LESSON 12: Subtract Integers [OBJECTIVEntnmath.kemsmath.com/LEVEL G TEACHER NOTES/Grade 7- Lesson...

Mathematics Success – Grade 7T248

LESSON 12: Subtract Integers

[OBJECTIVE]The student will explore subtraction with integers and apply this understanding to

solve problems in mathematical and real-world situations.

[PREREQUISITE SKILLS]Addition and subtraction of whole numbers, number line, addition of integers

[MATERIALS]Student pages S125–S137Red and yellow unit tiles for students (5 of each color)

Foldable from Lesson 11

[ESSENTIAL QUESTIONS]1. Explain how to subtract integers using algebra tiles.

2. Describe the process we can use to take away the second number in the

subtraction problem if there are not enough counters.

3. Will the following problems have the same solution? 4 – 6 and 4 + (−6) Justify

your answer.

[WORDS FOR WORD WALL]subtraction, zero pairs, take away, yellow- positive, red- negative, absolute value,

difference

[GROUPING]Cooperative Pairs (CP), Whole Group (WG), Individual (I)

[LEVELS OF TEACHER SUPPORT]Modeling (M), Guided Practice (GP), Independent Practice (IP)

[MULTIPLE REPRESENTATIONS]SOLVE, Algebraic Formula, Verbal Description, Pictorial Representation, Concrete

Representation, Graphic Organizer

[WARM-UP] (CP, IP, WG) S125 (Answers on T261.)• HavestudentsturntoS125intheirbookstobegintheWarm-Up.Students

will practice their basic addition skills with integers to prepare for subtracting

integers.MonitorstudentstoseeifanyofthemneedhelpduringtheWarm-Up.Give students time to complete the problems and then review the answers as a

class. {Verbal Description}

[HOMEWORK]Take time to go over the homework from the previous night.

[LESSON] [1 – 2 Days (1 day = 80 minutes) – M, GP, WG, CP, IP]

Mathematics Success – Grade 7 T249

SOLVE Problem (GP, WG) S126 (Answers on T262.)

HavestudentsturntoS126intheirbooks.ThefirstproblemisaSOLVEproblem.You are only going to complete the S step with students at this point. Tell students

that during the lesson they will learn how to subtract with integers in mathematical

and real-world situations. They will use this knowledge to complete this SOLVE

problem at the end of the lesson. {SOLVE, Graphic Organizer, Verbal Description}

Reviewing Absolute Value (WG, M, GP, CP) S126 (Answers on T262.)

WG, M, GP, CP: Students will use horizontal and vertical number lines to

review the concept of absolute value. Assign the roles of

Partner A and Partner B to students. {Verbal Description, Pictorial Representation}


MODELING

Reviewing Absolute Value

Step 1:HavestudentpairslookatthehorizontalnumberlinewithProblem1onthe bottom of S126.

• PartnerA,whatistherangeofthevaluesonthenumberline?(negativefivethroughpositivefive)

• Havestudentscirclethezeroonthenumberline. • PartnerB,describethechangeaswemovefromzerototherighton

the number line. (positive)

• PartnerA,describethechangeaswemovefromzerototheleftonthe number line. (negative)

0 5 -5 positivenegative

3 spaces3 spaces

Step 2: Partner B, identify the number of spaces from the zero in the positive

direction. (3 spaces)

• PartnerA,identifythepositiononthepositivesideofthenumberline.(3) • PartnerB,identifythenumberofspacesfromthezerointhenegative

direction. (3)

• PartnerA, identifythepositiononthenegativesideofthenumberline. (-3)



Step 3:Havepartnersdiscussthefollowingquestion:Ifthenumberofspacesfrom zero in both directions is 3, explain why one of the points is 3 and

the other is a negative 3. (When we move to the left we are moving in

the negative direction; when we move to the right we are moving in the

positive direction. The distance moved is 3 spaces for both. )

• PartnerB,identifywhatthisconceptiscalled.(absolute value) • PartnerA,explainwhatabsolutevaluemeans.(Absolutevalueisthe

distance a number is from zero on the number line.)

