mental math gr 1 4 copy

8/17/2019 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&ample7#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&ample7

#r / = > i# yu (nw / = is 1 and ne mre is 1!


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>=@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&ample7

#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&ample7

= is 12

5 = is 12

s ! = is !2


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/ = 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&ample7 = 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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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&ample72 = > 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&ample7

#r > = 5

thin( @ = @ is 1#r > = 5

thin( > = > = is 1

#r > = 5

thin( 5 = 5 9 is 1


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#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&ample7

#r 5 = /

thin( 5 = 5 is 1

s 5 = / is 1 = 1 is 1>


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!=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&ample7 #r > = !!

thin( 2 = !2 and > = ! is >2 = / r >/


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15=A@=1A

>=!A


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Ma(ing 12 9 Gr !


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&ample7 #r / = >

thin( / = = ! is 12 = ! r 1!


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/=5A5=A

>=5A


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Cmpensatin 9 Gr !


Meaning7 Dsing ther (nwn math #acts and

cmpensating+ Fr e&ample4 adding t anaddend and ta(ing away #rm the sum+

E&ample7 #r > = !!

thin( > = !> 9 is

@2 9 r >/


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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&ample7

= ! is the same as

! =


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Cmpati'le Num'ers 9 Gr !4


Meaning7 Cmpati'le num'ers are #riendly

num'ers )#ten assciated with cmpati'lenum'ers t > r 12*+

E&ample7 #r = ! students may thin( = 1is > and mre ma(es 5


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=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&ample7 for 3

x

4 think

for 12

÷3 think


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>&>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&ample7 & > 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&ample7

#r &

thin( 4 4 @4 /

s & is /


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&>A!&A

>&A


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er $rperty #Multiplicatin9 Gr


Meaning7 Multiplying a #actr 'y


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Multiplicati%e "dentity9 Gr


Meaning7Multiplying a #actr 'y ne will nt changeits %alue+

;i%iding a di%idend 'y ne will nt change its

%alue+E&ample7 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&ample7 #r ! & /thin( ! & > is 1> and s(ip cunt 'y

threes 1>4 1/4 14


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& 5 A

@ & /A/ & 5A

& /A



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;u'ling r Hal%ing9 Gr 4 >


Meaning7 Dsing (nwn #acts and du'ling r

hal%ing them t determine the answer+

E&ample7 #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



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Dsing the $attern #r s, Gr


Meaning7 .nwing the #irst digit # the

answer is ne less than the nn,nine #actrand the sum # the prductIs digits is nine+

E&ample7 #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



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Repeated ;u'ling9 Gr 4 >


Meaning7 Cntinually du'ling t get t an

answer+

E&ample7 #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 @



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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&ample7 #r !> 5

thin( 5 & A !>• s !> 5 is >


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!@ @ A

8hin( @ & A !@

5 A

8hin( 5 & A



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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&ample7 #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+

mental math gr 1 4 copy

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