems to share
with students
the
Debrief discussion.
I
"'",""""c
12
I
4
5
'}
J
5
8
SecHon 3 - Grade 8
if
I'2
Queens Printer for Ontario, 2004
(modifled by HeDSBI
i33
33..1: Let's Sharel
1
<
A group
.
friends buys 3 pizzas to share equally. Each friend
receIves
3 0 f a pIzza.
.
S
Your challenge is to show different ways to find the total number of
friends in the group.
e,,"
2. Amy, Sue, and Alex bought . kg of trail mix to share equally.
4
Your challenge is to show different ways to determine how much
trail mix each person will receive.
?
3. Sandra's printer can print 5 pages in .:. of a minute.
3
Your challenge is to show different ways to determine how many
pages Sandra's printer can print in one minute.
n •
i'V\
£
M'I\
(\/\10'1.
7
'"
S
+CJ'
4. The area of a rectangle is 2' square units. The length of the
8
1
rectangle is I . units.
4
Your challenge is to show different ways to determine the
the rectangle.
of
13
4
5.
Replace the triangle in each equation below to create a true statement
.-; 3
a)
c)
3 Li -5
5
~
2
3
TIPS Sedion :1 - Grade
_
= ,)
=
b)
1
4
d)
"",-
1
72
Queen's Printer for Ontario. 2004
1
Li 3
,.,5 ~
8
12
}3
4
(modified by HCDSBj
=
I!..
2
Page 134
Grade'
",,,tt,,,l"fi i... o
to cleveloo
'invert-and-multiply'mle
•
diviclimz two
rate qu,estltof1:s,
~nt
Wb911 Ct. ~ DIIcuHkm
rate: What is it?
Facilitate a whole class discussi<:m
is it
What are s(}me examplies?
que~stl(m 3 on BLM 31 L)
sotltware to org.ani,te c()ncept map of unit rate.
•
ActIonl
A unit rale IS the
Small irouDl ~ Probllm POIIOg
Each small group creates I or 2 unit rate
involve
writes
Dr(lblt:~ms on chart paper,
with
group to peer
and
edit CirlzulaLe, qllestionil,g
them refine the problems.
problem must require the calculation of a unit I'dte
Each
fractions. Ask: Is it easy to mentally
Tell them the next
.........""5 the
of two
easier to
bel,1:innmg the
that student,>
their callzul.llor'S.
how to
students conlplele BLM 34.1.
In
TIPS Section
~
• cllllrlplliper
• markers
• fiLM 34.1
Grade
e
Queens Printer lor Onlario, 2004
(modified by HCDSBl
If students are not
lJsedto
a
proceSS.
Page 135
Unit 5: Dar 9: Let's Think About Dividiny
Grade 8
Mmll Lurn1ns G U I , M , t t r i ' l f
.
•
tOdeVel.op~
• Use patterning
.. • .ies and algorithms for dividing
• Practise partitive and quotitive divisioo with fractions,
•
unit rates and mtio tabl,es to solve division of fraction
• BLM,. 5.9,1,
5.9.2
• chMt
•
A$se$sment
•
Minds On ".
WhO.' CIa"
=t Sh,rlng
Review stories from previous day and connect to Home Activity answers,
division summary of BLM 5.8.1 and multiplication Home
Compare
Activity. Just note the pattern at this time.
Discuss the role of the nnmerator and denominator ofa fraction. (The
den.omi:nator
fraction
th,e whole into parts indicating the siu of the
parts. The numerator shows tbe number oftbose parts).
Partitive dM'$ion:
Oetetminirlg equal
parts or flhares of
P,rtn,'1 NB =t Exglgmtign
Students explore some properties of multiplying and dividing
QuotiUw division:
(BLM 5.9.1).
lit wl1oiliI, e.g.,
share4~
among :3 people
(f
1t~$)
How·mtmy &hare&
be rMa$lJred
out of tNl whole?
OM:
Four~Me
divided into thirds,
e.g., How many
•
Action!
yvho., Cilis -+ Discussion
share&are
there?
