Ext 6-8 Sampler

34 Grade7 Operationswith Integers Operationswith integersare scaffolded inPartA. 53 ©Math Teachers Press, Inc., Reproduction by anymeans is strictly prohibited. Subtracting Integers You can use black andwhite cubes to subtract integers. Youmay have to add pairs of black andwhite cubes (eachpair has a sumof zero) tohave enough cubes to subtract. – 2 – ( – 3) 1. – 4 – ( – 1) =_________ 4. – 3– ( – 4) = _________ 7. 2 – ( – 1) = _________ 10. – 3 – 2=_________ 13. – 1 – ( – 4) =_________ 2. – 3– ( – 2) =_________ 5. – 2 – ( – 4) =_________ 8. – 2 –6= _________ 11. 2 – ( – 5) =_________ 14. 2– 5= _________ 3. 5 – ( – 1) =_________ 6. 1– ( – 3) =_________ 9. – 2– ( – 2) = _________ 12. – 4– ( – 2) = _________ 15. – 2– 1= _________ Drawpairsof black andwhitecubes for eachset so that you can subtract. The first problemhasbeendone for you. – 2 – ( – 3) = 1 –3 Build – 2with2white cubes. There aren’t enough tosubtract... There are not enough white cubes. Addpairs of numbershavinga sumof zero. Subtract3 white cubes. There is 1 black cube left. Study the solutions for the problems. Explain thepattern for subtracting negative integers and illustratewith anexample. 55 ©Math Teachers Press, Inc., Reproduction by anymeans is strictly prohibited. – 8÷4= = – 2 – 8÷ ( – 4) = =2 Dividing Integers 1. – 6÷ 2= ____________ = 5. 8÷ – 2= ____________ = 9. – 42÷ – 6= ____________ = 2. – 12÷ 3= ____________ = 6. – 15÷ – 3= ____________ = 10. – 35÷ 7= ____________ = 3. – 9÷ 3= ____________ = 7. 20÷5= ____________ = 11. 64÷8= ____________ = 4. – 15÷ – 5= ____________ = 8. 16÷ – 4= ____________ = 12. – 81÷ ( – 9) = ____________ = You can find the quotient of two integers by relating adivision fact to the related fact inmultiplication. Write themultiplicationsentence for eachdivisionsentence. Solve for . 13. Find theaveragemonthly loss of a companywitha loss of $36,000 for one year. _________ 14. Theprice of a stock fell $5a day for 5 days.What was the total change? _________ The quotient of two integerswith different signs is ____________. The quotient of two integerswith the same sign is ____________. 15. Explain thepattern formultiplyingor dividing two integerswith thesame sign andwithdifferent signs. Think 4 x = – 8 Think – 4 x = – 8 2 x = – 6 54 ©Math Teachers Press, Inc., Reproduction by anymeans is strictly prohibited. 3×4= s =3(4) =12 Patterns forMultiplying Integers Joan babysat for 3 hours. She earned $4 per hour. Howmuchdid she earn? Theproduct of two positive integers is positive. – 3× ( – 2) 3× ( – 5) = – 15 Find theproducts. – 3× ( – 2) = 6 1. – 2× 3= ____ 5. – s – 1= ____ 9. – 8(8) = ____ 2. – 4× ( – 2) = ____ 6. – s ???? 10. 5( – 8) = ____ 3. – 5× 2= ____ 7. s – 7= ____ 11. – 1× – 10= ____ 4. 2× ( – 3) = ____ 8. – s – 8) = ____ 12. – 4(6) = ____ Put together 3groupsof 4 black cubes. This ismultiplication. Put together 3groupsof 5white cubes. James is taking scuba diving lessons. The instructor says hewill descend 5 feet everyminute. How deepwill he be in 3minutes? Theproduct of apositive integer and anegative integer is negative. Theproduct of two negative integers is positive. Now remove3groupsof – 2. Thismeans tosubtract 3groupsof – 2. Start with6 zeropairs, which is the same as0. Explain the pattern formultiplying two integerswith the same sign andwith different signs. 56 ©Math Teachers Press, Inc., Reproduction by anymeans is strictly prohibited. The answer to an expression havingmixedoperations ( +, – , × , ÷ )will comeout differently, depending onwhich operation you do first. Example: s +2 or s +2 3 s 6=18 12 2 14 Order of Operations Do the operations in this order: 1. M ultiply and D ivide from left to right. 2. A dd and S ubtract from left to right. This rule is sometimes called the M y D ear A unt S ally rule (MDAS). Perform theoperations in the correct order. 1. 3(4) – 6 _____ 4. – 10 –12÷4 _____ 7. n s ????? 10. – 12÷4 – 2 _____ 13. 5(4)___ 2 _____ 16. – 10__ – 2 s ????? 19. 14+8(4) – 10 _____ 2. 3+ (6)(4) _____ 5. 64–14(2) _____ 8. s ????? 11. 40– 24÷ – 4 _____ 14. – 10__ 5 +8 _____ 17. 18__ 9 s ????? 20. – 70 – 15÷ 3 _____ 3. 13+ 4 – 2 _____ 6. 8+ (12)( – 2) _____ 9. – 5+6÷ 3 _____ 12. s ????? 15. 6(4) ___ – 2(6) _____ 18. – 81___ 3(3) – 5 _____ 21. 10(6) –12÷4 _____ Example: 16÷8–4 2–4= – 2 Example: 25+ (5)(2) 25+10=35 4HE CORRECT SOLUTION FOR n s IS A 0 B 2 C 12 D 18 Answer &IRSTMULTIPLY THE s Thenadd the 2. First add the4+2, then multiply the sum by3. Multiply before adding. Divide before subtracting. Journal Prompts encourage students to usewords andpictures toprepare for Smarter BalancedandPARCC Assessments. 53 55 54 56