• PartnerB,whatistheabsolutevalueof3?(3)Record. • PartnerA,whatistheabsolutevalueof-3? (3) Record.

Step 4:Havestudentpairscomplete thequestions forProblem2.Reviewthesymbol for absolute value.

Step 5: The absolute value of a number is always a (positive) value because the

absolute value represents the distance from (zero) on the number line

and a distance cannot be a (negative) value. Record.


MODELING

Subtracting Two Positive Values

Step 1:HavestudentslookatProblem1onS127. • PartnerA,whatistheproblemaskingustofind?(thedifference of

positive 4 and positive 1)

• PartnerB,explainhowwecanmodel theproblemusingunit tiles.(Place four yellow tiles on the space.)

• Havestudents identifysomeofthetermstheycanusetodescribesubtraction. (take away, remove, cross out)

• Whatdowewanttotakeawayfromthefouryellowtiles?(1yellowtile) • Modelhowtotakeawaytheoneyellowtile.

Step 2: What do we have left after we take the one yellow tile away? (3 yellow tiles)

• What do you notice about the color of the tiles? (They are allyellow.)

• Havestudentsdrawapictureofthe4yellowtilesintheboxbelowProblem 1 and talk about how to show subtraction. (Cross out 1 yellow

tile with an X.)

• Have students discuss howwe canmodel taking away the one Y.(Cross it out.)

• PartnerA,explainthecolorofthetiles.(allthesamecolor)Record. • PartnerB,whatoperationdidweuse?(subtraction) • PartnerA,whatisthedifference?(3yellows=3)Record.

Step 3: Direct students’ attention to the horizontal number line for Problem 1.

• PartnerA,explainhowtomodelthefirstvalueofpositive4.(Drawaline in the positive direction – to the right from the zero to the 4.)

• PartnerB,explainhowtomodelsubtractingthe1.(Drawalinestartingat the 4 and then moving one space in the negative direction.)

0 5-5

41

• PartnerA,whatisthedifferenceof4and1?(3)


Subtracting Integers (WG, M, GP, CP) S127, S128(Answers on T263, T264.)

WG, M, GP, CP: HavestudentsturntoS127.Passoutyellowandredunit tiles to student pairs. Students will use algebra unit

tiles and number lines to explore subtracting integers

and the relationship between subtraction and addition.

Be sure students know their role of Partner A or Partner

B. {Concrete Representation, Verbal Description, Pictorial Representation}


MODELING

Subtracting Two Negative Values

Step 1:HavestudentslookatProblem2onS127. • PartnerA,whatistheproblemaskingustofind?(thedifferenceof

negative 4 and negative 1)

• PartnerB,explainhowwecanmodeltheproblemusingalgebratiles.(Place four red tiles on the space.)


• Whatdowewanttotakeawayfromthefourredtiles?(1redtile) • Modelhowtotakeawaytheoneredtile.

Step 2: What do we have left after we take the one red tile away. (3 red tiles)

• What do you notice about the color of the tiles? (They are all red.)

• Have students draw a picture of the 4 red tiles in the box belowProblem 1 and talk about how to show subtraction. (Cross out 1 red

tile with an X.)

• Havestudentsusethetilestorepresent-4intermsofRs.(RRRR)Record. • Have students discuss howwe canmodel taking away the one R.

(Cross it out.)

• Partner A, explain the color of the tiles. (all the same color) Record.


Step 4: Direct students’ attention to the vertical number line for Problem 1.

• PartnerB,explainhowtomodelthefirstvalueofpositive4.(Drawaline in the positive direction up from the zero to the 4.)

• PartnerA,explainhowtomodelsubtracting1.(Drawalinefromthe4 one space in the negative direction which is down.)

