Ext 6-8 Sampler

37 Grade7 SolvingAddition/SubtractionEquations Lesson19, 7ETeacherGuide 58 Objective50: To solve additionor subtraction equations withmodels. Materials: Rectangular rods andblack andwhite cubes (orpositive andnegative integer squares and rods from Master 20), equal sign card (Master 20), brownpaper bags EquationswithAddition or Subtraction Model the equation x +5=8using rectangular rods, black andwhite cubes, and an equal sign card (from Master 20). Ask a student to translate the equation shown into words. (xplus 5 equals 8) Whatmustbedone toan equation tokeep itbalanced? (Whatever operation is doneonone sideof the equal signmust be repeatedon theother sideof the equal sign.) Theeasiestway to solveanequation is toget the variableby itself onone sideof theequal sign.What ison the same sideas thevariable, x ? (5) How canwe get ridof the5? (add – 5) The sumof anumberand its opposite is zero. Ifweadd – 5 to the left side,whatmustbedoneon the right sideof theequal sign? (add – 5)Model this by placing5white cubes on each side. Nowhowdoes the equation read? ( x +5–5=8–5) Ifweput together the like termsonboth sidesof theequal sign,whatdowe get? ( 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. Whatmustweget ridof toget n by itself onone sideof theequal sign? ( – 3) How canwedo this? (Add + 3.) Ifweadd + 3 to the left side,whatmustbedoneon 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) Ifwe substitute – 2 for n , is theequation true? (yes) Show the checkon theboard: Check: ( – 2) –3 = – 5 – 2+ ( – 3) = – 5 – 5 = – 5 = = Use rods or abrownbagwith x writtenon itwith black andwhite squares tomodel the two examples in the explanation.Ask a student volunteer to translate the equations inproblems 1 and2 intowords. For example, forproblem1, a studentmight say, “When anunknown number x has 2 added to it, the result is 4.What is thenumber?” Have studentsusemodels to solve theproblems. Student-AuthoredEquations Give each student ahalf-sheet of paper. Ask students to thinkof anumber,write a true sentence about thenumberusing aplus orminus sign, anddraw apictureof the sentenceor a sketchof abalance scale. Exchange equations and pictureswith the students in the class. Skill Builders 50-6 58 ©Math TeachersPress, Inc.,Reproduction by anymeans is strictly prohibited. SolvingAddition andSubtractionEquationswithModels 1. Build the equation with rods and cubes. 2. Isolate x by using the sum of zeromethod. Make the same change on the other side of the equation. 3. Simplify bymatching positive and negative pairs. x = 5 x = 7 Ex. x + 3 = 8 Ex. x – 2 = 5 Add – 3 to + 3 to get a sum zero. Add – 3 on the other side also. Add + 2 on this side also. Usemodels to solve the equations. 3. x +3 = – 6 x = _____ 6. x – 3 = 3 x = _____ 4. x – 4 = 5 x = _____ 7. 4 + x = 1 x = _____ 5. x – 2 = 6 x = _____ 8. – 4 + x = 3 x = _____ An equation is like a balance scale. If a change is made on one side, the same changemust bemade on the other side. If 1 pound (lb) is added to the left side, drawwhat must be done to balance the right side. 2 lb. 2 lb. 1 lb. Add + 2 to – 2 to get a sum zero. 1. x = _____ 2. x = _____ 10. Explain the pattern for solving equationswith addition and subtraction. Give an example of each. 2 9 -9 6 9 -3 8 7 Tosolve the equation, youneed toaddor subtract the same number to bothsides to isolate x. Exampleswill vary. 7.EE.4, 7.EE.4a