BNM3 Task 3 |Latest Update with Complete Solution
Understanding and Teaching Integers and Order of Operations
Number Sense and Functions-AOA2
Camille Winicky
The..order..of..operations..is..the..rules..that..tell..us..about..the..sequence..in..which..we..should..solve..a
n..expression..with..multiple..operations...The..order..is..parentheses,..exponents,..multiplication,..an
d..division..(from..left..to..right),..addition..and..subtraction..(from..left..to..right).
In..Response..One,..the..student..incorrectly..multiplied..2..x..2..before..dividing...According..to..the..
order..of..operations,..multiplication,..and..division..are..equal..operations..and..should..be..complete
d..from..left..to..right..as..they..appear..in..the..equation...Since..the..student..multiplied..first,..they..ende
d..up
1
with..2.. 4..–..2,..which..resulted..in..the..incorrect..answer..of..-1. .
÷ 2.
Response..Two..shows..the..correct..answer..but..does..not..follow..the..proper..order..of..operations...T
he..student..should..have..started..with..the..division..operation..and..then..moved..to..multiplication.
Instead,..they..subtracted..2..–
..2..first,..leaving..them..with..2..÷..2..x..0...Then,..the..student..correctly..moved..to..division,..calculati
ng..2..÷..2,..and..followed..with..multiplication...Although..this..process..resulted..in..the..correct..answ
er,..the..steps..taken..were..incorrect..because..the..student..did..not..adhere..to..the..proper..order..of..op
erations.
In..Response..Three,..the..student..skipped..the..first..step,..which..should..have..been..dividing..2÷2...I
nstead,..they..multiplied..2×2,..leaving..them..with..the..equation..2..÷..4−2...The..student..then..went..o
ut..of..order..by..subtracting..next,..which..left..them..with..2..÷..2..=..1...This..solution..is..also..incorrect..
because..the..proper..order..of..operations..was..not..followed.
In..Response..Four,..the..student..skipped..the..first..two..steps..in..the..order..of..operations—
division..and..multiplication—
and..subtracted..instead...This..left..them..with..the..equation..2..÷..2x0...At..this..point,..the..student..ma
de..another..mistake..by..multiplying..before..dividing...The..order..of..operations..requires..that..multip
lication..and..division..be..completed..from..left..to..right...Therefore,..the..division..should..have..been.
.completed..first...Instead,..the..student..multiplied..2..x..0,..leaving..them..with..2..÷.0...The..student..inc
orrectly..concluded..that..2..÷..0=not..possible,..but..dividing..by..zero..is..undefined.
The..problem..is..2..÷..2..×..2−2...To..make..Response..1..correct,..the..parentheses..would..have..to..be..place
d..around..the..multiplication..portion..of..the..problem...2..÷..(..2..×..2)−2...Adding..the..parentheses..means..t
hat..part..would..be..completed..first...2.÷..4−2...According..to..the..order..of..operations,..the..division..wo
uld..be
1. 1. 1.
completed. . next.. . 2.÷..4=.. .. . Finally,. . −2=−1.. .. . Adding. . these. . parentheses. . results. . in. . the. . s
ame
2 2 2
answer..the..student..achieved..in..response..1.
, The..problem..is..2..÷..2..×..2−2...To..make..Response..2..correct,..the..parentheses..would..have..to..be..place
d..around..the..subtraction..portion..of..the..problem.. . 2..÷..2..×..(..2−2).....Adding..the..parentheses..means..
that..part..would..be..completed..first...This..would..leave..the..problem. . 2..÷..2..×..0...Following..the..ord
er..of..operations,..the..student..would..divide..next...After..dividing..the..student..would..multiply..1.×.0=
0...This
Understanding and Teaching Integers and Order of Operations
Number Sense and Functions-AOA2
Camille Winicky
The..order..of..operations..is..the..rules..that..tell..us..about..the..sequence..in..which..we..should..solve..a
n..expression..with..multiple..operations...The..order..is..parentheses,..exponents,..multiplication,..an
d..division..(from..left..to..right),..addition..and..subtraction..(from..left..to..right).
In..Response..One,..the..student..incorrectly..multiplied..2..x..2..before..dividing...According..to..the..
order..of..operations,..multiplication,..and..division..are..equal..operations..and..should..be..complete
d..from..left..to..right..as..they..appear..in..the..equation...Since..the..student..multiplied..first,..they..ende
d..up
1
with..2.. 4..–..2,..which..resulted..in..the..incorrect..answer..of..-1. .
÷ 2.
Response..Two..shows..the..correct..answer..but..does..not..follow..the..proper..order..of..operations...T
he..student..should..have..started..with..the..division..operation..and..then..moved..to..multiplication.
Instead,..they..subtracted..2..–
..2..first,..leaving..them..with..2..÷..2..x..0...Then,..the..student..correctly..moved..to..division,..calculati
ng..2..÷..2,..and..followed..with..multiplication...Although..this..process..resulted..in..the..correct..answ
er,..the..steps..taken..were..incorrect..because..the..student..did..not..adhere..to..the..proper..order..of..op
erations.
In..Response..Three,..the..student..skipped..the..first..step,..which..should..have..been..dividing..2÷2...I
nstead,..they..multiplied..2×2,..leaving..them..with..the..equation..2..÷..4−2...The..student..then..went..o
ut..of..order..by..subtracting..next,..which..left..them..with..2..÷..2..=..1...This..solution..is..also..incorrect..
because..the..proper..order..of..operations..was..not..followed.
In..Response..Four,..the..student..skipped..the..first..two..steps..in..the..order..of..operations—
division..and..multiplication—
and..subtracted..instead...This..left..them..with..the..equation..2..÷..2x0...At..this..point,..the..student..ma
de..another..mistake..by..multiplying..before..dividing...The..order..of..operations..requires..that..multip
lication..and..division..be..completed..from..left..to..right...Therefore,..the..division..should..have..been.
.completed..first...Instead,..the..student..multiplied..2..x..0,..leaving..them..with..2..÷.0...The..student..inc
orrectly..concluded..that..2..÷..0=not..possible,..but..dividing..by..zero..is..undefined.
The..problem..is..2..÷..2..×..2−2...To..make..Response..1..correct,..the..parentheses..would..have..to..be..place
d..around..the..multiplication..portion..of..the..problem...2..÷..(..2..×..2)−2...Adding..the..parentheses..means..t
hat..part..would..be..completed..first...2.÷..4−2...According..to..the..order..of..operations,..the..division..wo
uld..be
1. 1. 1.
completed. . next.. . 2.÷..4=.. .. . Finally,. . −2=−1.. .. . Adding. . these. . parentheses. . results. . in. . the. . s
ame
2 2 2
answer..the..student..achieved..in..response..1.
, The..problem..is..2..÷..2..×..2−2...To..make..Response..2..correct,..the..parentheses..would..have..to..be..place
d..around..the..subtraction..portion..of..the..problem.. . 2..÷..2..×..(..2−2).....Adding..the..parentheses..means..
that..part..would..be..completed..first...This..would..leave..the..problem. . 2..÷..2..×..0...Following..the..ord
er..of..operations,..the..student..would..divide..next...After..dividing..the..student..would..multiply..1.×.0=
0...This