Take up the answers to BLM 5.9.1 and have students share their
and
for refierellCe.
their hypothesis for properties of fractions. Record and
Pal'l =t Prgblem SolYlng
Students solve problems that lire partitive
quotitive divisious, and
unit rates (BLM 5.9.2). They determine algorithms by reasoning,
unit
the numetlltorsldividin~ the denominators, and the common
rates,
12 iIlhafel'l)
Oivlslort$ U$ing
unit rete: A unit
ram Is the quantity
~at$dwltha
~riof
~
qI,Il!lntlty,
•.g., $a per hoor.
45 W<'lI'd$
minute.
~., of
a gallon
of water to fill a
full. how
•
Consolidate
Debrief
al/il;orithtiUS for
fractions
of1l:Yroble:ms that students
worked on and
ease of use. Do not introduce the invert~and~
many gal!onlil will
flIl the pall?
+3 ",.to
multiply algorithm yet
Common
dlilnomlnator
~gOOthm:
How many sets
arelni '7
I
~
Home Activib: or Further Classroom Consolidation
Complete the practice questions.
3iset$
Provide students
with appropriate
prat::tic0 questions.
TIPS4RM Grade 8 Insert after page 134 In Notable Strateglefl
5.9.. 1: Exploring Properties of Fractions
1. Investigate numbers that you can multiply
i
by to get a whole number answer.
i.e., 1>:?=8 whole number
:3
e.g.,
f J.
X
~
6'"
X
~ X l~ : ~
9: 3
EX;:\~:U :fe~3ed;nu~~\~~wo:r t~ fet'lproc4\)
2. Investigate numbers that you can multiply ! by to get a whole number answer.
4
Le., !X?
4-
e.g.,
8 whole number
~~~~~b
~x'3:~
~x16 '" ~
Explain how you determined numbers that worked.
~IAH;~\e( il~ ~
3. Investigate fractions that you can multipfy ~ by to get a whole number answer.
Le., ~x?
:3
e.g.,
a whole number
~x~
~:3 2 !O-
a 3 b
3x~ -:" =)
3
Explain how you determi~ed fractions that worked.
n~W,pb 0\
the
rec."plll(A\ 1
4. What fractions can you multiply the following
2 i
3 7
a) -x~ "",1
b) -:<-3
1
c)
5 <t.
7
TIPS4RM Grade 8 insert after page 134 In Notable Strategies
by to get a result of 17
5 n
-.x- ",1
d) 3x.!.
11 S
3
1
5.9.1: Exploring Properties of Fractions
(continued)
5. What number can you divide 2 by to get an answer of 1?
I.e.,
~ : ~ ::
;; 1
1
Explain your reasoning.
6. What do you divide 5 by to get an answer of 1?
Le.,
;; 1
~
S 5-;: \
7. a) What do you divide ~ by to get an answer of 17
Le.,
~+'!"" 1
.~ ~ ~ 3' 3-
3
)
b) What number do you divide any number by to get a result of 17
HStW
8. What fractions can you divide or multiply the following by to get a result of 17
2 ~.
..
2 5"
5 !)
5 \l
a) -+? ",,1
b) -x·~ ",,1
0) - + 1
d) -x c- 1
5
5 ""
;J
What do you \rtice?
\~
lS -tht
O\\~;I\~
11
\\1lftI\er
io
Make a hypothesis about dividing by a fraction:
~'illl~
0.
11
q
8W',)f,
rec·l~roc<l.\
~O'l is s·~\.r \0 ll\~\;~1i":l '"
Test your hypothesis on these divisions:
3 1
.') j '1\
7 3
a) 5"~1 :. S).t
b) 9
':
':"3
N
J1
TIPS4RM Grade 8 insert after page 134 in Notable Strategies
~
k rr..'"\~1
-t..~
.
2 1
0) 2 3 + 3
::
~ . \
2"\ <I
:3''3: "1
-::0
5.9.2: Thinking About Dividing
ParlA
For each question explain your thinking. Use words, pictures, or diagrams.
1. Some children left their shoes outside the door before entering the house.
if 10 shoes were left, how many children entered the house?
@ @ @ @@> ,,5 ch;\dfef\
~ .. 5
or
2. A teacher purchased 72 donuts for a class party.
a) If there are 24 students in the class, how many donuts did each student get?
n-3
.
a~x3:.7~
a~
b) What fraction of the donuts did each student get?
