mental math gr 1 4 copy
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Virginia Birch
MFNERC Numeracy Specialist
Mental Math StrategiesGrade 1 to 4
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Overview• Mental Math… what is it?•
Grade 1 t ! Strategies• "ndicatrs #rm the $r%incial Reprt
Card
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Mental Math… what is it• Cnceptual strategies that enhance
#le&i'le thin(ing and num'er sense andnum'er s(ills )critical numeracy*
• calculating mentally withut the use #e&ternal memry aids+
• pr%ides a crnerstne #r all estimatin
prcesses ##ering a %ariety # alternatealgrithms and nn,standard techni-ues#r #inding answers
. , Gr / Manit'a CurriculumFramewr( # 0utcmes 21! . , Gr / Manit'a CurriculumFramewr( # 0utcmes 21!
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• de%elping mental math s(ills andrecalling math #acts autmatically
• Facts 'ecme autmatic #r
students thrugh repeated e&psureand practice+
• 3hen #acts are autmatic4 students
are n lnger using strategies tretrie%e them #rm memry+
Mental Math… what is it
. , Gr / Manit'a CurriculumFramewr( # 0utcmes 21!
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• 0ne # the Math Cmpetencies #r
the Grade ! and Grade 5 Math6ssessment
• )see reprt templates*
Mental Math… what is it
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Mental Math7• Shuld nt 'e timed+ Students di##er n
the amunt # time they need t prcesscncepts+
•
Can 'e dne daily appr&imately #i%eminutes #r a daily math rutine+• Can 'e practiced with math games r
learning centers where students can
practice the strategies+• Create a Mental Math Bulletin Bard
• Create an Estimatin Bulletin Bard
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8he de%elpment # mental mathstrategies is greatly enhanced 'y
sharing and discussin+ Studentsshuld 'e gi%en the #reedm t adapt4cm'ine4 and in%ent their wnstrategies+
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Math 8ls yu can use…
• 8en Frames• Base 12 Blc(s• 122 9 Chart• Num'er :ine• 6rray Cards• ;mines• Finger $atterns• :in(ing cu'es
Ging #rm cncrete t pictrial t a'stract…
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Cunting 0n 9 Grade 1Cncept7 6dditin
Meaning7
Students 'egin with a num'er and cunt n t getthe sum+ Students shuld 'egin t recgni
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$ractising the strategy…=5A
=!A
!=1A
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Cunting Bac( 9 Grade 1
Cncept7 Su'tractin
Meaning7 Students 'egin with the minuendand cunt 'ac( t #ind the di##erence+
E&le7#r @ 9 thin( @ 9 1 9 1 is
thin( @4 >4
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$ractising the Strategy
,A
12,!A5,1A
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Dsing 0ne Mre 9 Gr 14 Cncept7 6dditin
Meaning7 Starting #rm a (nwn #act andadding ne mre+
E&le7
#r / = > i# yu (nw / = is 1 and ne mre is 1!
