lesson 11: add integers [objective - …ntnmath.kemsmath.com/level g teacher notes/grade 7- lesson...

Mathematics Success – Grade 7 T219

LESSON 11: Add Integers

[OBJECTIVE]The student will explore addition 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

[MATERIALS] Student pages S111–S124Red and yellow unit tiles for students (5 of each color)Paper for foldable (1 per student)

[ESSENTIAL QUESTIONS]1. Explain how to add integers that have the same signs.2. Explain how to add integers that have different signs.3. Describe real-life situations where you would need to use negative integers.

[WORDS FOR WORD WALL]zero pairs, “push together”, yellow - positive, red - negative, additive inverse property, commutative property, sum, addition

[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] (IP, WG) S111 (Answers on T232.)• Have students turn to S111 in their books to begin the Warm-Up. Students will

practice their basic addition and subtraction skills to prepare for adding integers. Monitor students to see if any of them need help during the Warm-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 7T220

SOLVE Problem (GP, WG) (GP, WG) S112 (Answers on T233.)

HavestudentsturntoS112intheirbooks.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 determine the rules for adding integers. They will use this knowledge to complete this SOLVE problem at the end of the lesson. {SOLVE, Graphic Organizer, Verbal Description}

Add Integers – Adding Opposites (WG, M, GP, CP) S112 (Answers on T233.)

WG, M, GP, CP: Students will use algebra tiles and number lines to explore integers and adding opposites to build a foundation for adding integers. Pass out red and yellow unit tiles to student pairs. Assign the roles of Partner A and Partner B to students.{Concrete Representation, Verbal Description, Pictorial Representation}

MODELING

Add Integers – Adding Opposites

Step 1: Review values of unit tiles with students. Have students identify the values of yellow tiles as positive and red tiles as negative. Ask students how to represent 4 with yellow tiles. Have students represent 2 with yellow tiles.

Have students represent -3 and then -5 with red unit tiles.

Step 2: Have student pairs read the word problem about Daniel and discuss what the $4.00 values represent in the problem.

• Partner A, explain themeaning of the word earn. (Earn will be apositive value because it is money you get by doing something.)

• Partner B, explain the meaning of the word owes. (Owes will bea negative value because it is money that you will have to pay someone.)




Step 3: Have student pairs discuss how they could use the unit tiles to represent the value that Daniel earned and create the model.

Have students discuss how they can use the unit tiles to represent the amount Daniel pays his brother and create the model.

If Daniel earns $4.00 but then has to pay his brother the $4.00, how much money does Daniel have left? (zero dollars)

Step 4: Show students one yellow and one red integer tile. Have them look at the number line and discuss how they would represent the one yellow tile using the number line.

• PartnerA,explainhowtorepresenttheoneyellowtileonthenumberline. (Move 1 to the right because we start with zero and move 1 in the positive direction.)

• PartnerB,ifwenowrepresenttheredintegertileonthenumberline,what value would we use? (Negative 1 because we start with zero and go one space in the negative direction.)

• Partner A, how could we describe the values of positive 1 andnegative 1? (They are opposites.) Explain your answer. (Both positive 1 and negative 1 are the same distance from zero but in opposite directions.)

Step 5: Go back to the yellow and red tiles. Ask students to discuss how they can connect the model of the negative one and positive one on the number line to the tiles.

• PartnerB,explaintherelationshipbetweentheyellowandredtiles.(They represent opposite values.)

• PartnerA,whatisthevalueofoneyellowandoneredtile?(zero)

• PartnerB,justifyyouranswer.(Ifwestartatzero,addoneandthentake it away we have zero.)


Step 6: Have student pairs draw the four unit tiles to represent the $4.00 Daniel earns and the four unit tiles that he pays his brother.

• PartnerA,whatcolorarethetilesthatrepresentthemoneyearned?(yellow)

• PartnerB,whatcolorarethetilesthatrepresentthemoneyhepaidhis brother? (red)

• Circleeachsetoftilesthatrepresentsasumofzero.

Step 7: Direct students’ attention to the horizontal number line.