• PartnerB,whatisthedifferenceof4−1?(3)

Step 5: Describe the relationship between subtraction and addition. (They are

opposite operations.) Record.

• Comparethehorizontalnumberlinebelowandthenumberlinefor4−1.(Thenumberlineslookthesame.)Record.

0 5-5

4-1

• Howcanyourepresentthenumberlinemodelabovewithaddition?[4 + (-1)=3]Record.

Step 6: What conclusion can you make based upon the horizontal number line

models? Subtraction is the same as adding the (opposite).

Howcanwewritethetwoproblems?[4−1=3]correspondsto[4+(-1)=3]Record.



• PartnerB,whatoperationdidweuse?(subtraction) • PartnerA,whatisthedifference?(3reds=-3) Record.


• PartnerA,explainhowtomodelthefirstvalueofnegative4.(Drawaline in the negative direction – to the left from the zero to the -4.)

• PartnerB,explainhowtomodelsubtractingthenegative1.(Ifwearesubtracting the negative we are moving in the opposite direction of

negative one which would be one space to the right.)

0 5-5

-41

• PartnerA,whatisthedifferenceofnegative4andnegative1?(-3)


• PartnerB,explainhowtomodelthefirstvalueofnegative4.(Drawaline in the negative direction down from the zero to the negative 4.)

• PartnerA,explainhowtomodelsubtractinganegative1.(Drawalinefrom the negative 4 one space up because we are doing the opposite

of subtracting one.)

• PartnerB,whatisthedifferenceofnegative4andnegative1?(-3)


opposite operations.)

• Comparethehorizontalnumberlinebelowandthenumberlinefor-4 + 1. (The number lines look the same.) Record.

0 5-5

-41

• Howcanyourepresentthenumberlinemodelabovewithaddition?(-4+1=-3) Record.


models?

Subtraction is the same as adding the (opposite).

How canwewrite the twoproblems? [-4 – (-1)= -3 corresponds to -4+1=-3]Record.



MODELING

Subtracting a Negative from a Positive


positive 4 and negative 1)

• PartnerB,explainhowwecanmodeltheproblemusingalgebratiles.(Place four yellow tiles on the space.)


• Whatdowewanttotakeawayfromthefouryellowtiles?(1redtile) • PartnerA, is itpossible to takeonered tileaway fromfouryellow

tiles? (No)

• PartnerB,whenwewereaddingintegers,whatdidwehavewhenwerepresented one red and one yellow? (a value of zero)

• Explaintostudentsthatwecallthatazero pair because the value is

zero.

Step 2:Havestudentsdiscusspossiblestrategiestouseazeropairto“createthe possibility” of taking away a red tile.

• What happens ifwe add one zero pair?Does the value of the tileschange? Explain your thinking. (No, the value does not change because

we can add or subtract the value of zero to a number without changing

the value.)

• Whatpropertydoesthisrelateto?(identitypropertyofzero)Step 3: Partner A, have we created the possibility of taking away one red tile? (Yes.)

• Whatdowehaveleftafterwetaketheoneredtileaway?(5yellowtiles) • Whatdoyounoticeaboutthecolorofthetiles?(Theyareallyellow.) • Havestudentsdrawapictureofthe4yellowtilesintheboxbelow

Problem 3 and talk about how to show subtraction. (Add the zero pair

and then cross out 1 red tile with an X.)

Step 4:HavestudentsusetheYstorepresentthetiles.(YYYY)Record. • HavestudentsdiscusshowwecanmodeltakingawaytheoneR.(Add

a YR to represent the zero pair and then cross out the R.)

• PartnerA,explainthecolorofthetiles.(allthesamecolor)Record. • PartnerB,whatoperationdidweuse?(subtraction) • PartnerA,whatisthedifference?(5yellows=5)Record.Step 5: Direct students’ attention to the horizontal number line for Problem 3.

• PartnerA,explainhowtomodelthefirstvalueofpositive4.(Drawaline in the positive direction to the right from the zero to the 4.)