'3
\
7i:~
3. A bake shop cuts each pie into 4 equal pieces to sell single servings.
a) If 6 pies were baked, how many servings can they sell?
Ef)
ffi -ffi -EBEB ffi
~ ~~ S'~J
b) If 8 people wanted to share the 6 pies equally, how many servings would each person
get and what fraction of the pies would each person receiv~ -:.
~ cD
E8 ED ffi EB
~:eJ
3
~ o~ ~
15
'eJ,
p\e
t~
eJ
4. You have been saving quarters. If you have $6, how many quarters haVe you saved?
fE
ffi EB
tEl ill EB=
~~~ ~ ~)£t ~av
~~ 9,~llrterf
(8 bXY: a~
5. The local pizza pla.ce cuts their pizzas into sixths, so that each slice is
1.
i29 ® ® ::1~
a) How many
~JQi\
slices are in an order of 4 pizzas?
S\;teJ
i
of the pizza.
U'.l _ 4 b f) U
-t ~ ro - T ~ T ~ 0( I
b) If 8 people share the four pizzas, how many slices does each person get?
How much of the four pizzas is this?
3S\\l..ed
a~; ~:.3 S\~~J
T1PS4RM Grade 8 Insert aftar page 134 In Notable Strategies
5..9.2: Thinking About Dividing
(continued)
PartS
For each rate question explain your thinking, Use words, symbols, pictures, tables, or
diagrams,
~
1. a) If it takes
of an hour to get
i
work done?
of the work done, how long does it take to g.et all the
.
~
.
2:.-J._~
SO; 3 - 5
1\\\lSWt ~S ONLY
C;~\'J\~Lt
-J.
-,]::
S
1..
'3
b
L
5
S.ll--:-
(-ct\
J.
?\:3
-7
b
or ( 2-)'
-5
1'5'
I
:!;
3. of an hour to do ~ of the work, how long does it take to do a~
5
3
1 1
,). -1..
':2. 3 ..."
'3
(;:A? 3
..,
\ \
'5 ~ '3
S' x"2 - ,; :: S'
~
~
Wof lc ODn.(.
b) If it takes
/
c)
t..
! :.
I,
~ De,scritJ<i.the parts of al.and b) \hat are,q>e sa'l'" an ~at dlf!e"'flt.
tlUh tlcn~ YQ~ -r,,,a \ 'The umi rate a
1'1"" f\u...\ \()\J
~r\et
1-0
itt ~tt#
i\ 1\
\t I~~S
d) How does ~sing a ~nit rate ~IP y~u think abo~t the~ que*\tions?
~OlA aaA e~
Uf\d
io jtt
to -me ~t
2. Sarah found out that if she walks really fast during her morning exercise she can cover
e!4 km in !5
of an hour. How far could she walk in one hour at this pace? Use the unit rate
r
Idea to solve this problem. [HInt: How far can she walk In
~\
t
~=
.!
of an hour?]
sk eo. .....)f ~.2S \(In in
1.
S
Ilt
Parte
1, The answers to the division questions are given. Determine a strategy to show how to
solve the.se questions:
\ (
(
a)
15 :
a
~
\l f H:S
b) 120 +£."" 20
49 1
c)
+.!
25
99 11
9
75
Use your strategy to solve:
25 +5
a) _.
28 7
TIPS4RM Gmde 8 Insert aftar page 134 in Notable StratElglf.1s
b) 10"", 2
21'"3""
\
&\ !'OK.
5.9..2: Thinking About Dividing
(continued)
Part D
1. The answers to the division questions are given. Determine a strategy to show how to
solve these questions:
b)
a)
15
3
15+3
s--16 16+16
"",5
c)
3 3 19 6
=:-+8 4 8 8
=19+6
2
1
19 3
6
6
2. Use your strategy to solve:
a)
24
4
5
b)
Summary
Describe all the ways that you have discovered to think about dividing.
TlPS4RM Grade 8 loser! after page 134 in Notabllil Str:ate!)ies
1 5 11
1-+2-=-+353 5
25 33
15
25+33= 25
Grade a
One More Way"
Math Learning GOlls
.