• PartnerA,whatdirectionispositiveonthenumberline?(totheright)

• PartnerB,whatdirectionisnegativeonthenumberline?(totheleft)

• Havestudentsstartatthepositionofzeroonthenumberline.

• PartnerA,whichdirectiondowemoveonthenumberlinetomodelthe amount Daniel earned? (to the right or positive)

• PartnerB,whichdirectiondowemoveonthenumberlinetomodelthe amount Daniel paid to his brother? (to the left or negative)

• Whatisthecombinedvalueofthepositivefourandnegativefour?(zero)

Step 8: Direct students’ attention to the vertical number line.

• PartnerA,whatdirectionispositiveonthenumberline?(up)

• PartnerB,whatdirectionisnegativeonthenumberline?(down)

• Havestudentsstartatthepositionofzeroonthenumberline.

• PartnerA,whichdirectiondowemoveonthenumberlinetomodelthe amount Daniel earned? (up or positive)

• PartnerB,whichdirectiondowemoveonthenumberlinetomodelthe amount Daniel paid to his brother? (down or negative)

• Whatisthecombinedvalueofthepositivefourandnegativefour?(zero)

Step 9: Conclusion: When we add a number and its opposite, what is the sum? (zero) Record.

• Thisisknownasthe(additive inverse) property. Record.


Adding Integers with Like Signs (WG, M, GP, CP) S113 (Answers on T234.)

WG, M, GP, CP: Have students turn to S113. Students will use integers tiles and number lines to explore adding integers with the same signs. Be sure students know their role of Partner A or Partner B. {Concrete Representation, Verbal Description, Pictorial Representation}



MODELING

Adding Integers with Like Signs – Positive Values

Step 1: Have students look at Problem 1 on S113.• PartnerA,whatistheproblemaskingustofind?(thesum of positive

3 and positive 2)• PartnerB,howmodeladdition in the problem using unit tiles? (3

yellow tiles and 2 yellow tiles.)• Explain to students that when we add items, we “push them

together.”• Modelhowtopush together the 3 yellow tiles and the 2 yellow tiles.

Step 2: What is the total number of tiles? (5)• What do you notice about the color of the tiles? (They are all

yellow.)• HavestudentsdrawapictureofthemodelintheboxbelowProblem

1.• Model for students how to use the Ys to represent the tiles.

(YYY + YY) Record.• PartnerA,explainthecolorofthetiles.(allthesamecolor)Record.• PartnerB,whatoperationdidweusetocombinethetiles?(addition)• Partner A, explain what we did with the tiles. (We pushed them

together to add them.) Record.• PartnerB,whatisthesum?(5yellows=5)Record.

Step 3: Direct students’ attention to the horizontal number line for Problem 1.• PartnerA,explainhowtomodelthefirstvalueofpositive3.(Drawaline

in the positive direction – to the right from the zero to the 3.) Record.• PartnerB,explainhowtomodeladdingthepositive2.(Drawaline

two spaces in the positive direction starting from the 3.) Record.

-5 0

3

2

5

• PartnerA,whatisthesumof3+2?(5)

Step 4: Direct students’ attention to the vertical number line for Problem 1.• PartnerB,explainhowtomodelthefirstvalueofpositive3.(Drawa

line in the positive direction – up from the zero to the 3.) Why?• PartnerA,explainhowtomodeladdingthepositive2.(Drawaline

starting at 3 and moving two spaces in the positive direction, which is up.)

• PartnerB,whatisthesumof3+2?(5)


MODELING

Adding Integers with Like Signs – Negative Values

Step 1: Have students look at Problem 2 on S113.• PartnerA,whatistheproblemaskingustofind?(thesumofnegative

3 and negative 2)• PartnerB,explainhowwecanmodeltheproblemusingunittiles.(3

red tiles and 2 red tiles)• Explain to students that when we add items, we “push them

together.”• Modelhowtopushtogetherthe3redtilesandthe2redtiles.