• PartnerB,explainhowtomodelsubtractingthenegative1.(Ifwearesubtracting the negative we are moving in the opposite direction of

negative one which would be one space to the right.)

0 5-5

41



• PartnerA,whatisthedifferenceofpositive4andnegative1?(5)


• PartnerB,explainhowtomodelthefirstvalueofpositive4.(Drawaline in the positive direction – up from the zero to the positive 4.)

• PartnerA,explainhowtomodelsubtractinganegative1.(Drawalinefrom the positive 4 one space up because we are doing the opposite

of subtracting one.)

• PartnerB,whatisthedifferenceofpositive4andnegative1?(5)


opposite operations.) Record.

• Comparethehorizontalnumberlinebelowandthenumberlinefor 4 + 1. (The number lines look the same.) Record.

0 5-5

41

• Howcanyourepresentthenumberlinemodelabovewithaddition?(4+1=5)Record.


models?

(Subtraction is the same as adding the opposite.) Record.

How can we write the two problems? [4 – (-1) = 5 corresponds to4+1=5]Record.



MODELING

Subtracting a Positive from a Negative


negative 4 and positive 1)

• PartnerB,explainhowwecanmodeltheproblemusingalgebratiles.(Place four red tiles on the space.)


• What dowewant to take away from the four red tiles? (1 yellowtile)

• PartnerA, is itpossible to takeoneyellowtileaway fromfour redtiles? (No)

• PartnerB,whenwewereaddingintegers,whatdidwehavewhenwerepresented one red and one yellow? (a value of zero)

• Havestudentsexplainwhyitiscalledazeropair.

Step 2:Havestudentsdiscusspossiblestrategiestouseazeropairto“createthe possibility” of taking away a yellow tile.

• Whathappens ifweaddonezeropair?Doesthevalueof thetileschange? Explain your thinking. (No, the value does not change

because we can add or subtract the value of zero to a number without

changing the value.)

• Whatpropertydoesthisrelateto?(identitypropertyofzero)

Step 3: Partner A, have we created the possibility of taking away one yellow tile?

(Yes)

• Whatdowehaveleftafterwetaketheoneyellowtileaway?(5redtiles)

• Whatdoyounoticeaboutthecolorofthetiles?(Theyareallred.) • Have students draw a picture of the 4 red tiles in the box below

Problem 4 and talk about how to show subtraction. (Add the zero pair

and then cross out 1 yellow tile with an X.)


Step 4:HavestudentsmodelhowtousetheRstorepresentthetiles.(RRRR)Record.

• HavestudentsdiscusshowwecanmodeltakingawaytheoneY.(Adda YR to represent the zero pair and then cross out the Y.)

• PartnerA,explainthecolorofthetiles.(allthesamecolor)Record. • PartnerB,whatoperationdidweuse?(subtraction) • PartnerA,whatisthedifference?(5red=-5) Record.


• PartnerA,explainhowtomodelthefirstvalueofnegative4.(Drawalinein the negative direction – to the left from the zero to the negative 4.)

• PartnerB,explainhowtomodelsubtractingthepositive1.(Moveonespace to the left.)

0 5-5

-41

• PartnerA,whatisthedifferenceofnegative4andpositive1?(-5)


• PartnerB,explainhowtomodelthefirstvalueofnegative4.(Drawaline in the negative direction down from the zero to the negative 4.)

• PartnerA,explainhowtomodelsubtractingapositive1.(Drawalinefrom the negative 4 one space down.)

• PartnerB,whatisthedifferenceofnegative4andpositive1?(-5)


opposite operations.)

• Comparethehorizontalnumberlinebelowandthenumberlinefor -4 + -1. (The number lines look the same.) Record.

0 5-5

-4-1

• Howcanyourepresentthenumberlinemodelabovewithaddition?(-4 + -1=-5) Record.


models? Subtraction is the same as adding the (opposite). Record.