• Develop _ _ r", dividm$ !racti0llS
• Prneti$¢ division of fractions.
with • unit .... model.
l_dll,
.BLM 5.10.1,
5.10.2
•
Assessment
•
Minds OIL,
Whit, Ctall ~ Discussion
Sul'llll'larize the straregi.es for division of fractions using a concept map.
Pose some questions that demonstrate that certain
are more useful
with some types
Ask: Whicb
is most efficient?
Pose some
out
that can be tested and in.clude questions that do not
W ill the
work?
~uslngthe
Smartldess
tlOftwllll'$
or CfMte
the~map
on mart p$pef,
Thle~
a raoonate
explOOng to
de.... one more
tM:tllod.
•
Actionl
PaJrl§bll! % erobltm §oMrm
Pairs complete BLM 5.10.1. Each pair compares strategies with another
and describes an algorithm so that they aU agree.
To belp stuaen.ts understand why the invert-MId-multiply algorithm works, start
with unit fraction
and build to unit rate, using ratio tables.
Curriculum Elpeetatlofls/ObservationiRating Scale: Observe students as
share
can be shared
•
Consolidate
Debrief
for division. Probe to highlight different
al~orithms that
Consolidate/Debrief.
The idHS nee<:k:ld
MI'$ explored on
O$y9.
An altemative
~thOO to help
studoots
~tandthe
algorlthm is to
wrlte the equation
In an equrvl!llent
form.
Whote Cl'ts -+ Pitgullion
Groups share their thinking and the
that
groups
the explanation in their own words.
Add the new
to the
Students create a
of the
Minds OrL. that
not work out
these questiOlrlS e1'ficiently.
develolled. Several
map.
map in their notes. Use the
in
and
that the new strate~ solves
A teactler
provided
is
can
~shanldto
challenge students
Home ActiVit( it Further Cl'ssroom Consolidation
Complete the practice questions, using the strategies t.hat you find moot
efficient Use your
map as a reference.
Provide st\Jdl:IDts
wIlh appropriate
practice ql.ml1l00nll,
TIPS4RM - GradE/8 - insert after page 134 in Notable Stral.egies
5.10.. 1: Finding One More Way
1, Generalizing a rate problem:
If ~ gallons of water is poured into a small pail, it will be
i
full. How many gallons of
water will the pail hold if it is filled completely?
a} Determine how many gallons of water it takes for the pail to be
.18
full? Explain,
b) Determine how many gallons of water it takes for the pail to then be completely
full
(!.
8
full)? Explain.
Ratio Table
c) This question can be written as a division problem:
~+r
3 8
Use the thinking of parts a} and b) to complete the division,
2
3
1
8
1
2, Consider the problem:
~+~'"
8
J
1
Write the equation as a multiplication: ~ ""
5
6
To solve this equation: multiply both sides by
~
5
-x-=
3 6
4 5
~x~=[
Explain the steps and determine the answer.
3. Recall the pattern that you noted in the previous lesson,
Will this pattern work for
3 3 8 and
~+~ ~
4, Use 1, 2, and 3 to create an algorithm for division and use it to solve:
a)
5 3
85
-+-
TIPS4RM., Grade 8
. 5 3
b) -+64
.
c)
insert after page 134 In Notable Strategies
2 4
35
2-+-
.3 1
d) 3-+146
3x~""8,
3
5.. 10..2: Finding One More Way
Consider this solution:
:3 4 3+4
7""5+7
=,i
but
4
4
4
4
-::::::;:
=
and 3
3
7
3x1
7
1
21
""20
so 3 4
5
-
3 7
4
21
20
Explain why this works.
TIPS4RM - Grade 8 - Insert after page 134 in Notable Strategies
(Teacher)
OM 34: Just One Please
Consolidate
Debrief
Grade 8
M.g,. ~ DIMugkm
the
in the
on BLM 34.1 and the context from onc
student-created unit rate problems to pose a fraction problem
for the
Student,; must
several
as multiplying
the reCipr(lCa!
f
I
a} 2 . :3
.'
.
! ~ 11Sks us to
'.
the
number of I ?3
3
,In a 2 1 -SI:1':e
,
P,,,,tn!",,,lhl
"'"
Add "reciprocal" to
the eliaS'll.