Step 2: What is the total number of tiles? (5)• Whatdoyounoticeaboutthecolorofthetiles?(Theyareallred.)• HavestudentsdrawapictureofthemodelintheboxbelowProblem

1.• Model for students how to use the Rs to represent the tiles.

(RRR + RR) Record.• PartnerA,explainthecolorofthetiles.(allthesamecolor)Record.• PartnerB,whatoperationdidweusetocombinethetiles?(addition)• Partner A, explain what we did with the tiles. (We pushed them

together to add them.) Record.• PartnerB,whatisthesum?(5reds=-5) Record.

Step 3: Direct students’ attention to the horizontal number line for Problem 2.• PartnerA,explainhowtomodelthefirstvalueofnegative3.(Drawa

line in the negative direction – to the left from the zero to the -3.)• PartnerB,explainhowtomodeladdingthenegative2.(Drawaline

two spaces in the negative direction – to the left starting from the -3.)

-2-3

-5 -4 -3 -2 -1 0 1 2 3 4 5

• PartnerA,whatisthesumof-3 + -2? (-5)

Step 4: Direct students’ attention to the vertical number line for Problem 1.• PartnerB,explainhowtomodelthefirstvalueofnegative3.(Drawa

line in the negative direction – down from the zero to the -3.)• PartnerA,explainhowtomodeladdingthenegative2.(Drawaline

from the -3 two spaces in the negative direction which is down.)• PartnerB,whatisthesumof-3 + -2? (-5)




MODELING

Adding Integers with Like Signs – Conclusions

Step 1: Direct students’ attention to the questions on the bottom of S113.

• Have partners discuss the first four questions and be prepared toshare their responses with the whole group.

• PartnerA,whatdidyounoticeaboutProblem1andProblem2?(InProblem 1 both values were positive and in Problem 2 both values were negative.) Record.

• PartnerB,inProblem1whenyouaddedtwopositiveintegers,whatwasthesum?(Itwasapositivefive.)Record.

• PartnerA,inProblem2whenyouaddedtwonegativeintegers,whatwasthesum?(Itwasanegativefive.)

• PartnerB,whatisyourconclusion?(Whenweaddtwopositiveintegersthe sum will be positive. When you add two negative integers the sum will be negative.) Record.

Step 2:Havestudentsuseoneofthenumberlinemodelstojustifytheiranswer.(When we add two positive values, we start at zero and because both values are positive we are moving in the positive direction; so our answer must be positive. When we add two negative values, we start at zero and because both values are negative we are moving in the negative direction; so our answer must be negative.) Record.

Adding Integers with Unlike Signs (WG, M, GP, CP) S114 (Answers on T235.)

WG, M, GP, CP: Have students turn to S114. Students will use algebra tiles and number lines to explore adding integers with the different signs. Be sure students know their role of Partner A or Partner B. {Concrete Representation, Verbal Description, Graphic Organizer}



MODELING

Adding Integers with Unlike Signs

Step 1: Have students look at Problem 3 on S114.• PartnerA,whatistheproblemaskingustofind?(thesumofpositive

3 and negative 2)• PartnerB,explainhowwecanmodeltheproblemusingunittiles.(3

yellow tiles and 2 red tiles)• PartnerA,whenweaddedinProblems1and2,whatdidwedowith

our tiles? (We pushed them together.)• Modelhowtopushtogetherthe3yellowtilesandthe2redtiles.

Step 2: What do you notice about the color of the tiles? (They are not all the same color.)• HavestudentsdrawapictureofthemodelintheboxbelowProblem3.• When we were adding opposites at the beginning of the lesson,

what did we do when we had yellow and red tiles? (We created zero pairs.)

• PartnerB,canwemakeanyzeropairswiththeyellowandredtiles?(Yes)• Havestudentscirclethezeropairs.

Step 3: After removing the zero pairs, what do we have left? (1 yellow tile)• ModelforstudentshowtousetheYsandRstorepresentthetiles.

