EXT 3-6 Sampler

64 Grade6 PartB Lesson26, 6ETeacherGuide 75 Objective56: To solve additionor subtraction equations withmodels. PD Materials: Rectangular rods andblack andwhite cubes (or positive andnegative integer squares and rods,Master 22), balance scaleon inside front cover of student book EquationswithAddition or Subtraction In this lessonwewill usemodels to solveequations involvingadditionand subtraction.To solveanequation wemust get the variable, orunknownnumber x , by itself onone sideof theequation. Writeon theboard: I am thinkingof anumber. If I add5 to thenumber, itwill equal 8.What is thenumber? Have students place rodswithblack andwhite cubes on thebalance scale shownon the inside front cover of the student book. Model the equation x +5=8with rods and cubes as shown. Ask a student to translate the equation shown into words. ( x plus 5 equals 8) What is thevalueof x that makes theequation true? (3) Inorder tokeepanequation balanced, the sameoperationmustbedoneonboth sides of theequal sign. Theeasiestway to solveanequation is toget the variableby itself onone sideof theequal sign.What ison the same sideas thevariable, x ? (5) How canweget ridof the5? (add – 5) Ifweadd – 5 to the left side,whatmustbe doneon the right sideof theequal sign? (add – 5)Model this byplacing5white cubes on each side. Nowhowdoes theequation read? ( x +5–5=8–5) Ifweput together the like termsonboth sidesof theequal sign,whatdo weget? ( x =3) Letus checkouranswer. Ifweput 3 in for x , is the equation true? (Yes) Why? (because3+5=8) Model the equation n –3= – 5with rods and cubes as shownbelow. Ask a student to translate the equation shown into words. Whenanunknownnumberhas3 subtracted from it, the result is – 5.Whatmustweget ridof toget n by itself onone sideof theequal sign? ( – 3) How canwedo this? (Add + 3.) Ifweadd + 3 to the left side,whatmustbe doneon the right sideof theequal sign? (Add + 3.) = = Model this byplacing3black cubes on each side. Now howdoes theequation read? ( n –3+3= – 5+3) Simplify theequationbyputting together the like termsonboth sidesof theequal sign.What arewe leftwith? ( n = – 2) Ifweput – 2 in for n , is theequation true? (yes) Show the checkon theboard: Check: ( – 2) –3 = – 5 – 2+ ( – 3) = – 5 – 5 = – 5 Use rods and cubes tomodel the example at the topof thepage.Ask a student volunteer to translate the equations inproblems 1 and2 intowords. For example, forproblem 1, a studentmight say, “When anunknownnumber x has 2 added to it, the result is 4.What is thenumber?” Have studentsusemodels to solve theproblems. Skill Builders 56-2, 56-7 75 ©Math TeachersPress, Inc.,Reproduction by anymeans is strictly prohibited. Equations InvolvingAddition andSubtraction Think of a balance scale as amodel of an equation. Whatever you do to one side, you must do to the other side to keep the balance. An equation has an equal sign and tells you that both sides of the equation have the same value. Cass said, “I am thinking of a number. If you subtract 3 from the number you will have 5 left. What is the number?” n – 3 = 5 n – 3 = 5 n = = = Usemodels tomake the equation. 1. = x = _____ 2. = x = _____ 3. x + 2 = 5 x = _____ 6. x – 2 = – 3 x = _____ 4. x – 3 = 4 x = _____ 7. x + 1 = – 4 x = _____ 5. x – 2 = 8 x = _____ 8. n + 10 = 24 n = _____ 9. Lane added 10 stamps to his stamp collection. He now has 50 stamps. Howmany stamps did he have before? ________ 10. I am thinking of a number. If you take 3 away from that number, therewill be 11 left. What was the original number? ________ Write a number sentence. Solve for the unknown. Let n equal the number. To get n by itself, add3 to the left side. Add3 to the right side to keep the balance. 11. Why is a teeter-totter a good example of an equation?How do you keep the balancewhen you add a 70 pound person to one side? 2 3 –1 7 40stamps 14 –5 10 14 9 8 x +40=50 x –3= 11 x +2=4 x –3=6 To keep a teeter-totter in balance, youmust have the same amount on each side. Add a 70 pound person to the other side to keep the balance. 6.EE.5, 6.EE.7 EquationsUsingAdditionorSubtraction Studentsplace cubeson the BalanceScale (foundon the inside front cover) to solve anequation.