WalL
there are
how many
groups
there are in
represents a Whole
solution,
In
1
2"" solution
Is
represented by
I
:3
b) 2 ~
2
the width ofa rec,tanigle
I- asks us to
:3
1
area 2-
if its
3
,
is I - em, Pictorially,
3
soluticlms above arc not easy ways to determine
is needed. From the workshC(;~t,
computational
divisinn bv ;4 fraction results in the same answer as
Th,erefbre,
I
2.~
I
2
has the same answer as
w')
be detemuned
The answer can then
or USIng an lIrea
Curriculam ExpeetationtlQuizlRubrk:
on
I :3
3 5
divisl.on
responses lhml a mmer·anC1,
fhlclions.
Hgme Advttv or Further Cf,pf;OOm Co!!!oUd'tion
Solve the unit rate problems created by your peers,
TIPS Section:3
Grade 8
Provide student·
created problems
I from the activity.
136
34.1: What's the Pattern?
Determine the answer to each question, using a calculator.
1
2
4+2=
4x-.=
b) I 6+3=
6x 1_
3-
c)
I 8+4=
1
8x-,-
4-
2
3
4x
4+I
i
1
-+2
4
1
+
I
2
J 1
-x-=
4 2
--
I
1
-x?
1
4
4 2
'"
I" +4
5
1
2 1 +}2
1
"""3
3
3
3
5
-
xl
4
3
5
?-x-
3
What do you notice about the answers in each row?
Show how you could find an answer to 2 1
3
12 without using a calculator,
3
)( 3
TIPS Section 3
Grade 8
Queen's Printer lor Ontario, 2004
(modified by HenSB)
137
Grade.
Dtscriplqn
• IJse resources
TIPS continuum on
Mlttri."
• fiLM :t) I
• da!J~ pmjlXlOf
to corlsoIidate
~ment
Vfb9JI Cm ~ DMVllion
Each student receives a fractional
Compare the "wholes."
ne()eSllarily the same
Discuss how the sizes
COl1npared e.g, 12 is four times the size
of one
same area but not
two
can be
ROlming fill! ~ f!mllllm 80Iving
flairs of students compare their fractions in two ways, Students record the
!mother
and
and mark
Currieumm ESpedadoufABipmutlMarkiug kheme:
individual responses,
•
gmun ~ Luming c.ntrn
Action!
Structure different stations ofactivities
to the
from TIPS
your students,
some stul:1en:LS,
Processes page 6
page 9
page 14
- Extend Your
Tme? page 22
-Is This
•
Consolidate
Debrief
interests of
fractil)l1S fbr
Whole Cm ~ Cgncem Map
Summarize the big ideas of this unit
a
map, COll1sil:1er
Smart Ideas software for this process,
Familiarize students with the
and process fbr
37: Smnmative Assessment),
Home A~ or further Cla$8room Con$oUdatJon
Make a review booklet as you study fbi the assessrnenL
Section
- Grade 8
Printer for Ontario, 2004
(modified by
MlAJ<:JI:H
138
35"1: Cracker Fractions (Teacher)
Each piece is a fraction of the whole cracker, All pieces are drawn to scale,
Distribute the fractional pieces and ask students to determine what one Whole looks like. The
"whole" answers may not look the same but they should all have the same area.
Ask students to make two comparative statements about their pieces. For example:
lo. 2,
' 0 f tlo.lie ....
1piece,
.
T lie
pIece '4
IS t'Imes th
'. e size
3
6
lo. 2 . . 1
lo.
lo.l.
T 'ie - pIece IS more b ,an b ,e .... pIece.
3
2
6
-65
2 1 ::::.4
-+
3 6
211
-
3 6
2
....5
..---
6
2
-3
1
.......
3
Ii I
Queens Printer fO! On1ario, :2004
(modified by HCDSB)
139
35.. 1: Cracker Fra.ctions (Teacher) (continued)
-76
2
-
3
1
~
2
2
-3
T!PS Section ::I - Grade
Queen's Printer for OntariO, 2004
(modified by Hrr;R!=l\
140
ltea
GradeS
JIIttriI18
."MXlI·"
composite nmnbers as products
numbers to
common mtJtltilples,
• Solve PH)lolems
the lowest common multiple,
YYJr'V",
• datil projector
•
Aaa• •ment
OpportuniU_
rID'i MY'" 121Jd1q..