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$ractising the Strategy
>=@A@=5A
/=A
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Dsing 0ne :ess , Gr 14 Cncept7 6dditin
Meaning7 Starting #rm a (nwn #act andta(ing ne away+
E&le7
#r / = @ i# yu (nw
/ = 5 is 1> and ne less is 1
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$ractising the strategy
5=@A=/A
@=>A
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Ma(ing 12 9 Gr 14
Cncept7 6dditin4 Su'tractin
Meaning7 Students use cm'inatins that
add up t ten and can e&tend this tmultiples # ten in later grades+
E&le7
= is 12
5 = is 12
s ! = is !2
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$ractising the strategy
/ = A !21> =A2
1@ = A 2
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Starting #rm .nwn
;u'les 9 Gr 1Cncept7 6dditin4 Su'tractin
Meaning7Students need t wr( t (nw their du'les#acts+
E&le7 = is and 9 is
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$ractising the strategy!=!A 4 s ,!A
=A 4 s ,A
/=/A 4 s ,/A
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$ractising the Strategy
1!,5A ?4 thin( 5 =A 1!11,@A ? 4 thin( @ =A11
1>,5A ? 4 thin( 5=A 1>
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8he er $rperty #
6dditin 9 Gr Cncept7 6dditin4 Su'tractin
Meaning7.nwing that adding 2 t an addend des ntchange its %alue4 and ta(ing 2 #rm a minuenddes nt change the %alue+
E&le72 = > A >
11 9 2 A 11
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Dsing ;u'les 9 Gr 4 !Cncept7 6dditin4 Su'tractin
Meaning7 Students learn du'les4 and use this t e&tend#acts7
using du'les
du'les plus ne )r tw*
du'les minus ne )r tw*
E&le7
#r > = 5
thin( @ = @ is 1#r > = 5
thin( > = > = is 1
#r > = 5
thin( 5 = 5 9 is 1
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$ractising the strategy
#r @= /4thin( du'les
#r @ = /4 thin( du'le @ plus tw
#r @ = /4 thin( du'le / minustw
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Building n .nwn
;u'les 9 Gr 4 !Cncept7 6dditin4 Su'tractin
Meaning7 Students learn du'les4 and usethis t e&tend #acts+
E&le7
#r 5 = /
thin( 5 = 5 is 1
s 5 = / is 1 = 1 is 1>
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$ractising the Strategy
!=A5=@A
/=A
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6dding #rm :e#t t
Right 9 Gr !Cncept7 6dditin
Meaning7 Dsing place %alue understanding tadd ,digit numerals+
E&le7 #r > = !!
thin( 2 = !2 and > = ! is >2 = / r >/
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$ractising the Strategy
15=A@=1A
>=!A
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Ma(ing 12 9 Gr !
Cncept7 6dditin4 Su'tractin
Meaning7 Students use cm'inatins that
add up t ten t calculate ther math #actsand can e&tend this t multiples # ten inlater grades+
E&le7 #r / = >
thin( / = = ! is 12 = ! r 1!
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$ractising the strategy
/=5A5=A
>=5A
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Cmpensatin 9 Gr !
Cncept7 6dditin4 Su'tractin
Meaning7 Dsing ther (nwn math #acts and
cmpensating+ Fr e&le4 adding t anaddend and ta(ing away #rm the sum+
E&le7 #r > = !!
thin( > = !> 9 is
@2 9 r >/
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$ractising the strategy
5=A1/=1>A
!=15A
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Cmmutati%e $rperty 9 Gr !
Cncept7 6dditin
Meaning7Switching the rder # the tw num'ers'eing added will nt a##ect the sum+
E&le7
= ! is the same as
! =
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Cmpati'le Num'ers 9 Gr !4
Cncept7 6dditin4 Su'tractin
Meaning7 Cmpati'le num'ers are #riendly
num'ers )#ten assciated with cmpati'lenum'ers t > r 12*+
E&le7 #r = ! students may thin( = 1is > and mre ma(es 5
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$ractising the Strategy
=5A=/A
5=/A
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6rray 9 Gr !
Cncept7 Multiplicatin4 ;i%isinMeaning7 Dsing an rdered arrangement tshw multiplicatin r di%isin )similar tarea*+E&le7 for 3
x
4 think
for 12
÷3 think
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$ractising the strategy
>&>A!&A
&A
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Cmmutati%e $rperty 9 Gr !Cncept7 Multiplicatin
Meaning7 Switching the rder r the twnum'ers 'eing multiplied will nt a##ect theprduct+
E&le7 & > is the same as
> &
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S(ip Cunting 9 Gr !
