Ext 6-8 Sampler

36 Lesson18, 7ETeacherGuide 57 Objective50: Towrite equations frommodels or from sentences. Materials: Rectangular rods (orpositive rectangular rods fromMaster 20), black andwhite cubes (orpositive and negative integer squares fromMaster 20), equal sign card (Master 20), brownpaper bag Vocabulary: equation, equal sign Comparing aPhrase to anEquation In these activities, studentswrite equations fromwords andmodels. In equations, the variable represents a specific unknownnumber. Writeon theboard: x +4 Display1brownbagmarked x (or one rectangular rod) and4black cubes tomodel the expression. What is thevalueof x ? (The value canbe anynumber.) Writeon theboard: x +4=6 Next to the1 rectangular rod and4black cubes, put an equal sign followedby6black cubes. Ask a student volunteer to explain themeaningof the models inhis/her ownwords. (We startwith anunknown number, add4 to thenumber and it equals 6.) Whatnumberwouldyouadd to4andget 6? (2) Is thereanyothernumber? (no) Howmanydifferent valuesof x willmake the statement true? (onlyone, x =2) Emphasize that the equal sign turns thephrase into a sentenceor equation inwhichonlyone valueof x will make the equation true. Displayother combinationswith rectangular rods and cubes and an equal sign, asking students toguess and check to find the valueof x thatmakes the statement true. = x Read andmodel the explanation at the topof thepage together.Use rectangular rods, cubes, and equal signs to model and solve the equations. Have student volunteersuse rods and cubes tomodel problems 1 and2.Ask student volunteers to read and identifykeyoperationalwords inproblems 7–18. Students may complete thepageon their own. UsingGuess andCheck Students enjoy solvingproblems in avarietyofways. Explain that onewayof solving an equation is tokeep substitutingdifferent numbers for the variableuntil you find theone thatmakes the equation true.Ask students to use guess and check to solve several problems. Skill Builders 50-2, 50-3 57 ©Math TeachersPress, Inc.,Reproduction by anymeans is strictly prohibited. Anequationmay bewritten fromwords. The sum of three times a number and 4 is 10. 3 n + 4= 10 An equation is a sentencewithan equal sign. In amathematical sentence, the words “is equal to” are replacedby the equal sign. The equal sign tells you that both sides of the equation have the same value. Write anequation for eachpictureor phrase. Use x as the variable. 1. = ________ 3. = ________ 5. + = ________ 2. = ________ 4. = ________ 6. = + ________ 7. A number plus 5 is 8. 9. 10more than a number is 45. 11. A numberminus 20 is 80. 13. A number divided by 2 is 12. 15. Twice the number is 12. 17. A number decreasedby 4 is 50. 8. A number less 6 is 34. 10. A number increasedby 6 is 58. 12. 2 times a number less 5 is 7. 14. 3 times a number decreasedby 4 is 23. 16. 11 less than a number is 7. 18. 4 times anumber is 40. An equation can bewritten from amodel or picture of amodel. x –4= 5 x + 5 =8 = Joanhad somemoney inher purse. Shewent to the storeand bought aCD for $18.When she got home, Joanhad $10 left. Pick theequation that showswhat happened. A n –18= 10 C 18+ n =10 B n – 10= 8 D n +8=10 Answer WritingEquations fromModelsorWords x –3=4 Summeans toadd. 3x +4= -2 2x +2=8 2x +2=3x –4 x +4+ x =2x +4 x + 10=45 x +6=58 x –6=34 x –20=80 2x –5= 7 x ÷2= 12 3x –4=23 2x = 12 x – 11 = 7 x –4=50 4x =40 2x +2x –4=4x –4 7.EE.4 WritingEquations Grade7