8
Students work in pairs to solve this problem:
I ofhis
nlavit1t~
9
I
garnes,
- of
8
but less
time that
cornpttter games,
Find different possil,mties
",In",n"
games,
9
16
144
1
s
S'1,
~
9
III
1
•
ActionI
S
WhQIJ CI_ -+ DtscU!8lm!
Facilitate a discussion on multiple
to the initial
a common denominator. Discuss other
solution that involves
pre,ble~ms that
the lowest common multiple of two numbers,
Itar tl1/0 I1UJOI1,f,
tltt' two moons art'
in lint' Hitlt
:f
tUller afttl with
"fUl1. fWtJOlt ! ('em
Self11(;'
ItJcati(1!t elle~'v
iYOO/t 2 call be view(y! ilt tltis same locatioll eve,}' I.'
IflIfen if the "t:t:t timc! ,helt both l!ttJons will b(;~ thif .f(lme !(Jcaticm?
i',
In
student find a solution to the Zerk problem.
answer is 30,
the
lowest common multiple.]
Demonstrate
the class a process for
the lowest common nntltl.ple
website:
F()c/(}r
\."flVU~ Index
n"t'(' 7> Choose Numbt'l:s' & (),JtJltttimtj'
Students work in
with
one
is the recorder. StlJldents
ex<:l1aJnge roles.
Cumcldum ExpeetatmuIRee....rded SolutmDJlJblbric::
•
Consolidate
Debrief
WhQIJ CI_ "':t Dileu.ton
210"'2>:
>:5>:1
Summarize the process used in the virtual,
Write
mnrlners
~" .. _;.,,~.~
exponents when needed. Discuss how the
common multiple) was very
when
c~tlculators became common.
tools.
this
l'k
Wit. h an
I e: 37 + 53 L'
.;)tud,. ents use
to CIlCCK1'1t le answer
210 90
Discuss
the skiJI is still important
90"'2"
x5
The lowest
is: :2 x 3" " 5
which is 630
210
Home Activity or Further C._room Consolidation
Create and solve one "easy" question and one "flOHm-easy" qwest!lon that
_ either a lowest comrnon multiple or a
cormmm
If Internet access is
show someone the website you used in class and
discuss how calculators can be used for fraction arithmetic,
C:nntinue
on your review booklet.
TIPS Section 3
Grade 8
Queen'S Printer fot Onlario, :2004
(modified by
M\",U::H:li
the other ellery 90
minutes How
often wlUthe
events occur at the
same time?
Answer:
minutes (the
141
Da 37: Summatlve Assessment
GradeS
DetcriRtk!l
•
•
MaI!dII8
Administer II
summlltive assessment
• SUl11l1l1ilive
Ilssessme!lt
• 1111111ipuhulves
• cll!\;ullllOfS
Auenmem
Whole CIIB -7. PtlBd09 fo·, Allwment
Do a whole class relaxation/calming activity prior to the assessment
Di5~tril:'lute the assessment Students scan the assessmentl()r unliuniliar
wIJ'rds~/instnlctiiol1s. Remind students that t.he class word waH
he useful
criteria.
•
Action!
Injfyklyal -7 SYmmatlve.An'.'mtnt
Students complete the assessment using manipulatives and calculators as
•
Consolidate
Debrief
Whole ((lIB -7 DifcuH12n
Assessments are opportunities for reflection and pbulnirlg
how the
of this assessment can
next
''''tid,,,,r)
Hmn ~.g[Fyrth ... gl-mom ConlOlkiltion
Complete the challenge:
Students who
complele the
llummatillE!
Julia :r mollter is () math teacher: She
1;'/;'/"IJ'~w nn(Jbi't"!J1
Discuss
and their
8ssellsmfmt task
early can
this assignment
based On
commtmicatittf!, co,ltt,?lt':n;!'J' ,:In,ci (YJ/'!'(?ctl1C<.I:r
l'oold1111 tWlh j~{tllh/
TIPS Seclion
.~
Grade
(modified by HenSEl)
142
Summatlve Assessment - Fractions
Name:
Date:
Instructions:
1, Answer all of the questions as completely as possible.