(YYY + RR) Record.• PartnerA,explainthecoloroftheletters.(Redtilesarenegative,and

yellow tiles are positive.)• PartnerB,dowehavezeropairsthatwecancombine?(Yes)• ModelthezeropairsbycrossingoutthematchingRandYpairs.• PartnerB,whatoperationdidweusetocombinethetiles?(addition)• PartnerA,explainwhatwedidwiththeRsandYs.(Addedthem.)Record.• PartnerB,whatisthesum?(1yellow=1)Record.

Step 4: Direct students’ attention to the horizontal number line for Problem 3.• PartnerA,explainhowtomodelthefirstvalueofpositive3.(Drawa

line in the positive direction – to the right from the zero to the 3.)• PartnerB,explainhowtomodeladdingthenegative2.(Drawaline

from the 3 two spaces in the negative direction – to the left)

-2

3

-5 0 5

• PartnerA,whatisthesumof3+-2? (1)



Step 5: Direct students’ attention to the vertical number line for Problem 3.• PartnerB,explainhowtomodelthefirstvalueofpositive3.(Drawa

line in the positive direction – up from the zero to the 3.)• PartnerA,explainhowtomodeladdingthenegative2.(Drawaline

from the 3 two spaces in the negative direction which is down.) • PartnerB,whatisthesumof3+-2? (1)

Step 6: Have students look at Problem 4 on S114.• PartnerA,whatistheproblemaskingustofind?(thesumofnegative

3 and positive 2)• PartnerB,explainhowwecanmodeltheproblemusingunittiles.(3

red tiles and 2 yellow tiles)• PartnerA,whenweaddedinProblems1and2,whatdidwedowith

our tiles? (We pushed them together.)• Modelhowtopushtogetherthe3redtilesandthe2yellowtiles.

Step 7: What do you notice about the color of the tiles? (They are not all the same color.)• HavestudentsdrawapictureofthemodelintheboxbelowProblem4.• Whenwewereaddingoppositesatthebeginningofthelesson,what

did we do when we had yellow and red tiles? (We created zero pairs.)• PartnerB,canwemakeanyzeropairswiththeredandyellowtiles?(Yes)• Havestudentscirclethezeropairs.

Step 8: After removing the zero pairs, what do we have left? (1 red tile)• ModelforstudentshowtousetheYsandRstorepresentthetiles.

(RRR + YY) Record.• PartnerA,explainthecolorofthetiles.(Thereareredandyellowtiles.)• PartnerB,dowehavezeropairsthatwecancombine?(Yes)• ModelthezeropairsbycrossingoutthematchingRandYpairs.• PartnerB,whatoperationdidweusetocombinethetiles?(addition)• PartnerA,explainwhatwedidwiththetiles.(Addedthem.)Record.• PartnerB,whatisthesum?(1red=-1) Record.

Step 8: Direct students’ attention to the horizontal number line for Problem 4.• PartnerA,explainhowtomodelthefirstvalueofnegative3.(Drawa

line in the negative direction – to the left from the zero to the -3.)• PartnerB,explainhowtomodeladdingthepositive2.(Drawaline

from the -3, two spaces in the positive direction – to the right)

2

-5

-3

0 5

• PartnerA,whatisthesumof-3 + 2? (-1)



Step 10: Direct students’ attention to the vertical number line for Problem 4.• PartnerB,explainhowtomodelthefirstvalueofnegative3.(Drawa

line in the negative direction – down from the zero to the -3.)• PartnerA,explainhowtomodeladdingthepositive2.(Drawaline

from the -3 two spaces in the positive direction which is up.) • PartnerB,whatisthesumof-3 + 2? (-1)

Step 11: What did you notice about Problem 3 and Problem 4? (In both problems one integer was positive and one was negative.) Record.

• InProblem3whenyouaddedthetwointegers,whatwasthesum?(It was a positive one.) Record.

• InProblem4whenyouaddedthetwointegers,whatwasthesum? (It was a negative one.)

Adding Integers with Unlike Signs – Exploring Rules and the Commutative Property (WG, M, GP, CP, IP) S115, S116 (Answers on T236, T237.)

