Ext 6-8 Sampler

42 PartB Grade7 Lesson25, 7ETeacherGuide 70 Objective51: To solve inequalities involving additionor subtraction. Materials: Rectangular rods (orpositive rectangular rods fromMaster 20), black andwhite cubes (orpositive and negative integer squares fromMaster 20), inequality symbols< and> fromMaster 20 Solving Inequalities:Addition or Subtraction Writeon theboard: x –3>2 Model x –3>2with rods and cubes as shownbelow. Have a student translate themodel into the inequality. When solvingalgebraic inequalities,we solve them the samewayaswe solveequations.Whatmustwedo toget x onone sideof thegreater than signby itself? (Add+3 toboth sides.)Model as shownbelow: Whenwe combine like termsonboth sides, howdoes the inequality read? ( x is greater than5.)Model this. Draw anumber lineon theboard tograph the solution. Ask studentswhat numbersmake the equation true and write their responses. Do the solutions lie to the left or right of 5on thenumber line? Explain thatwe can show the solutions to the inequalitybyplacing anopendot on5 and extending aheavy line to the right of 5. Why is thedot above5not shaded in? (because5 isnot part of the solution set). Use rods and cubes to solve the two examples in the explanation.Graph each solutionon anumber line. To show n >2, draw anunshadeddot at 2 and aheavily shaded line to the right. Ask students to suggest numbers thatwill satisfy the inequality. (2.5, 3, 4, 5, etc.) > > > 2 3 4 5 6 7 8 ( x > 5) – 2 – 1 0 1 2 3 4 ( n > 2) To show n ≤6, draw a shadeddot at 6 and aheavily shaded line to the left. Ask students to suggest numbers thatwouldmake the inequality true. (5.5, 5, 4.5, 4, etc.) Workproblems 1 and5with the class.Have students complete thepageon their own. WritingSolutions From aGraph Draw agraph showing the solutionof several inequalities on theboard.Ask students towrite the inequality shownon this graph. A. B. C. Skill Builders 51-1 0 – 3 – 2 – 1 0 1 2 3 ( x > 1) – 4 – 3 – 2 – 1 0 1 2 3 4 ( x < 2 ) – 3 – 2 – 1 0 1 2 3 ( x ≤ – 1 ) 70 ©Math TeachersPress, Inc.,Reproduction by anymeans is strictly prohibited. 1. 3. n –6 – 4 5. n – 3 7 7. n +4 – 2 2. 4. n +5 5 6. n + 6 – 8 8. n – 3 – 2 You can use rectangular rods andblack andwhite cubes to solve inequalities. Solveand graph. n +3 5 n – 2 4 n 2 n 6 Solving Inequalities InvolvingAdditionor Subtraction Use rods andblack andwhitecubes to solve each inequality. Graph the solution. 9. The sumof a number n and5 is less than – 10.Writean inequality and solve for n . ______________, ______________ 10. A number n less 4 is greater than or equal to2.Write an inequality and solve for n . ______________, ______________ – 4 – 3 – 2 – 1 0 1 2 3 4 5 6 – 2 – 1 0 1 2 3 4 5 6 7 8 – 3 – 2 – 1 0 1 2 3 – 3 – 2 – 1 0 1 2 3 – 15 – 10 – 5 0 5 10 15 – 6 – 4 – 2 0 2 4 6 – 15 – 10 – 5 0 5 10 15 – 3 – 2 – 1 0 1 2 3 – 15 – 10 – 5 0 5 10 15 – 3 – 2 – 1 0 1 2 3 Explain how solving anaddition or subtraction inequality is similar to solvinganaddition or subtractionequation. Explain how it is different. Add3white cubes to bothsides. 2 isnotasolution. Thedot isnotshaded. 6 isasolution. Thedot isshaded. ) means less than or equal to. Add2 black cubes to bothsides. Part B n+5< -10 n –4 * 2 n> 1 n>2 n ) 10 n> -6 n<5 n * 0 n> -14 n ) 1 n * 6 n< -15 7.EE.3, 7.EE.4, 7.EE.4b Solving Inequalities