Howcanwewritethetwoproblems?[-4–1=-5 corresponds to -4 + -1

=-5]Record.




Subtracting Integers and Corresponding Addition Problems (WG, M, IP, GP, CP) S129 (Answers on T265.)

WG, M, GP, CP: HavestudentsturntoS129.Studentswillbewritingthe corresponding addition problem for each subtraction

problem. Be sure students know their role of Partner A

or Partner B. {Verbal Description, Pictorial Representation, Concrete Representation, Graphic Organizer}

MODELING

Subtracting Integers and Corresponding Addition Problems

Step 1:Directstudents’attentiontotheboxonthetopofS129. • Have student pairs look at Problem1andwrite the corresponding

addition problem.

• Havestudentssubtract4–1andwritethedifference.(3)Record. • Havestudentpairsmodelthecorrespondingadditionproblemusing

integer tiles or a pictorial model.

• PartnerA,whatisthesumof4+(-1)? (3) Record.

• PartnerB,howarethetwoproblemssimilar?(Theanswersarethesame.) Record.

• PartnerA,howarethetwoproblemsdifferent?(Oneissubtractingapositive 1, and the other is adding a negative 1.) Record.

Step 2:HavestudentscompleteProblems2–4andthenreviewtheanswersasa whole group.

Step 3: What conclusion can you make about the problems above? (Subtracting

an integer is the same as adding the opposite value.) Record.

CP, IP, WG: HavestudentscompleteProblems5–8.Studentsmayuse tiles or a pictorial model, if necessary, and should

be prepared to explain the difference for each problem.

ReviewanswerstoProblems5–8asawholegroup.{Pictorial Representation, Verbal Description, Graphic Organizer}


Integer Rules (WG, GP) S130 (Answers on T266.)

HavestudentsturntoS130toaddtotheIntegerRulesgraphicorganizer.Askstudents to look back at the problems they have completed during the lesson.

Havestudentscompletethefirstsentence.(Subtractionisthesameasaddingthe opposite.) Record.

Discuss with students their ideas and come up with a rule that makes sense to

them. Allow them to write it in their own words. (1. Change subtraction sign to an

addition sign. 2. Change the sign of the second number to its opposite.) Record.

Afterthesetwosteps:(Followtherulesforadditionofintegers.)Record.

This page will be used again as students discover the rules for each operation on

integers. {Verbal Description, Graphic Organizer}

MODELING

Integer Foldable – Subtracting Integers

Step 1:Havestudentsgetouttheirintegerfoldable.

Step 2:Ontheinside,ontherightsideofthesecondflap,havestudentswritethe rules for subtracting integers. On the left side, have students write

examplesforsubtractingintegers.Usetheteacherexampleasamodelfor students.

Integer Foldable – Subtracting Integers (M, GP)


SOLVE Problem (WG. GP) S131 (Answers on T267.)

Remind students that the SOLVE problem is the same one from the beginning

of the lesson. Complete the SOLVE problem with your students. Ask them for

possible connections from the SOLVE problem to the lesson. (Step L involves

subtracting integers.) {SOLVE, Graphic Organizer, Verbal Description}

Real - World Application with Integer Subtraction (CP, IP, WG) S132, S133, S134, S135 (Answers on T268, T269, T270, T271.)

This activity includes four SOLVE problems that give students the opportunity to

practice subtracting integers with real - world applications. {SOLVE, Graphic Organizer, Verbal Description}

Thereareavarietyofwaystocompletetheseproblems.Hereareafewsuggestionswhicharealternativestohavingstudentscompleteall4problemsinstudentpairs:• Have students work in groups of 4 or 5 and assign them one of the SOLVE

problems to complete as a group. Students can then transfer answers to chart

paper and present to the whole group.

LESSON 12: Subtract Integers [OBJECTIVEntnmath.kemsmath.com/LEVEL G TEACHER NOTES/Grade 7- Lesson...

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