2, Your answers will be assessed for understanding, communication, and
correctness.
3, If you think you can explain your reasoning much better by talking to me
or by showing something to me, then draw a speaker symbol beside the
question.
<»)
4, If you need me to read something to you, show me the sign language
symbol for R.
5, If you need manipulatives, show me the sign language symbol for M.
6, You may use a calculator for any part of this assessment.
Au• •ment Checkbric
Making convincing arguments, explanations and
cations
rating narrative and mathematical forms
Representing a situation mathematically
Selecting and applying
problem~solving
str
A.aessment feedback
Strengths
Areas for Improvement
Next Steps
TIPS Section 3
Grade 8
Qwaen's Printer for Ontario, 2004
(modifted by HeOSEl)
143
Unit Assessment - Fractions (continued)
Quick Lasagne
1. Preheat oven to 325°F.
2. Grease a rectangular
pan.
3. Pre-cook the pasta.
4. Une the bottom of the
pan with the square
pasta pieces.
Spread spaghetti sauce
evenly over the top of the
pasta.
6, Sprinkle mozzarella
cheese over the sauce,
7, Bake for 30 minutes,
Small square pieces of pasta
1 can spaghetti sauce
Grated mozzarella cheese
Julia is making "Quick Lasagne." She starts to cover her greased pan with the cooked pasta.
Julia discovers that she needs to use part of a pasta piece to complete the row, The picture
below is a scale model of the sheet with first row of pasta pieces,
1, Circle the answer that best represents the number of pasta pieces in the first row,
9
b)
1
9~·
Queen's Printer for
9
2004
1
'"}
,k
(modified by MeaSEl)
d)
9~
4
144
The picture below is a scale model of the sheet covered with pasta pieces.
Determine the number of pasta pieces on the sheet. Showyour work.
1
9 2 pasta pieces
across the top
1
6- pasta pieces
4
down the side
)(
"::
3. Forty pasta pieces cover two4hirds of a rectangUlar pan.
Circle the expression that gives the number of pasta pieces that will cover all of the pan.
a)
,
40 -
ry
b)
4
+40
Queen's Printer for Qntarlo. 2004
,
- +4U
3
(modified by HensEll
Page 145
4, When Jamel makes the uQuick lasagne~ recipe he uses a rectangular pan that holds
pasta pieces, Each pasta piece has an area of 36 cm 2 ,
Circle the expression that gives the total area of the rectangular pan in
b)
1
9
1
9
+ ~\j-
5, Miguel has a very small rectangular pan on which he can place 51 pasta pieces across the
3
top and
1 pasta pieces dawn the side, He has a package of 36 pasta pieces and wants to
2
know if he has enough pasta pieces to make two pans of "Quick lasagne:' Justifyyour
reasoning,
"::
TIPS Sectlon:5
,
Grade 8
(modifltld by HenSB)
146
6. Kaye cuts her ~auick Lasagne» into pieces of different shapes and sizes.
The diagram below is a geoboard model of Kaye's pan of lasagne.
The lasagne was made with 12 pasta pieces but it is cut into 8 pieces for serving - A, B, C,
0, E, F, G, and H.
a) Which piece(s) is/are
~. of the pan of lasagne?
.JlIstifyyour reasoning.
Hint
The dashed lines show the 12 pasta pieces.
\"'.:::>
Q<""c:.
7
'II
'\ ,0
If Julia eats a piece that is : of the pan and another piece that is ,1_ of the pan, then what
fraction of the whole pan of lasagne does she eat?
.JlIstlfyyoar reasoning.
-t--
\
TIPS Section
Grade 8
Oueen's Printer for Ontario, 2004
(modified by HCDSSI
147
Assessment Checkbric - "Look Foran
Record observations from student work.
Computing and
carrying out
procedures
Making convincing
arguments.
explanations and
justifications
Integrating
narrative and
mathematical
forms
Representing a
situation
mathematically
Selecting and
applying problem
e>nh/lnn strategies
Queen's Printer for Ontano, 2004
(modified by HenSe)
148

Gr.8 Fractions - SGDSBMathLearningPartners

Transcription

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