Cncept7 Multiplicatin
Meaning7 Dsing the cncept # multiplicatin
as a series # e-ual gruping t determine aprduct+
E&le7
#r &
thin( 4 4 @4 /
s & is /
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$ractising the Strategy
&>A!&A
>&A
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er $rperty #Multiplicatin9 Gr
Cncept7 Multiplicatin
Meaning7 Multiplying a #actr 'y
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Multiplicati%e "dentity9 Gr
Cncept7 Multiplicatin
Meaning7Multiplying a #actr 'y ne will nt changeits %alue+
;i%iding a di%idend 'y ne will nt change its
%alue+E&le7 1 & 1 is 1
1 1 is 1
( C #
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S(ip,Cunting #rm a.nwn Fact9 Gr 4 >
Cncept7 Multiplicatin4 ;i%isin
Meaning7 Similar t the cunting n strategy#r additin+ Dsing a (nwn #act and s(ipcunting #rward r 'ac(ward t determinethe answer+
E&le7 #r ! & /thin( ! & > is 1> and s(ip cunt 'y
threes 1>4 1/4 14
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& 5 A
@ & /A/ & 5A
& /A
$ractising the Strategy
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;u'ling r Hal%ing9 Gr 4 >
Cncept7 Multiplicatin4 ;i%isin
Meaning7 Dsing (nwn #acts and du'ling r
hal%ing them t determine the answer+
E&le7 #r 5 & 4
thin( the du'le # 5 & is /
#r / @4
thin( the du'le # @ is /
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/ & A
thin( du'le / & A
! A
thin( du'le 1@ A
$ractising the Strategy
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Dsing the $attern #r s, Gr
Cncept7 Multiplicatin4 ;i%isin
Meaning7 .nwing the #irst digit # the
answer is ne less than the nn,nine #actrand the sum # the prductIs digits is nine+
E&le7 #r 5 &
thin( ne less than 5 is @
and @ plus ! is nine4
s 5 & is @!
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& A !@
> & A >
@ & A >
5 & A @!/ & A 5
$ractising the Strategy
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Repeated ;u'ling9 Gr 4 >
Cncept7 Multiplicatin
Meaning7 Cntinually du'ling t get t an
answer+
E&le7 #r ! & /4
thin( ! & is @4@ & is 14
1 & is
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8 Jnd / K /4 Jrst Jnd K /4 then du'le4 thendu'le again+
K / A 1@
K / is du'le K /
1@ = 1@ A ! s4
K / A !
/ K / is du'le K /! = ! A @ s4
/ K / A @
$ractising the Strategy
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Dsing multiplicatin t di%ide ,Gr
Cncept7 ;i%isinMeaning7 8his is a #rm # part,part,whlerepresentatin+ 8hin(ing # additin as7
part & part A whle8hin(ing # su'tractin as7
whle part A part
E&le7 #r !> 5
thin( 5 & A !>• s !> 5 is >
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!@ @ A
8hin( @ & A !@
5 A
8hin( 5 & A
$ractising the Strategy
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;istri'uti%e prperty 9 Gr 4 >
Cncept7 MultiplicatinMeaning7 "n arithmetic r alge'ra4 when yudistri'ute a #actr acrss the 'rac(ets7
a & )' = c* A a & ' = a & c )a = '* & )c = d* A ac = ad = 'c = 'd
E&le7 #r & 1>
thin( & 122 plus & >2 plus & is
22 = 122 = / r !2/
Pl b
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Place a straw between two
columns.
3hat des it nw shw?
a & )' = c* A a & ' = a & c
Recrd it as ! & 5 A ! & = ! & >
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13 x 12
A )12 = !* & )12 = *A )12 & 12* = )12 & *
= )! & 12* = )! & *
)a = '* & )c = d* A ac = ad = 'c = 'd
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Hw d yu assess #r
mental math strategies?• Dse chec(lists• 0'ser%e strategies students are
using thrugh games• Ma(e anecdtal ntes while
cn%ersing with a student•
Cllect student sample wr(
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"ndicatrs #rm the $r%incialReprt Card )Gr 1 t /*
• ;etermines an answer using multiplemental math strategies
• 6pplies mental math strategies that aree##icient4 accurate4 and #le&i'le
• Ma(es a reasna'le estimate # %alue r
-uantity using 'enchmar(s and re#erents+• Dses estimatin t ma(e
mathematical Ludgments in daily li#e+