WG, M, GP, CP: Have students turn to S115. Students will use the information from Problems 3 and 4 on S114 to explore the rules for adding integers and how adding integers works with the commutative property. Be sure students know their role of Partner A or Partner B. {Verbal Description, Pictorial Representation, Graphic Organizer}

MODELING

Adding Integers with Unlike Signs – Exploring Rules and the Commutative Property

Step 1: Have students look at Problem 3 on the top of S115.• Partner A, when we added the two values, where did we start on the

number line? (zero) Record.• PartnerB,whichdirectiondidwemovefirst?(totherighttorepresent

the positive three) Record.• PartnerA,howdidwemodeladdingthenegativetwo?(bymovingto

the left) Record.• Partner B, when we move to the right on the number line, what

operation are we modeling? (addition) Record.• PartnerA,whenwemovetotheleftonthenumberline,whatoperation

are we modeling? (subtraction) Record.• PartnerB, ifwelookatthenumbervalueswithoutthesigns,what

operation did we use to determine the answer in this problem? (subtraction) Record.

• PartnerA,howwasthesignofthesumdetermined?(Thesignofthesum is the sign of the value with the greater absolute value.) Record.



Step 2: Have students complete the questions under Problem 4. Review the answers as a whole group.

Step 3: Direct students to the section at the bottom of the page entitled, “Adding Integers with Property Application.”• HavestudentslookattheProblem3column.Wouldthesumchange

if the order of the addends was switched? Have students be prepared to explain and defend their answer using the number line.

• PartnerA,wasthesumthesameforbothproblems?(Yes)Record.• PartnerB,didtheorderoftheaddendschangethesum?(No)Record.• Whatpropertyarewerepresenting?(thecommutative property of

addition) Record.

Step 4: Have students complete the questions about property application in the column for Problem 4 and then review answers as a whole group.

CP, IP, WG: Have students turn to S116 in their books. Students will complete Problems 1 – 4. They can use a pictorial model of tiles, Ys and Rs or number lines as needed. They will also complete Problems 5 – 8 without using a model, but students should be prepared to explain the sum for each problem. Review answers to Problems 1 – 8 as a whole group. {Pictorial Representation, Verbal Description, Graphic Organizer}

Integer Rules (WG, CP, GP) S117 (Answers on T238.)

HavestudentsturntoS117,wheretheywillfindagraphicorganizer in which to write all of the integer rules that they will learn. Ask students to look back at the problems they have completed during the lesson. Have students complete thefirstsentencetocreatearuleforaddingintegerswiththe same signs. 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. Have students complete the second sentence to create a rule for adding integers with different signs. Again, discuss this as a class and develop a rule that makes sense to students. Allow them to write it in their own words. This page will be used again as students discover the rules for each operation on integers. {Verbal Description, Graphic Organizer}



Adding Integers Foldable (M, GP)

Use the following activity to help students begin their integer foldables. Students will complete this foldable as they learn about the other operations on integers in future lessons.

MODELING

Adding Integers Foldable

Step 1: Give each student one sheet of paper. Have them fold their papers hamburger style and then have them fold it hamburger style again.

Step 2: Next, have students unfold their papers and then do a hot-dog fold. Students should see four equal sections, separated by a fold. Have studentscuteachofthesefoldsonthefrontflaponly(whereyouseethe dotted line).

Step 3:Ontheoutsideofeachflap,havestudentswritetheoperationnames(Addition, Subtraction, Multiplication, Division). Inside, on the right side ofthefirstflap,havestudentswritetherules foradding integers.Onthe left side, have students write examples for adding integers. Use the teacher example as a model for students.

SOLVE Problem (WG. GP) S118 (Answers on T239.)

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

Real - World Application with Integer Addition (WG, GP) S119, S120, S121, S122 (Answers on T240, T241, T242, T243.)

This activity includes four SOLVE problems that give students the opportunity to practice adding integers with real - world applications. {SOLVE, Graphic Organizer, Verbal Description}

There are a variety of ways to complete these problems. Here are a few suggestions which are alternatives to having students complete all 4 problems in student pairs:

lesson 11: add integers [objective - …ntnmath.kemsmath.com/level g teacher notes/grade 7- lesson...

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